This work presents an approach for detecting mathematical formulas in scanned document images. The proposed approach is end-to-end trainable. Since many OCR engines cannot reliably work with the formulas, it is essential to isolate them to obtain the clean text for information extraction from the document. Our proposed pipeline comprises a hybrid task cascade network with deformable convolutions and a Resnext101 backbone. Both of these modifications help in better detection. We evaluate the proposed approaches on the ICDAR-2017 POD and Marmot datasets and achieve an overall accuracy of 96% for the ICDAR-2017 POD dataset. We achieve an overall reduction of error of 13%. Furthermore, the results on Marmot datasets are improved for the isolated and embedded formulas. We achieved an accuracy of 98.78% for the isolated formula and 90.21% overall accuracy for embedded formulas. Consequently, it results in an error reduction rate of 43% for isolated and 17.9% for embedded formulas.

Synthetic Aperture Radar (SAR) is an active type of microwave remote sensing. Using the microwave imaging system, remote sensing monitoring of the land and global ocean can be done in any weather conditions around the clock. Detection of SAR image targets is one of the main needs of radar image interpretation applications. In this paper, an improved two-parameter CFAR algorithm based on Rayleigh distribution and morphological processing is proposed to perform ship detection and recognition in high resolution SAR images. Through simulation experiments, comprehensive study of the two algorithms for high resolution SAR image target detection is achieved. Finally, the results of ship detection experiments are compared and analyzed, and the effects of detection are evaluated according to the Rayleigh distribution model and algorithms.

Biodiversity conservation questions human practices towards biodiversity and, therefore, largely conflicts with ordinary societal aspirations. Decisions on the location of protected areas, one of the most convincing conservation tools, reflect such a competitive endeavor. Operations Research (OR) brings a set of analytical models and tools capable of resolving the conflicting interests between ecology and economy. Recent technological advances have boosted the size and variety of data available to planners, thus challenging conventional approaches bounded on optimized solutions. New models and methods are requested to use such a massive amount of data in integrative schemes addressing a large variety of concerns. Here, we provide an overview on the past, present and future challenges that characterize spatial conservation models supported by OR. By enlarging the spatial, temporal, taxonomic and societal horizons of biodiversity conservation planners navigate around multiple bio-socioeconomic equilibria and are able to decide on cost-effective strategies to improve biodiversity persistence.

The Physics Informed Neural Networks framework is applied to the understanding of the dynamics of Coronavirus of 2019. To provide the governing system of equations used by the framework, the Susceptible-Infected-Recovered-Death mathematical model is used. The study focused on finding the patterns of the dynamics of the disease which involves predicting the infection rate, recovery rate and death rate; thus predicting the active infections, total recovered, susceptible and deceased at any required time. The study used data that was collected on the dynamics of COVID-19 from the Kingdom of Eswatini between March 2020 and September 2021. The obtained results showed less errors thus making highly accurate predictions.

The inherent value and use of hydrocarbon from waste plastics and solvents can be extended through open-loop chemical recycling as this process converts plastic to range of non-plastic materials. This process is enhanced by first creating plastic-solvent-combinations from multiple sources which are then streamlined through single process stream. We report on the relevant mechanics for streamlining industrially relevant polymers such as polystyrene (PS), polypropylene (PP), high-density polyethylene (HDPE) and acrylonitrile butadiene styrene (ABS) into chemical slurries mixed with various organic solvents such as toluene, xylene and cyclohexane. The miscibility of the polymer feedstock within the solvent was evaluated using the Relative Energy Difference method, and the dissolution process was evaluated using the “Molecular theories in a continuum framework” model. These models were used to design a batch process yielding 1 tonne/h slurry by setting appropriate assumptions including constant viscosity of solvents, disentanglement-controlled dissolution mechanism and linear increase of the dissolved polymer’s mass fraction over time. Solvent selection was found to be the most critical parameter for the dissolution process. The characteristics of the ideal solvent are high affinity to the desired polymer and low viscosity. This work serves as a universal technical guideline for open-loop chemical recycling of plastics avoiding the growth of waste plastic in a circular economy framework.

Nitric oxide (NO) is a key molecule in cardiovascular homeostasis and its abnormal delivery is highly associated with the occurrence and development of cardiovascular disease (CVD). The assessment and manipulation of NO delivery is crucial to the diagnosis and therapy of CVD, such as endothelial dysfunction, atherosclerotic progression, pulmonary hypertension, and cardiovascular manifestations of Coronavirus (COVID-19). However, due to the low concentration and fast reaction characteristics of NO in cardiovascular system, the clinical applications centered on the NO delivery are challenging. In this tutorial review, we first summarized the methods to estimate the in vivo NO delivery process based on the clinical images and mathematical modeling to assess the endothelial function and vulnerability of atherosclerotic plaque. Then, the emerging bioimaging technologies that have the potential to directly measure the arterial NO concentration were discussed, including the Raman spectroscopy and electrochemical sensor. Aside from the diagnostic methods, therapies aimed at controlling NO delivery to regulate CVD were reviewed, including the inhaled NO therapy to treat the pulmonary hypertension and COVID-19, stem cell therapy and NO-releasing platform to treat endothelial dysfunction and atherosclerosis.

Targeted radionuclide therapy (TRT) has recently seen a surge in popularity, with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results – an example being chimeric antigen receptor (CAR) T-cells therapy in hematologic malignancies. Moreover, TRT and CAR T therapies possess unique features that require special consideration when determining how to dose, time, and sequence combination treatments, including the distribution of TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate additive or synergistic effects of combination therapies and warrant a mathematical treatment which includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here we combine two previously published mathematical models in a multiple myeloma setting to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell based therapies. We find that for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR T therapies.

A method for calibrating models of agricultural production and resource use presented by Howitt [1] for policy analysis is proposed to leverage multidisciplinary agricultural research at the National Center for Alluvial Aquifer Research (NCAAR). An illustrative example for Sunflower County, MS is presented to show how plot-level research can be extended to draw systemic region or basin wide implications. A hypothetical improvement in yields for dryland soybean varieties is incorporated to the model and shown to have a positive impact on aquifer outcomes and producer profits. The example illustrates that a change in one practice-crop combination can have system-wide impacts as evidenced by the change in acreages for all crops and practices.

The Epithelial- Mesenchymal Transition (EMT) is a biological phenomenon associated with explicit phenotypic and molecular changes in cellular traits. Unlike the earlier-held popular belief of it being a binary process, EMT is now thought of as a landscape including diverse hybrid E/M phenotypes manifested by varying degrees of the transition. These hybrid cells can co-express both epithelial and mesenchymal markers and/or functional traits, and can possess the property of collective cell migration, enhanced tumor-initiating ability, and immune/targeted therapy-evasive features, all of which are often associated with worse patient outcomes. These characteristics of the hybrid E/M cells have led to a surge in studies that map their biophysical and biochemical hallmarks that can be helpful in exploiting their therapeutic vulnerabilities. This review discusses recent advances made in investigating hybrid E/M phenotype(s) from diverse biophysical and biochemical aspects by integrating live cell-imaging, cellular morphology quantification and mathematical modeling, and highlights a set of questions that remain unanswered about the dynamics of hybrid E/M states.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

Gastric emptying rate (GER) may impact diabetes and obesity in humans and could provide a method to reduce canine weight gain. Starch, the most common source of carbohydrates (CHOs) in pet food, is classified as rapidly or slowly digestible, or resistant to digestion. This study investigated starch source effects in commercial extruded dog foods on the GER of 11 healthy adult Siberian Huskies (5.63±0.72 years; mean±SEM). Test diets were classified as traditional, grain-free, whole-grain, and vegan. Dogs received each diet once, a glucose control twice, and acetaminophen (Ac) as a marker for GER in a randomized, partially-replicated, 6x6 Latin square design. Pre- and post-prandial blood samples were collected at 16 timepoints from -15 to 480 minutes. Serum Ac concentrations were assessed via standard spectrophotometric assays and fitted with a mathematical model to estimate parameters of GER. Data was analyzed using a repeated measures ANOVA, followed by a Tukey-Kramer post-hoc test when significant (p<0.05). More total emptying (p= 0.0430) occurred at faster rate (p=0.0668) in dogs fed the grain-free diet, which contained the lowest total starch (34.03 ± 0.23%) and highest resistant starch (0.52 ± 0.007%). This research may benefit future diet formulations to reduce the prevalence of canine weight gain.

