A study of stage structured model of fish population is presented. This model focuse on the anchovy population in the Bay of Biscay (Engraulis encrasicolus L.) is presented. The method of study is based on an intermediate complexity mathematical model, taking into account the spatialisation, the environmental conditions and the stage-structure of the fishes. First, to test the model, we show mathematical properties, such as unicity of the solution of structural stability. Then we provide numerical simulations, to validate (...) the model and to test the dynamics according to the variations of the parameters. (shrink)

There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural (...) instability with a recent argument against causal decision theory proposed by Caspar Hare and Brian Hedden. We show that their argument is undermined by considerations arising from decision instability and structural instability. (shrink)

There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural (...) instability with a recent argument against causal decision theory proposed by Caspar Hare and Brian Hedden. We show that their argument is undermined by considerations arising from decision instability and structural instability. (shrink)

Climate modelling plays a crucial role for understanding and addressing the climate challenge, in terms of both mitigation and adaptation. It is therefore of central importance to understand to what extent climate models are adequate for relevant purposes, such as providing certain kinds of climate change projections in view of decision-making. In this perspective, the issue of the stability of climate models under small relevant perturbations in their structure seems particularly important. Within this framework, a debate has emerged in (...) the philosophy of science literature about the relevance for climate modelling of the mathematical notion of structural stability. This paper adresses several important foundational and epistemological questions that arise in this context, in particular about the the role of abstract mathematical considerations of a qualitative nature for concrete modelling projects with mainly quantitative purposes. (shrink)

In this article, we focus on an extended model M ¯ of bounded rationality. Based on a rationality function with lower semicontinuity, we analyze the relationship between structural stability and robustness of Ω ¯. To further demonstrate the applicability of our theory, we introduce a model Ω ¯ 0 containing an abstract rationality function and generalize abstract fuzzy economies. We demonstrate the structural stability of the extended model Ω ¯ 0 at ξ ¯, ɛ. That is (...) to say, Ω ¯ 0 is robust to the ξ ¯, ɛ -equilibria. (shrink)

Quantum mechanical and molecular dynamics methods were used to analyze the structure and stability of neutral and zwitterionic configurations of the extracted active site sequence from a Burkholderia cepacia lipase, histidyl-seryl-glutamin (His86-Ser87-Gln88) and its mutated form, histidyl-cysteyl-glutamin (His86-Cys87-Gln88) in vacuum and different solvents. The effects of solvent dielectric constant, explicit and implicit water molecules and side chain mutation on the structure and stability of this sequence in both neutral and zwitterionic forms are represented. The quantum mechanics computations represent (...) that the relative stability of zwitterionic and neutral configurations depends on the solvent structure and its dielectric constant. Therefore, in vacuum and the considered non-polar solvents, the neutral form of the interested sequences is more stable than the zwitterionic form, while their zwitterionic form is more stable than the neutral form in the aqueous solution and the investigated polar solvents in most cases. However, on the potential energy surfaces calculated, there is a barrier to proton transfer from the positively charged ammonium group to the negatively charged carboxylat group or from the ammonium group to the adjacent carbonyl oxygen and or from side chain oxygen and sulfur to negatively charged carboxylat group. Molecular dynamics simulations (MD) were also performed by using periodic boundary conditions for the zwitterionic configuration of the hydrated molecules in a box of water molecules. The obtained results demonstrated that the presence of explicit water molecules provides the more compact structures of the studied molecules. These simulations also indicated that side chain mutation and replacement of sulfur with oxygen leads to reduction of molecular flexibility and packing. (shrink)

We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.

Ecologists are challenged by the need to bridge and synthesize different approaches and theories to obtain a coherent understanding of ecosystems in a changing world. Both food web theory and regime shift theory shine light on mechanisms that confer stability to ecosystems, but from different angles. Empirical food web models are developed to analyze how equilibria in real multi-trophic ecosystems are shaped by species interactions, and often include linear functional response terms for simple estimation of interaction strengths from observations. (...) Models of regime shifts focus on qualitative changes of equilibrium points in a slowly changing environment, and typically include non-linear functional response terms. Currently, it is unclear how the stability of an empirical food web model, expressed as the rate of system recovery after a small perturbation, relates to the vulnerability of the ecosystem to collapse. Here, we conduct structural sensitivity analyses of classical consumer-resource models in equilibrium along an environmental gradient. Specifically, we change non-proportional interaction terms into proportional ones, while maintaining the equilibrium biomass densities and material flux rates, to analyze how alternative model formulations shape the stability properties of the equilibria. The results reveal no consistent relationship between the stability of the original models and the proportionalized versions, even though they describe the same biomass values and material flows. We use these findings to critically discuss whether stability analysis of observed equilibria by empirical food web models can provide insight into regime shift dynamics, and highlight the challenge of bridging alternative modelling approaches in ecology and beyond. (shrink)

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. (...) These sub-collections, called organizations, correspond to the groups of species that can survive together in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. (shrink)

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called chemical organization theory sheds new light on the longstanding complexity–stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. (...) These sub-collections, called organizations, correspond to the groups of species that can survive together in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the complexity–stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. (shrink)

