ResearchPad - differential-equations https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry]]> https://www.researchpad.co/article/elastic_article_14654 Locusts aggregate in swarms that threaten agriculture worldwide. Initially these aggregations form as aligned groups, known as hopper bands, whose individuals alternate between marching and paused (associated with feeding) states. The Australian plague locust (for which there are excellent field studies) forms wide crescent-shaped bands with a high density at the front where locusts slow in uneaten vegetation. The density of locusts rapidly decreases behind the front where the majority of food has been consumed. Most models of collective behavior focus on social interactions as the key organizing principle. We demonstrate that the formation of locust bands may be driven by resource consumption. Our first model treats each locust as an individual agent with probabilistic rules governing motion and feeding. Our second model describes locust density with deterministic differential equations. We use biological observations of individual behavior and collective band shape to identify numerical values for the model parameters and conduct a sensitivity analysis of outcomes to parameter changes. Our models are capable of reproducing the characteristics observed in the field. Moreover, they provide insight into how resource availability influences collective locust behavior that may eventually aid in disrupting the formation of locust bands, mitigating agricultural losses.

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<![CDATA[Exact flow of particles using for state estimations in unmanned aerial systems` navigation]]> https://www.researchpad.co/article/Nb8d1b185-24ca-4749-9cc9-bbc7ade34d0a

The navigation is a substantial issue in the field of robotics. Simultaneous Localization and Mapping (SLAM) is a principle for many autonomous navigation applications, particularly in the Global Navigation Satellite System (GNSS) denied environments. Many SLAM methods made substantial contributions to improve its accuracy, cost, and efficiency. Still, it is a considerable challenge to manage robust SLAM, and there exist several attempts to find better estimation algorithms for it. In this research, we proposed a novel Bayesian filtering based Airborne SLAM structure for the first time in the literature. We also presented the mathematical background of the algorithm, and the SLAM model of an autonomous aerial vehicle. Simulation results emphasize that the new Airborne SLAM performance with the exact flow of particles using for recursive state estimations superior to other approaches emerged before, in terms of accuracy and speed of convergence. Nevertheless, its computational complexity may cause real-time application concerns, particularly in high-dimensional state spaces. However, in Airborne SLAM, it can be preferred in the measurement environments that use low uncertainty sensors because it gives more successful results by eliminating the problem of degeneration seen in the particle filter structure.

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<![CDATA[SimKinet: A free educational tool based on an electrical analogy to solve chemical kinetic equations]]> https://www.researchpad.co/article/5c8c1982d5eed0c484b4d822

In this article we introduce the software SimKinet, a free tool specifically designed to solve systems of differential equations without any programming skill. The underlying method is the so-called Network Simulation Method, which designs and solves an electrical network equivalent to the mathematical problem. SimKinet is versatile, fast, presenting a real user-friendly interface, and can be employed for both educational and researching purposes. It is particularly useful in the first courses of different scientific degrees, mainly Chemistry and Physics, especially when facing non-analytic or complex-dynamics problems. Moreover, SimKinet would help students to understand fundamental concepts, being an opportunity to improve instruction in Chemistry, Mathematics, Physics and other Sciences courses, with no need of advanced knowledge in differential equations. The potency of SimKinet is demonstrated via two applications in chemical kinetics: the photochemical destruction of stratospheric ozone and the chaotic dynamics of the peroxidase-oxidase reaction.

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<![CDATA[Modeling financial interval time series]]> https://www.researchpad.co/article/5c6f148ad5eed0c48467a270

In financial economics, a large number of models are developed based on the daily closing price. When using only the daily closing price to model the time series, we may discard valuable intra-daily information, such as maximum and minimum prices. In this study, we propose an interval time series model, including the daily maximum, minimum, and closing prices, and then apply the proposed model to forecast the entire interval. The likelihood function and the corresponding maximum likelihood estimates (MLEs) are obtained by stochastic differential equation and the Girsanov theorem. To capture the heteroscedasticity of volatility, we consider a stochastic volatility model. The efficiency of the proposed estimators is illustrated by a simulation study. Finally, based on real data for S&P 500 index, the proposed method outperforms several alternatives in terms of the accurate forecast.