This paper presents a novel architecture for detecting mathematical formulas in document images, which is an important step for reliable information extraction in several domains. Recently, Cascade Mask R-CNN networks have been introduced to solve object detection in computer vision. In this paper, we suggest a couple of modifications to the existing Cascade Mask R-CNN architecture: First, the proposed network uses deformable convolutions instead of conventional convolutions in the backbone network to spot areas of interest better. Second, it uses a dual backbone of ResNeXt-101, having composite connections at the parallel stages. Finally, our proposed network is end-to-end trainable. We evaluate the proposed approach on the ICDAR-2017 POD and Marmot datasets. The proposed approach demonstrates state-of-the-art performance on ICDAR-2017 POD at a higher IoU threshold with an f1-score of 0.917, reducing the relative error by 7.8%. Moreover, we accomplished correct detection accuracy of 81.3% on embedded formulas on the Marmot dataset, which results in a relative error reduction of 30%.

Information can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum information.

The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps of researches. The methodology of research is Systematic Literature review through peer review papers which are published in high ranking journals. In this paper, First, we search all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar, then, screening papers based on the criteria such as subject of paper, journals impact factor which is published in-should be peer review journal- and relative content of the papers. Finally, we selected 245 papers with three steps screening through 2806 papers that they have enough quality and relative to our research goals for context analysis. Through context analysis, first we categorized the information of the papers and drew the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and found the gapes, then, offered new suggestions like implementing SSCMs models in pollutant industries like casting industry, Heavy industry, coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells and CAR T cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T cells and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load and tumor burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the ‘mathematical names’ in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the ‘conscious procedures’ that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the ‘names in mathematics’ as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of ‘mathematical names’ in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.

Monitoring volatile organic compounds (VOCs) places a crucial role in environmental pollutants control and indoor air quality. In this study, a metal-oxide (MOx) sensor detector (used in a commercially available monitor) was employed to delineate the composition of air containing three common VOCs (ethanol, acetone and hexane) under various concentrations. Experiments with a single component and double components were conducted to investigate how the solvents interact with the metal oxide sensor. The experimental results revealed that the affinity between VOC and sensor was in the following order: acetone > ethanol > n-hexane. A mathematical model was developed, based on the experimental findings and data analysis, to convert the output resistance value of the sensor into concentration values, which in turn can be used to calculate a VOC-based air quality index. Empirical equations were established based on inferences of vapor composition versus resistance trends, and on an approach of using original and diluted air samples to generate two sets of resistance data per sample. The calibration of numerous model parameters allowed matching simulated curves to measured data. As such, the predictive mathematical model enabled quantifying not only the total concentration of sensed VOCs, but also estimating the VOC composition. This first attempt to obtain semi-quantitative data from a single MOx sensor, despite remaining selectivity challenges, is aimed at expanding the capability of mobile air pollutants monitoring devices.

Mathematical literacy is a very hot issue in the development of mathematics learning, apart from mathematical literacy, another interesting thing is the entrepreneurial spirit that must be given from an early age, especially for vocational students. This research was conducted at SMK Rosma Karawang in the Department of Computer and Network Engineering, West Java Province with the XI grade students. The teaching materials developed by applying the principles of the development model developed with the ADDIE model consist of analysis, design, development, implementation and evaluation. This research and development model is considered suitable for developing teaching tools and materials which is used for the purposes of the learning process. Based on the results of data analysis and processing that have been carried out in this study, the development of teaching materials using the ADDIE model has met the appropriate and valid criteria by media, language and media expert valuators. Another result of developing this teaching material besides meeting the eligibility criteria is that the teaching materials developed are able to increase mathematical literacy and instill entrepreneurial spirit for students.

Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient’s T lymphocytes are genetically manipulated to recognize tumor-specific antigens increasing tumor elimination efficiency. In the last years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate on patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable to be mathematically modeled. In this work, we developed a three population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities were considered as uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on some specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reduce and optimize the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such in silico laboratory was made available in a Shiny R-based platform called CARTmath. It is an open-source, easy to run simulator, available at github.com/tmglncc/CARTmath or directly on the webpage cartmath.lncc.br, containing this manuscript results as examples and documentation. The developed model, together with the CARTmath platform, provides potential use for assessing different CAR-T cell immunotherapy protocols and associated efficacy, becoming an accessory towards in silico trials.

This is a short introductory review on quantum-like modeling of cognition with applications to decision making and rationality. The aim of the review is twofold: a) to present briefly the apparatus of quantum information and probability theory useful for such modeling; b) to motivate applications of this apparatus in cognitive studies and artifical intelligence, psychology, decision making, social and political sciences. We define quantum rationality as decision making that is based on quantum information processing. Quantumly and classically rational agents behaves differently. A quantum-like agent can violate the Savage Sure Thing Principle, the Aumann theorem on impossibility of agreeing to disagree.Such an agent violates the basic laws of classical probability, e.g., the law of total probability and the Bayesian probability inference. In some contexts, ``irrational behavior'' (from the viewpoint of classical theory of rationality) can be profitable, especially for agents who are overloaded by a variety of information flows. Quantumly rational agents can save a lot of information processing resources. At the same time, this sort of rationality is the basis for quantum-like socio-political engineering, e.g., social laser. This rationality plays the important role in the process of decision making not only by biosystems, but even by AI-systems. The latter equipped with quantum(-like) information processors would behave irrationally, from the classical viewpoint. As for biosystems, quantum rational behavior of AI-systems has its advantages and disadvantages. Finally, we point out that quantum-like information processing in AI-systems can be based on classical physical devices, e.g., classical digital or analog computers.

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

Outbreaks of Ebola ebolavirus (EBOV) have been associated with high morbidity and mortality. Milestones have been reached recently in the management of EBOV disease (EVD) with licensure of an EBOV vaccine and two monoclonal antibody therapies. However, neither vaccines nor therapies are available for other disease-causing filoviruses. In preparation for such outbreaks, and for more facile and cost-effective management of EVD, we seek a cocktail containing orally available and room temperature stable drugs with strong activity against multiple filoviruses. We previously showed that (bepridil + sertraline) and (sertraline + toremifene) synergistically suppress EBOV in cell cultures. Here we describe steps towards testing these combinations in a mouse model of EVD. We identified a vehicle suitable for oral delivery of the component drugs and determined that, thus formulated the drugs are equally active against EBOV as preparations in DMSO, and they maintain activity upon storage in solution for up to seven days. Pharmacokinetic (PK) studies indicated that the drugs in the oral delivery vehicle are well tolerated in mice at the highest doses tested. Collectively the data support advancement of these combinations to tests for synergy in a mouse model of EVD. Moreover, mathematical modeling based on human oral PK projects that the combinations would be more active in humans than their component single drugs.

