Coronavirus disease 2019 (COVID-19), the emissary behind the worst global pandemic of the 21st century, is primarily a respiratory disease-causing virus called SARS-CoV-2 which is responsible for millions of new cases (incidence) and deaths (mortalities), worldwide. Many factors have played a role in the differential morbidity and mortality experienced by nations and ethnicities against SARS-CoV-2, such as the quality of primary medical health facilities or enabling economies. Nevertheless, the most important variable, i.e., the subsequent ability of individuals to be immunologically sensitive or resistant to the infection, was not properly discussed before. Therefore, an astounding issue arose when some developed countries experienced higher morbidity and mortality, compared with their relatively underdeveloped counterparts, despite having excellent medical health facilities. Hence this investigative review attempts to analyze the issue from an angle of previously undiscussed genetic, epigenetic, and molecular immune resistance mechanisms in correlation with the pathophysiology of SARS-CoV-2 and varied ethnicity-based immunological responses against it. The biological factors discussed here include the overall landscape of human microbiota, endogenous retroviral genes spliced into the human genome, copy number variation, and how they could modulate the innate and adaptive immune systems, which put a particular ethnic genetic architecture at a higher risk of SARS-CoV-2 infection than others. Considering an array of these factors in their entirety may help explain the geographic disparity of disease incidence, severity, and subsequent mortality associated with the disease while at the same time encouraging scientists to design new experimental approaches to investigation.

Fluid flow and chemokine gradients play a large part in not only regulating homeostatic processes in the brain, but also in pathologic conditions by directing cell migration. Tumor cells in particular are superior at invading into the brain resulting in tumor recurrence. One mechanism that governs cellular invasion is autologous chemotaxis, whereby pericellular chemokine gradients form due to interstitial fluid flow (IFF) leading cells to migrate up the gradient. Glioma cells have been shown to specifically use CXCL12 to increase their invasion under heightened interstitial flow. Computational modeling of this gradient offers better insight into the extent of its development around single cells, yet very few conditions have been modelled. In this paper, a computational model is developed to investigate how a CXCL12 gradient may form around a tumor cell and what conditions are necessary to affect its formation. Through finite element analysis using COMSOL and coupled convection-diffusion/mass transport equations, we show that velocity (IFF magnitude) has the largest parametric effect on gradient formation, multidirectional fluid flow causes gradient formation in the direction of the resultant which is governed by IFF magnitude, common treatments and flow patterns have a spatiotemporal effect on pericellular gradients, exogenous background concentrations can abrogate the autologous effect depending on how close the cell is to the source, that there is a minimal distance away from the tumor border required for a single cell to establish an autologous gradient, and finally that the development of a gradient formation is highly dependent on specific cell morphology.

We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

The number of diabetic patients worldwide is increasing rapidly. Prevention of diabetic reti-nopathy (DR), a leading cause of blindness, is a serious issue. We examined the effects of prophy-lactic pattern scanning laser retinal photocoagulation on DR development in 16 Spontaneously Diabetic Torii (SDT) fatty rats. Photocoagulation was applied to the right eyes of 8-week SDT fatty rats, and the left eyes served as the untreated controls. Electroretinography at 9 and 39 weeks of age and pathological examination of the retinal thickness and number of retinal folds, and immunohistochemistry of vascular endothelial growth factor and glial fibrillary acidic pro-tein at 24 and 40 weeks of age were performed bilaterally. No significant differences were seen between the left and right eyes in the apex latency and the amplitude of the oscillatory potential wave in the SDT fatty rats at 9 and 39 weeks of age and in the pathology and immunohistochem-istry in the SDT fatty rats at 24 and 40 weeks of age. Prophylactic pattern scanning retinal laser photocoagulation did not affect the development of DR in SDT fatty rats.

CC chemokine receptor 6 (CCR6) is one of the members of G protein-coupled receptor (GPCR) family that is upregulated in many immune-related cells, including B lymphocytes, effector and memory T cells, regulatory T cells, and immature dendritic cells. Coordination between CCR6 and its ligand CC motif chemokine ligand 20 (CCL20) is deeply involved in the pathogenesis of various diseases, such as cancer, autoimmune diseases, and psoriasis. Therefore, CCR6 is an attractive target for therapy and is being investigated as a diagnostic marker for patients. In a previous study, we developed an anti-mouse CCR6 (mCCR6) monoclonal antibody (mAb), C6Mab-13 (rat IgG1, kappa), applicable for flow cytometry by immunizing a rat with N-terminal peptide of mCCR6. This study investigated the binding epitope of C6Mab-13 using enzyme-linked immunosorbent assay (ELISA) and surface plasmon resonance (SPR) methods with the synthesized point mutated-peptides within 1-20 amino acids region of mCCR6. In ELISA, C6Mab-13 lost the reaction to the alanine-substituted peptide of D11A. The epitope of C6Mab-13 was identified to be Asp11 in ELISA. Furthermore, in SPR analysis, the dissociation constants (KD) could not be calculated for G9A and D11A mutants due to lack of binding. The SPR analysis demonstrated that the C6Mab-13 epitope comprises Gly9 and Asp11. Taken together, the key binding epitope of C6Mab-13 was determined to be around Asp11 on mCCR6. Based on the epitope information, C6Mab-13 could be useful for further functional analysis of mCCR6 in future studies.

In this study, we deal with a nonlinear system of neutral Volterra integro-differential equations (NVIDEs) with infinite delay. We study stability, uniform stability and instability of zero solution of the system of NVIDEs with infinite delay. We obtain three new results with regard to these concepts via two new Lyapunov– Krasovskii functionals (LKFs), respectively. As the main contributions of this work, we improve and generalize some earlier results in the relevant database from the linear case to more general nonlinear cases.

(1) Background: Angiotensin II, a major culprit in cardiovascular disease, activates mediators that are also involved in pathological cardiac remodelling. We aimed at investigating the effects of two of them: aldosterone (Ald) and transforming growth factor-beta-1 (TGF-β1 ), on cardiac remodelling in an in vivo model. (2) Methods: Six-week-old male wild-type (WT) and TGF-β1 -overexpressing transgenic (TGF-β1 -TG) mice were infused with subhypertensive doses of Ald for 2 weeks, and/or treated orally with eplerenone from postnatal day 21. Heart’s ventricles were examined: by morphometry, immunoblotting to assess intracellular signalling pathways, RT qPCR to determine hypertrophy and fibrosis marker genes. (3) Results: TGF-β1 -TG mice spontaneously developed cardiac hypertrophy and interstitial fibrosis, exhibited higher baseline phosphorylation of p44/42 and p38 kinases, fibronectin and ANP mRNA expression. Ald induced a comparable increase in ventricular heart weight-to-body-weight ratio and cardiomyocyte diameter in both strains, but less pronounced increase in interstitial fibrosis in transgenic compared to WT mice (23.6% vs 80.9%, p<0.005). Ald increased phosphorylation of p44/42 and p38 in WT but not TGF-β1 -TG mice. While eplerenone-enriched chow partially prevented Ald-induced cardiac hypertrophy in both genotypes and interstitial fibrosis in WT controls, it completely protected from additional fibrosis in transgenic mice. (4) Conclusions: Ald appears to induce cardiac hypertrophy independently of TGF-β1 , while in case of fibrosis downstream signalling pathways of these two factors probably converge

In this work, we offer a novel and accurate method in order to find the solution of the linear differential equations over the intervals [0, 1) based on the generalization of Legendre wavelets. The mechanism is still upon workable implementation of the operational matrix of integration and its derivatives. This method reduces the problems into algebraic equations via the properties of generalized Legendre wavelet (GLW) together with the operational matrix of integration. The function approximation has been picked out in such a way so as to enumerate the connection coefficients in an facile manner. The proposed numerical technique, based on the GLW, has been examined on three linear problems as a consequence of this investigation. The outcomes have shown that this method, as opposed to some other existing numerical and analytical methods, is a very useful and advantageous for tackling such problems.