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<![CDATA[Threshold response to stochasticity in morphogenesis]]> https://www.researchpad.co/article/5c5b52e0d5eed0c4842bd1b9

During development of biological organisms, multiple complex structures are formed. In many instances, these structures need to exhibit a high degree of order to be functional, although many of their constituents are intrinsically stochastic. Hence, it has been suggested that biological robustness ultimately must rely on complex gene regulatory networks and clean-up mechanisms. Here we explore developmental processes that have evolved inherent robustness against stochasticity. In the context of the Drosophila eye disc, multiple optical units, ommatidia, develop into crystal-like patterns. During the larva-to-pupa stage of metamorphosis, the centers of the ommatidia are specified initially through the diffusion of morphogens, followed by the specification of R8 cells. Establishing the R8 cell is crucial in setting up the geometric, and functional, relationships of cells within an ommatidium and among neighboring ommatidia. Here we study an PDE mathematical model of these spatio-temporal processes in the presence of parametric stochasticity, defining and applying measures that quantify order within the resulting spatial patterns. We observe a universal sigmoidal response to increasing transcriptional noise. Ordered patterns persist up to a threshold noise level in the model parameters. In accordance with prior qualitative observations, as the noise is further increased past a threshold point of no return, these ordered patterns rapidly become disordered. Such robustness in development allows for the accumulation of genetic variation without any observable changes in phenotype. We argue that the observed sigmoidal dependence introduces robustness allowing for sizable amounts of genetic variation and transcriptional noise to be tolerated in natural populations without resulting in phenotype variation.

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<![CDATA[Intervention on default contagion under partial information in a financial network]]> https://www.researchpad.co/article/5c478c36d5eed0c484bd0d24

We study the optimal interventions of a regulator (a central bank or government) on the illiquidity default contagion process in a large, heterogeneous, unsecured interbank lending market. The regulator has only partial information on the interbank connections and aims to minimize the fraction of final defaults with minimal interventions. We derive the analytical results of the asymptotic optimal intervention policy and the asymptotic magnitude of default contagion in terms of the network characteristics. We extend the results of Amini, Cont and Minca’s work to incorporate interventions and adopt the dynamics of Amini, Minca and Sulem’s model to build heterogeneous networks with degree sequences and initial equity levels drawn from arbitrary distributions. Our results generate insights that the optimal intervention policy is “monotonic” in terms of the intervention cost, the closeness to invulnerability and connectivity. The regulator should prioritize interventions on banks that are systematically important or close to invulnerability. Moreover, the regulator should keep intervening on a bank once having intervened on it. Our simulation results show a good agreement with the theoretical results.

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<![CDATA[Detection of a sudden change of the field time series based on the Lorenz system]]> https://www.researchpad.co/article/5989db53ab0ee8fa60bdcaf0

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.

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<![CDATA[Modeling Radicalization Phenomena in Heterogeneous Populations]]> https://www.researchpad.co/article/5989dab5ab0ee8fa60bacb9c

The phenomenon of radicalization is investigated within a mixed population composed of core and sensitive subpopulations. The latest includes first to third generation immigrants. Respective ways of life may be partially incompatible. In case of a conflict core agents behave as inflexible about the issue. In contrast, sensitive agents can decide either to live peacefully adjusting their way of life to the core one, or to oppose it with eventually joining violent activities. The interplay dynamics between peaceful and opponent sensitive agents is driven by pairwise interactions. These interactions occur both within the sensitive population and by mixing with core agents. The update process is monitored using a Lotka-Volterra-like Ordinary Differential Equation. Given an initial tiny minority of opponents that coexist with both inflexible and peaceful agents, we investigate implications on the emergence of radicalization. Opponents try to turn peaceful agents to opponents driving radicalization. However, inflexible core agents may step in to bring back opponents to a peaceful choice thus weakening the phenomenon. The required minimum individual core involvement to actually curb radicalization is calculated. It is found to be a function of both the majority or minority status of the sensitive subpopulation with respect to the core subpopulation and the degree of activeness of opponents. The results highlight the instrumental role core agents can have to hinder radicalization within the sensitive subpopulation. Some hints are outlined to favor novel public policies towards social integration.

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<![CDATA[A Simple, Realistic Stochastic Model of Gastric Emptying]]> https://www.researchpad.co/article/5989db4bab0ee8fa60bda3a6

Several models of Gastric Emptying (GE) have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations), considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.

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<![CDATA[On Three-Dimensional Flow and Heat Transfer over a Non-Linearly Stretching Sheet: Analytical and Numerical Solutions]]> https://www.researchpad.co/article/5989dadcab0ee8fa60bba026

This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.

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<![CDATA[Within-Host Dynamics of Multi-Species Infections: Facilitation, Competition and Virulence]]> https://www.researchpad.co/article/5989da13ab0ee8fa60b7a6e4

Host individuals are often infected with more than one parasite species (parasites defined broadly, to include viruses and bacteria). Yet, research in infection biology is dominated by studies on single-parasite infections. A focus on single-parasite infections is justified if the interactions among parasites are additive, however increasing evidence points to non-additive interactions being the norm. Here we review this evidence and theoretically explore the implications of non-additive interactions between co-infecting parasites. We use classic Lotka-Volterra two-species competition equations to investigate the within-host dynamical consequences of various mixes of competition and facilitation between a pair of co-infecting species. We then consider the implications of these dynamics for the virulence (damage to host) of co-infections and consequent evolution of parasite strategies of exploitation. We find that whereas one-way facilitation poses some increased virulence risk, reciprocal facilitation presents a qualitatively distinct destabilization of within-host dynamics and the greatest risk of severe disease.