Estrogen receptor α (ERα) is a ligand‐dependent transcription factor that regulates the expression of estrogen‐responsive genes. Approximately 70% of patients with breast cancer are ERα positive. Estrogen stimulates cancer cell proliferation and contributes to tumor progression. Endocrine therapies, which suppress the ERα signaling pathway, significantly improve the prognosis of patients with breast cancer. However, the development of de novo or acquired endocrine therapy resistance remains a barrier to breast cancer treatment. Therefore, understanding the regulatory mechanisms of ERα is essential to (...) overcome the resistance to treatment. This review focuses on the regulation of ERα expression, including copy number variation, epigenetic regulation, transcriptional regulation, and stability, as well as functions from the point of view post‐translational modifications. (shrink)

A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set of (...) models is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)

The ArgumentThis essay attempts to show the decisive importance of the “scientific discipline” for any historical or sociological analysis of modern science. There are two reasons for this:1. A discontinuity can be observed at the beginning of modern science: the “discipline,” which up until that time had been a classificatorily generated unit of the ordering of knowledge for purposes of instruction in schools and universities, develops into a genuine and concrete social system of scientific communication. Scientific disciplines as concrete systems (...) (Realsysteme) arise as a result of (a) the communicative stabilization of “scientific communities” at the end of the eighteenth century and the formation of “appropriate” roles and organizational structures (in universities); (b) the structural differentiation of the new scientific disciplines from the established professions (law, theology, medicine) in Europe; (c) the formation of scientific communication in the standardized form of scientific publication; the distinction of the separate action-type “scientific research” and the differentiation of these two elementary acts of all future scientific endeavor in relation to each other.2. The scientific discipline as primary unit of the internal differentiation of science has, since its genesis, been stabilized by two conditions: (a) The fact of a science differentiated into a plurality of (competing, mutually stimulating) disciplinary perspectives becomes the chief causal factor underlying the developmental dynamism of modern science; (b) Similar to the way in which the discipline functions as a cognitive address within the system of science, science also links the discipline up as a structural unit (utilized in both systems) with curricular structures in the system of education — i.e., it is stabilized by the central system/environment relation of science. (shrink)

The calibration solution to the stability of the world despite eye movements depends, according to Bridgeman et al., upon a combination of three factors which presumably all need to operate to achieve the goal of stability. Although the authors admit (sect. 4.3, para. 5) that the relative contributions of retinal and extraretinal factors will depend on the particular viewing situation, Figure 5 (sect. 4.3) makes it clear in its representation that the role of perceptual factors is relatively minor (...) compared to extraretinal ones. It is with this representation that this commentary wishes to take issue, believing that it occurs as a result of some assumptions about terminology that may be ambiguous, as well as some misconceptions about the circumstances in which there is a need for stability. (shrink)

Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

Adopting deep approaches to learning can have a profound impact on learning outcomes. The extent of change in the learning approach could be attributed to the effect of contextual factors. After a substantive review, it was found that research interested in investigating the longitudinal effect of deep approaches to learning on learning outcomes were rarely directly concerned with the longitudinal state and trend of the approach itself. Moreover, the limitations of past analytical methods, has not been appropriately acknowledged. This study (...) examined deep approaches to learning in students from kindergarten to third grade using a multilevel structural equation modeling indicator-specific growth model. This was used to highlight the methodological issues to investigate the effect of context and the states, stability, and changes in deep approaches to learning over this developmental period. The current study comprised of a large-scale sample of 21,490 kindergarteners in kindergarten. Results showed: there was a contextual effect on the longitudinal changes of deep approaches to learning; deep approaches to learning was high but showed considerable individual differences; most indicators relating to deep approaches to learning declined, whereas the trend were relatively stable over time. Corresponding suggestions were proposed at the end of this article. (shrink)

Cognitive Science, Volume 45, Issue 11, November 2021.

The physical and relational structure of the biologic continuum (both internal and external to the organism) creates the information signature that is the basis for the origination of meaning in the living system. A meaning metric can be grounded in the significance of that information to the stability of the system during the process of adaptive reconciliation of divergences from the steady state condition. From this perspective, an information-theoretic formulation of the process for translating incident information into adaptive action (...) is proposed that can be practically used in defining and quantifying the meaning of that information for the living system. (shrink)

In this paper we build a prey–predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage and present some general mathematical results. In the last part, (...) we will assume that the dynamics of the prey is fast compared to the predator’s one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result. (shrink)

Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying (...) term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems. (shrink)

Today, economic theory is a mathematical theory, but that was not always the case. Major changes in the ways economists presented their arguments to one another occurred between the late 1930s and the early 1950s; over that period the discipline became mathematized. Professor Weintraub, a noted scholar of the modern history of economic thought, argues that those changes were not merely cosmetic: The mathematical forms of the arguments significantly altered the substance of the arguments. Stabilizing Dynamics is particularly concerned with (...) the ways in which the rich and confusing talk of the 1930s evolved, over a fifteen-year period, into technical analysis of some mathematical structures. The author describes the context for the history of that change, locating it in the broader intellectual currents, and shows how the history of modern economics can be seen as a confluence of several disparate traditions. Historiographically, this book offers one of the first constructivist accounts of modern economic analysis. (shrink)

§1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.The class of simple theories includes stable theories, but also many more, such as the theory of the random graph. Moreover, many of the theories of particular (...) algebraic structures which have been studied recently turn out to be simple. The interest is basically that a large amount of the machinery of stability theory, invented by Shelah, is valid in the broader class of simple theories. Stable theories will be defined formally in the next section. An exhaustive study of them is carried out in [33]. Without trying to read Shelah's mind, we feel comfortable in saying that the importance of stability for Shelah lay partly in the fact that an unstable theory T has 2λ many models in any cardinal λ ≥ ω1 + |T|. (shrink)