ExuR and UxuR are paralogous proteins belonging to the GntR family of transcriptional regulators. Both are known to control hexuronic acid metabolism in a variety of Gammaproteobacteria but the relative impact of each of them is still unclear. Here, we apply 2D difference electrophoresis followed by mass-spectrometry to characterise the changes in the Escherichia coli proteome in response to the uxuR or exuR deletion. Our data clearly show that the effects are different: deletion of uxuR resulted in significantly enhanced expression of D-mannonate dehydratase UxuA and flagellar protein FliC, and inhibition of outer membrane porin OmpF, while the absence of ExuR did not significantly alter the spectrum of detected proteins.This suggests that the roles of proteins predicted as homologs are far from identical. Effects of uxuR deletion were largely dependent on the cultivation conditions: during growth with glucose, UxuA and FliC were dramatically altered, while during growth with glucuronate activation of both was not so prominent. During growth on glucose, the maximal activation was detected for FliC. This was further confirmed by expression analysis and physiological tests thus suggesting involvement of UxuR in the regulation of bacterial motility and biofilm formation.

Background: Left ventricular hypertrophy (LVH) may be due to different causes, ranging from benign secondary forms to severe cardiomyopathies. Transthoracic Echocardiography (TTE) and ECG are the first level examination for LVH diagnosis. Cardiac magnetic resonance (CMR) defines accurately LVH type, extent and severity. Objectives: to evaluate the diagnostic and prognostic role of CMR in patients with TTE and/or ECG evidence of LVH. Methods: We performed CMR in 300 consecutive patients with echocardiographic and/or ECG signs of LVH. Results: Overall, 275 patients had TTE evidence of LVH with initial suspicion of hypertrophic cardiomyopathy (HCM) in 132 (44%), cardiac amyloidosis in 41 (14%), hypertensive LVH in 48 (16%), aortic stenosis in 4 (1%), undetermined LVH in 50(16%). The initial echocardiographic diagnostic suspicion of LVH was confirmed in 172 patients (57.3%) and changed in 128 patients (42.7%, p<0.0001): the diagnosis of HCM increased from 44% to 71% of patients; hypertensive and undetermined LVH decreased significantly (respectively to 4% and 5%). CMR allowed a diagnosis in 41 out of 50 (82%) with undetermined LVH at TTE. CMR also identified HCM in 17 out of 25 patients with apparently normal echo but with ECG criteria for LVH. Finally, the reclassification of the diagnosis by CMR was associated with a change of survival risk of patients: after CMR reclassification no events occurred in patients with undetermined or hypertensive LVH. Conclusions: CMR changed echocardiographic suspicion in almost half of patients with LVH. In the subgroup of patient with abnormal ECG, CMR identified LVH (particularly HCM) in 80% of patients. This study highlights the indication of CMR to better characterize the type, extent and severity of LVH detected at echocardiography and suspected with ECG.

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques also opened the door to study the optical properties of these nanomaterials. We present a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS₂, MoSe₂, WS₂ and WSe₂, with thickness ranging from one layer up to six layers. We analyze the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provides a route to employ differential reflectance spectroscopy for determining the number of layers of MoS₂, MoSe₂, WS₂ and WSe₂.

The possibility of the life origin in the stellar systems, located at a distance of ~ 200 pc from the solar system, was investigated. The stars, in the spectrums of which C (carbon), O (oxygen), N (nitrogen), and P (phosphorus) are found, are called DNA–stars. Based on stellar abundances a new method for searching for habitable exoplanets has been developed and a list of 48 DNA–stars in the solar neighborhood, on which life is possible, has been defined. The quota of DNA–stars is equal 1.3% of the total amount of Hypatia Stellar Catalog. Only three DNA–stars out of selected 48 stars belong to the spectral class as our Sun (G2V). The closest to the solar system is the DNA-star with the number HIP 15510, which belongs to the G8V class and is 6 pc away from the solar system. Nine DNA--stars, which have the highest chemical similarity with solar spectrum, were identified. It is identified that one of these nine stars, HIP 24681, has six planets.

In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of solution are given. At the same time, modifying the classical definitions of continuous dependence and Ga^teaux differentiability, some results on continuous dependence and Ga^teaux differentiable of solution relative to the initial value also are presented in new topology sense. For the autonomous impulsive system, the periodicity of solution is given. As an application, properties of solution for a type of controlled nonlinear ordinary differential equation with impulses at variable times is obtained. These results are foundation to study optimal control problems of systems governed by the differential equations with impulses at variable times.

In this paper, we propose a partial differential equation model based on phase-field for sentiment analysis in the field of hotel comment texts. The comment texts are converted into word vectors using the Word2Vec tool, and then we utilize the multifractal detrended fluctuation analysis (MF-DFA) model to extract the generalized Hurst exponent of the word vector time series to achieve dimensionality reduction of the word vector data. The dimensionality reduced data is represented in a two-dimensional computational domain, and the modified Allen-Cahn (AC) function is used to evolve the phase values of the data to obtain a stable nonlinear boundary, thereby achieving automatic classification of hotel comment texts. The experimental results show that the proposed method can effectively classify positive and negative samples and achieve excellent results in classification indicators. We compared our proposed classifier with traditional machine learning models and the results indicate that our method possesses a better performance.

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

Background: Gut-Brain-Axis provides bidirectional communicational route; imbalance of which can have pathophysiological consequences. It is a frontier in autism research, affects 85% of autistic children (NIH report). Their microbiome has few overall microbes and smaller number of health promising microbes than their neurotypical peers. We hypothesize autism gut might play a role in manifestation of autism behaviours and on treatment, can revert back to normal behaviour considerably. The aim is to better understand to what degree gut microbiota of autism subjects differs from controls and identify bacterial species present exclusively in autism. Materials and Methods: 16s-rRNA-sequence of autism-subjects were retrieved from the American Gut Project Archive. Taxonomic assignment was inferred by similarity based methods using Quantitative Insights Into Microbial Ecology (QIIME). Species abundance was characterized and co-occurrence network was built to infer species interaction using measures of diversity. Statistical parameters were considered to validate the findings. Result: A total of 206 (1.8%) of American Gut Project datasets onstituted of autistic samples. Various bacteria such as Akkermansia sp., and Prevotella sp., were harboured in higher abundance in autistic children with statistical significance than in controls. Conclusion: These findings indicate connecting-link between gut-microbiome-brain-axis and autistic behaviour which can result in improved management

Flavonoids, compounds present in many dietary supplements, affect growth of different bacterial species when tested as purified or synthetic substances. Here, we asked if soy isoflavone extracts, commonly used in many products sold as anti-menopausal dietary supplements, influence bacterial growth similarly to synthetic isoflavone, genistein. Four commercially available products were tested in amounts corresponding to genistein concentrations causing inhibition of growth of Vibrio harveyi (a model bacterium sensitive to this isoflavone) and Escherichia coli (a model bacterium resistant to genistein). Differential effects of various extracts on V. harveyi and E. coli growth, from stimulation, through no changes, to inhibition, were observed. Moreover, contrary to genistein, tested extracts caused a decrease (to different extends) in viability of human dermal fibroblasts. These results indicate that effects of various soy isoflavone extracts on bacterial growth and viability of human cells are different, despite similar declared composition of the commercially available products.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

In this work we present some driving strategies for a type of omnidirectional mobile robot, the offset-differential robot. This system presents omnidirectionality while using any type of standard wheels, allowing for applications in all terrain. The work is based on the full kinematic and dynamic analysis of the robot, including the passive elements, to explain some unexpected behaviors that appear during its motion. The stable and unstable behaviors are characterized and some driving strategies are stated in order to achieve the desired performance regarding precise positioning and speed.