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<![CDATA[Mathematical Model for Growth Regulation of Fission Yeast Schizosaccharomyces pombe]]> https://www.researchpad.co/article/5989da77ab0ee8fa60b973e5

Regulation of polarised cell growth is essential for many cellular processes including spatial coordination of cell morphology changes during the division cycle. We present a mathematical model of the core mechanism responsible for the regulation of polarised growth dynamics during the fission yeast cell cycle. The model is based on the competition of growth zones localised at the cell tips for a common substrate distributed uniformly in the cytosol. We analyse the bifurcations in this model as the cell length increases, and show that the growth activation dynamics provides an explanation for the new-end take-off (NETO) as a saddle-node bifurcation at which the cell sharply switches from monopolar to bipolar growth. We study the parameter sensitivity of the bifurcation diagram and relate qualitative changes of the growth pattern, e.g. delayed or absent NETO, to previously observed mutant phenotypes. We investigate the effects of imperfect asymmetric cell division, and show that this leads to distinct growth patterns that provide experimentally testable predictions for validating the presented competitive growth zone activation model. Finally we discuss extension of the model for describing mutant cells with more than two growth zones.

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<![CDATA[Mathematical Modeling of Influenza A Virus Dynamics within Swine Farms and the Effects of Vaccination]]> https://www.researchpad.co/article/5989dabeab0ee8fa60bafb23

Influenza A virus infections are widespread in swine herds across the world. Influenza negatively affects swine health and production, and represents a significant threat to public health due to the risk of zoonotic infections. Swine herds can act as reservoirs for potentially pandemic influenza strains. In this study, we develop mathematical models based on experimental data, representing typical breeding and wean-to-finish swine farms. These models are used to explore and describe the dynamics of influenza infection at the farm level, which are at present not well understood. In addition, we use the models to assess the effectiveness of vaccination strategies currently employed by swine producers, testing both homologous and heterologous vaccines. An important finding is that following an influenza outbreak in a breeding herd, our model predicts a persistently high level of infectious piglets. Sensitivity analysis indicates that this finding is robust to changes in both transmission rates and farm size. Vaccination does not eliminate influenza throughout the breeding farm population. In the wean-to-finish herd, influenza infection may persist in the population only if recovered individuals become susceptible to infection again. A homologous vaccine administered to the entire wean-to-finish population after the loss of maternal antibodies eliminates influenza, but a vaccine that only induces partial protection (heterologous vaccine) has little effect on influenza infection levels. Our results have important implications for the control of influenza in swine herds, which is crucial in order to reduce both losses for swine producers and the risk to public health.

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<![CDATA[Dynamics of the Ethanolamine Glycerophospholipid Remodeling Network]]> https://www.researchpad.co/article/5989dac5ab0ee8fa60bb20cc

Acyl chain remodeling in lipids is a critical biochemical process that plays a central role in disease. However, remodeling remains poorly understood, despite massive increases in lipidomic data. In this work, we determine the dynamic network of ethanolamine glycerophospholipid (PE) remodeling, using data from pulse-chase experiments and a novel bioinformatic network inference approach. The model uses a set of ordinary differential equations based on the assumptions that (1) sn1 and sn2 acyl positions are independently remodeled; (2) remodeling reaction rates are constant over time; and (3) acyl donor concentrations are constant. We use a novel fast and accurate two-step algorithm to automatically infer model parameters and their values. This is the first such method applicable to dynamic phospholipid lipidomic data. Our inference procedure closely fits experimental measurements and shows strong cross-validation across six independent experiments with distinct deuterium-labeled PE precursors, demonstrating the validity of our assumptions. In constrast, fits of randomized data or fits using random model parameters are worse. A key outcome is that we are able to robustly distinguish deacylation and reacylation kinetics of individual acyl chain types at the sn1 and sn2 positions, explaining the established prevalence of saturated and unsaturated chains in the respective positions. The present study thus demonstrates that dynamic acyl chain remodeling processes can be reliably determined from dynamic lipidomic data.

