Mathematically modelling and controlling prostate cancer under intermittent hormone therapy

In this review, we summarize our recently developed mathematical models that predict the effects of intermittent androgen suppression therapy on prostate cancer （PCa）. Although hormone therapy for PCa shows remarkable results at the beginning of treatment, cancer cells frequently acquire the ability to grow without androgens during long-term therapy, resulting in an eventual relapse. To circumvent hormone resistance, intermittent androgen suppression was investigated as an alternative treatment option. However, at the present time, it is not possible to select an optimal schedule of on- and off-treatment cycles for any given patient. In addition, clinical trials have revealed that intermittent androgen suppression is effective for some patients but not for others. To resolve these two problems, we have developed mathematical models for PCa under intermittent androgen suppression. The mathematical models not only explain the mechanisms of intermittent androgen suppression but also provide an optimal treatment schedule for the on- and off-treatment periods.

A dynamic soil freezing characteristic curve model for frozen soil

The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.

A Statistical Approach Designed for Finding Mathematically Defined Repeats in Shotgun Data and Determining the Length Distribution of Clone-Inserts

The large amount of repeats, especially high copy repeats, in the genomes of higher animals and plants makes whole genome assembly (WGA) quite difficult. In order to solve this problem, we tried to identify repeats and mask them prior to assembly even at the stage of genome survey. It is known that repeats of different copy number have different probabilities of appearance in shotgun data, so based on this principle, we constructed a statistical model and inferred criteria for mathematically defined repeats (MDRs) at different shotgun coverages. According to these criteria, we developed software MDRmasker to identify and mask MDRs in shotgun data. With repeats masked prior to assembly, the speed of assembly was increased with lower error probability. In addition, clone-insert size affects the accuracy of repeat assembly and scaffold construction. We also designed length distribution of clone-inserts using our model. In our simulated genomes of human and rice, the length distribution of repeats is different, so their optimal length distributions of clone-inserts were not the same. Thus with optimal length distribution of clone-inserts, a given genome could be assembled better at lower coverage.

Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Optimizing multistage processes,such as distillation or absorption,is a complex mixed-integer nonlinear programming(MINLP)problem.Relaxing integer into continuous variables and solving the easier nonlinear programming(NLP)problem is an optimization idea for the multistage process.In this article,we propose a relaxation method based on the efficiency parameter.When the efficiency parameter is 1or 0,the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage.And non-integer efficiency represents partial existence.A multi-component absorption case shows a natural penalty for non-integer efficiency,which can assist the efficiency parameter converging to 0 or 1.However,its penalty is weaker than the existing relaxation models,such as the bypass efficiency model.In a simple distillation case,we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.

MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

Cognitive function among military veterans with STEM occupations

Dear Editor,There is limited research on the relationship between science,technology,engineering,and mathematics(STEM)occupational history and cognitive function in later life,especially among military veterans,who may be at greater risk for later-life cognitive decline.This study examines a nationally representative sample of military veterans to address this gap in knowledge.

Effect of solvent on the initiation mechanism of living anionic polymerization of styrene:A computational study

For living anionic polymerization(LAP),solvent has a great influence on both reaction mechanism and kinetics.In this work,by using the classical butyl lithium-styrene polymerization as a model system,the effect of solvent on the mechanism and kinetics of LAP was revealed through a strategy combining density functional theory(DFT)calculations and kinetic modeling.In terms of mechanism,it is found that the stronger the solvent polarity,the more electrons transfer from initiator to solvent through detailed energy decomposition analysis of electrostatic interactions between initiator and solvent molecules.Furthermore,we also found that the stronger the solvent polarity,the higher the monomer initiation energy barrier and the smaller the initiation rate coefficient.Counterintuitively,initiation is more favorable at lower temperatures based on the calculated results ofΔG_(TS).Finally,the kinetic characteristics in different solvents were further examined by kinetic modeling.It is found that in benzene and n-pentane,the polymerization rate exhibits first-order kinetics.While,slow initiation and fast propagation were observed in tetrahydrofuran(THF)due to the slow free ion formation rate,leading to a deviation from first-order kinetics.

