A Vertex Network Model of Arabidopsis Leaf Growth

Biology provides many examples of complex systems whose properties allow organisms to develop in a highly reproducible,or robust,manner.One such system is the growth and development of flat leaves in Arabidopsis thaliana.This mechanistically challenging process results from multiple inputs including gene interactions,cellular geometry,growth rates,and coordinated cell divisions.To better understand how this complex genetic and cellular information controls leaf growth,we developed a mathematical model of flat leaf production.This two-dimensional model describes the gene interactions in a vertex network of cells which grow and divide according to physical forces and genetic information.Interestingly,the model predicts the presence of an unknown additional factor required for the formation of biologically realistic gene expression domains and iterative cell division.This two-dimensional model will form the basis for future studies into robustness of adaxial-abaxial patterning.

RBF neural network regression model based on fuzzy observations

A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.

The calculation and optimal allocation of transmission capacity in natural gas networks with MINLP models

The transmission capacity of gas pipeline networks should be calculated and allocated to deal with the capacity booking with shippers. Technical capacities, which depend on the gas flow distribution at routes or interchange points, are calculated with a multiobjective optimization model and form a Pareto solution set in the entry/exit or point-to-point regime. Then, the commercial capacities, which can be directly applied in capacity booking, are calculated with single-objective optimization models that are transformed from the above multiobjective model based on three allocation rules and the demand of shippers.Next, peak-shaving capacities, which are daily oversupply or overdelivery amounts at inlets or deliveries,are calculated with two-stage transient optimization models. Considering the hydraulic process of a pipeline network and operating schemes of compressor stations, all the above models are mixed-integer nonlinear programming problems. Finally, a case study is made to demonstrate the ability of the models.

Evaluation of a mathematical model using experimental data and artificial neural network for prediction of gas separation

In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming＇s study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network （ANN） technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network

Mathematical Model Validation of Search Protocols in MP2P Networks

Broadcasting is a basic technique in Mobile ad-hoc network(MANET),and it refers to sending a packet from one node to every other node within the transmission range.Flooding is a type of broadcast where the received packet is retransmitted once by every node.The naive flooding technique,floods the network with query messages,while the random walk technique operates by contacting the subsets of every node’s neighbors at each step,thereby restricting the search space.One of the key challenges in an ad-hoc network is the resource or content discovery problem which is about locating the queried resource.Many earlier works have mainly focused on the simulation-based analysis of flooding,and its variants under a wired network.Although,there have been some empirical studies in peer-to-peer(P2P)networks,the analytical results are still lacking,especially in the context of P2P systems running over MANET.In this paper,we describe how P2P resource discovery protocols perform badly over MANETs.To address the limitations,we propose a new protocol named ABRW(Address Broadcast Random Walk),which is a lightweight search approach,designed considering the underlay topology aimed to better suit the unstructured architecture.We provide the mathematical model,measuring the performance of our proposed search scheme with different widely popular benchmarked search techniques.Further,we also derive three relevant search performance metrics,i.e.,mean no.of steps needed to find a resource,the probability of finding a resource,and the mean no.of message overhead.We validated the analytical expressions through simulations.The simulation results closely matched with our analyticalmodel,justifying our findings.Our proposed search algorithm under such highly dynamic self-evolving networks performed better,as it reduced the search latency,decreased the overall message overhead,and still equally had a good success rate.

Mathematical Modeling of a Metabolic Network to Study the Impact of Food Contaminants on Genomic Methylation and DNA Instability

Environmental contamination of food is a worldwide public health problem. Folate mediated one- carbon metabolism plays an important role in epigenetic regulation of gene expression and mutagenesis. Many contaminants in food cause cancer through epigenetic mechanisms and/or DNA instability i.e. default methylation of uracil to thymine, subsequent to the decrease of 5-methylte- trahydrofolate (5 mTHF) pool in the one-carbon metabolism network. Evaluating consequences of an exposure to food contaminants based on systems biology approaches is a promising alternative field of investigation. This report presents a dynamic mathematical modeling for the study of the alteration in the one-carbon metabolism network by environmental factors. It provides a model for predicting “the impact of arbitrary contaminants that can induce the 5 mTHF deficiency. The model allows for a given experimental condition, the analysis of DNA methylation activity and dumping methylation in the de novo pathway of DNA synthesis.

Modeling of Ship Maneuvering Motion Using Neural Networks

In this paper, Neural Networks （NNs） are used in the modeling of ship maneuvering motion. A nonlinear response model and a linear hydrodynamic model of ship maneuvering motion are also investigated. The maneuverability indices and linear non-dimensional hydrodynamic derivatives in the models are identified by using two-layer feed forward NNs. The stability of parametric estimation is confirmed. Then, the ship maneuvering motion is predicted based on the obtained models. A comparison between the predicted results and the model test results demonstrates the validity of the proposed modeling method.