Partial differential equations (PDEs) are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and quantum mechanics. By solving PDEs, we can ob- tain insights into the behavior of the system and make predictions about its future evolution. Conventional numerical methods for obtaining the approximate solutions of PDEs may re- quire extensive computational resources and time, especially for complex PDEs and large- scale problems. The recently developed physics-informed neural network (PINN) has shown promise in a variety of scientific and engineering fields by incorporating physical laws into the loss functions of the neural network (NN). In addition, the training of PINN does not require ground truth data, but it has poor generalization ability to unseen domains. On the other hand, a convolutional neural network (CNN) has fast inference and better generalization ability, but it requires a large amount of training data. Taking the advantages of PINN and CNN by using Legendre multiwavelets (LMWs) as basis functions, we introduce a new method to approach the PDEs in this paper, namely Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), in order to continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any pre- computed training data, simultaneously providing fast and continuous solutions that gener- alize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, incompressible Navier-Stokes (N- S) equation, and two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

Background Polycystic ovary syndrome (PCOS) is a common hormonal disorder worldwide among women of reproductive age. It is characterized by endocrine, reproductive, and metabolic abnormalities. Insulin resistance (IR) is one of its most important clinical features, associated with metabolic disorders and increased risk of type 2 diabetes (T2D). This study aimed to explore the whole blood gene expression profiling related to IR in PCOS patients compared to controls. Methods Blood RNA was extracted from 5 PCOS and 5 non-PCOS women with matched age and BMI. Homeostasis model assessment (HOMA-IR) was used to estimate the IR. The expression of IR genes was analyzed by Profiler PCR array. Results Both groups have similar levels of HOMA-IR (p>0.05). However, differential expression levels were observed between them. Fourteen genes were upregulated and 26 genes were downregulated in PCOS samples. Among the upregulated genes (>2 fold-change, p-value<0.05) are ADIPOQ, ADIPOR1, OLR, IGF-1, and APOE. Downregulated genes (>-2 fold-change, p-value<0.05) include HK-2, IRS1, and SERPINE1. These genes are involved in insulin and adipokines signaling, commonly dysregulated in T2D. They are also involved in innate immunity and inflammatory processes and are essential for lipid and carbohydrate metabolism. Conclusion Our finding suggests that despite both groups having no difference in IR level, there are differentially expressed genes involved in the IR pathway.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix, and the Laplace transform. The fundamental solution is presented in a form of the convolutional powers of the kernel matrix in the manner of a convolutional exponential matrix function. The fundamental solution combined with a solution representation gives an exact expression in explicit form for the solution of a RFDE. Algebraic graph theory is applied to the RFDE in the form of a weighted loop-digraph to illuminate the system structure and system dynamics and to identify the strong and weak components. Examples are provided in the document to elucidate the behavior of the fundamental solution. The paper introduces fundamental solutions of other functional differential equations.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

This paper showed that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literature has stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We showed the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. With this understanding, the closed Reynolds Navier-Stokes turbulence equations of incompressible flows were formulated. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".

Traditional potential transformers have problems of large volume, difficulty in insulation, iron core saturation, ferroresonance overvoltage and poor transient response characteristics. The voltage sensor based on the principle of electric field coupling and differential input structure does not need to contact the measured object or ground, and can avoid the above problems. However, it requires a sufficiently high capacitance between the differential electrodes to obtain sufficient accuracy and a high voltage division ratio. The existing method of using mutual capacitance between the differential electrodes will cause many problems and fail to meet the practical needs. To solve the above problems, this paper innovatively uses multi-layer ceramic capacitor to replace the mutual capacitance and designs a new type of voltage sensor. In addition, by using single bypass small resistance grounding method to increase the input impedance of the differential signal processing circuit, error of the sensor is further reduced. The experimental results show that the sensor has excellent accuracy and great transient response characteristics. The ratio error under power frequency is within ±0.5% and the phase error is within 1. The ratio error in the range of 500 Hz∼30 kHz is within ±5% and the phase error is within 5. Moreover, it has the advantages of low cost, miniaturization, flexible shape and easy to adjust the voltage division ratio. These characteristics indicate that the sensor has good voltage measurement and sensor network potential.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

We classify all the topologically non-equivalent phase portraits of the quadratic polynomial differential system dx/dt = (1-2x)(y-x), dy/dt =y (2-g y-(5g-4)x/(g-1)), in the Poincaré disc for all the values of the parameter g in R\{1}. The differential system dx/dt = y-x, dy/dt =y (2-g y-(5g-4)x/(g-1))/(1-2x), when the parameter g in (1,2] models the structure equations of a static star in general relativity in the case of the existence of a homologous family of solutions, being x = m(r)/r where m(r)>= 0 is the mass inside the sphere of radius r of the star, y = 4pi r^2 rho where rho is the density of the star, and t = ln (r/R) where R is the radius of the star. We classify the possible values of m(r)/r and 4pi r^2 rho when r-->0.

Ageing is associated with a decline in both Nrf2 activity and DNA repair efficiency, leading to the accumulation of DNA damage and an increased risk of cancer. Understanding the mechanisms behind the increased level of damaged DNA during ageing is crucial for developing interventions to mitigate age-related cancer risk and improve overall health in older individuals. (Poly)phenols are plant-derived bioactive compounds that undergo metabolism into simpler phenolic catabolites following ingestion. While these compounds have been associated with various health benefits, further analysis of their bioavailable catabolites is necessary. To this end, four phenolic catabolites derived from colonic microbiota were investigated for their ability to reduce DNA damage in response to oxidative challenge and modulate the Nrf2-Antixoidant Response Element pathway. Normal and adenocarcinoma colonocyte cell lines (CCD 841 CoN, & HT29 respectively) were exposed to sub cytotoxic concentrations (>10 µM,) of hydroxylated (4-hydroxybenzoic acid, 3-(3’-hydroxyphenyl) propionic acid) and non-hydroxylated (benzoic acid or 3-phenylpropionic acid) phenolic acids. Using the COMET assay, each catabolite demonstrated significant (p<0.001) geno-protective activity, albeit with varying potency. They also significantly modulated expression of key genes in the Nrf2-ARE pathway, including Nrf2, Heme oxygenase-1 (HO-1), and NAD(P)H dehydrogenase quinone 1 (NQO1). Hydroxylation of the phenolic acids appeared to have a limited effect with respect to bioactivity. Overall, the colon derived phenolic metabolites, when assessed at physiologically relevant concentrations, reduced DNA damage in both normal and adenocarcinoma colonic cells in response to oxidative challenge, mediated – at least in part via upregulation of the Nrf2-ARE pathway.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.

The Pashmina and Barbari are two famous goat breeds found in the wide areas of the Indo-Pak region. Pashmina is famous for its long hair-fiber (Cashmere) production while Barbari is not-selected for this trait. So, the mRNA expression profiling in the skin samples of both breeds would be an attractive and judicious approach for detecting putative genes involved in this valued trait. Here, we performed differential gene expression analysis on publicly available RNA-Seq data from both breeds. Out of 44,617,994 filtered reads of Pashmina and 55,995,999 of Barbari which are 76.48% and 73.69% mapped to the ARS1 reference transcriptome assembly respectively. A pairwise comparison of both breeds resulted in 47,159 normalized expressed transcripts while 8,414 transcripts are differentially expressed above the significant threshold. Among these, 4,788 are upregulated in Pashmina while 3,626 transcripts are upregulated in Barbari. Fifty-nine transcripts harbor 57 genes including 32 LOC genes and 24 are annotated genes which were selected on the basis of TMM counts > 500. Genes with ectopic expressions other than uncharacterized and LOC symbol genes are Keratins (KRT) and Keratin Associated Proteins (KRTAPs), CystatinA&6, TCHH, SPRR4, PPIA, SLC25A4, S100A11, DMKN, LOR, ANXA2, PRR9 and SFN. All of these genes are likely to be involved in keratinocyte differentiation, sulfur matrix proteins, dermal papilla cells, hair follicles proliferation, hair curvature, wool fiber diameter, hair transition, hair shaft differentiation and its keratinization. These differentially expressed reported genes are critically valuable for enhancing the quality and quantity of the pashmina fiber and overall breed improvement. This study will also provide important information on hair follicle differentiation for further enrichment analyses and introducing this valued trait to other goat breeds as well.

