Dynamics of opinion forming in structurally balanced social networks

A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.     

Evolution: geometrical and dynamical aspects.

We develop a possible axiomatic approach to the evolution theory that has been previously discussed in Freguglia [2002]. The axioms synthesize the fundamental ideas of evolution theory and allow a geometrical and dynamical interpretation of the generation law. Using the axioms we derive a simple reaction-diffusion model which introduces the species as self-organized stationary distribution of a finite population and simulates the evolution of a phenotypic character under the effect of an external perturbing action. The dynamical properties of the model are briefly presented using numerical simulations.     

Qualitative modelling of the interplay of inflammatory status and butyrate in the human gut: a hypotheses about robust bi-stability

Background

Gut microbiota interacts with the human gut in multiple ways. Microbiota composition is altered in inflamed gut conditions. Likewise, certain microbial fermentation products as well as the lipopolysaccharides of the outer membrane are examples of microbial products with opposing influences on gut epithelium inflammation status. This system of intricate interactions is known to play a core role in human gut inflammatory diseases. Here, we present and analyse a simplified model of bidirectional interaction between the microbiota and the host: in focus is butyrate as an example for a bacterial fermentation product with anti-inflammatory properties.

Results

We build a dynamical model based on an existing model of inflammatory regulation in gut epithelial cells. Our model introduces both butyrate as a bacterial product which counteracts inflammation, as well as bacterial LPS as a pro-inflammatory bacterial product. Moreover, we propose an extension of this model that also includes a feedback interaction towards bacterial composition. The analysis of these dynamical models shows robust bi-stability driven by butyrate concentrations in the gut. The extended model hints towards a further possible enforcement of the observed bi-stability via alteration of gut bacterial composition. A theoretical perspective on the stability of the described switch-like character is discussed.

Conclusions

Interpreting the results of this qualitative model allows formulating hypotheses about the switch-like character of inflammatory regulation in the gut epithelium, involving bacterial products as constitutive parts of the system. We also speculate about possible explanations for observed bimodal distributions in bacterial compositions in the human gut. The switch-like behaviour of the system proved to be mostly independent of parameter choices. Further implications of the qualitative character of our modeling approach for the robustness of the proposed hypotheses are discussed, as well as the pronounced role of butyrate compared to other inflammatory regulators, especially LPS, NF- κB and cytokines.

     

Nanosecond Motions in Proteins Impose Bounds on the Timescale Distributions of Local Dynamics

We elucidate the physics of protein dynamical transition via 10-100-ns molecular dynamics simulations at temperatures spanning 160-300 K. By tracking the energy fluctuations, we show that the protein dynamical transition is marked by a crossover from nonstationary to stationary processes that underlie the dynamics of protein motions. A two-timescale function captures the nonexponential character of backbone structural relaxations. One timescale is attributed to the collective segmental motions and the other to local relaxations. The former is well defined by a single-exponential, nanosecond decay, operative at all temperatures. The latter is described by a set of processes that display a distribution of timescales. Although their average remains on the picosecond timescale, the distribution is markedly contracted at the onset of the transition. It is shown that the collective motions impose bounds on timescales spanned by local dynamical processes. The nonstationary character below the transition implicates the presence of a collection of substates whose interactions are restricted. At these temperatures, a wide distribution of local-motion timescales, extending beyond that of nanoseconds, is observed. At physiological temperatures, local motions are confined to timescales faster than nanoseconds. This relatively narrow window makes possible the appearance of multiple channels for the backbone dynamics to operate.     

Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep

Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calculation of dimensionality estimates the degrees of freedom of a signal. Nevertheless, it is difficult to decide from this kind of analysis whether a process is quasiperiodic or chaotic. Therefore, we performed a new analysis by calculating the first positive Lyapunov exponent L ₁ from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L ₁ is zero for periodic as well as quasiperiodic processes, but positive in the case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L ₁ for sleep EEG segments of 15 healthy men corresponding to the sleep stages I, II, III, IV, and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor a simple noise. Moreover, we found statistically significant differences between the values of L ₁ for different sleep stages. All together, this kind of analysis yields a useful extension of the characterization of EEG signals in terms of nonlinear dynamical system theory.     

On the robustness of update schedules in Boolean networks

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems.     

New approach to the probabilistic-statistical analysis of turbulent transport processes in plasma

It is proposed to apply the statistical analysis of the increments of fluctuating particle fluxes to examine the probability characteristics of turbulent transport processes in plasma. Such an approach makes it possible to pass over to the analysis of the dynamical probability characteristics of the process under study. It is shown that, in the plasmas of the L-2M stellarator and the TAU-1 linear device, the increments of local fluctuating particle fluxes are stochastic in character and their distributions are scale mixtures of Gaussians. In particular, in TAU-1, the increments obey a Laplacian distribution (which is a scale mixture of Gaussians with an exponential mixing distribution). A mathematical model is proposed to explain such distributions. Possible physical mechanisms responsible for the random character of the increments of fluctuating particle fluxes are discussed.     

