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.

Synergy of radiation and immune system is currently receiving significant attention in oncology as numerous studies have shown that cancer irradiation can induce strong antitumor immune responses. It remains unclear, however, what are the best radiation fractionation protocols to maximize the therapeutic benefits of this synergy. Here, we present a novel mathematical model that can be used to predict and dissect the complexity of the immune-mediated response at multiple tumor sites after applying focal irradiation and systemic immunotherapy. We successfully calibrate the proposed framework with published experimental data, in which two tumors were grown in mice at two spatially separated sites from which only one was irradiated using various radiation fractionation protocols with and without concurrent systemic immunotherapy. The proposed model is calibrated to fit the temporal dynamics of tumor volume at both sites and can predict changes in immune infiltration in the non-irradiated tumors. The model was then used to investigate additional radiation fractionation protocols. Model simulations suggest that the optimal radiation doses per fraction to maximize antitumor immunity are between 10-13 Gy, at least for the experimental setting used for model calibration. This work provides the framework for evaluating radiation fractionation protocols for radiation-induced immune-mediated systemic antitumor responses.

Academic publishing appears to be the most important key of the academic functions (academic research, excellence in teaching and learning and community services). Selecting the right journal to publish research results is a challenge to academics. Yet, there is inadequate knowledge about a model specifically directed at the topic of the journal selection process with a mathematical certainty. The objectives of this research are: to identify the main factors that an author or researchers consider when selecting an academic journal for submitting a manuscript, and, to develop a mathematical algorithm of journal selection that provide the best journal choice with a mathematical certainty based on difficulty of each factor. Quantitative research through questionnaires has been applied as an appropriate instrument base to address the researcher’s identification of the factors that should be considered when selecting a journal. Questionnaire developed and emailed to academics in 31 public and private universities in the developing countries. Academics reported that the most important publication difficulty factors were publishing in reputable journals, and publishing in a journal that has an impact factor. However, the most least publication difficulty factors were found to be: number of issues per year and if the journal is an open access. The proposed mathematical algorithm of journal’s publication difficulty factors was developed and tested.

The managers’ strategic behavior of commercial real estate in a competitive environment is discussed. The means of this research are methods of mathematical and experimental game theory. Illustrates an example of a decision-theoretic game problem with two players engaged in the management of competing shopping centers. The strategies of these players are determined by the costs of the development. Since the number of visitors is constantly and changing the quality of shopping centers, managers actually pull visitors from each other, the game-theoretical formulation of the problem of management of shopping centers corresponds to the zero-sum game. The model example shows that with the help of mathematical modeling it is possible to determine the theoretical expected behavior of agents. The model of the software module created specifically for experimental research is described. The experiments are designed to compare the theoretically predicted behavior with the real actions of people. The novelty is that at significant costs of the Manager for the development and promotion of shopping and entertainment centers, the strategies of managers are resistant to each other's actions, in contrast to changes in the external environment is shown.

The “Crisis of Reproducibility” has received considerable attention both within the scientific community and without. While factors associated with scientific culture and practical practice are most often invoked, I propose that the Crisis of Reproducibility is ultimately a failure of generalization with a fundamental scientific basis in the methods used for biomedical research. The Denominator Problem describes how limitations intrinsic to the two primary approaches of biomedical research, clinical studies and pre-clinical experimental biology, lead to an inability to effectively characterize the full extent of biological heterogeneity, which compromises the task of generalizing acquired knowledge. Drawing on the example of the unifying role of theory in the physical sciences, I propose that multi-scale mathematical and dynamic computational models, when mapped to the modular structure of biological systems, can serve a unifying role as formal representations of what is conserved and similar from one biological context to another. This ability to explicitly describe the generation of heterogeneity from similarity addresses the Denominator Problem and provides a scientific response to the Crisis of Reproducibility.

Increasing of the imaging rate of conventional atomic force microscopy (AFM) is almost impossible without impairing of the imaging quality, since the probe tip tends to lose contact with the sample. We propose to apply the additional nonlinear force on the upper surface of a cantilever, which will help to keep the tip and surface in contact. In practice this force can be produced by the precisely regulated airflow. Such an improvement affects the AFM system dynamics, which were evaluated using a mathematical model presented in this paper. The model defines the relationships between the additional nonlinear force, the pressure of the applied air stream and the initial air gap between the upper surface of the cantilever and the end of the air duct. It was found that the nonlinear force created by the stream of compressed air (aerodynamic force) prevents the contact loss caused by the high scanning speed or higher surface roughness, and at the same time has minimal influence on the interaction force, thus maintaining stable contact between the probe and the surface. This improvement allows to effectively increase the scanning speed by at least 10 times using a soft (spring constant of 0.2 N/m) cantilever by applying the air pressure of 40 Pa. If a stiff cantilever (spring constant of 40 N/m) is used, the potential of accuracy improvement reaches 92 times. This method is suitable for use with different types of AFM sensors and can be implemented practically without essential changes in AFM sensor design.

