Analyzing reciprocity dynamics in supply chains of public goods: a stochastic evolutionary game approach.

To start with an infinitely repeated game of supply chains of public goods, a stout reciprocity mechanism is introduced into income games to build a matric dynamic equation. The conventional evolutionary game method is employed to propose a model called the evolutionary game for the cooperative strategy of both the manufacturer and the seller groups in the supply chain of public goods. Also, white Gaussian noise (WGN) is added to reflect random interference in the evolution process. Then, a stochastic dynamic system is established, and Ito's differential equation is used to analyze both sides' strategy evolution in a game, interpret changes in system stability when random disturbance is added, and finally test the influence of different situations on the system stability by running a numerical simulation. The research shows that the stronger the reciprocity coefficient is, and the system is subjected to random interference, the greater the strategy choice change in players' decision-making procedures when the repeated game of public goods is conducted.

Revealing endogenous conditions for Peto's paradox via an ordinary differential equation model.

Cancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto's paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto's paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.

Modelling the spatial risk pattern of dementia in Denmark using residential location data: A registry-based national cohort.

Dementia is a major global public health concern that is increasingly leading to morbidity and mortality among older adults. While studies have focused on the risk factors and care provision, there is currently limited knowledge about the spatial risk pattern of the disease. In this study, we employ Bayesian spatial modelling with a stochastic partial differential equation (SPDE) approach to model the spatial risk using complete residential history data from the Danish population and health registers. The study cohort consisted of 1.6 million people aged 65 years and above from 2005 to 2018. The results of the spatial risk map indicate high-risk areas in Copenhagen, southern Jutland and Funen. Individual socioeconomic factors and population density reduce the intensity of high-risk patterns across Denmark. The findings of this study call for the critical examination of the contribution of place of residence in the susceptibility of the global ageing population to dementia.

Study on Calculation Method of Bending Performance of Concrete Sandwich Composite Slab.

In order to explore the flexural behavior of a concrete sandwich panel under concentrated boundary conditions, based on Kirachhoff's elastic thin plate theory in this paper, the geometric deformation, physical conditions, and equilibrium relationship of a sandwich panel are deduced by constructing the layered analysis model of the sandwich panel, the basic differential equation of the flexural deformation of the concrete sandwich thin plate is obtained, and the mathematical expression of the internal force and displacement under the boundary condition of concentrated support is given. Combined with an engineering example, the proposed calculation method is verified. The results show that, in the arrangement of reliable connectors for concrete sandwich panels, the concrete wythes bear the load while the contribution of the core layer to the bending capacity of the structure can be ignored. When subjected to a laterally distributed load, the sandwich panel mainly experiences out-of-plane bending deformation, and the bending normal stress in the concrete panel layer shows a linear non-uniform distribution along the thickness direction of the panel. The bending deformation performance and bearing efficiency of a concrete sandwich slab with the change in concentrated support position have significant effects, and the load transfer efficiency can be improved by optimizing the arrangement of supports. Except for small local areas near the supports, the bending stress distribution and deformation behavior of the concrete sandwich panel can be accurately analyzed by the calculation method established in this paper.

Strong delayed negative feedback.

In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit.

Towards a single parameter for the assessment of EEG oscillations.

The single macroscopic flow on the boundary of a closed curve equals the sum of the countless microscopic flows in the enclosed area. According to the dictates of the Green's theorem, the counterclockwise movements on the border of a two-dimensional shape must equal all the counterclockwise movements taking place inside the shape. This mathematical approach might be useful to analyse neuroscientific data sets for its potential capability to describe the whole cortical activity in terms of electric flows occurring in peripheral brain areas. Given a map of raw EEG data to coloured ovals in which different colours stand for different amplitudes, the theorem suggests that the sum of the electric amplitudes measured inside every oval equals the amplitudes measured just on the oval's edge. This means that the collection of the vector fields detected from the scalp can be described by a novel, single parameter summarizing the counterclockwise electric flow detected in the outer electrodes. To evaluate the predictive power of this parameter, in a pilot study we investigated EEG traces from ten young females performing Raven's intelligence tests of various complexity, from easy tasks (n = 5) to increasingly complex tasks (n = 5). Despite the seemingly unpredictable behavior of EEG electric amplitudes, the novel parameter proved to be a valuable tool to to discriminate between the two groups and detect hidden, statistically significant differences. We conclude that the application of this promising parameter could be expanded to assess also data sets extracted from neurotechniques other than EEG.