The epithelial-mesenchymal (E/M) hybrid state has emerged as an important mediator of elements of cancer progression, facilitated by epithelial mesenchymal plasticity (EMP). We review here evidence for the presence, prognostic significance, and therapeutic potential of the E/M hybrid state in carcinoma. We further assess modelling predictions and validation studies to demonstrate stabilised E/M hybrid states along the spectrum of EMP, as well as computational approaches for characterising and quantifying EMP phenotypes, with particular attention to the emerging realm of single-cell approaches through RNA sequencing and protein-based techniques.

This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.

In March 2020, the World Health Organization declared coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2, to be a pandemic. Since the declaration, Nigeria economy has been greatly impacted thus resulting in a recession. This paper considers a couple of misconceptions among Nigerian people in the COVID-19 pandemic era thereby causing the spread of the novel virus and hence making the situation difficult for the government to handle. In particular, we discuss the first and second waves of the pandemic as it affects the Nigerian people. The impact of the pandemic on animals and the role of mathematical epidemiologists in combatting the spread is discussed herein. We give some recommendations that could be adopted by the government and the good people of Nigeria to reduce the further spread of the virus.

The thymus hosts the development of a specific type of adaptive immune cells called T cells. T cells orchestrate the adaptive immune response through recognition of antigen by the highly variable T-cell receptor (TCR). T-cell development is a tightly coordinated process comprising lineage commitment, somatic recombination of Tcr gene loci and selection for functional, but non-self-reactive TCRs, all interspersed with massive proliferation and cell death. Thus, the thymus produces a pool of T cells throughout life capable of responding to virtually any exogenous attack while preserving the body through self-tolerance. The thymus has been of considerable interest to both immunologists and theoretical biologists due to its multiscale quantitative properties, bridging molecular binding, population dynamics and polyclonal repertoire specificity. Here, we review mathematical modelling strategies that were reported to help understand the flexible dynamics of the highly dividing and dying thymic cell populations. Furthermore, we summarize the current challenges to estimating in vivo cellular dynamics and to reaching a next-generation multiscale picture of T-cell development.

This paper presents multidisciplinary and innovative research concerning fighting against coronavirus through wastewater collection and treatment. Studies suggest that coronavirus exists in the wastewaters. Untreated wastewater is proved to spread the virus. Coronavirus is attacking people globally and shrinking the economy. This paper highlights the idea that the coronavirus shall be defeated with the help of wastewater collection and treatment as well. The question addressed by this paper is will communities defeat the coronavirus without well-collected and treated wastewaters? This research aims to display the role of wastewaters in the spread of coronavirus in cities and to require their collection. The methods to achieve the goals are theoretical surveys, case study strategy, mathematical modeling, statistical procedures, forecasting of future, and dialectical discussions. The findings of this research demonstrate the need for carefully collected and treated wastewaters to overcome the coronavirus. This paper gives suitable techniques to collect and treat wastewater such as wastewater stabilization ponds, bacterial reactors, and anaerobic ponds. The innovative idea of this paper, its suggested indicators to select a certain wastewater treatment technique in every city, and its outcome will assist the global community to fight the coronavirus more effectively.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

{\bf Abstract.} \\ {\bf Background:} Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 burden among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. \noindent{\bf Methodology and Findings:} To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious Recovered (SEIR) transmission model. All the values of different parameters used in this model were from the Bangladesh Government’s database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and good fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be good control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number ($ \mathcal{R}_{0} $) has been estimated to be 0.7563. \noindent{\bf Conclusion:} Our analysis suggests that, due to the extensive precautions from the Bangladesh government as well as other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. Although detailed and pragmatic preparedness should be adopted for the worst scenario.

A mechanical ventilation system is a big support for breathing complications, in which an external solution is quite necessary to keep oxygen compensation in the patients. Its knowledge is well widespread and different equipment has been developed. However, they are very expensive and their quantity in medical centers is not sufficient, especially in Peru. Hence, it has been required to develop new methods to provide oxygen by a low cost equipment; Protofy, a research group from Spain, designed one of the first low cost mechanical ventilation systems which was medically validated by its government. In this sense, a redesign of the mechanical ventilation system was carried out according to the local requirements and available technology, a different airbag resuscitator with different properties and geometry, but maintaining its working concept based on a cam compression mechanism. Sensors and a display were added to improve the performance with a control algorithm for the rotation frequency and to show the ventilation curves over time to the medical staff. It was necessary to develop a mathematical model to relate the behavior between ventilation curves for a patient and physical variables of the design, especially in the epidemic COVID 19, that many countries are dealing with at the time research is being conducted. The mechanical ventilation system was redesigned, fabricated, and tested measuring its ventilation curves over time. Results indicate that this redesign provides a sturdy equipment able to work during a longer lifetime than the original. The replicability of the ventilation curves behavior is assured, while the mechanism dimensions are adapted for a particular airbag resuscitator. The mathematical model of the whole system can predict satisfactorily the ventilation curves over time and was used to provide the air pressure, volume, and flow as a function of the rotation angle measured by sensors.

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial successes against B-cell malignancies, what has led to a growing scientific and clinical interest on extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immuno-suppressive tumour microenvironment, that is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, accounting for their immunosuppressive capabilities. Using the mathematical model, we show that the use of large numbers of CAR-T cells targeting the solid tumour antigens could overcome the cancer immunosuppressive potential. To achieve such high levels of CAR-T cells we propose and study computationaly, the manufacture and injection of CAR-T cells targeting two antigens: CD19 and a tumour-associated antigen. We study in-silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive generation of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its inmune suppression capabilities. That strategy could benefit from the combination with PD-1 inhibitors and of low tumour loads. Our computational results provide a theoretical support for the treatment of different types of solid tumours using T-cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD1 drugs after completion of classical cytoreductive treatments.

Determination of the presence in the blood of antibodies specific to the causative agent of a particular disease (serodiagnosis) is an effective approach in medical analytical chemistry. Serodiagnostics performed in the lateral flow immunoassay format (immunochromatography) meet the modern requirements for point-of-care testing and are supported by existing technologies of large-scale diagnostic tests production—thus raising increased attention in a tense epidemiological situation. For traditional lateral flow serodiagnostics formats, a large number of nonspecific immunoglobulins in the sample significantly reduces the degree of detectable binding. To overcome these limitations, an assay based on the formation of immobilized antigen— specific antibody—labeled antigen complexes detection was proposed. However, the requirements for its implementation, providing maximum sensitivity, have not been established. This article describes the mathematical model for the above assay. The influence of the ratio of reagent concentrations on the analysis results is considered. It is noted that the formation of specific antibody complexes with several labeled antigens is the main limiting factor in reducing the detection limit, and methods are proposed to minimize this factor. Recommendations for the choice of the assay conditions, following from the analysis of the model, are confirmed experimentally.

The developments of confirmed daily Sars-CoV-2 infections can be modeled a posteriori in a comparatively simple and satisfactory way by means of a special exponential function: its exponential coefficient varies exponentially with time itself. This property enables the function to directly simulate the „daily case“ curve fragments observed for the first waves of the current epidemics in a number of counties and countries. Linear combinations of two or more of the functions allow for the modeling of the complete curves observed in the vast majority of all regions for which case number developments have been tabulated.