Different bacterial species have dramatically different generation times, from 20-30 minutes in Escherichia coli to about two weeks in Mycobacterium leprae. The translation machinery in a cell needs to synthesize all proteins for a new cell in each generation. The three subprocesses of translation, i.e., initiation, elongation, and termination, are expected to be under stronger selection pressure to optimize in short-generation bacteria (SGB) such as Vibrio natriegens than in the long-generation Mycobacterium leprae. The initiation efficiency depends on the start codon decoded by the initiation tRNA, the optimal Shine-Dalgarno (SD) decoded by the anti-SD (aSD) sequence on small subunit rRNA, and the secondary structure that may embed the initiation signals and prevent them from being decoded. The elongation efficiency depends on the tRNA pool and codon usage. The termination efficiency in bacteria depends mainly on the nature of the stop codon and the nucleotide immediately downstream of the stop codon. By contrasting SGB with long-generation bacteria (LGB), we predict that 1) SGB to have more ribosome RNA operons to produce ribosomes, and more tRNA genes for carrying amino acid to ribosomes, 2) SGB to have a higher percentage of genes using AUG as start codon and UAA as stop codon than LGB, 3) SGB to exhibit better codon and anticodon adaptation than LGB, and 4) SGB to have weaker secondary structure near translation initiation signals than LGB. These differences between SGB and LGB should be more pronounced in highly expressed genes than lowly expressed genes. We present empirical evidence in support of these predictions.

The Standard Model is not a complete description of reality; it omits the existence of dark matter, dark energy, and an explanation as to why no CP violation has been observed. However, some of these phenomena could be explained through a new force mediated by a new boson. If such a boson were massless it would result in a power law potential and if massive the interaction would be Yukawa-like. A previous experiment employing a micro-mechanical oscillator and a spherical test mass interactions was successful in placing the best limits on a mass-mass Yukawa-like interaction, but the data was never analyzed in the context of a power law. Here that data is analyzed considering a power law for powers n = 1-5 where n is the number of boson exchanges. The results show that the limits obtained through power law analysis of this data are not better than the currently accepted limits. A discussion of an experiment design capable of producing better limits on power law extensions to the Standard Model is presented, and suggests micro mechanical oscillators based experiment remains capable of improving the limits by at least one order of magnitude.

This study aimed at exploring what role artificial intelligence techniques could play in the futural numerical analysis. In this paper, a convolutional neural network techniques based on modified loss function is proposed as a surrogate of finite element method(FEM). Several surrogate-based physics-informed neural networks(PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). Results from the proposed surrogate-based approach are in good agreement with ones from conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is indicated that to some extent the artificial intelligence technique could replace conventional numerical analysis as a great surrogate model.

The triple-negative breast cancer (TNBC) subtype is one of the most aggressive forms of breast cancer that has poor clinical outcome and still remains as an unmet clinical challenge. Accumulating evidence suggests that intratumoral heterogeneity or the presence of phenotypically heterogeneous cell populations within a tumor plays a crucial role in chemoresistance, tumor progression and metastasis. Increased understanding of the molecular regulators of intratumoral heterogeneity will enable the development of effective therapeutic strategies in TNBC. We have identified a molecular mediator involved in intratumoral heterogeneity in breast cancer using an unbiased approach. We isolated two heterogeneous tumor cell populations from the 4T1 TNBC tumor model and phenotypic characterization revealed that the cells are distinct in terms of their morphology, proliferation and self-renewal ability in vitro; as well as primary tumor formation and metastatic potential in vivo. Further, RNA sequencing on both cell populations was performed to identify the molecular mediators underlying this heterogeneity. Bioinformatic analysis performed on the differentially expressed genes along with the Kaplan-Meier survival analysis in TNBC patients identified Metastasis associated colon cancer 1 (Macc1) as the top candidate gene mediating the aggressive phenotype. The role of Macc1 in regulating the proliferative phenotype was validated using siRNA mediated gene knockdown. The role of Macc1 in the aggressive cancer cell phenotypes and disease progression is being studied further using a small molecule transcriptional inhibitor of Macc1 in cell line and animal models, thus increasing our understanding of the molecular underpinnings of intratumoral heterogeneity in breast cancer that is critical to the improvement in the treatment of women currently living with the highly aggressive TNBC subtype.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

Patients who have undergone surgery in early life may be at elevated risk for neuropathic pain in later life. The risk factors for this susceptibility are not fully understood. Here, we used a mouse chronic pain model to test the hypothesis that early exposure to general anesthetic (GA) causes cellular and molecular alterations in dorsal spinal cord (DSC) and dorsal root ganglion (DRG) that produces a predisposition to neuropathic pain via an upregulation of the mammalian target of the rapamycin (mTOR) signaling pathway. Mice were exposed to isoflurane at postnatal day 7 (P7) and underwent spared nerve injury at P28 which causes chronic pain. Selected groups were treated with rapamycin, an mTOR inhibitor, for eight weeks. Behavioral tests show early isoflurane exposure enhances susceptibility to chronic pain, and rapamycin treatment improves outcomes. Immunohistochemistry, Western blotting, and q-PCR indicates that isoflurane upregulates mTOR expression and neural activity in DSC and DRG. Accompanying upregulation of mTOR and rapamycin-reversible changes in chronic pain-associated markers, including N-cadherin, cAMP response element-binding protein (CREB), purinergic P2Y12 receptor, glial fibrillary acidic protein (GFAP) in DSC; and connexin 43, phospho-extracellular signal-regulated kinase (p-ERK), GFAP, Iba1 in DRG, were observed. We conclude that early GA exposure alters the development of pain circuits such that mice are subsequently more vulnerable to chronic neuropathic pain states.

The present study aimed to investigate the effect of cold deformation on the precipitation kinetics of a binary CuSc alloy containing 0.4 wt.% scandium using the experimental analysis method of differential scanning calorimetry (DSC). Non-deformed and 75% cross-section reduced cold-rolled, supersaturated specimens were tested at non-isothermal DSC runs at up to five different heating rates. The DSC results showed that cold deformation significantly accelerated the precipitation process in the binary alloy, leading to a decrease in the initial and peak temperatures of the exothermic reactions. The activation energies calculated with the Kissinger method, indicated that the precipitation activation energy decreased with increasing cold deformation. The findings of this study provide worthy implications to further optimize the processing of Cu-Sc alloys with improved mechanical properties.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

In this study dual PET and contrast enhanced MRI were combined to investigate their correlation per voxel in patients at initial diagnosis with suspected glioblastoma. Correlation with contrast enhancement (CE) as an indicator of BBB leakage was further used to evaluate whether PET signal is likely caused by BBB disruption alone, or rather attributable to specific binding after BBB passage. PET images with [18F]GE180 and the amino acid [18F]FET were acquired and normalized to healthy background (TBR). Contrast enhanced images were normalized voxel by voxel with the pre-contrast T1-weighted MRI to generate relative CE values (rCE). Voxel-wise analysis revealed a high PET signal even within the sub-volumes without detectable CE. No to moderate correlation of rCE with TBR voxel-values and a small overlap as well as a larger distance of the hotspots delineated in rCE and TBR-PET images were detected. In contrast, voxel-wise correlation between both PET modalities was strong for most patients and hotspots showed a moderate overlap and distance. The high PET signal in tumor sub-volumes without CE observed in voxel-wise analysis as well as the discordant hotspots emphasize the specificity of the PET signals and the relevance of combined differential information from dual PET and MRI images.