Modeling the heterogeneous apoptotic response of caspase-mediated signaling in tumor cells.

Resisting apoptosis is a hallmark of cancer. For this reason, it may be possible to force cancer cells to die by targeting components along the apoptotic signaling pathway. However, apoptosis signaling is challenging to understand due to dynamic and complex behaviors of ligands, receptors, and intracellular signaling components in response to cancer therapy. In this work, we forecast the apoptotic response based on the combined impact of these features. We expanded a previously established mathematical model of caspase-mediated apoptosis to include extracellular activation and receptor dynamics. In addition, three potential threshold values of caspase-3 necessary for the activation of apoptosis were selected to forecast which cells become apoptotic over time. We first vary ligand and receptor levels with the number of intracellular signaling proteins remaining consistent. Then, we vary the intracellular protein molecules in each simulated tumor cell to forecast the response of a heterogeneous population. By leveraging the benefits of computational modeling, we investigate the combined effect of several factors on the onset of apoptosis. This work provides quantitative insights for how the apoptotic signaling response can be forecasted, and precisely triggered, amongst heterogeneous cells via extracellular activation.

LordNet: An efficient neural network for learning to solve parametric partial differential equations without simulated data.

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be 40× faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.

Applying Neural ODEs to Derive a Mechanism-Based Model for Characterizing Maturation-Related Serum Creatinine Dynamics in Preterm Newborns.

Serum creatinine in neonates follows complex dynamics due to maturation processes, most pronounced in the first few weeks of life. The development of a mechanism-based model describing complex dynamics requires high expertise in pharmacometric (PMX) modeling and substantial model development time. A recently published machine learning (ML) approach of low-dimensional neural ordinary differential equations (NODEs) is capable of modeling such data from newborns automatically. However, this efficient data-driven approach in itself does not result in a clinically interpretable model. In this work, an approach to deriving an interpretable model with reasonable PMX-type functions is presented. This "translation" was applied to derive a PMX model for serum creatinine in neonates considering maturation processes and covariates. The developed model was compared to a previously published mechanism-based PMX model whereas both models had similar mechanistic structures. The developed model was then utilized to simulate serum creatinine concentrations in the first few weeks of life considering different covariate values for gestational age and birth weight. The reference serum creatinine values derived from these simulations are consistent with observed serum creatinine values and previously published reference values. Thus, the presented NODE-based ML approach to model complex serum creatinine dynamics in newborns and derive interpretable, mathematical-statistical components similar to those in a conventional PMX model demonstrates a novel, viable approach to facilitate the modeling of complex dynamics in clinical settings and pediatric drug development.

Theoretical analysis of J-transform decomposition method with applications of nonlinear ordinary differentialequations.

One of the most noteworthy differential equations of the first order is the Riccati differential equation. It is applied in various branches of mathematics, including algebraic geometry, physics, and conformal mapping theory. The J-transform Adomian decomposition method is employed in the current study to find exact solutions for different kinds of nonlinear differential equations. We give thorough detailed proofs for new theorems related to the J-transform technique. The Adomian decomposition method and the J-transform method serve as the foundation for this technique. For certain differential equations, the theoretical analysis of the J-transform Adomian decomposition method is examined and is computed using readily computed terms. Our findings are contrasted with exact solutions found in the literature that were produced using alternative techniques. The significant features of the J-transform Adomian decomposition method are described in the article. It has been shown that the J-transform Adomian decomposition method is very efficient, useful, and adaptable to a broad variety of linear and nonlinear differential equations. Most of the symbolic and numerical calculations were performed using Mathematica.

Investigation of Bandgap Properties of a Piezoelectric Phononic Crystal Plate Based on the PDE Module in COMSOL.