Dynamics parametrically controlled by image correlations organize robot navigation

Behavior-based robot designs confront the problem of how different elementary behaviors can be integrated. We address two aspects of this problem: the stabilization of behavioral decisions that are induced by changing sensory information and the fusion of multiple sources of sensory information. The concrete context is homing and obstacle avoidance in a vision-guided mobile robot. Obstacle avoidance is based on extracting time-to-contact information from optic flow. A dynamical system controls heading direction and velocity. Time-to-contact estimates parametrically control this dynamical system, the attractors of which generate robot movement. Decisions come about through bifurcations of the dynamics and are stabilized through hysteresis. Homing is based on image correlations between memorized and current views. These control parametrically a dynamics of ego-position estimation, which converges in closed loop so as to position the robot at the home position. Unreliable visual information and more continous open-loop dead-reckoning information are integrated within this dynamics. This permits vision-based homing, but also stabilizes the behavior during periods of absent or erroneous visual information through the internal state of the dynamical system. The navigation scheme is demonstrated on a robot platform in real time. Received: 2 May 1995 / Accepted in revised form: 10 June 1996     

Solitary wave and spatially locked solitary pattern in a chemical reaction system

We investigate the behavior of a one-dimensional two component dynamical system. The dynamical equations are obtained by extracting an essence out of equations which describe the behavior of a biochemical reaction catalyzed by an allosteric protein. The obtained dynamical equations are similar to van der Pol equations. The dynamical equations are solved numerically. In the continuous system, a solitary wave is found to occur in certain ranges of the parameter space. The condition of occurrence of the solitary wave is investigated. The solitary wave can be induced by various initial perturbations, including rectangular ones with space-wise length longer than a certain critical value. The property of the solitary wave is similar to that of the impulses in nervous systems. In the discrete system, a spatially locked solitary pattern is found to occur in certain ranges of the parameter space.     

Abstract heterarchy: time/state-scale re-entrant form

A heterarchy is a dynamical hierarchical system inheriting logical inconsistencies between levels. Because of these inconsistencies, it is very difficult to formalize a heterarchy as a dynamical system. Here, the essence of a heterarchy is proposed as a pair of the property of self-reference and the property of a frame problem interacting with each other. The coupling of them embodies a one-ity inheriting logical inconsistency. The property of self-reference and a frame problem are defined in terms of logical operations, and are replaced by two kinds of dynamical system, temporal dynamics and state-scale dynamics derived from the same "liar statement". A modified tent map serving as the temporal dynamics is twisted and coupled with a tent map serving as the state-scale dynamics, and this results in a discontinuous self-similar map as a dynamical system. This reveals that the state-scale and temporal dynamics attribute to the system, and shows both robust and emergent behaviors.     

GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of state transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools.     

La Dynamique Posturale Non-Linéaire. Partie I : bases et fondements

The different sensorial systems involved in the postural control form a super system preserving the static and dynamical equilibrium of a standing human being, motionless or moving. Now, the human posture captors are endowed with conditions that are sufficient to constitute a dynamical system. Then, we can show that: (i) generic properties of dynamical systems may be applied to the postural system, (ii) we may benefit from conceptual justifications to postural interactions experienced at a clinical level. Moreover, concerning the issue of the multi-causal chain in posturology, it is possible to infer and characterize a certain number of generic properties relative to these postural interactions. From this theoretical grounding, based on the knowledge of dynamical systems, it appears licit to introduce the concept of Non-linear Postural Dynamics (NPD). In a first part of this paper, the bases and foundations of NPD are presented, while the second part deals with different possible modes of NPD. Indeed, because the postural system is comparable to the structure of a dynamical system, it turns out that the former, natural seat of non-linear interaction dynamics, exhibits four dynamical modes and only four, « solutions » to the whole postural system. These four modes are as follows: (1) the quasi-linear mode, (2) the stationary mode, (3) the non-linear convergent mode, and (4) the chaotic mode. The present paper is devoted to the definition and articulation of these postural dynamic's modes. A codification of the clinical elements of their recognition should constitute a logically indispensable sequel. However, by their very constitutive principles themselves, some of these modes call for a functional multi-disciplinary approach. As a consequence, in the search for therapeutic protocols, not blindly but rather built on the interplay of various medical fields relative to posture and its physio-dynamical equilibrium, it is necessary to identify in a first step, and as surely as possible, the postural mode in which the patient stands.     