A plant’s early response to pathogen stress is a vital indicator of its disease resistance. In order to study the response mechanism of resistant and susceptible flax cultivars to Fusarium oxysporum f. sp. lini (Foln), we applied RNA-sequencing to analyze transcriptomes of flax with Foln 0.5, 2 and 8 hours post inoculation (hpi). We found a significant difference in the number of differential expression genes (DEGs) between resistant and susceptible flax clutivars. The number of DEGs in the Fusarium-resistant cultivar increased dramatically at 2 hpi, and a large number of DEGs participated in the Fusarium-susceptible cultivar response to Foln infection 0.5 hpi. GO enrichment analysis determined that the up-regulated DEGs of both flax cultivars were enriched such as oxidoreductase activity and oxidation-reduction process. At the same time, the genes involved in diterpenoid synthesis were up-regulated in resistant cultivar, while those involved in extracellular region, cell wall and organophosphate ester transport were down-regulated in susceptible cultivar. KEGG enrichment analysis showed the genes encoded WRKY 22 and WRKY33 which involved in MAPK signaling pathway were up-regulated expressed in S-29 and down-regulated expressed in R-7, negatively regulated the disease resistance of flax; The genes encoded Hsp 90 family which in involved in plant pathogen interaction pathway were up-regulated in R-7 and down-regulated in S-29, which positively regulated the disease resistance of flax; The genes encoded MYC2 transcription factor and TIFY proteins which involved in plant hormone signaling pathway were up-regulated in R-7, and regulated the jasmonic acid metabolism of flax and the signal transduction of plant hormones. Meanwhile seven regulatory genes with the most correlation were screened out, Among Lus10025000.g and Lus10026447.g regulated other genes expressed both in plant hormone signal transduction pathway and MAPK signal pathway. In conclusion, these findings will facilitate further studies on the function of these candidate genes in flax of response to Fusarium stress, and the breeding of disease-resistant flax cultivar.

Indiana Vesiculovirus (IVV; formerly as Vesicular stomatitis virus and Vesicular stomatitis Indiana virus) causes a disease in livestock that is very similar to the foot and mouth disease thereby an outbreak may lead to significant economic loss. Long-read sequencing (LRS) -based approaches revealed a hidden complexity of the transcriptomes in several viruses already. This technique was utilized already for the sequencing of the IVV genome, but our study is the first for the application of this technique for the profiling of IVV transcriptome. Since LRS is able to sequence full-length RNA molecules, and thereby providing more accurate annotation of the transcriptomes than the traditional short-read sequencing methods. The objectives of this study were to assemble the complete transcriptome of using nanopore sequencing, to ascertain cell-type specificity and dynamics of viral gene expression and to evaluate host gene expression changes induced by the viral infection. We carried out a time-course analysis of IVV gene expression in human glioblastoma and primate fibroblast cell lines using a nanopore-based LRS approach and applied both amplified and direct cDNA sequencing, as well as cap-selection for a fraction of samples. Our investigations revealed that, although the IVV genome is simple, it generates a relative complex transcriptomic architecture. In this study, we also demonstrated that IVV transcripts vary in structure and exhibit differential gene expression patterns in the two examined cell types.

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for a) describing the dynamics and b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and non-linearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of non-linearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

Fungal keratitis (FK) is an invasive infection of the cornea primarily associated with Aspergillus and Fusarium species. FK is treated empirically with a limited selection of topical antifungals with varying levels of success. Though clinical infections are typically characterized by a dense network of mature mycelium, traditional models used to test antifungal susceptibility of FK isolates exclusively evaluate susceptibility in fungal cultures derived from asexual spores known as conidia. The purpose of this study was to characterize differences in fungal response when topical antifungal treatment is initiated at progressive phases of fungal development. We compared efficacy of voriconazole and luliconazole against in vitro cultures of A. flavus and F. keratoplasticum at 0, 24, and 48 h of fungal development. A porcine cadaver corneal model was used to compare antifungal efficacy of voriconazole and luliconazole in ex vivo tissue cultures of A. flavus and F. keratoplasticum at 0, 24, and 48 h of fungal development. Our results demonstrate phase-dependent susceptibility of both A. flavus and F. keratoplasticum to both azoles in vitro as well as ex vivo. We conclude that traditional antifungal susceptibility testing with conidial suspensions does not correlate with fungal susceptibility in cultures of a more advanced developmental phase. A revised method of antifungal susceptibility testing that evaluates hyphal susceptibility may better predict fungal response in the clinical setting where treatment is often delayed until days after the initial insult.

Water stress is one of the main factors affecting the development of agricultural crops. An inno-vative alternative to improve tolerance to water stress is the application of biostimulants. In the present study, the efficacy and physiological and biochemical responses of different biostimulants were evaluated in beans under moderate and severe stress. The treatments consisted of three types of irrigation: FC100, without water stress, FC75, irrigation reduced by 25% (moderate water stress) and FC50, irrigation reduced by 50% (severe water stress). In the treatments with water deficit, foliar biostimulants were applied: zinc oxide nanoparticles plus chitosan, Codasil®, Osmoplant®, Stimplex® and salicylic acid. Foliar application of ZnO + chitosan nanoparticles benefited biomass accumulation and yield under moderate water stress (FC75) and Codasil® and Osmoplant® under severe water stress (FC50). Proline, free sugars and gas exchange were higher under the application of ZnO + chitosan nanoparticles under moderate water stress and under Codasil® and Osmoplant® under severe water stress. Depending on the severity of water stress, ZnO + chitosan nanoparticles, Codasil® and Osmoplant® are viable products to increase tolerance in green bean cv. Strike plants.

Partial Differential Equations (PDEs) constitute a fundamental framework for modeling various physical phenomena across diverse fields such as physics, engineering, and finance. Solving PDEs accurately and efficiently remains a significant challenge, particularly when dealing with complex systems or high-dimensional data. In this paper, we present a novel approach based on deep learning techniques to investigate the effective factors in solving PDEs. Our methodology leverages the expressive power of deep neural networks to learn and represent the underlying relationships between input parameters and the solutions of PDEs. By incorporating domain knowledge into the network architecture and training process, our approach aims to provide insights into the key factors influencing the solution of PDEs. We demonstrate the effectiveness of our method through numerical experiments on various PDEs, showcasing its capability to identify important features and improve predictive accuracy. Our findings suggest that deep learning techniques offer a promising avenue for understanding and analyzing the complex dynamics inherent in PDEs, paving the way for enhanced computational methods in scientific and engineering applications.

Differential diagnosis of solid pancreatic lesions (SPLs) using B-mode endoscopic ultrasonography (EUS) is challenging. Detective flow imaging (DFI) offers the potential for detecting low-flow vessels in the pancreas, thus enhancing diagnostic accuracy. This study aimed to investigate DFI-EUS findings of SPLs and analyze their differential diagnostic accuracy for pancreatic cancer. This retrospective study included patients with pathologically confirmed SPLs who underwent EUS between April 2021 and June 2023. Expert endosonographers, blinded to the patients’ clinical data, evaluated images obtained through B-mode, eFLOW, and DFI-EUS. Frame rate and vessel detection sensitivity between eFLOW and DFI were compared, and diagnostic criteria for pancreatic cancer were established. This study included 104 patients, most diagnosed with pancreatic cancer. DFI-EUS demonstrated a significantly higher vessel visualization rate (96%) in SPLs compared to eFLOW (27%). Additionally, DFI showed a superior frame rate, sensitivity (99%), and accuracy (88%) in detecting pancreatic cancer, although with a modest specificity (43%). On DFI-EUS, characteristics such as hypovascular, peritumoral, or spotty vessel findings were suggestive of pancreatic cancer. DFI-EUS significantly improved the visualization of vascular structures within the SPLs, highlighting its efficacy as a diagnostic modality for pancreatic cancer.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

The work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

To guide analysts to select the right tool and parameters in differential gene expression analysis of single-cell RNA sequencing (scRNA-seq) data, we developed a novel simulator that recapitulates the data characteristics of real scRNA-seq datasets while accounting for all the relevant sources of variation in a multi-subject, multi-condition scRNA-seq experiment: the cell-to-cell variation within a subject, the variation across subjects, the variability across cell types, the mean/variance relationship of gene expression across genes, library size effects, group effects, and covariate effects. By applying it to benchmark 12 differential gene expression analysis methods (including cell-level and pseudo-bulk methods) on simulated multi-condition, multi-subject data of the 10x Genomics platform, we demonstrated that methods originating from the negative binomial mixed model such as glmmTMB and NEBULA-HL outperformed other methods. Utilizing NEBULA-HL in a statistical analysis pipeline (https://github.com/interactivereport/scRNAseq_DE) for single cell analysis will enable scientists to better understand cell-type specific transcriptomic response to disease or treatment effects and to discover new drug targets. Further, application to two real datasets showed the outperformance of our differential expression (DE) pipeline, with unified findings of differentially expressed genes (DEG) and a pseudo-time trajectory transcriptomic result. In the end, we made recommendations of filtering strategies of cells and genes based on simulation results to achieve optimal experimental goals.