Aiming to address the vibration noise problems on ships, we constructed a piezoelectric phononic crystal (PC) plate structure model, solved the governing equations of the structure using the partial differential equations module (PDE) in the finite element softwareCOMSOL6.1, and obtained the corresponding energy band structure, transmission curves, and vibration modal diagrams. The application of this method to probe the structural properties of two-dimensional piezoelectric PCs is described in detail. The calculation results obtained using this method were compared with the structures obtained using the traditional plane wave expansion method (PWE) and the finite element method (FE). The results were found to be in perfect agreement, which verified the feasibility of this method. To safely and effectively adjust the bandgap within a reasonable voltage range, this paper explored the order of magnitude of the plate thickness, the influence of the voltage on the bandgap, and the dependence between them. It was found that the smaller the order of magnitude of the plate thickness, the smaller the order of magnitude of the band in which the bandgap was located. The magnitude of the driving voltage that made the bandgap change became smaller accordingly. The new idea of attaching the PC plate to the conventional plate structure to achieve a vibration damping effect is also briefly introduced. Finally, the effects of lattice constant, plate width, and thickness on the bandgap were investigated.

Systematic simulation of tumor cell invasion and migration in response to time-varying rotating magnetic field.

Cancer invasion and migration play a pivotal role in tumor malignancy, which is a major cause of most cancer deaths. Rotating magnetic field (RMF), one of the typical dynamic magnetic fields, can exert substantial mechanical influence on cells. However, studying the effects of RMF on cell is challenging due to its complex parameters, such as variation of magnetic field intensity and direction. Here, we developed a systematic simulation method to explore the influence of RMF on tumor invasion and migration, including a finite element method (FEM) model and a cell-based hybrid numerical model. Coupling with the data of magnetic field from FEM, the cell-based hybrid numerical model was established to simulate the tumor cell invasion and migration. This model employed partial differential equations (PDEs) and finite difference method to depict cellular activities and solve these equations in a discrete system. PDEs were used to depict cell activities, and finite difference method was used to solve the equations in discrete system. As a result, this study provides valuable insights into the potential applications of RMF in tumor treatment, and a series of in vitro experiments were performed to verify the simulation results, demonstrating the model's reliability and its capacity to predict experimental outcomes and identify pertinent factors. Furthermore, these findings shed new light on the mechanical and chemical interplay between cells and the ECM, offering new insights and providing a novel foundation for both experimental and theoretical advancements in tumor treatment by using RMF.

TauFlowNet: Revealing latent propagation mechanism of tau aggregates using deep neural transport equations.

Mounting evidence shows that Alzheimer's disease (AD) is characterized by the propagation of tau aggregates throughout the brain in a prion-like manner. Since current pathology imaging technologies only provide a spatial mapping of tau accumulation, computational modeling becomes indispensable in analyzing the spatiotemporal propagation patterns of widespread tau aggregates from the longitudinal data. However, current state-of-the-art works focus on the longitudinal change of focal patterns, lacking a system-level understanding of the tau propagation mechanism that can explain and forecast the cascade of tau accumulation. To address this limitation, we conceptualize that the intercellular spreading of tau pathology forms a dynamic system where each node (brain region) is ubiquitously wired with other nodes while interacting with the build-up of pathological burdens. In this context, we formulate the biological process of tau spreading in a principled potential energy transport model (constrained by brain network topology), which allows us to develop an explainable neural network for uncovering the spatiotemporal dynamics of tau propagation from the longitudinal tau-PET scans. Specifically, we first translate the transport equation into a GNN (graph neural network) backbone, where the spreading flows are essentially driven by the potential energy of tau accumulation at each node. Conventional GNNs employ a l2-norm graph smoothness prior, resulting in nearly equal potential energies across nodes, leading to vanishing flows. Following this clue, we introduce the total variation (TV) into the graph transport model, where the nature of system's Euler-Lagrange equations is to maximize the spreading flow while minimizing the overall potential energy. On top of this min-max optimization scenario, we design a generative adversarial network (GAN-like) to characterize the TV-based spreading flow of tau aggregates, coined TauFlowNet. We evaluate our TauFlowNet on ADNI and OASIS datasets in terms of the prediction accuracy of future tau accumulation and explore the propagation mechanism of tau aggregates as the disease progresses. Compared to the current counterpart methods, our physics-informed deep model yields more accurate and interpretable results, demonstrating great potential in discovering novel neurobiological mechanisms through the lens of machine learning.

Identifying Key Regulatory Genes in Drug Resistance Acquisition: Modeling Pseudotime Trajectories of Breast Cancer Single-Cell Transcriptome.