Studies performed at single-cell resolution have demonstrated the physiological significance of cell-to-cell variability. Various types of mathematical models and systems analyses of biological networks have further been used to gain a better understanding of the sources and regulatory mechanisms of such variability. In this work, we present a novel sensitivity analysis method, called molecular density function perturbation (MDFP), for the dynamical analysis of cellular heterogeneity. The proposed analysis is based on introducing perturbations to the density or distribution function of the cellular state variables at specific time points, and quantifying how such perturbations affect the state distribution at later time points. We applied the MDFP analysis to a model of signal transduction pathway involved in TRAIL (tumor necrosis factor-related apoptosis-inducing ligand)-induced apoptosis in HeLa cells. The MDFP analysis showed that caspase-8 activation regulates the timing of the switch-like increase of cPARP (cleaved poly(ADP-ribose) polymerase), an indicator of apoptosis. Meanwhile, the cell-to-cell variability in the commitment to apoptosis depended on mitochondrial outer membrane permeabilization (MOMP) and events following MOMP, including the release of Smac (second mitochondria-derived activator of caspases) and cytochrome-C from mitochondria, the inhibition of XIAP (X-linked inhibitor of apoptosis) by Smac and the formation of apoptosome.

This paper investigates existing mathematical morphology based techniques applied for performing malaria parasites detection and identification in both Giemsa and Leishman stained blood smears images. Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis; this kind of visual inspection is subjective, errorprone and time consuming. In order to cope with such issues, computer-aided methods have been increasingly evolved for abnormal erythrocyte and/or parasites detection, segmentation and semi/fully automated classification. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection.

The pennate diatom Phaeodactylum tricornutum is a model organism able to synthesize industrially-relevant molecules. Commercial-scale cultivation currently requires large monocultures, prone to bio-contamination. However, little is known about the identity of the invading organisms. To reduce the complexity of natural systems, we systematically investigated the microbiome of non-axenic P. tricornutum cultures from a culture collection in reproducible experiments. The results revealed a dynamic bacterial community that developed differently in “complete” and “minimal” media conditions. In complete media, we observed an accelerated “culture crash”, indicating a more stable culture in minimal media. The identification of only four bacterial families as major players within the microbiome suggests specific roles depending on environmental conditions. From our results we propose a network of putative interactions between P. tricornutum and these main bacterial factions. We demonstrate that, even with rather sparse data, a mathematical model can be reconstructed that qualitatively reproduces the observed population dynamics, thus indicating that our hypotheses regarding the molecular interactions are in agreement with experimental data. Whereas the model in its current state is only qualitative, we argue that it serves as a starting point to develop quantitative and predictive mathematical models, which may guide experimental efforts to synthetically construct and monitor stable communities required for robust upscaling strategies.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex anti-tumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these fields of research for more efficient development and effective treatments.

This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics – namely, category theory – and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms – a language completely devoid of arbitrariness – then we would make possible a synthetical argument about the essential human activity of “the aesthetics”, and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.

This economic evaluation aims to support policy-making on the combined use of pre-exposure prophylaxis (PrEP) with HIV vaccines by evaluating the potential cost-effectiveness of implementation that would support the design of clinical trials for assessment of combined product safety and efficacy. The target study population is a cohort of men who have sex with men (MSM) in the United States. Policy strategies considered include standard HIV prevention, daily oral PrEP, HIV vaccine, and their combination. We constructed a Markov model based on clinical trial data and published literature. We used a payer perspective, monthly cycle length, a lifetime horizon, and a 3% discount rate. We assumed a price of $500 per HIV vaccine series in the base case. HIV vaccines dominated standard care and PrEP. At current prices,PrEP was not cost-effective alone or in combination. A combination strategy had the greatest health benefit but was not cost-effective (ICER=$463,448/QALY) as compared to vaccination alone. Sensitivity analyses suggest a combination may be valuable for higher-risk men with good adherence. Vaccine durability and PrEP drug prices were key drivers of cost-effectiveness. Results suggest that boosting potential may be key to HIV vaccine value.

Arc sensors have been used in seam tracking and widely studied since the 80s; commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and swing or rotate speed.

The accurate wellbore pressure control not only prevents from lost circulation/blowout and fracturing formation by managing density of drilling fluid, but also improves productivity by mitigating reservoir damage. The geothermal pressure calculated by constant parameters for geothermal well would bring big error easily, as the changes of physical, rheological and thermal properties of drilling fluids with temperature were neglected. This paper researches the wellbore pressure coupling by calculating the temperature distribution with existed model, fitting the rule of density of drilling fluid with temperature and establishing mathematical models to stimulate the wellbore pressures, which is expressed as the variation of Equivalent Circulating Density (ECD) under different conditions. With this method, temperature and ECDs in the wellbore of the first medium-deep geothermal well ZK212 Yangyi Geothermal Field in Tibet were determined, and the sensitivity analysis was simulated by assumed parameters, i.e. circulating time, flow rate, geothermal gradient, diameters of wellbore, rheological models and regimes, the results indicated the geothermal gradient and flow rate were the most influence parameters on the temperature and ECD distribution, and additives added in drilling fluid should be careful which would change the properties of drilling fluid and induce the temperature redistribution. To make sure the safe drilling, velocity of pipes tripping into the hole, depth and diameter of wellbore are considered to control the surge pressure.

Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.