Recently, hybrid logic circuits based on magnetic tunnel junctions (MTJs) have been widely investigated to realize zero standby power. However, such hybrid CMOS/MTJ logic circuits suffer from a severe sensing reliability due to the limited tunnel magnetoresistance ratio (TMR≤150%) of the MTJ and the large process variation in the deep sub-micrometer technology node. In this paper, a novel differential sensing amplifier (DSA) is proposed, in which two PMOS transistors are added to connect the discharging branches and evaluation branches. Owing to the positive feedback realized by these two added PMOS transistors, it can achieve a large sensing margin. By using an industrial CMOS 40 nm design kit and a physics-based MTJ compact model, hybrid CMOS/MTJ simulations have been performed to demonstrate its functionality and evaluate its performance. Simulation results show that it can achieve a smaller sensing error rate of 9% in comparison with the previously proposed DSAs with the TMR ratio of 100% and process variation of 10%, while maintaining almost the same sensing delay of 74.5 ps and sensing energy of 1.92 fJ/bit.

In this study, we first present a time-fractional L$\hat{e}$vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L$\hat{e}$vy-time fractional diffusion equation of European-style options. Introduce a more general model from the models based on the L$\hat{e}$vy-time fractional diffusion equation and review some recent findings regarding of the Europe option pricing of risk-neutral free.

Veratrum californicum is a rich source of steroidal alkaloids such as cyclopamine, a known inhibitor of the Hedgehog (Hh) signaling pathway. Here we provide a detailed analysis of the alkaloid composition of V. californicum by plant part through quantitative analysis of cyclopamine, veratramine, muldamine and isorubijervine in the leaf, stem and root/rhizome of the plant. To determine if additional alkaloids in the extracts contribute to Hh signaling inhibition, we replicated the concentrations of these alkaloids observed in extracts using commercially available standards and compared the inhibitory potential of the extracts to alkaloid standard mixtures using Shh-Light II cells. Alkaloid combinations enhanced Hh signaling pathway antagonism compared to cyclopamine alone, and significant differences were observed in the Hh pathway inhibition between the stem and root/rhizome extracts and their corresponding alkaloid standard mixtures, indicating that additional alkaloids present in these extracts contribute to Hh signaling inhibition.

In this study we sought to investigate the impact of urbanization, presence of concrete river bottom, and nutrient pollution on microbial communities along the L.A. River. Six molecular markers were evaluated for identification of bacteria, plants, fungi, fish, and invertebrates in 90 samples. PCA (principal components analysis) was used with PAM (partitioning around medoids) clustering to reveal community structure and an NB (Negative binomial) model in DESeq2 was used for differential abundance analysis. PCA and factor analysis exposed the main axes of variation but were sensitive to outliers. Differential abundance of Proteobacteria was associated with soft bottom sites, and there was an apparent balance in the abundance of organisms responsible for nitrogen cycling. Nitrogen cycling was explained by differential abundance of ammonia oxidizing archaea, the complete ammonia oxidizers Nitrospira sp., nitrate reducing bacteria Marmoricola sp., and nitrogen fixing bacteria Devosia sp. which were differentially abundant at soft-bottom sites (p adj &lt; 0.002). In contrast, differential abundance of several Cyanobacteria and other anoxygenic phototrophs was associated with the concrete bottom sites, which suggested the accumulation of excess nitrogen. The soft bottom sites tended to be represented by differential abundance of aerobes, whereas the concrete-associated species tended to be alkaliphilic, saliniphilic, calciphilic, sulfate dependent, and anaerobic. In Glendale Narrows, downstream from multiple water reclamation plants, there were differential abundance of cyanobacteria and algae, however indicator species for low nutrient environments and ammonia-abundance were also present. There was differential abundance of ascomycetes associated with Arroyo Seco and a differential abundance of Scenedesmaceae green algae and cyanobacteria in Maywood, in the analysis which compared suburban with urban river communities. The proportion of Ascomycota to Basidiomycota within the LA River differed from the expected proportion based on published worldwide freshwater and river 18S data; the shift in community structure was most likely associated with the extremes of urbanization. This study indicates that extreme urbanization can result in overrepresentation of cyanobacterial species that could cause reductions in water quality and safety.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

Recent years brought great focus in the field of development of extracellular vesicles (EVs) based drug-delivery systems. Considering possible applications of EVs as a drug carriers the isolation process is a crucial step. To solve problems related with EV isolation, we created and validated a new EVs isolation method – Low Vacuum Filtration (LVF) and compared it with two commonly applied procedures - differential centrifugation (DC) and ultracentrifugation (UC). EVs isolated from endothelial cells culture media have been characterized by a) transmission electron microscopy (TEM) b) nanoparticle tracking analysis (NTA), c) western blot and d) Fourier-Transform Infrared Spectroscopy (FTIR). Additionally, the membrane surface have been imaged with Environmental Scanning Electron Microscopy (ESEM). We showed that LVF is reproducible and efficient method for EVs isolation form conditioned media. Additionally, we observed correlation between ATR-FTIR spectra quality and the EVs and proteins concentration. ESEM imaging confirmed that actual pore diameter are close to the values calculated theoretically. LVF method is an easy, fast and inexpensive EVs isolation method which allows for isolation of both ectosomes and exosomes from high volume sources with good repeatability. We think that it could be an efficient alternative for commonly applied methods.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

The article proposes an indirect measurement method based on a dimensional and shape analysis of forgings for the evaluation of the manufacture and the proper operation of the key elements of the crank press, in which after modernization, a quick tool assembly based on SMED (Single Minute Exchange of Die) was implemented. As a result of the introduced changes aiming at improving the forging aggregate and increasing the production efficiency, errors were observed on the manufactured products-forgings in the form of twists and joggles. The preliminary analysis showed that they can be clearances and dynamic deformation in the kinematic chain, the occurrence of side forces during automatic forging of the forging in a two-component system (a long, thin element), as well as the design and construction errors in the joining of the SMED instrument with the table tops of the press. In order to solve the presented problem, in the first place, a separate dimensional and shape analysis was made of selected elements of the press and the instrumentation with the use of the 3D scanning method with the purpose to analyze the construction tolerances of the key elements of the press geometry. Next, an evaluation of the effect of clearances and dynamic deformations of the press as well as the force distribution during the forging process was made through numerical modelling. Despite all of the above, such an approach did not make it possible to solve the problem. A proprietary method with the use of 3d reverse scanning was proposed, which allowed to solve the problem of forgings errors. Based on the measurement results and analyses for a few variants of production cycles the necessary changes was obtained, making it possible to minimize the errors and obtain proper products in respect of geometry and quality.