Single-cell RNA-sequencing (scRNA-seq) technology has provided significant insights into cancer drug resistance at the single-cell level. However, understanding dynamic cell transitions at the molecular systems level remains limited, requiring a systems biology approach. We present an approach that combines mathematical modeling with a pseudotime analysis using time-series scRNA-seq data obtained from the breast cancer cell line MCF-7 treated with tamoxifen. Our single-cell analysis identified five distinct subpopulations, including tamoxifen-sensitive and -resistant groups. Using a single-gene mathematical model, we discovered approximately 560-680 genes out of 6000 exhibiting multistable expression states in each subpopulation, including key estrogen-receptor-positive breast cancer cell survival genes, such as RPS6KB1. A bifurcation analysis elucidated their regulatory mechanisms, and we mapped these genes into a molecular network associated with cell survival and metastasis-related pathways. Our modeling approach comprehensively identifies key regulatory genes for drug resistance acquisition, enhancing our understanding of potential drug targets in breast cancer.

Numerical simulation and study on heat and mass transfer in a hybrid ultrasound/convective dryer.

Susceptibility of airborne ultrasonic power to augment heat and mass transfer during hot air dehydration of peppermint leaves was investigated in the present study. To predict the moisture removal curves, a unique non-equilibrium mathematical model was developed. For the samples dried at temperatures of 40‒70 °C and the power intensities of 0‒104 kW m-3, the diffusion of moisture inside the leaves and coefficients for of mass and heat transfer varied from 0.601 × 10-4 to 5.937 × 10-4 s-1, 4.693 × 10-4 to 7.975 × 10-4 m s-1 and 49.2 to 78.1 W m-2 K-1, respectively. In general, at the process temperatures up to 60 °C, all the studied transfer parameters were augmented in the presence of ultrasonic power.

A simple and fast method for estimating bat roost locations.

Bats play a pivotal role in pest control, pollination and seed dispersal. Despite their ecological significance, locating bat roosts remains a challenging task for ecologists. Traditional field surveys are time-consuming, expensive and may disturb sensitive bat populations. In this article, we combine data from static audio detectors with a bat movement model to facilitate the detection of bat roosts. Crucially, our technique not only provides a point prediction for the most likely location of a bat roost, but because of the algorithm's speed, it can be applied over an entire landscape, resulting in a likelihood map, which provides optimal searching regions. To illustrate the success of the algorithm and highlight limitations, we apply our technique to greater horseshoe bat (Rhinolophus ferrumequinum) acoustic data acquired from six surveys from four different UK locations and over six different times in the year. Furthermore, we investigate what happens to the accuracy of our predictions in the case that the roost is not contained within the area spanned by the detectors. This innovative approach to searching rural environments holds the potential to greatly reduce the labour required for roost finding, and, hence, enhance the conservation efforts of bat populations and their habitats.

An optimal investment consumption model for retirees with no health insurance.

Retirees meet a number of problems as they are growing older which needs persistent attention. Hence, without a doubt, the outcomes of the financial markets influence the choices that people make when nearing retirement. In our model, the stock price dynamics follow Geometric Brownian motion (GBM) and our goal was to optimize the expected discounted utility of consumption and terminal wealth whilst considering health expenses. The investment return process comprises risk free asset and risky assets, and the health expenses. We choose power utility functions where comprehensive solutions for Hyperbolic Absolute Risk Aversion (HARA) utility functions are obtained and optimal investment, consumption and health expenditure strategies are derived by applying dynamic programming and variable change technique on the Hamilton-Jacobi-Bellman (HJB) equations. In our numerical results it showed various effects of some economic and market parameters on the optimal investment, consumption and health expense strategies. The inflation price market risk governs the amount invested in stock, bond and also how much to be put in health to sustain a given period of the retiree's lifetime. As the health welfare rate R increases, the proportion of wealth invested in the stock increases. We also investigated the effects of the high correlation coefficients and low correlation coefficients on consumption and income rate respectively. As the constant variance discounting coefficient increases, seasoned enterprise annuity retirees decrease their allocation to the risky assets. Finally, a numerical example is presented to depict the effects of financial parameters on the optimal investment strategy with health expenditure.