Artificial intelligence methods may help in unveliling information hidden in high-dimensional oncological data. Flow cytometry studies of haematological malignancies provide quantitative data with the potential to be used for the construction of response biomarkers. Many computational methods from the bioinformatics toolbox can be applied to these data but have not been exploited in their full potential in leukaemias, specifically for the case of childhood B-cell acute lymphoblastic leukemia. In this paper we analysed flow cytometry data obtained on diagnosis from 54 paediatric B-cell acute lymphoblastic leukemia patients from two local institutions. We constructed classifiers based on the Fisher’s Ratio to quantify differences in expression levels of immunophenotypical markers between patients with relapsing and non-relapsing disease. The distribution of the marker CD38 was found and validated to have a strong discriminating power between both patient cohorts, thus providing a classifier.

In this paper, the computational fluid dynamics (CFD) method has been used to simulate the gas flow and the catalytic hydrogenation process of the C-2 hydrogenation adiabatic reactor in a practical ethylene production unit of a chemical plant. The laminar finite-rate model was used for the chemical reaction model. The standard two-equation model was used for the turbulence model. The exponent-function kinetic model was used for the reaction dynamics model. The simulation results were in good agreement with the actual industrial data obtained from the C-2 hydrogenation reactor, and the distributions of reaction parameters such as temperature and component concentrations in the reactor were further analyzed. Based on the validated CFD models, the structure and operating conditions of the reactor, as well as hydrogen load distribution ratios, are simulated for comparing the comprehensive performance metrics of ethylene selectivity and acetylene conversion rate; as a result, we can obtain the optimal temperature of 312 K, the optimal hydrogen/acetylene ratio of 0.10 as well as the optimal hydrogen load distribution ratio of 4:4:2, and the diameter/height ratio exerts a marginal effect on the selectivity, conversion rate and harmonic mean of the reactor.

Medical Trust-Network is one of the most promising fields of study in network science. Establishment of trust within medical entities ensures better treatment and increases better medical facilities. The word ‘Trust’ signifies a very important behavioral aspect between any human entities, especially among doctors and patients. To represent such relationships Trust Network Models are built to express the interactions between human entities within such networks. Though the idea of a Trust-Network has traditionally been one of the major areas of research, yet the concept of a medical trust network model is relatively a new domain. In this paper, we introduce an overall multilayered Trust Network to represent the entire healthcare architecture. More specifically our model is based on an evolutionary graph system with a discrete relationship between the three most important entities of any healthcare system, namely – Doctors, Departments, and Hospitals. Observations indicate that based on our model, the medical healthcare system is a multilayered model unlike a feed-forward model as indicated by previous studies.

We try to solve three decades-old physics challenges. List all elementary particles. Describe dark matter. Describe mechanisms that govern the rate of expansion of the universe. We propose new modeling. The modeling uses extensions to harmonic oscillator mathematics. The modeling points to all known elementary particles. The modeling suggests new particles. Based on those results, we do the following. We explain observed ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. We interrelate the masses of some elementary particles. We interrelate the strengths of electromagnetism and gravity. Our work seems to offer new insight regarding applications of harmonic oscillator mathematics. Our work seems to offer new insight regarding three branches of physics. The branches are elementary particles, astrophysics, and cosmology.

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.

Materials characterised by magnetorheological properties are non-classic engineering materials. A significant increase in the interest of scientific community in materials from this group can be observed over the recent several years. The results of research presented in this article are oriented on the examination of said materials’ mechanical properties. In order to do so, stress relaxation tests were conducted on cylindrical samples of magnetorheological elastomers loaded with compressive stress for various values of magnetic induction (B1 = 0 mT, B2 = 32 mT, B3 = 48 mT, and B4 = 64 mT) and temperature (T1 = 25° C, T2 = 30° C, and T3 = 40° C). The results of these tests indicate that the stiffness of examined samples increases along with the increase of magnetic field induction and decreases along with the increase of temperature. On this basis, it has been determined that: the biggest stress amplitude change caused by the influence of magnetic field was σ0ΔB = 12.7% and the biggest stress amplitude change caused by the influence of temperature was σ0ΔT = 11.3%. As a result of applying a mathematical model, it has been indicated that the stress relaxation in the examined magnetorheological elastomer for the adopted time range (t = 3600 s) has a hyperbolic decline nature. The collected test results point to examined materials being characterised by extensive rheological properties, which leads to a conclusion that it is necessary to conduct further tests in this scope.

In central Senegal malaria incidences have declined from 2000 to 2010 in response to scaling-up of control measures and then remained stable, making elimination improbable. Additional control measures are needed to reduce transmission. We simulated chemoprophylaxis interventions targeting malaria hotspots, using a meta-population mathematical model based on differential equation framework and incorporating human mobility. The model was fitted to weekly malaria incidences from 45 villages. Three approaches for selecting intervention targets were compared: a) villages with malaria cases during the low transmission season of the previous year; b) villages with highest incidences during the high transmission season of the previous year; c) villages with highest connectivity with adjacent populations. Our modeling, considering human mobility, showed that the intervention strategies targeting hotspots would be effective in reducing malaria incidence in both targeted and untargeted areas. But whatever the intervention, pre-elimination stage (1-5 cases per 1,000 per year) would not be reached without simultaneously increasing vector control by more than 10%. Targeted interventions allow increasing overall malaria control and elimination potential.

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

Modern medicine adopted four presumptions when it evolved from ancient experienced-based mind-body medicine. To understand its failure in finding cures for chronic diseases, we examined four presumptions, and found that statistical population of health properties does not exist for most research purposes, mathematical models are misused to model intensive properties, synthetic drugs are inherently more dangerous than nature-made medicines under their respective application conditions, and reductionist treatments are inferior and inherently dangerous. We found that clinical trials are valid only for research where treatment effect is much stronger than the total effects of all interfering or co-causal factors or errors introduced by misused mathematical models can be tolerated. In all other situations, clinical trials introduce excessive errors and fail to detect treatment effects, or produce biased, incorrect or wrong results. We further found that chronic diseases are manifestation of small departures in multiple process attributes in distinctive personal biological pathways networks, that modern medicine lacks required accuracy for accurately characterizing chronic diseases, and that reductionist treatments are good at controlling symptoms and safe for short term uses. For all stated reasons, as long as modern medicine continues relying on the flawed presumptions, it can never find predictable cures for chronic diseases. By implication, predictable cures to chronic diseases are adjustments to lifestyle, dietary, emotional, and environmental factors to slowly correct departures in process attributes responsible for chronic diseases.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Despite great advances in understanding the dynamics of viral epidemics, the emergence of rapidly spreading, highly pathogenic viruses remains a realistic and catastrophic possibility, which current health systems may not be able to fully contain. An intriguing feature in many recent zoonotic viral outbreaks is the presence of superspreaders, which are infected individuals that cause dramatically more new cases than the average. Here I study the effect of superspreaders on the early dynamics of emerging viruses that have not gained the capacity for efficient human-to-human transmission, i.e viruses with R0 < 1. I show that superspreaders have a higher chance of rapid extinction, but under crowded conditions can lead to outbreaks, causing far more cases than regular viruses. I suggest that outbreaks of highly pathogenic superspreaders are more likely when they coincide in time and space with an unrelated outbreak leading to increased hospital admission rates. These superspreader outbreaks may be difficult to detect, especially in the context of a different epidemic in progress, and can significantly affect mortality patterns observed in affected areas.