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

Consistent and Accurate TDOA Localization in Dynamic NLOS Environments via Prior Information Independent Estimation

In the time-difference-of-arrival(TDOA)localization,robust least squares(LS)problems solved by mathematical programming were proven to be superior in mitigating the effects of non-line-of-sight(NLOS)propagation.However,the existing algorithms still suffer from two disadvantages:1)The algorithms strongly depend on prior information;2)The approaches do not satisfy the mean square error(MSE)optimal criterion of the measurement noise.To tackle the troubles,we first formulate an MSE minimization model for measurement noise by taking the source and the NLOS biases as variables.To obtain stable solutions,we introduce a penalty function to avoid abnormal estimates.We further tackle the nonconvex locating problem with semidefinite relaxation techniques.Finally,we incorporate mixed constraints and variable information to improve the estimation accuracy.Simulations and experiments show that the proposed method achieves consistent performance and good accuracy in dynamic NLOS environments.

An Implementation of Multiscale Line Detection and Mathematical Morphology for Efficient and Precise Blood Vessel Segmentation in Fundus Images

Diagnosing various diseases such as glaucoma,age-related macular degeneration,cardiovascular conditions,and diabetic retinopathy involves segmenting retinal blood vessels.The task is particularly challenging when dealing with color fundus images due to issues like non-uniformillumination,low contrast,and variations in vessel appearance,especially in the presence of different pathologies.Furthermore,the speed of the retinal vessel segmentation system is of utmost importance.With the surge of now available big data,the speed of the algorithm becomes increasingly important,carrying almost equivalent weightage to the accuracy of the algorithm.To address these challenges,we present a novel approach for retinal vessel segmentation,leveraging efficient and robust techniques based on multiscale line detection and mathematical morphology.Our algorithm’s performance is evaluated on two publicly available datasets,namely the Digital Retinal Images for Vessel Extraction dataset(DRIVE)and the Structure Analysis of Retina(STARE)dataset.The experimental results demonstrate the effectiveness of our method,withmean accuracy values of 0.9467 forDRIVE and 0.9535 for STARE datasets,aswell as sensitivity values of 0.6952 forDRIVE and 0.6809 for STARE datasets.Notably,our algorithmexhibits competitive performance with state-of-the-art methods.Importantly,it operates at an average speed of 3.73 s per image for DRIVE and 3.75 s for STARE datasets.It is worth noting that these results were achieved using Matlab scripts containing multiple loops.This suggests that the processing time can be further reduced by replacing loops with vectorization.Thus the proposed algorithm can be deployed in real time applications.In summary,our proposed system strikes a fine balance between swift computation and accuracy that is on par with the best available methods in the field.

采用解析和数值方法分析浮动式矩形浮箱的波浪诱导载荷研究

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave,sway,and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response.The analytical expressions for the radiation potentials,wave forces,and hydrodynamic coefficients are presented based on matched eigenfunction expansion method(MEFEM).The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH.In addition,the present result is compared with the existing published experimental results available in the literature.The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force,horizontal wave force,torque,added mass,and damping coefficients due to the heave,sway,and roll motions,and the comparison analysis between the forces is also analyzed in detail.Further,the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

Model informed precision medicine of Chinese herbal medicines formulas-A multi-scale mechanistic intelligent model

Recent trends suggest that Chinese herbal medicine formulas(CHM formulas)are promising treatments for complex diseases.To characterize the precise syndromes,precise diseases and precise targets of the precise targets between complex diseases and CHM formulas,we developed an artificial intelligence-based quantitative predictive algorithm(DeepTCM).DeepTCM has gone through multilevel model calibration and validation against a comprehensive set of herb and disease data so that it accurately captures the complex cellular signaling,molecular and theoretical levels of traditional Chinese medicine(TCM).As an example,our model simulated the optimal CHM formulas for the treatment of coronary heart disease(CHD)with depression,and through model sensitivity analysis,we calculated the balanced scoring of the formulas.Furthermore,we constructed a biological knowledge graph representing interactions by associating herb-target and gene-disease interactions.Finally,we experimentally confirmed the therapeutic effect and pharmacological mechanism of a novel model-predicted intervention in humans and mice.This novel multiscale model opened up a new avenue to combine“disease syndrome”and“macro micro”system modeling to facilitate translational research in CHM formulas.