Modeling the spread of circulating vaccine-derived poliovirus type 2 outbreaks and interventions: A case study of Nigeria.

Background: Despite the successes of the Global Polio Eradication Initiative, substantial challenges remain in eradicating the poliovirus. The Sabin-strain (live-attenuated) virus in oral poliovirus vaccine (OPV) can revert to circulating vaccine-derived poliovirus (cVDPV) in under-vaccinated communities, regain neurovirulence and transmissibility, and cause paralysis outbreaks. Since the cessation of type 2-containing OPV (OPV2) in 2016, there have been cVDPV type 2 (cVDPV2) outbreaks in four out of six geographical World Health Organization regions, making these outbreaks a significant public health threat. Preparing for and responding to cVDPV2 outbreaks requires an updated understanding of how different factors, such as outbreak responses with the novel type of OPV2 (nOPV2) and the existence of under-vaccinated areas, affect the disease spread. Methods: We built a differential-equation-based model to simulate the transmission of cVDPV2 following reversion of the Sabin-strain virus in prolonged circulation. The model incorporates vaccinations by essential (routine) immunization and supplementary immunization activities (SIAs), the immunity induced by different poliovirus vaccines, and the reversion process from Sabin-strain virus to cVDPV. The model's outcomes include weekly cVDPV2 paralytic case counts and the die-out date when cVDPV2 transmission stops. In a case study of Northwest and Northeast Nigeria, we fit the model to data on the weekly cVDPV2 case counts with onset in 2018-2021. We then used the model to test the impact of different outbreak response scenarios during a prediction period of 2022-2023. The response scenarios included no response, the planned response (based on Nigeria's SIA calendar), and a set of hypothetical responses that vary in the dates at which SIAs started. The planned response scenario included two rounds of SIAs that covered almost all areas of Northwest and Northeast Nigeria except some under-vaccinated areas (e.g., Sokoto). The hypothetical response scenarios involved two, three, and four rounds of SIAs that covered the whole Northwest and Northeast Nigeria. All SIAs in tested outbreak response scenarios used nOPV2. We compared the outcomes of tested outbreak response scenarios in the prediction period. Results: Modeled cVDPV2 weekly case counts aligned spatiotemporally with the data. The prediction results indicated that implementing the planned response reduced total case counts by 79% compared to no response, but did not stop the transmission, especially in under-vaccinated areas. Implementing the hypothetical response scenarios involving two rounds of nOPV2 SIAs that covered all areas further reduced cVDPV2 case counts in under-vaccinated areas by 91-95% compared to the planned response, with greater impact from completing the two rounds at an earlier time, but it did not stop the transmission. When the first two rounds were completed in early April 2022, implementing two additional rounds stopped the transmission in late January 2023. When the first two rounds were completed six weeks earlier (i.e., in late February 2022), implementing one (two) additional round stopped the transmission in early February 2023 (late November 2022). The die out was always achieved last in the under-vaccinated areas of Northwest and Northeast Nigeria. Conclusions: A differential-equation-based model of poliovirus transmission was developed and validated in a case study of Northwest and Northeast Nigeria. The results highlighted (i) the effectiveness of nOPV2 in reducing outbreak case counts; (ii) the need for more rounds of outbreak response SIAs that covered all of Northwest and Northeast Nigeria in 2022 to stop the cVDPV2 outbreaks; (iii) that persistent transmission in under-vaccinated areas delayed the progress towards stopping outbreaks; and (iv) that a quicker outbreak response would avert more paralytic cases and require fewer SIA rounds to stop the outbreaks.

The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature.

It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature.

Annealed fractional Lévy-Ito diffusion models for protein generation.

Protein generation has numerous applications in designing therapeutic antibodies and creating new drugs. Still, it is a demanding task due to the inherent complexities of protein structures and the limitations of current generative models. Proteins possess intricate geometry, and sampling their conformational space is challenging due to its high dimensionality. This paper introduces novel Markovian and non-Markovian generative diffusion models based on fractional stochastic differential equations and the Lévy distribution, allowing for a more effective exploration of the conformational space. The approach is applied to a dataset of 40,000 proteins and evaluated in terms of Fréchet distance, fidelity, and diversity, outperforming the state-of-the-art by 25.4%, 35.8%, and 11.8%, respectively.