PCSK9 is implicated in familial hypercholesterolemia via targeting the cell surface PCSK9-LDLR complex toward lysosomal degradation. The M2 repeat in the PCSK9's C-terminal domain is essential for its extracellular function, potentially through its interaction with an unidentified “protein X”. The M2 repeat was recently shown to bind an R-x-E motif in MHC-class-I proteins (implicated in the immune system), like HLA-C, and causing their lysosomal degradation. These findings suggested a new role of PCSK9 in the immune system and that HLA-like proteins could be “protein X” candidates. However, the participation of each member of the MHC-I protein family in this process and their regulation of PCSK9's function have yet to be determined. Herein, we compared the implication of MHC-I-like proteins such as HFE (involved in iron homeostasis) and HLA-C on the extracellular function of PCSK9. Our data revealed that the M2 domain regulates the intracellular sorting of the PCSK9-LDLR complex to lysosomes, and that HFE is a new target of PCSK9 that inhibits its activity on the LDLR, whereas HLA-C enhances its function. This work suggests the potential modulation of the PCSK9 functions through interactions of HFE and HLA-C.

Purpose: To examine the effectiveness of patterned laser trabeculoplasty (PSLT) as an additional treatment for patients of open-angle glaucoma (OAG) receiving maximized ocular hypotensive medications (OHM). Methods: Forty eyes of 33 patients (average age 72.7±10.7 years) who had not previously undergone open glaucoma surgery or laser trabeculoplasty and were treated with maximized OHM between June 2018 and March 2022 were included. A 360-degree PSLT was conducted and postoperative intraocular pressure (IOP) and survival curves at 1, 3, 6, 9, and 12 months were evaluated. Results: According to the Kaplan-Meier survival analysis, the average survival time was 8.1 months with death defined as postoperative IOP reduction of less than 10% or requiring additional treatment. The average survival time was 4.9 months with death defined as postoperative IOP reduction of less than 20% or requiring additional treatment. In the 31 eyes which received no additional treatment after PSLT, the mean preoperative IOP was 18.5±3.9 mmHg, which reduced to 15.3±4.1 mmHg (p=1.62 x 10-6)), 15.5±3.4 mmHg (p=1.51 x 10-5), 15.7±4.0 mmHg (p=1.75 x 10-5), 14.7±4.38 (p=2.89 x 10-6), and 15.0±4.0 mmHg (p=5.74 x 10-9) at 1, 3, 6, 9 and 12 months after PSLT, respectively. The IOP reduction rate one year after PSLT was 18.7%. Thirteen of the 31 eyes (42%) achieved a 20% reduction in IOP compared to the baseline. Conclusion: Adjunctive treatment with PSLT in OAG patients receiving maximized OHM may be effective over 12-months of follow-up.

Evolutionary algorithms find applicability in reinforcement learning of neural networks due to their independence from gradient-based methods. To achieve successful training of neural networks using evolutionary algorithms, careful considerations must be made to select appropriate algorithms due to the availability of various algorithmic variations. In Part1 and Part2, the author previously reported experimental evaluations on Genetic Algorithm and Evolution Strategy for reinforcement learning of neural networks, utilizing the Acrobot control task. This article constitutes Part3 of the series of comparative research. In this study, Differential Evolution is adopted as the third instance of major evolutionary algorithms. The experimental results show a statistically significant superiority of DE over both GA and ES (p < .01). In addition, DE exhibits its robustness to variations in hyperparameter configurations (the number of offsprings and generations). In the previous experiments, both ES and GA showed significant performance differences depending on the configurations, whereas in the experiment reported in this article, such differences are not detected for DE.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of corona-virus disease 19 (COVID-19) and employs angiotensin-converting enzyme 2 (ACE2) as the recep-tor. Although the expression of ACE2 is crucial for cellular entry, we found that the interaction of ACE2 with the Spike (S) protein in the same cells led to its downregulation through degradation in the lysosomal compartment via the endocytic pathway. Interestingly, the ability of the S protein from previous variants of concern (VOCs) to downregulate ACE2 was variant-dependent and correlated with disease severity. The S protein from the Omicron variant, associated with milder disease, exhibited a lower capacity to downregulate ACE2 than that of the Delta variant, which is linked to a higher risk of hospitalization. Chimeric studies between the S proteins from the Delta and Omicron variants revealed that both the receptor-binding domain (RBD) and S2 subunit played crucial roles in the reduced ACE2 downregulation activity observed in the Omicron var-iant. In contrast, three mutations (L452R/P681R/D950N) located in the RBD, S1/S2 cleavage site, and HR1 domain were identified as essential for the higher ACE2 downregulation activity ob-served in the Delta variant than that in the other VOCs. Our results suggested that dysregulation of the renin-angiotensin system due to the ACE2 downregulation activity of the S protein of SARS-CoV-2 may play a key role in the pathogenesis of COVID-19.

A systematic and comprehensive review of critical applications of Blockchain Technol-ogy with Differential Privacy integration lies within the privacy and security enhancement. This paper aims to highlight the research issues in the e-health domain (e.g., Electronic Medical Rec-ords) and to review the current research directions in Differential Privacy integration with Blockchain Technology.(1) Background: The current state of the art in the e-health domain is identified as follows: (a) healthcare information poses a high level of security and privacy concerns due to its sensitivity; (b) due to vulnerabilities surrounding the healthcare system, a data breach is common and presents a risk for attacks by an adversary; and (c) the current privacy and security apparatus needs further fortification. (2) Methods: The methodology uses a systematic literature review (SLR) to identify and select relevant research papers and academic journals in DP and BT. (3) Results: The results are categorized into: e-Health Record Privacy, Real-Time Health Data, and Health Survey Data Protection to identify inherent issues with Differential Privacy integra-tion with Blockchain and technical challenges.(4) Conclusion: This review thoroughly surveyed and summarized Differential Privacy mechanisms in EMR privacy, real-time health data, and health survey data protection while highlighting challenges.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

The theory of electron spin has been proposed for a century, but the study of quantum effects in biological molecules is still in its infancy. Chirality-induced spin selectivity (CISS) is a very modern theory that can explain many biochemical phenomena. In this paper, we propose a new theoretical model based on CISS theory and quantum chemistry theory, which can well explain the theoretical explanation of the chiral selectivity of chiral proteins. Moreover, this theory can predict the spin state of corresponding chiral molecules. Taking L-DOPA and AADC enzyme as examples, this theoretical model solves the theoretical explanation of AADC enzyme's chiral catalysis selectivity problem and successfully predicts the spin state of L-DOPA and D-DOPA's valence electrons.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

The aim of this study was to identify the differentially expressed genes (DEG) from the skeletal muscle and liver samples of animal model for metabolic diseases in human. To perform the study, the fatty acid (FA) profile and RNA sequencing (RNA-Seq) data of 35 samples of liver tissue (SOY1.5, n=17 and SOY3.0, n=18) and 36 samples of skeletal muscle (SOY1.5, n=18 and SOY3.0, n=18) of Large White pigs were analyzed. The FA profile of the tissues was modified by the diet, mainly those related to monounsaturated (MUFA) and polyunsaturated (PUFA) FA. The skeletal muscle transcriptome analysis revealed 45 DEG (FDR 10%), and the functional enrichment analysis identified network maps related to inflammation, immune process, and pathways associated with the oxidative stress, type 2 diabetes and metabolic dysfunction. For the liver tissue, the transcriptome profile analysis revealed 281 DEG, which participate in network maps related to neurodegenerative diseases. With this nutrigenomics study, we verified that different levels of soybean oil in the pig diet, an animal model for metabolic diseases in humans, affected the transcriptome profile of skeletal muscle and liver tissue. These findings may help to better understand the biological mechanisms that can be modulated by the diet.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

The refractive index of a liquid serves as a fundamental parameter reflecting its composition, thereby enabling the determination of component concentrations in various fields such as chemical research, food industry, and environmental monitoring. Traditional methods for refractive index (RI) measurement rely on light deflection angles at interfaces between the liquid and a material of known refractive index. In this paper, the authors present a new differential refractometer for highly sensitive measurement of RI differences between two liquid samples. Using a configuration with two cells equipped with flat parallel plates as measuring elements, the instrument facilitates accurate analysis. Namely, the sensor signals from both the solution and the solvent cuvette are generated simultaneously with one laser pulse, reducing the possible fluctuations of the laser radiation intensity. Our evaluation shows the high sensitivity of RI measurements (< 7 · 106), so this differential refractometer can be proposed not only as a high-sensitivity sensing tool that can be used for mobile detection of nanoparticles in solution samples, but also to determine the level of environmental nano-pollution using water (including rain, snow) samples from various natural as well as industrial sources, thus helping to solve some important environmental problems.