The corrected mechanism model of battery voltammetric function is helpful to guide the development and application of battery. There are two scientific issues that need to be answered: First, how many mechanisms do batteries have; Second, how to establish the mechanism model separately under the overlapping of these mechanisms. Volt-ampere characteristics of both linear state and nonlinear state exist; the monotonic decreasing of volt-ampere characteristics indicates that the battery have only three kinds of mechanisms. Without changing the basic form of the function and under the principle of the mechanism function’s working region considered, we propose a mechanism function which satisfies the monotonic decreasing characteristic of the voltammetric curve of battery, via the derivative law of each mechanism function in the voltammetric function of battery. By using the voltammetric data, the obtained cell mechanism function can accurately predict the potential (current or voltage) when the independent variable of the cell is zero, and provide the theoretical basis for the internal working mechanism of the cell, which can guide the practice.

Social networking applications such as Twitter have increasingly gained significance in terms of socio-economic, political, and religious as well as entertainment sectors. This in turn, has witnessed a wide gamut of information explosion in the social networking realm that can tend to be both useful as well as misleading at the same point of time. Spam detection is one such solution that caters to this problem through identification of irrelevant users and their data. However, existing research has so far laid primary focus on user profile information through activity detection and relevant techniques that may underperform when these profiles exhibit characteristics of temporal dependency, poor reflection of generated content from the user profile, etc. This is the primary motivation for this paper that addresses the aforementioned problem of user profiles by focusing on both profile information and content-based spam detection. To this end, this work delivers three significant contributions. Firstly, exhaustive use of Natural language processing (NLP) techniques has been rendered towards creation of a new comprehensive dataset with a wide range of content-based features. Secondly, this dataset has been fed into a customized state-of-art hybrid machine learning model that has been exclusively built using a combination of both machine learning and deep learning techniques. Extensive simulation based analysis not only records over 98% accuracy but also establishes the practical applicability of this proposal by proving that modeling based on the mixed profile and content-generated data is more capable of spam detection in contrast to each of these standalone approaches. Finally, a novel methodology based on logistic regression is proposed and supported by analytical formulations. This paves the way for the custom-built dataset to be analyzed and corresponding probabilities to be obtained that differentiate legitimate users from spammers. The obtained mathematical outcome can henceforth be used for future prediction of user categories through appropriate parameter tuning for any given dataset. This makes our method a truly generic one capable of identifying and classifying different user categories.

: Arboviruses transmitted by Aedes aegypti and Ae. albopictus have been introduced to Florida on many occasions. Infrequently, these introductions lead to sporadic local transmission and, more rarely, sustained local transmission. Both mosquito species are present in Florida, with spatio-temporal variation in population composition. We developed a 2-vector compartmental, deterministic model to investigate factors influencing Chikungunya virus (CHIKV) establishment. The model includes a non-linear, temperature-dependent mosquito mortality function based on minimum mortality in a central temperature region. Latin Hypercube sampling was used to generate parameter sets used to simulate transmission dynamics, following the introduction of one infected human. The analysis was repeated for 3 values of the mortality function central temperature. Mean annual temperature was consistently important in the likelihood of epidemics, and epidemics increased as the central temperature increased. Ae. albopictus recruitment was influential at the lowest central temperature while Ae. aegypti recruitment was influential at higher central temperatures. Our results indicate that the likelihood of CHIKV establishment may vary, but overall Florida is permissive for introductions. Model outcomes were sensitive to the specifics of mosquito mortality. Mosquito biology parameters are variable, and improved understanding of this variation will improve our ability to predict the outcome of introductions.

The quantified residence time distribution (RTD) provides a numerical characterization of mixing in the continue casting tundish, thus allowing the engineer to better understand the metallurgical performance of the reactor. This paper describes a computational fluid dynamic (CFD) modelling study for analyzing the flow pattern and the residence time distribution in a five-strand tundish. Two passive scalar transport equations are applied to separately calculate the E-curve and F-curve in the tundish. The numerical modelling results are compared to the water modelling results for the validation of the mathematical model. The volume fraction of different flow regions (plug, mixed and dead) and the intermixing time during the ladle changeover are calculated to study the effects of the flow control device (FCD) on the tundish performance. The result shows that a combination of the U-baffle with deflector holes and the turbulence inhibitor has three major effects on the flow characteristics in the tundish: i) reduce the extent of the dead volume; ii) evenly distribute the liquid streams to each strand and iii) shorten the intermixing time during the ladle changeover operation.

In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, still remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.

In the present time, the biggest problem of the world is the outbreak of novel coronavirus. Novel coronavirus (COVID-19), this one name has become a part of our daily lives over the past few months. Beyond the boundaries of medical science, coronavirus is now the main subject of research in all fields like Applied Mathematics, Economy, Philosophy, Sociology, Politics upto living room. The epidemic has brought unimaginable changes in our traditional habits and daily routines. Thousands of people in our country are fighting with the rest of the world to survive in various new situations. There are different kinds of coronavirus appeared in different times. In this time, Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is responsible for the coronavirus disease of 2019 (COVID-19). This virus was first identified towards the end of 2019 in the city of Wuhan in the province of Hubei in China. Within very short duration of time and very fast, it has spread throughout a large part of the world. In this study, the main aim is to investigate the spreading rate, death rate, recovery rate due to corona virus infection and to study the future of the coronavirus in India by using mathematical modeling based on the previous data. Mathematical models, in this situation, are the important tools in recruiting effective strategies to fight this epidemic. India is at high risk of spreading the disease and is facing many losses in socio-economic aspects. With current infection rates and existing levels of personal alertness, the number of infected people in India will increase at least in the next three months. Proper social awareness, maintain of social distance, large rate of testing and separation may break the chain of the Coronavirus-2.

The outburst of the CoVid-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities' strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the CoVid-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. %\vspace{1mm} Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number, ${\cal R}_0$. Based on the senegalese territory CoVid-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.

A compartmental epidemiological model with seven groups is introduced herein, to account for the dissemination of diseases similar to the Coronavirus disease 2019 (COVID-19). In its simplified version, the model contains ten parameters, four of which relate to characteristics of the virus, whereas another four are transition probabilities between the groups; the last two parameters enable the empirical modelling of the effective transmissibility, associated in this study with the cumulative number of fatalities due to the disease within each country. The application of the model to the fatality data (the main input herein) of five countries (to be specific, of those which had suffered most fatalities by April 30, 2020) enabled the extraction of an estimate for the basic reproduction number $R_0$ for the COVID-19 disease: $R_0=4.91(33)$.

We develop and apply new physics theory. The theory suggests specific unfound elementary particles. The theory suggests specific constituents of dark matter. We apply those results. We explain ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. The theory points to relationships between masses of elementary particles. We show a relationship between the strength of electromagnetism and the strength of gravity. The mathematics basis for matching known and suggesting new elementary particles extends mathematics for harmonic oscillators.

Objective: To use mathematical models to predict the epidemiological impact of lifting the lockdown in London, UK, and alternative strategies to help inform policy in the UK. Methods: A mathematical model for the transmission of SARS-CoV2 in London. The model was parametrised using data on notified cases, deaths, contacts, and mobility to analyse the epidemic in the UK capital. We investigated the impact of multiple non pharmaceutical interventions (NPIs) and combinations of these measures on future incidence of COVID-19. Results: Immediate action at the early stages of an epidemic in the affected districts would have tackled spread. While an extended lockdown is highly effective, other measures such as shielding older populations, universal testing and facemasks can all potentially contribute to a reduction of infections and deaths. However, based on current evidence it seems unlikely they will be as effective as continued lockdown. In order to achieve elimination and lift lockdown within 5 months, the best strategy seems to be a combination of weekly universal testing, contact tracing and use of facemasks, with concurrent lockdown. This approach could potentially reduce deaths by 48% compared with continued lockdown alone. Conclusions: A combination of NPIs such as universal testing, contact tracing and mask use while under lockdown would be associated with least deaths and infections. This approach would require high uptake and sustained local effort but it is potentially feasible as may lead to elimination in a relatively short time scale.