Community detection on elite mathematicians’collaboration network

Purpose:This study focuses on understanding the collaboration relationships among mathematicians,particularly those esteemed as elites,to reveal the structures of their communities and evaluate their impact on the field of mathematics.Design/methodology/approach:Two community detection algorithms,namely Greedy Modularity Maximization and Infomap,are utilized to examine collaboration patterns among mathematicians.We conduct a comparative analysis of mathematicians’centrality,emphasizing the influence of award-winning individuals in connecting network roles such as Betweenness,Closeness,and Harmonic centrality.Additionally,we investigate the distribution of elite mathematicians across communities and their relationships within different mathematical sub-fields.Findings:The study identifies the substantial influence exerted by award-winning mathematicians in connecting network roles.The elite distribution across the network is uneven,with a concentration within specific communities rather than being evenly dispersed.Secondly,the research identifies a positive correlation between distinct mathematical sub-fields and the communities,indicating collaborative tendencies among scientists engaged in related domains.Lastly,the study suggests that reduced research diversity within a community might lead to a higher concentration of elite scientists within that specific community.Research limitations:The study’s limitations include its narrow focus on mathematicians,which may limit the applicability of the findings to broader scientific fields.Issues with manually collected data affect the reliability of conclusions about collaborative networks.Practical implications:This study offers valuable insights into how elite mathematicians collaborate and how knowledge is disseminated within mathematical circles.Understanding these collaborative behaviors could aid in fostering better collaboration strategies among mathematicians and institutions,potentially enhancing scientific progress in mathematics.Originality/value:The study adds value to understanding collaborative dynamics within the realm of mathematics,offering a unique angle for further exploration and research.

Research on Maneuver Decision-Making of Multi-Agent Adversarial Game in a Random Interference Environment

The strategy evolution process of game players is highly uncertain due to random emergent situations and other external disturbances.This paper investigates the issue of strategy interaction and behavioral decision-making among game players in simulated confrontation scenarios within a random interference environment.It considers the possible risks that random disturbances may pose to the autonomous decision-making of game players,as well as the impact of participants’manipulative behaviors on the state changes of the players.A nonlinear mathematical model is established to describe the strategy decision-making process of the participants in this scenario.Subsequently,the strategy selection interaction relationship,strategy evolution stability,and dynamic decision-making process of the game players are investigated and verified by simulation experiments.The results show that maneuver-related parameters and random environmental interference factors have different effects on the selection and evolutionary speed of the agent’s strategies.Especially in a highly uncertain environment,even small information asymmetry or miscalculation may have a significant impact on decision-making.This also confirms the feasibility and effectiveness of the method proposed in the paper,which can better explain the behavioral decision-making process of the agent in the interaction process.This study provides feasibility analysis ideas and theoretical references for improving multi-agent interactive decision-making and the interpretability of the game system model.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.

Accelerating Factor Xa inhibitor discovery with a de novo drug design pipeline

Small-molecule drugs are essential for maintaining human health. The objective of this study is to identify a molecule that can inhibit the Factor Xa protein and be easily procured. An optimization-based de novo drug design framework, Drug CAMD, that integrates a deep learning model with a mixed-integer nonlinear programming model is used for designing drug candidates. Within this framework, a virtual chemical library is specifically tailored to inhibit Factor Xa. To further filter and narrow down the lead compounds from the designed compounds, comprehensive approaches involving molecular docking,binding pose metadynamics(BPMD), binding free energy calculations, and enzyme activity inhibition analysis are utilized. To maximize efficiency in terms of time and resources, molecules for in vitro activity testing are initially selected from commercially available portions of customized virtual chemical libraries. In vitro studies assessing inhibitor activities have confirmed that the compound EN300-331859shows potential Factor Xa inhibition, with an IC_(50)value of 34.57 μmol·L^(-1). Through in silico molecular docking and BPMD, the most plausible binding pose for the EN300-331859-Factor Xa complex are identified. The estimated binding free energy values correlate well with the results obtained from biological assays. Consequently, EN300-331859 is identified as a novel and effective sub-micromolar inhibitor of Factor Xa.

Using Improved Particle Swarm Optimization Algorithm for Location Problem of Drone Logistics Hub

Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.