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<![CDATA[A Hybrid of the Chemical Master Equation and the Gillespie Algorithm for Efficient Stochastic Simulations of Sub-Networks]]> https://www.researchpad.co/article/5989db4cab0ee8fa60bda822

Modeling stochastic behavior of chemical reaction networks is an important endeavor in many aspects of chemistry and systems biology. The chemical master equation (CME) and the Gillespie algorithm (GA) are the two most fundamental approaches to such modeling; however, each of them has its own limitations: the GA may require long computing times, while the CME may demand unrealistic memory storage capacity. We propose a method that combines the CME and the GA that allows one to simulate stochastically a part of a reaction network. First, a reaction network is divided into two parts. The first part is simulated via the GA, while the solution of the CME for the second part is fed into the GA in order to update its propensities. The advantage of this method is that it avoids the need to solve the CME or stochastically simulate the entire network, which makes it highly efficient. One of its drawbacks, however, is that most of the information about the second part of the network is lost in the process. Therefore, this method is most useful when only partial information about a reaction network is needed. We tested this method against the GA on two systems of interest in biology - the gene switch and the Griffith model of a genetic oscillator—and have shown it to be highly accurate. Comparing this method to four different stochastic algorithms revealed it to be at least an order of magnitude faster than the fastest among them.

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<![CDATA[Flow Past a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Two-Phase Model]]> https://www.researchpad.co/article/5989da43ab0ee8fa60b8ad9f

The steady two-dimensional flow and heat transfer over a stretching/shrinking sheet in a nanofluid is investigated using Buongiorno’s nanofluid model. Different from the previously published papers, in the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations are transformed into nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. The effects of some governing parameters on the fluid flow and heat transfer characteristics are graphically presented and discussed. Dual solutions are found to exist in a certain range of the suction and stretching/shrinking parameters. Results also indicate that both the skin friction coefficient and the local Nusselt number increase with increasing values of the suction parameter.

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<![CDATA[Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series]]> https://www.researchpad.co/article/5989da3dab0ee8fa60b88a5c

Stochastic chemical reaction networks constitute a model class to quantitatively describe dynamics and cell-to-cell variability in biological systems. The topology of these networks typically is only partially characterized due to experimental limitations. Current approaches for refining network topology are based on the explicit enumeration of alternative topologies and are therefore restricted to small problem instances with almost complete knowledge. We propose the reactionet lasso, a computational procedure that derives a stepwise sparse regression approach on the basis of the Chemical Master Equation, enabling large-scale structure learning for reaction networks by implicitly accounting for billions of topology variants. We have assessed the structure learning capabilities of the reactionet lasso on synthetic data for the complete TRAIL induced apoptosis signaling cascade comprising 70 reactions. We find that the reactionet lasso is able to efficiently recover the structure of these reaction systems, ab initio, with high sensitivity and specificity. With only < 1% false discoveries, the reactionet lasso is able to recover 45% of all true reactions ab initio among > 6000 possible reactions and over 102000 network topologies. In conjunction with information rich single cell technologies such as single cell RNA sequencing or mass cytometry, the reactionet lasso will enable large-scale structure learning, particularly in areas with partial network structure knowledge, such as cancer biology, and thereby enable the detection of pathological alterations of reaction networks. We provide software to allow for wide applicability of the reactionet lasso.

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<![CDATA[Consensus or Deadlock? Consequences of Simple Behavioral Rules for Coordination in Group Decisions]]> https://www.researchpad.co/article/5989dac3ab0ee8fa60bb1713

Coordinated collective behaviors often emerge from simple rules governing the interactions of individuals in groups. We model mechanisms of coordination among ants during cooperative transport, a challenging task that requires a consensus on travel direction. Our goal is to determine whether groups following simple behavioral rules can reach a consensus using minimal information. Using deterministic and stochastic models, we investigate behavioral factors that affect coordination. We define and investigate three types of behavioral rules governing individual behavior that differ in the information available: individuals either 1) have no information, 2) can measure transport success, or 3) measure success while also knowing whether they are aligned with the majority. We find that groups break deadlocks only if individuals more readily give up when they are going against the majority, corresponding to rule type 3 –such groups are “informed.” These behavioral rules succeed through positive and negative feedbacks that are implemented in our model via a single mechanism: individuals only need to measure the relative group sizes to make effective decisions. We also find that groups reach consensus more quickly if they have either a shared bias, high sensitivity to group behavior, or finely tuned persistence. Each of these is a potential adaptation for efficient cooperative transport. This flexibility makes the behavioral rules in the informed case relatively robust to deficiencies in the individuals’ capabilities. While inspired by ants, our results are generalizable to other collective decisions with deadlocks, and demonstrate that groups of behaviorally simple individuals with no memory and extremely limited information can break symmetry and reach a consensus in a decision between two equal options.

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<![CDATA[Applying diffusion-based Markov chain Monte Carlo]]> https://www.researchpad.co/article/5989db50ab0ee8fa60bdbf11

We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the presence of nonlinear models and non-conjugate priors. Also, it requires comparatively little problem-specific tuning. We implement the algorithm and assess its performance for both a test case and a glaciological application. Our results demonstrate that in some settings, diffusion MCMC is a faster alternative to a general Metropolis-Hastings algorithm.

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<![CDATA[Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order]]> https://www.researchpad.co/article/5989dab1ab0ee8fa60bab4e2

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.

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