A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.

The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.

In this research work, we present a mathematical model for novel coronavirus -19 (NCOVID-19) which is consisted on three different compartments susceptible, infected and recovered classes abbreviated as under convex incident rate involving and emigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then by mean of nonstandard finite difference scheme (NSFD), we simulate the results against the data of Wuhan city for the sixty days. By means of simulation, we show how protection, exposure, emigration, death and cure rates affect the susceptible, infected and recovered population with the passage of time involving emigration. On the basis of simulation, we observe the dynamical behavior due to emigration of susceptible and infected classes or one of these two.

In attempting to predict the further course of the novel coronavirus (COVID-19) pandemic caused by SARS-CoV-2, mathematical models of different types are frequently employed and calibrated to reported case numbers. Among the major challenges in interpreting these data is the uncertainty about the amount of undetected infections, or conversely: the detection ratio. As a result, some models include assumptions about the percentage of detected cases among total infections while others completely neglect undetected cases. Here, we illustrate how model projections about case and fatality numbers vary significantly under varying assumptions on the detection ratio. Uncertainties in model predictions can be significantly reduced by representative testing, both for antibodies and active virus RNA, to uncover past and current infections that have gone undetected thus far.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

The outbreak of coronavirus disease 2019 (COVID-19) was identified in Wuhan, China, in December 2019. As of April 17, 2020, more than 2 million cases of COVID-19 have been reported worldwide. Northern Italy is one of the world’s centers of active coronavirus cases. In this study, we predicted the spread of COVID-19 and its burden on hospital care under different conditions of social distancing in Lombardy and Emilia-Romagna, the two regions of Italy most affected by the epidemic. To do this, we used a Susceptible-Exposed-Infectious-Recovered (SEIR) deterministic model, which encompasses compartments relevant to public health interventions such as quarantine. A new compartment L was added to the model for isolated infected population, i.e., individuals tested positives that do not need hospital care. We found that in Lombardy restrictive containment measures should be prolonged at least until early July to avoid a resurgence of hospitalizations; on the other hand, in Emilia-Romagna the number of hospitalized cases could be kept under a reasonable amount with a higher contact rate. Our results suggest that territory-specific forecasts under different scenarios are crucial to enhance or take new containment measures during the epidemic.

The proximal part of the colon offers opportunities to prolong the absorption window following oral administration of a drug. In this work, we used computer simulations to understand how the hydrodynamics in the proximal colon might affect the release from dosage forms designed to target the colon. For this purpose, we developed and compared three different models: a completely-filled colon, a partially-filled colon and a partially-filled colon with a gaseous phase present (gas-liquid model).The highest velocities of the liquid were found in the completely-filled model, which also shows the best mixing profile, defined by the distribution of tracking particles over time. No significant differences with regard to the mixing and velocity profiles were found between the partially-filled model and the gas-liquid model. The fastest transit time of an undissolved tablet was found in the completely-filled model. The velocities of the liquid in the gas-liquid model are slightly higher along the colon than in the partially-filled model. The filling level has an impact on the exsisting shear forces and shear rates, which are decisive factors in the development of new drugs and formulations.

Background: The world, now in an emergency of preventing the drastic spread of COVID-19. After the infection was first reported in December 2019, almost every country did not pay attention to this highly contaminated disease and failed to react swiftly. Now the whole universe is in an vulnerable state, loosing a great loss of lives and facing difficulties in all socio-economic aspects. That is why we have the urge to develop an efficient mathematical model (quarantine) based on social consciousness to control the epidemic. Methods: This is a quarantine mathematical model. The outcome of the system is dependent on social consciousness. We have calculated the awareness level by considering various socio-economic factor of each country. In our model, the parameters are Education Index, GDP per capita, population density, high literacy and stable economy. To maximize the efficiency of the model, it has to be implemented in initial stage. However, strict application of the method in vigorous stage of epidemic will also bring a satisfactory outcome. Results: Higher social consciousness will decrease the number of infected population dramatically while minimal or lower awareness will do a outburst. Conclusion: Outbreak will be in control of health care system, lower the death rate and will ensure social and economic stability.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

The first case of Corona Virus Disease 2019 (COVID-19) was reported in Wuhan, China in December 2019. Since then, COVID-19 has quickly spread out to all provinces in China and over 150 countries or territories in the world. With the first level response to public health emergencies (FLRPHE) launched over the country, the outbreak of COVID-19 in China is achieving under control in China. We develop a mathematical model based on epidemiology of COVID-19, incorporating the isolation of healthy people, confirmed cases and close contacts. We calculate the basic reproduction numbers 2.5 in China (excluding Hubei province) and 2.9 in Hubei province with the initial time on January 30 which show the severe infectivity of COVID-19, and verify that the current isolation method effectively contains the transmission of COVID-19. Under the isolation of healthy people, confirmed cases and close contacts, we find a noteworthy phenomenon that is the potential second epidemic of COVID-19, and estimate the peak time and value and the cumulative number of cases. Simulations show that the isolation of close contacts tracked measure can efficiently contain the transmission of the potential second epidemic of COVID-19. With isolation of all susceptible people or all infected people or both, there is no potential second epidemic of COVID-19. Furthermore, resumption of work and study can increase the transmission risk of the potential second epidemic of COVID-19.

Physics theory has yet to settle on specific descriptions for new elementary particles, for dark matter, and for dark energy forces. Our work extrapolates from the known elementary particles. The work suggests well-specified candidate descriptions for new elementary particles, dark matter, and dark energy forces. This part of the work does not depend on theories of motion. This work embraces symmetries that correlate with motion-centric conservation laws. The candidate descriptions seem to explain data that prior physics theory seems not to explain. Some of that data pertains to elementary particles. Our theory suggests relationships between masses of elementary particles. Our theory suggests a relationship between the strengths of electromagnetism and gravity. Some of that data pertains to astrophysics. Our theory seems to explain ratios of dark matter effects to ordinary matter effects. Our theory seems to explain aspects of galaxy formation. Some of that data pertains to cosmology. Our theory suggests bases for inflation and for changes in the rate of expansion of the universe. Generally, our work proposes extensions to theory in three fields. The fields are elementary particles, astrophysics, and cosmology. Our work suggests new elementary particles and seems to explain otherwise unexplained data.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.

The Universe has a gravitational horizon with a radius R_h = c/H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaitre-Robertson-Walker spacetime, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model R_h = ct. As of today, this cosmology has passed over 20 observational tests, often better than LCDM. The gravitational radius R_h therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to mc². This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches R_h. In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.

Using classical clinical observations, we first outline an elementary conceptual model for the Mind Representation System, then move to a more elaborate mathematical model that refers to discrete cofibration with enriched fibers.

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

This note first summarizes the history of the manuscript "On a Continuum Model for Avalanche Flow and Its Simplified Variants" by Grigorian and Ostroumov―published in the Special Issue on snow avalanche dynamics of Geosciences―since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor's personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian's stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian–Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment.

We develop a mathematical model to provide epidemic predictions for the 2019-nCov epidemic in Wuhan, China. We use reported case data up to January 31, 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model we identify the number of unreported cases. We then use the model to project the epidemic forward with varying level of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling 2019-nCov epidemics.

Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Computational simulation using mathematical models is a useful method for understanding the complex behavior of a living system. The majority of studies using mathematical models to reveal biological mechanisms uses one of the two main approaches: the bottom-up or the top-down approach. When we aim to analyze a large-scale network, such as a comprehensive knowledge-integrated model of a target phenomenon, for example a whole-cell model, the variation of analyses is limited to particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we developed a hybrid method that combines both approaches. To construct a mathematical model, we extracted network motifs, subgraph structures that recur more often in a metabolic network or gene regulatory network than in a random network, from a large-scale regulatory network, detected regulatory motifs among them, and combined these motifs. We confirmed that the model reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop which has not been focused on. The model extracted by our hybrid method has the potential to reveal the critical mechanisms of neural differentiation. The hybrid method is applicable to other biological events.

In the present paper, a measure of the influence of irregularities of the underlying surface (for instance, the real terrain profile) on the dynamics of air flow is estimated. It is shown that these irregularities significantly perturbing the pressure, density, velocity and temperature of air flow; for perturbed pressure, density, velocity and temperature of air flow the closed formulas in the Fourier integral form are obtained. In addition, in the present paper, it is proved that due to these perturbations, at a certain altitude of the atmosphere some surface of the "sturdy wall" form appears, on which the vertical and horizontal components of the air flow velocity become infinitesimal and infinitely large, respectively.

The ongoing electrification of the heat and transport sectors is expected to lead to a substantial increase in peak electricity demand over the coming decades, which may drive significant investment in network reinforcement in order to maintain a secure supply of electricity to consumers. The traditional way of security provision has been based on conventional investments such as the upgrade of the capacity of electricity transmission or distribution lines. However, the energy storage technology can also provide security of supply, thereby constituting a cost-efficient alternative to expensive conventional reinforcements. In this context, the current paper presents a methodology for the economic quantification of the security contribution of energy storage. This methodology makes use of mathematical optimization for the calculation of the F-factor metric, which reflects the optimal amount of peak demand reduction as compared to the power capability of the energy storage asset. In this context, a case study is presented in which the security contribution of energy storage is analyzed as a function of its power capability, energy capacity and efficiency as well as of characteristics of load patterns.

Industrial pig farming is associated with negative technological pressure on the bodies of pigs. Leg weakness and lameness are the sources of significant economic loss in raising pigs. Therefore, it is important to identify predictors of limb condition. This work presents assessments of the state of limbs using indicators of growth and meat characteristics of pigs based on machine learning algorithms. We have evaluated and compared the accuracy of prediction for several ML classification algorithms (Random Forest, K-Nearest Neighbors, Artificial Neural Networks, C50Tree, Support Vector Machines, Naive Bayes, Generalized Linear Models, Boost, and Linear Discriminant Analysis) and have identified the Random Forest and K-Nearest Neighbors as the best performing algorithms for predicting pig leg weakness using a small set of simple measurements that can be taken at an early stage of animal development. Muscle Thickness, Back Fat amount, and Average Daily Gain serve as significant predictors of conformation of pig limbs. Our work demonstrates the utility and relative ease of using machine learning algorithms to assess the state of limbs in pigs based on growth rate and meat characteristics.

The molecular study of fat cell development in the human body is essential for our understanding of obesity and related diseases. Mesenchymal stem/stromal cells (MSC) are the ideal source to study fat formation as they are the progenitors of adipocytes. In this work, we used human MSCs, received from surgery waste, and differentiate them into fat adipocytes. The combination of several layers of information coming from lipidomics, metabolomics and proteomics enabled comprehensive analysis of the biochemical pathways in adipogenesis. Simultaneous analysis of metabolites, lipids and proteins in cell culture is challenging due to the compound’s chemical difference so that most studies involve separate analysis with unimolecular strategies. In this study, we employed a multimolecular approach using a two–phase extraction to monitor the crosstalk between lipid metabolism and protein-based signaling in a single sample (~105 cells). We developed an innovative analytical workflow including standardization with in-house produced 13C-isotopically labeled compounds, hyphenated high-end mass spectrometry (high-resolution Orbitrap MS) and chromatography (HILIC, RP) for simultaneous untargeted screening and targeted quantification. Metabolite and lipid concentrations ranged over 3-4 orders of magnitude and were detected down to the low fmol (absolute on column) level. Biological validation and data interpretation of the multiomics workflow was performed based on proteomics network reconstruction, metabolic modelling (MetaboAnalyst 4.0) and pathway analysis (OmicsNet). Comparing MSCs and adipocytes, we observed significant regulation of different metabolites and lipids such as triglycerides, gangliosides and carnitine with 113 fully reprogrammed pathways. The observed changes are in accordance with literature findings dealing with adipogenic differentiation of MSC. These results are a proof of principle for the power of multimolecular extraction combined with orthogonal LC-MS assays and network construction. Considering the analytical and biological validation performed in this study, we conclude that the proposed multiomics workflow is ideally suited for comprehensive follow-up studies on adipogenesis and is fit for purpose for different applications.

Background: Accurate prediction of patients’ response to therapy is clinically indispensable, howbeit challenging. With increased understanding of the human genome and malignancies, there is the renaissance of in silico pharmacogenomics with renewed interest in drug response predictability based on gene-drug interaction. Objective: Evidence-based transcript-proteome profiling is essential for synthesizing clinically applicable algorithms for predicting response to anticancer therapy, including immune checkpoint blockade (ICBT); thus, saving physicians’ time, reducing polypharmacy, and curtailing unnecessary treatment expense. In this study, we tested and validated the hypothesis that a selected proteomic signature in ICBT-naïve patients is sufficient for the prediction of response to ICBT. Methods: Using a multimodal approach consisting of computational pharmacogenomics, transcript-proteome analytics, mathematical modeling, and machine learning systems; we delineated therapy-sensitivity and stratified patients into graduated response groups based on their proteomic profile. Protein expression levels in our cohort tissue specimens were evaluated based on T cell- and non-T cell- inflamed phenotypes by immunohistochemistry. Results: We established β-catenin, PDL1, CD3 and CD8 expression-based ICBT response model. Statistical regression models validated the predictive association between our predefined algorithms and therapeutic outcome. Interestingly, our 4-gene prediction classifier was constitutively independent of tumor tissue origin, correctly stratified patients into high-, low-, and non- responders pre-treatment, with high prediction accuracy, and exhibited good association with patients’ performance status and prognosis (p < 0.01). Conclusion: Our findings demonstrate the possibility of accurate proteomics based ICBT response prediction and provide a putative basis for drug response prediction based on selective proteome profile in untreated cancer patients.

An autonomous endogenous time-keeping is ubiquitous across many living organisms known as circadian clock when it has a period of about 24 hours. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus \textit{Neurospora crassa} is a well established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of \textit{Neurospora} is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedbacks among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 hrs. Our model reveals a switch between WC1 induced transcription and FFC assisted inactivation of WC1. Using the new model we also study possible mechanisms of glucose compensation. A fairly simple model with just 3 non-linearities helps to elucidate clock dynamics revealing a mechanism of rhythms production. The model can further be utilized to study entrainment and temperature compensation.

This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.

Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR, however its application to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies which focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria, and utilized our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture, and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap on the dynamics of transformation and transduction, and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.

