Analysis of stable two-dimensional patterns in contractile cytogel

Summary Contractile actomyosin systems play a central role in the generation of intracellular patterns. Models for pattern formation have benefited greatly from the application of mechanochemical theory. However, investigations of the patterns have been primarily qualitative in nature; the two-dimensional nature of the evolving patterns has not yet been addressed mathematically, nor has the evolution of stable heterogeneous steady-state solutions. We consider these issues, supporting our analytical predictions with numerical simulations in one and two spatial dimensions. We show how, for certain gels, the two and three-dimensional tensor equation which describes a balance of forces can be reduced to a reaction-diffusion equation.     

Huddling behavior as critical phase transition triggered by low temperatures

Huddling is a grouping behavior where animals maintain close bodily contact and save energy. We tested the hypothesis that this thermoregulatory behavior behaves as a system with continuous (second‐order phase) transition called critical when the environmental temperature (driving parameter) is near a critical value. To do so, we followed theoretical and experimental approaches, examining data from geometrical models, metabolic rate during huddling in small mammals, and also conducting an experiment on thermoregulatory huddling behavior with white mice. Our results support all predictions for systems under continuous‐phase transition triggered by low temperatures, a phenomenon reported for first time in a biological system. We suggest that huddling behavior in social animals, a recognized adaptive behavior, may be considered a self‐organized system coupled with an external driving parameter. © 2011 Wiley Periodicals, Inc. Complexity, 2011     

Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model

We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In particular, a conjecture of Cantrell, Cosner and Lou on concentration phenomena is resolved under mild conditions. Applications to a related parabolic competition system are also discussed.     

Reverse-engineering country risk ratings: a combinatorial non-recursive model

The central objective of this paper is to develop a transparent, consistent, self-contained, and stable country risk rating model, closely approximating the country risk ratings provided by Standard and Poor’s (S&P). The model should be non-recursive, i.e., it should not rely on the previous years’ S&P ratings. The set of variables selected here includes not only economic-financial but also political variables. We propose a new model based on the novel combinatorial-logical technique of Logical Analysis of Data (which derives a new rating system only from the qualitative information representing pairwise comparisons of country riskiness). We also develop a method allowing to derive a rating system that has any desired level of granularity. The accuracy of the proposed model’s predictions, measured by its correlation coefficients with the S&P ratings, and confirmed by k-folding cross-validation, exceeds 95%. The stability of the constructed non-recursive model is shown in three ways: by the correlation of the predictions with those of other agencies (Moody’s and The Institutional Investor), by predicting 1999 ratings using the non-recursive model derived from the 1998 dataset applied to the 1999 data, and by successfully predicting the ratings of several previously non-rated countries. This study provides new insights on the importance of variables by supporting the necessity of including in the analysis, in addition to economic variables, also political variables (in particular “political stability”), and by identifying “financial depth and efficiency” as a new critical factor in assessing country risk.     

QUALITATIVE ANALYSIS ON A CLASS OF ECOSYSTEM

In this paper, we give complete qualitative analysis on a class of biological system and prove the nonexistence, existence and uniqueness of a limit cycle for the system.     

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities.

Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations.     

一类两种群均有收获率的HollingⅡ类生物捕食系统的定性分析

对一类两种群均有收获率的具HollingⅡ类功能反应的食饵-捕食系统作定性分析,利用常微分方程定性,稳定性及分支理论,得到此类生物捕食系统平衡点的性态和极限环的存在,不存在的条件及开发研究的结论,补充和完善了前人的结果.     

Semiqualitative modelling of bioprocesses

This paper deals with semiqualitative modelling of bioprocesses with a view to their supervision. An analysis of several approaches for modelling shows the difficulties involved in taking into account in a same framework, quantitative and qualitative knowledge, generally available about a process that we want to control. We propose an original approach, placed in the context of semiqualitative modelling, that is supported by a knowledge model the variables and parameters of which are defined by intervals. For these semiqualitative models, we study their properties in simulation and prediction, and more precisely, their fitting based on experimental data. We show that pertinent predictions in a short time can be obtained, making of these semiqualitative models interesting tools for the development of systems for bioprocess supervision     

具有HollingⅡ型功能反应的捕-食模型的定性分析及最优收获策略

利用微分方程的定性理论和Pontryagin最大值原理,讨论了一类食饵-捕食者种群都具有密度制约并且都具有收获的HollingⅡ型功能反应模型的性质,得到了存在边界平衡点、唯一正平衡点及各平衡点全局渐进稳定的条件,分析了相应的生物学意义,给出了最优可持续收获策略,并且用mathematica对特定参数下的系统进行了模拟.     

Agent-based and multi-agent simulations: coming of age or in search of an identity?