Modeling epithelial cell homeostasis: Assessing recovery and control mechanisms

Critical to epithelial cell viability is prompt and direct recovery, following a perturbation of cellular conditions. Although a number of transporters are known to be activated by changes in cell volume, cell pH, or cell membrane potential, their importance to cellular homeostasis has been difficult to establish. Moreover, the coordination among such regulated transporters to enhance recovery has received no attention in mathematical models of cellular function. In this paper, a previously developed model of proximal tubule (Weinstein, 1992, Am. J. Physiol. 263, F784–F798), has been approximated by its linearization about a reference condition. This yields a system of differential equations and auxiliary linear equations, which estimate cell volume and composition and transcellular fluxes in response to changes in bath conditions or membrane transport coefficients. Using the singular value decomposition, this system is reduced to a linear dynamical system, which is stable and reproduces the full model behavior in a useful neighborhood of the reference. Cost functions on trajectories formulated in the model variables (e.g., time for cell volume recovery) are translated into cost functions for the dynamical system. When the model is extended by the inclusion of linear dependence of membrane transport coefficients on model variables, the impact of each such controller on the recovery cost can be estimated with the solution of a Lyapunov matrix equation. Alternatively, solution of an algebraic Riccati equation provides the ensemble of controllers that constitute optimal state feedback for the dynamical system. When translated back into the physiological variables, the optimal controller contains some expected components, as well as unanticipated controllers of uncertain significance. This approach provides a means of relating cellular homeostasis to optimization of a dynamical system.     

Control of computational dynamics of coupled integrate-and-fire neurons

 Generation and control of different dynamical modes of computational processes in a net of interconnected integrate-and-fire neurons are demonstrated. A net architecture resembling a generic cortical structure is formed from pairs of excitatory and inhibitory units with excitatory connections between and inhibitory connections within pairs. Integrate-and-fire model neurons derived from detailed conductance-based models of neocortical pyramidal cells and fast-spiking interneurons are employed for the excitatory and inhibitory units, respectively. Firing-rate adaptation is incorporated into the excitatory units based on the regulation of the slow afterhyperpolarization phase of action potentials by intracellular calcium ions. Saturation of synaptic conductances is implemented for the interconnections between units. It is shown that neuronal adaptation of the excitatory units can generate richer net dynamics than relaxation to fixed-point attractors in a pattern space. At strong adaptivity, i.e. when the neuronal excitability is strongly influenced by the preceding activity, complex dynamics of either aperiodic or limit-cycle character are generated in both the pattern space and the phase space of all dynamical variables. This regime corresponds to an exploratory mode of the system, in which the pattern space can be searched. At weak adaptivity, the dynamics are governed by fixed-point attractors in the pattern space, and this corresponds to a mode for retrieval of a particular pattern. In the brain, neuronal adaptivity can be regulated by various neuromodulators. The results are in accordance with those recently obtained by means of more abstract models formulated in terms of mean firing rates. The increased realism makes the present model reveal more detailed mechanisms and strengthens the relevance of the conclusions to biological systems. The simplicity and realism of the coupled integrate-and-fire neurons make the present model useful for studies of systems in which the temporal aspects of neural coding are important. Received: 8 December 1995 / Accepted in revised form: 23 January 1997     

Agential autonomy and biological individuality

What is a biological individual? How are biological individuals individuated? How can we tell how many individuals there are in a given assemblage of biological entities? The individuation and differentiation of biological individuals are central to the scientific understanding of living beings. I propose a novel criterion of biological individuality according to which biological individuals are autonomous agents. First, I articulate an ecological–dynamical account of natural agency according to which, agency is the gross dynamical capacity of a goal-directed system to bias its repertoire to respond to its conditions as affordances. Then, I argue that agents or agential dynamical systems can be agentially dependent on, or agentially autonomous from, other agents and that this agential dependence/autonomy can be symmetrical or asymmetrical, strong or weak. Biological individuals, I propose, are all and only those agential dynamical systems that are strongly agentially autonomous. So, to determine how many individuals there are in a given multiagent aggregate, such as multicellular organism, a colony, symbiosis, or a swarm, we first have to identify how many agential dynamical systems there are, and then what their relations of agential dependence/autonomy are. I argue that this criterion is adequate to the extent that it vindicates the paradigmatic cases, and explains why the paradigmatic cases are paradigmatic, and why the problematic cases are problematic. Finally, I argue for the importance of distinguishing between agential and causal dependence and show the relevance of agential autonomy for understanding the explanatory structure of evolutionary developmental biology.     

On the decomposition of a dynamical system into non-interacting subsystems

It is shown that, under rather general conditions, it is possible to formally decompose the dynamics of ann-dimensional dynamical system into a number of non-interacting subsystems. It is shown that these decompositions are in general not simply related to the kinds of observational procedures in terms of which the original state variables of the system are defined. Some consequences of this construction for reductionism in biology are discussed.     

一种非线性多阶段动力系统的最优控制及数值优化

针对间歇发酵过程的非线性多阶段动力系统,建立了以初始浓度为控制变量、以生产强度为性能指标的最优控制模型.证明了非线性多阶段动力系统的主要性质、最优控制的存在性及达到最优解的必要条件.构造了优化算法并应用于实际数据计算,其数值结果表明了本文模型与算法的有效性.