Mathematical Modeling of Carcinogenesis Based on Chromosome Aberration Data

Objective： The progression of human cancer is characterized by the accumulation of genetic instability. An increasing number of experimental genetic molecular techniques have been used to detect chromosome aberrations. Previous studies on chromosome abnormalities often focused on identifying the frequent loci of chromosome alterations, but rarely addressed the issue of interrelationship of chromosomal abnormalities. In the last few years, several mathematical models have been employed to construct models of carcinogenesis, in an attempt to identify the time order and cause-and-effect relationship of chromosome aberrations. The principles and applications of these models are reviewed and compared in this paper. Mathematical modeling of carcinogenesis can contribute to our understanding of the molecular genetics of tumor development, and identification of cancer related genes, thus leading to improved clinical practice of cancer.

Finding the Optimal Percentage of Cluster Heads from a New and Complete Mathematical Model on LEACH

Network lifetime is one of the important metrics that indicate the performance of a sensor network. Different techniques are used to elongate network lifetime. Among them, clustering is one of the popular techniques. LEACH (Low-Energy Adaptive Clustering Hierarchy) is one of the most widely cited clustering solutions due to its simplicity and effectiveness. LEACH has several parameters that can be tuned to get better performance. Percentage of cluster heads is one such important parameter which affects the network lifetime significantly. At present it is hard to find the optimum value for the percentage of cluster head parameter due to the absence of a complete mathematical model on LEACH. A complete mathematical model on LEACH can be used to tune other LEACH parameters in order to get better performance. In this paper, we formulate a new and complete mathematical model on LEACH. From this new mathematical model, we compute the value for the optimal percentage of cluster heads in order to increase the network lifetime. Simulation results verify both the correctness of our mathematical model and the effectiveness of computing the optimal percentage of cluster heads to increase the network lifetime.

Physical Network Approach Applied to Wind Turbine Modeling with Simscape Language

Model-Based Design is an efficient and cost-effective way to develop controls, signal processing, image processing, communications, mechatronics, and other embedded systems. Rather than re-lying on physical prototypes and textual specifications, Model-Based Design uses a system model as an executable specification throughout development. It supports system- and component-level design and simulation, automatic code generation, and continuous test and verification. This paper is focused firstly on the so-called model-based design and aims at presenting an up-to-date state of the art in this important field. Secondly, it develops a model based design for wind energy systems. Mathematical formulations and numerical implementations for different components of wind energy systems are highlighted with Simscape language. Finally, results are derived from simulations.

Observations of Passenger Flow and Verification of a Crowd Dynamics Model

This paper reports observations of passenger flow in the Wuchang railway station in Wuhan, China during the Chinese Traditional Spring Festival in 2006. The data collected are used to verify a crowd dynamics model previously developed. The crowd dynamics model is based on simulating the global movement of each individual under the influence of the surrounding crowd, and the good agreement between the predictions and observations validates the prediction model. The crowd dynamics model suggests that the crowd movement speed is dominated by two factors： the front-back inter-person effect, and the pedestrian＇s self-motive. The first effect gives logarithmic relationship between the crowd speed and crowd density. The second factor depends on the individual motive driven with which people try to divorce themselves from the control of the crowd movement. The prediction model are helpful to guide the design of public traffic systems for effective crowd dispersal.

Surging footprints of mathematical modeling for prediction of transdermal permeability

In vivo skin permeation studies are considered gold standard but are difficult to perform and evaluate due to ethical issues and complexity of process involved. In recent past, a useful tool has been developed by combining the computational modeling and experimental data for expounding biological complexity. Modeling of percutaneous permeation studies provides an ethical and viable alternative to laboratory experimentation. Scientists are exploring complex models in magnificent details with advancement in computational power and technology. Mathematical models of skin permeability are highly relevant with respect to transdermal drug delivery, assessment of dermal exposure to industrial and environmental hazards as well as in developing fundamental understanding of biotransport processes.Present review focuses on various mathematical models developed till now for the transdermal drug delivery along with their applications.