The promise of agent-based for explicating properties of social systems has not yet been fully realized. Agent models sometimes provide only a veneer of, rather than substantive engagement with, social behavior. The problem will be illustrated with Axelrod’s model for evolution of ethnocentrism (a biological model) versus Schelling’s model for spatial segregation based on preferences (a cultural model). The examples show the need to incorporate both the biological and cultural basis for behavior through a schema that includes behavior based on cultural/cognitive processing of information and behavior based on biological/cognitive processing of information. An example of an agent-based model that implements decision making in this manner is discussed. The model accounts for heterogeneity in behavior outcomes and leads to two main predictions: (1) small scale, hunter-gatherer societies in resource scarce environments will have stable adaptations less affected by variation in resource abundance in comparison to groups in resource rich regions where inter-group conflict is more likely and (2) the relationship between community size, population size and administrative complexity will have two distinct patterns, one for patrilineally organized societies and the other for matrilineally organized societies. Both predictions have been verified empirically.     

Dynamic properties of the oregonator model with delay

Delayed feedbacks are quite common in many physical and biological systems and in particular many physiological systems. Delay can cause a stable system to become unstable and vice versa. One of the well-studied non-biological chemical oscillators is the Belousov-Zhabotinsky(BZ) reaction. This paper presents an investigation of stability and Hopf bifurcation of the Oregonator model with delay. We analyze the stability of the equilibrium by using linear stability method. When the eigenvalues of the characteristic equation associated with the linear part are pure imaginary, we obtain the corresponding delay value. We find that stability of the steady state changes when the delay passes through the critical value. Then, we calculate the explicit formulae for determining the direction of the Hopf bifurcation and the stability of these periodic solutions bifurcating from the steady states, by using the normal form theory and the center manifold theorem. Finally, numerical simulations results are given to support the theoretical predictions by using Matlab and DDE-Biftool.     

Belief and probability: A general theory of probability cores

This paper considers varieties of probabilism capable of distilling paradox-free qualitative doxastic notions (e.g., full belief, expectation, and plain belief) from a notion of probability taken as a primitive. We show that core systems, collections of nested propositions expressible in the underlying algebra, can play a crucial role in these derivations. We demonstrate how the notion of a probability core can be naturally generalized to high probability, giving rise to what we call a high probability core, a notion that when formulated in terms of classical monadic probability coincides with the notion of stability proposed by Hannes Leitgeb [32]. Our work continues by one of us in collaboration with Rohit Parikh [7]. In turn, the latter work was inspired by the seminal work of Bas van Fraassen [46]. We argue that the adoption of dyadic probability as a primitive (as articulated by van Fraassen [46]) admits a smoother connection with the standard theory of probability cores as well as a better model in which to situate doxastic notions like full belief. We also illustrate how the basic structure underlying a system of cores naturally leads to alternative probabilistic acceptance rules, like the so-called ratio rule initially proposed by Isaac Levi [34].Core systems in their various guises are ubiquitous in many areas of formal epistemology (e.g., belief revision, the semantics of conditionals, modal logic, etc.). We argue that core systems can also play a natural and important role in Bayesian epistemology and decision theory. In fact, the final part of the article shows that probabilistic core systems are naturally derivable from basic decision-theoretic axioms which incorporate only qualitative aspects of core systems; that the qualitative aspects of core systems alone can be naturally integrated in the articulation of coherence of primitive conditional probability; and that the guiding idea behind the primary qualitative features of a core system gives rise to the formulation of lexicographic decision rules.     

Mortality density forecasts: An analysis of six stochastic mortality models

This paper develops a framework for developing forecasts of future mortality rates. We discuss the suitability of six stochastic mortality models for forecasting future mortality and estimating the density of mortality rates at different ages. In particular, the models are assessed individually with reference to the following qualitative criteria that focus on the plausibility of their forecasts: biological reasonableness; the plausibility of predicted levels of uncertainty in forecasts at different ages; and the robustness of the forecasts relative to the sample period used to fit the model. An important, though unsurprising, conclusion is that a good fit to historical data does not guarantee sensible forecasts. We also discuss the issue of model risk, common to many modelling situations in demography and elsewhere. We find that even for those models satisfying our qualitative criteria, there are significant differences among central forecasts of mortality rates at different ages and among the distributions surrounding those central forecasts.     

An analysis of heart rhythm dynamics using a three-coupled oscillator model

Rhythmic phenomena represent one of the most striking manifestations of the dynamic behavior in biological systems. Understanding the mechanisms responsible for biological rhythms is crucial for the comprehension of the dynamics of life. Natural rhythms could be either regular or irregular over time and space. Each kind of dynamical behavior may be related to both normal and pathological physiological functioning. The cardiac conducting system can be treated as a network of self-excitatory elements and, since these elements exhibit oscillatory behavior, they can be modeled as nonlinear oscillators. This paper proposes a mathematical model to describe heart rhythms considering three modified Van der Pol oscillators connected with time delay couplings. Therefore, the heart dynamics is represented by a system of differential difference equations. Numerical simulations are carried out presenting qualitative agreement with the general heart rhythm behavior. Normal and pathological rhythms represented by the ECG signals are reproduced. Pathological rhythms are generated by either the coupling alterations that represents communications aspects in the heart electric system or forcing excitation representing external pacemaker excitation.     