The article presents the results of tests of minor head losses through PVC and PP elbows for a flow of water and mixtures of water and sand with grain sizes of up to 0.5 mm and concentrations of 5.6 g∙L-1, 10.84 g∙L-1, and 15.73 g∙L-1. The tests were carried out at variable flow velocities for three elbow diameters of 63, 75, and 90 mm. The flow rate, pressure difference in the tested cross-sections, and temperature of the fluids were measured and automatically recorded. The results of the measurements were used to develop mathematical models for determining the minor head loss coefficient as a function of elbow diameter, sand concentration in the liquid, and Reynolds number. The mathematical model was developed by cross validation. It was shown that when the concentration of sand in the liquid was increased by 1.0 g∙L-1, the coefficient of minor head loss through the elbows increased, in the Reynolds number range of 4.6∙104 − 2.1∙105, by 0.3−0.01% for PP63, 0.6−0.03 % for PP75, 1.1−0.06 % for PP90, 0.8−0.01 % for PVC63, 0.8−0.02 % for PVC75, and 0.9−0.04 % for PVC90. An increase in Re from 5∙104 to 2∙106 for elbows with diameters of 63, 75 and 90 mm caused a 7.3 %, 6.8 %, and 6.0 % decrease in the minor head loss coefficient, respectively.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

Multiple lines of evidence indicate that CD8$^+$ T cells are important in the control of HIV-1 (HIV) replication. However, CD8$^+$ T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8$^+$ T-cell responses induced during the course of HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8$^+$ T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8$^+$ T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8$^+$ T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8$^+$ T cells in the chronic infection. The breadth of HIV-specific CD8$^+$ T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8$^+$ T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8$^+$ T-cell responses and the presence of intra- and interclonal competition between multiple CD8$^+$ T-cell responses; such competition may limit the magnitude of CD8$^+$ T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8$^+$ T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

In this work a new pre-tuning multivariable PID controllers method for quadrotors is put forward. A procedure based on LQR/LQG theory is proposed for attitude and altitude control. With the aim of analyzing performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, togheter with sensors drift/bias properties and noise characteristics of low-cost comercial sensors typically used in this type of applications (such as MARG with MEMS technology and LIDAR) are considered. In order to estimate the state vector and compensate bias/drift effects on rate gyros of the MARG, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robutsness analysis of the control system is carried out by means of numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show that the proposed pre-tuning method for multivariable PID controller is robust with respect to: a) parametric uncertainty in the plant model, b) disturbances acting at the plant input, c) sensors measurement and estimation errors.

Auxin and ethylene pathways cooperatively regulate a variety of developmental processes in plants. Growth responses to ethylene are largely dependent on auxin, the key regulator of plant morphogenesis. Auxin, in turn, is capable of inducing ethylene biosynthesis and signaling making the interaction of these hormones reciprocal. Recent studies discovered a bunch of molecular events underlying auxin-ethylene crosstalk. In this review, we summarize the results of fine-scale and large-scale experiments on interaction of auxin and ethylene pathways in Arabidopsis. We integrate the knowledge on the molecular crosstalk events, their tissue specificity and associated phenotypic responses to decipher the crosstalk mechanisms at a systems level. We also discuss the prospects of applying systems biology approaches to study the mechanisms of crosstalk between plant hormones.

Hidden markov models are a very useful tool in the modelling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden markov model to analyze the underlying structure of an ancient and complex manuscript, known as Voynich's manuscript, that remains still undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscript we train the network by means of the $\alpha$ and $\beta$-pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices in order to compare with known languages concerning the frequency of consonant and vowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

Human African Trypanosomiasis (HAT) commonly known as sleeping sickness, is a neglected tropical vector borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments while in the human population, the HAT is modelled by four compartments. The next generation matrix approach is used to derive the basic reproduction number, R₀, and also it is proved that if R₀ ≤ 1 the disease free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persist in the population if the value of R₀ > 1. Furthermore, the optimal control model is determined by using the Pontryagin’s maximum principle with control measures such as education, treatment and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures are very efficient and effective to eliminate HAT in Africa.

This paper addresses the modeling of the iron ore direct reduction process, a process likely to reduce CO₂ emissions from the steel industry. The shaft furnace is divided into three sections (reduction, transition, and cooling), and the model is two-dimensional (cylindrical geometry for the upper sections and conical geometry for the lower one), to correctly describe the lateral gas feed and cooling gas outlet. This model relies on a detailed description of the main physical–chemical and thermal phenomena, using a multi-scale approach. The moving bed is assumed to be comprised of pellets of grains and crystallites. We also take into account eight heterogeneous and two homogeneous chemical reactions. The local mass, energy, and momentum balances are numerically solved, using the finite volume method. This model was successfully validated by simulating the shaft furnaces of two direct reduction plants of different capacities. The calculated results reveal the detailed interior behavior of the shaft furnace operation. Eight different zones can be distinguished, according to their predominant thermal and reaction characteristics. An important finding is the presence of a central zone of lesser temperature and conversion.

This work is located in a growing sector within the field of renewable energies, wave energy converters (WECs). Specifically, it focuses on one of the point absorbers wave (PAWs) of the hybrid platform W2POWER. With the aim of maximising the mechanical power extracted from the waves by these WECs and reduce their mechanical fatigue, the design of five different model predictive controllers (MPCs) with hard and soft constraints has been carried out. As contribution of this paper, two of the MPCs have been designed with the addition of an embedded integrator. In order to validate the MPCs, an exhaustive study on performance and robustness is realized through simulations carried out in which uncertainties in the WEC dynamics are considered. Furthermore, looking for realistic in these simulations, an identification methodology for PAWs is proposed and validated by means of real time series of a scale prototype.

Intercellular transport of auxin is driven by PIN-formed (PIN) proteins. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping it into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM. Which of these two mechanisms dominates is a matter of debate. Here we addressed the issue with a mathematical modeling approach. We demonstrate that the efficiency of secretory transport depends on SV size, half-life of PINs on the PM, pH, exocytosis frequency and PIN density. 3D-SIM microscopy was used to determine PIN density on the PM. Combing this data with published values of the other parameters, we show that the transport activity of PINs in SVs would have to be at least 1000x greater than on the PM in order to produce a comparable macroscopic auxin transport. If both transport mechanisms operated simultaneously and PINs were equally active on SVs and PM, the contribution of secretion to the total auxin flux would be negligible. In conclusion, while secretory vesicle-mediated transport of auxin is intriguing and theoretically possible model, it unlikely to be a major mechanism of auxin transport in planta.

The manuscript studies the release kinetic of fluorescein from colloidal liquid crystals made up from monoglyceride and different non-ionic surfactants. The release experiments were carried out under sink conditions, and mathematical models were described as extrapolations from solutions of diffusion equation in different initial and boundary conditions imposed by pharmaceutical formulations. The diffusion equation was solved, using Laplace and Fourier transformed functions for the release kinetic from infinite reservoirs in a semi-infinite medium. Solutions represents a general square root law and can be applied for the release kinetic of fluorescein from monoglyceride colloidal liquid crystals. Akaike, Schwartz and Imbimbo criteria were used to establish the appropriate mathematical model and the hierarchy of performances of different models applied to the release experiments. The Fisher statistic test was applied to perform significance of differences among mathematical models. Differences evaluated by mathematical criteria demonstrated that small or no significant statistic differences were carried out between various applied models and colloidal formulations. Phenomenological models were preferred over to empirical and semi-empirical ones. The general square root model shows that the diffusion-controlled release of fluorescein is the mathematical models extrapolated for monoglyceride colloidal liquids, in the first part of the process.