The National Institute of Justice reported that current methods for processing sexual assault samples have a high failure rate, with 60 to 80 percent of tested kits unable to produce usable DNA profiles. Even when samples test positive for male DNA, 34 percent of sexual assault kits (SAK) do not yield recovered male DNA after differential extraction. Less than 30% recovery of available sperm DNA contributes to this low success rate. The SpermX™ method (SX) has been shown to recover 80 percent or more of sperm DNA from sexual assault samples. An interlaboratory evaluation compared SX to standard differential extraction (DE) protocols. Mock samples with known ratios of female epithelial cells and sperm cells were processed using both methods. Results revealed that SX consistently provided CODIS up-loadable DNA profiles, even with as few as 25 sperm cells, whereas DE failed to produce usable results. On average, SX yielded a seven-fold increase in the recovery of unshared male alleles compared to DE. In conclusion, SX outperformed DE in recovering higher quantities of male DNA with minimal female carryover in sexual assault-type samples. This improved success rate in obtaining usable DNA profiles can significantly aid in solving sexual assault cases. Keywords: Differential extraction, Sexual Assault Kit (SAK), Sperm DNA, STRmix™, Combined DNA Index System (CODIS), Forensic DNA analysis, Low Sperm Samples, DNA Mixtures, Autosomal STR Analysis, SpermX.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

The reduction of biodiversity loss is one of the targets of the 2030 Agenda for Sustainable Development. The protection of endangered species is critical for conserving global biodiversity. Asian elephants，as one of the last few mega-herbivores on Earth, are currently threatened by climate changes and anthropogenic modifications. The modelling of their living habitats is of top priority to the conservation of Asian elephant. In this study, we used the maximum entropy model (MaxEnt) to identify the current and potential future habitats of Asian elephants in South and Southeast Asia. We performed analyses for future projections with 17 scenarios by using the present results as baseline. To optimise the modelling results, we delineated the core habitats by using the Core Mapper Tool and compared them with existing protected areas (PAs) through gap analysis. The results showed that the current total area of core habitats is 491,455 km2 in size and will be reduced to 332,544 km2 by 2090 under SSP585 (the shared socioeconomic pathway). The projection analysis under differential scenarios suggested that most of the core habitats in the current protected areas would remain stable and suitable for elephants in the future. However, the remaining 75.17% of the core habitats lay outside the current PAs, and finally we mapped approximately 219,545 km2 of suitable habitats as priority protected areas in the future. Although our model did not perform well in some regions, our analyses and findings still could provide useful references to the planning of protected areas and conservation of Asian elephant.

Structural and biochemical studies have recently revealed a range of rationally engineered nanobodies with efficient neutralizing capacity against SARS-CoV-2 virus and resilience against mutational escape. In this work, we combined atomistic simulations and conformational dynamics analysis with the ensemble-based mutational profiling of binding interactions for a diverse panel of SARS-CoV-2 spike complexes with nanobodies. Using this computational toolkit, we identified dynamic signatures and binding affinity fingerprints for the SARS-CoV-2 spike protein complexes with nanobodies Nb6 and Nb20, VHH E, a pair combination VHH E+U, a biparatopic nanobody VHH VE, and a combination of CC12.3 antibody and VHH V/W nanobodies. Through ensemble-based deep mutational profiling of stability and binding affinities, we identify critical hotspots and characterize molecular mechanisms of SARS-CoV-2 spike protein binding with single ultra-potent nanobodies, nanobody cocktails and biparatopic nanobodies. By quantifying dynamic and energetic determinants of the SARS-CoV-2 S binding with nanobodies, we also examine the effects of circulating variants and escaping mutations. We found that mutational escape mechanisms may be controlled through structurally and energetically adaptable binding hotspots located in the host receptor-accessible binding epitope that are dynamically coupled to the stability centers in the distant epitope targeted by VHH U/V/W nanobodies. The results of this study suggested a mechanism in which through cooperative dynamic changes, nanobody combinations and biparatopic nanobody can modulate the global protein response and induce the increased resilience to common escape mutants.

Tularemia is a zoonotic disease caused by {\it Francisella tularensis} bacteria, a gram-negative coccobacillus-shaped bacterium. There are multiple transmission routes of the infection to humans such as consumption of contaminated food or water, handling of infected animals or bites from {\it haematophagous} arthropods (such as ticks, deer flies, or mosquitoes). In this study we focus on transmission via the bites of ticks and developed a deterministic model of ordinary and impulsive differential equations to gain insight in the differential effect of prescribed fire on {\it Demacenta variablis} and {\it Amblyomma americanum} ticks and the prevalence of tularemina. We found that prescribed fire differentially reduce the number of the two ticks with {\it A. americanum} reduced the least compare to {\it D. variablis} subsequently leading to differential increase of tularemia new infected cases in humans and rodents. Our result further indicates that the spatial arrangement of burn against unburn areas may not matter as either arrangement led to fewer ticks and reduction in tularemia transmission when prescribed fire was implemented. The results of this study provide important new understandings of the intricate effect of prescribed fire on tick species, and the dynamics of the tick-borne disease, tularemia disease in this study.

Transposable elements (TEs) are repetitive elements which make up around 45% of the human genome. A class of TEs known as SINE-VNTR-Alu (SVA) demonstrate the capacity to mobilise throughout the genome, resulting in SVA polymorphisms for presence or absence within the population. Although studies have previously highlighted the involvement of TEs within neurodegenerative diseases, such as Parkinson’s disease and amyotrophic lateral sclerosis (ALS), however the exact mechanism has yet to be identified. In this study we used whole genome sequencing and RNA sequencing data of ALS patients and healthy controls from the New York Genome Center ALS Consortium, to elucidate the influence of reference SVA elements on gene expression genome-wide within central nervous system (CNS) tissues. To investigate this, we applied matrix expression quantitative trait loci analysis and demonstrated that reference SVA insertion polymorphisms can significantly modulate the expression of numerous genes, preferentially in the trans position, and in a tissue-specific manner. We also highlight that SVAs significantly regulate mitochondrial genes as well as genes within the HLA and MAPT loci, previously associated within neurodegenerative disease. In conclusion, this study continues to bring to light the effects of polymorphic SVAs on gene regulation and further highlights the importance of TEs within disease pathology.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. This asymptotic phenomena is observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem.

This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.

Ditching-rotary tiller was widely used in tillage and ditching furrow during rapeseed sowing. As its ditching furrow system (consist of four identical ditching plows) would bear great drag resistance from the soil during operation, the ditching plow was optimized based on differential geometry analysis and EDEM simulation. Resistance-velocity simulation indicated the plow with parabolic type guide curve had better reduce-drag characteristics. Differential geometry analysis indicated decay rate of E and growth rate of G could represent the variable regularity of drag resistance with the increase of velocity. The L value could represent the magnitude of drag resistance. The smaller L value, decay rate of E and growth rate of G, the better drag-reduce characteristics. Quadratic rotation orthogonal combination design shown the optimal structural parameter values were: Δθ=15°, θmin=45°, h=250mm, l=100mm. The minimum average drag resistance was 230.1N. The differential geometry analysis of optimal ditching plow shown |dE/dκ| and |dG/dκ| could obtain minimum value, indicating growth rate of drag resistance for optimal plow was the lowest within the experimental level. Field experiment indicated the operation effect of optimized ditching furrow system could met the requirements of rapeseed sowing. The research provided in-depth theoretical guidance for Drag-reduce design of plow.