Simultaneous synthesis of sub and above-ambient heat exchanger networks including expansion process based on an enhanced superstructure model

Synthesis of heat exchanger networks including expansion process is a complex task due to the involvement of both heat and work.A stream that expands through expanders can produce work and cold load,while expansion through valves barely affects heat integration.In addition,expansion through expanders at higher temperature produces more work,but consumes more hot utility.Therefore,there is a need to weigh work production and heat consumption.To this end,an enhanced stage-wise superstructure is proposed that involves synchronous optimization of expander/valve placement and heat integration for each pressure-change sub-stream in stages.A mixed-integer nonlinear programming(MINLP)model is established for synthesizing sub and aboveambient heat exchanger networks with multi-stream expansion,which explicitly considers the optimized selection of end-heaters and end-coolers to adjust temperature requirement.Our proposed method can commendably achieve the optimal selection of expanders and valves in a bid for minimizing exergy consumption and total annual cost.Four example studies are conducted with two distinct objective function(minimization of exergy consumption and total annual cost,respectively)to illustrate the feasibility and efficacy of the proposed method.

Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model

Based on the T-S fuzzy model,this paper presents a new model of non-linear network control system with stochastic transfer delay.Sufficient criterion is proposed to guarantee globally asymptotically stability of this two-levels T-S fuzzy model.Also a T-S fuzzy observer of NCS is designed base on this two-levels T-S fuzzy model.All these results present a new approach for networked control system analysis and design.

Context-Aware System Modeling Based on Boolean Control Network

Boolean control network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean network is used for modeling complex system. In this paper, we have presented a model of a context-aware system used in smart home based on Boolean control networks. This modeling describes the relationship between the context elements (person, time, location, and activity) and services (Morning Call, Sleeping, Guarding, Entertainment, and normal), which is effective to logical inference. We apply semi tensor matrix product to describe the dynamic of the system. This matrix form of expression is a convenient and reasonable way to design logic control system.

Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

A Neural Study of the Fractional Heroin Epidemic Model

This works intends to provide numerical solutions based on the nonlinear fractional order derivatives of the classical White and Comiskey model(NFD-WCM).The fractional order derivatives have provided authentic and accurate solutions for the NDF-WCM.The solutions of the fractional NFD-WCM are provided using the stochastic computing supervised algorithm named Levenberg-Marquard Backpropagation(LMB)based on neural networks(NNs).This regression approach combines gradient descent and Gauss-Newton iterative methods,which means finding a solution through the sequences of different calculations.WCM is used to demonstrate the heroin epidemics.Heroin has been on-growth world wide,mainly in Asia,Europe,and the USA.It is the fourth foremost cause of death due to taking an overdose in the USA.The nonlinear mathematical system NFD-WCM discusses the overall circumstance of different drug users,such as suspected groups,drug users without treatment,and drug users with treatment.The numerical results of NFD-WCM via LMB-NNs have been substantiated through training,testing,and validation measures.The stability and accuracy are then checked through the statistical tool,such asmean square error(MSE),error histogram,and fitness curves.The suggested methodology’s strength is demonstrated by the high convergence between the reference solutions and the solutions generated by adding the efficacy of a constructed solver LMB-NNs,with accuracy levels ranging from 10?9 to 10?10.

A mathematical model for environmental risk assessment in manufacturing industry

Environmental conscious manufacturing has become an important issue in industry because of market pressure and environmental regulations. An environmental risk assessment model was developed based on the network analytic method and fuzzy set theory. The "interval analysis method" was applied to deal with the on site monitoring data as basic information for assessment. In addition, the fuzzy set theory was employed to allow uncertain, interactive and dynamic information to be effectively incorporated into the environmental risk assessment. This model is a simple, practical and effective tool for evaluating the environmental risk of manufacturing industry and for analyzing the relative impacts of emission wastes, which are hazardous to both human and ecosystem health. Furthermore, the model is considered useful for design engineers and decision maker to design and select processes when the costs, environmental impacts and performances of a product are taken into consideration.

Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system(VHDNS)along with the numerical treatment of artificial neural networks(ANNs)techniques supported by Levenberg-Marquardt backpropagation(LMQBP),known as ANNs-LMQBP.This mechanism is physically appropriate,where the number of infected people is increasing along with the limited health services.Furthermore,the biological effects have fadingmemories and exhibit transition behavior.Initially,the model is developed by considering the two and three categories for the humans and the vector species.The VHDNS is constructed with five classes,susceptible humans Sh(t),infected humans Ih(t),recovered humans Rh(t),infected vectors Iv(t),and susceptible vector Sv(t)based system of the fractional-order nonlinear ordinary differential equations.To solve the number of variations of the VHDNS,the numerical simulations are performed using the stochastic ANNs-LMQBP.The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training,verifying,and testing data to decrease the mean square error(MSE).An extensive analysis is provided using the correlation studies,MSE,error histograms(EHs),state transitions(STs),and regression to observe the accuracy,efficiency,expertise,and aptitude of the computing ANNs-LMQBP.