Competition of three species in an advective environment

Individuals in advective environments, for example rivers, coastlines, or the gut, are subject to movement with directional bias. We study how this movement bias shapes community composition by considering how the strength of movement bias affects the outcome of competition among three species. Our model is a system of three reaction-advection-diffusion equations with Danckwerts boundary conditions. Our key tool in this study is to use the dominant eigenvalue of the diffusion-advection operator in order to reduce the spatially explicit model to a spatially implicit ordinary differential equation model. After an in-depth analysis of the implicit model, we use numerical simulations of the explicit model to test the predictions obtained from the analysis. In general, we find a good qualitative agreement between the explicit and the implicit model. We find that varying the strength of advection can fundamentally alter the outcome of competition between the three species, and we characterize the possible transitions. In particular, water extraction and flow control can destabilize existing species communities or facilitate invasions of non-native species.     

Hydrodynamic Models and Confinement Effects by Horizontal Boundaries

Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces with the confining boundaries. When contact happens, we show that the model evolution can lead to the dependent variables developing singularities in finite time. The conditions and the nature of these singularities are illustrated in several cases, progressing from a single-layer homogeneous fluid with a constant-pressure free surface and flat bottom, to the case of a two-fluid system contained between two horizontal rigid plates, and finally, through numerical simulations, to the full Euler stratified system. These demonstrate the qualitative and quantitative predictions of the models within a set of examples chosen to illustrate the theoretical results.

     

An alternative model of a nonlinear business cycle

The purpose of this paper is to develop a piecewise linear model to understand complex dynamics that arise out of sophisticated nonlinear macrodynamic models developed by Hicks and Goodwin. This piecewise analogue has several advantages: (i) it is a natural extension of a linear accelerator; (ii) it exhibits all the qualitative results of Goodwin's model; (iii) it enables one to conveniently derive newer bounds on output; and (iv) students find its representation appealing and understandable. The use of computer software is advocated for complex economic models that are described by systems of differential equations. To this end, the usefulness of STELLA (a Macintosh-based software) in verifying the qualitative predictions of the analysis, is illustrated.     

Representation and interpretation of quantum mixtures in the ESR model

The interpretation of mixtures is problematic in quantum mechanics (QM) because physical properties are nonobjective in this theory. An extended semantic realism model was recently developed, restoring objectivity by reinterpreting quantum probabilities as conditional on detection and embodying the QM mathematical formalism in a broader noncontextual (hence local) framework. In this model, each generalized observable is represented by a family of positive operator-valued measures parameterized by the pure states of the considered physical system Ω. We here propose a new proof that each proper mixture is represented by a family of density operators parameterized by the macroscopic properties characterizing Ω. We then show that this representation implies some predictions differing from the QM predictions and avoids the problems following from the standard QM representation of proper mixtures. We also recall that the state transformations induced by idealized nondestructive measurements can be obtained using a nontrivial generalization of the Lüders postulate.     

Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons

Many reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction–diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate.     

CONSERVATION OF ENDANGERED ENDEMIC SEABIRDS WITHIN A MULTI‐PREDATOR CONTEXT: THE BARAU'S PETREL IN RÉUNION ISLAND

Abstract Seabirds breeding on islands are vulnerable to introduced predators, such as rats and cats, and the removal of such predators is generally viewed as a priority for seabird conservation and restoration. However, multiple invasive mammal species interacting may generate unexpected outcomes following the removal (eradication) of one species. Generally these indirect interactions are not well understood or demonstrated. We propose and study a prey (seabird)‐mesopredator (rat)‐superpredator (cat) model, taking into account the juvenile stages in the prey population, in order to direct conservation management for seabird conservation. We give a more biologically realistic differential system than those studied before (Courchamp et al. [1999] ; Fan et al. [2005] ), in particular for long‐lived seabird species. We present a theoretical study and show existence and uniqueness of a positive solution as well as a qualitative study of the equilibria that may appear. Because standard numerical methods, usually implemented in scientific softwares, can fail to give the right biological approximations ( Anguelov et al. [2009] ), we propose a reliable algorithm that preserves most of the qualitative properties of the continuous system, using the theory of nonstandard finite difference methods. Finally, we use biologically realistic parameters available for the representative Barau's petrel (Pinet et al. [2008] ), an endemic species from Réunion island, to present numerical simulations that support the theoretical study. Cats play the major role in seabird prey population dynamics. Seasonality in seabird breeding delays but does not prevent extinction. In all scenarios, cat control (or preferably eradication) is imperative to prevent extinction of vulnerable long‐lived seabirds, like the Barau's petrel.