General Dynamical Properties Research Articles

Beyond Boolean: Ternary networks and dynamics.

Boolean networks introduced by Kauffman, originally intended as a prototypical model for gaining insights into gene regulatory dynamics, have become a paradigm for understanding a variety of complex systems described by binary state variables. However, there are situations, e.g., in biology, where a binary state description of the underlying dynamical system is inadequate. We propose random ternary networks and investigate the general dynamical properties associated with the ternary discretization of the variables. We find that the ternary dynamics can be either ordered or disordered with a positive Lyapunov exponent, and the boundary between them in the parameter space can be determined analytically. A dynamical event that is key to determining the boundary is the emergence of an additional fixed point for which we provide numerical verification. We also find that the nodes playing a pivotal role in shaping the system dynamics have characteristically distinct behaviors in different regions of the parameter space, and, remarkably, the boundary between these regions coincides with that separating the ordered and disordered dynamics. Overall, our framework of ternary networks significantly broadens the classical Boolean paradigm by enabling a quantitative description of richer and more complex dynamical behaviors.

Admissible Reversing and Extended Symmetries for Bijective Substitutions

In this paper, we deal with reversing and extended symmetries of subshifts generated by bijective substitutions. We survey some general algebraic and dynamical properties of these subshifts and recall known results regarding their symmetry groups. We provide equivalent conditions for a permutation on the alphabet to generate a reversing/extended symmetry, and algorithms how to compute them. Moreover, for any finite group H and any subgroup P of the d-dimensional hyperoctahedral group, we construct a bijective substitution which generates an aperiodic subshift with symmetry group {mathbb {Z}}^{d}times H and extended symmetry group ({mathbb {Z}}^{d} rtimes P)times H. A similar construction with the same symmetry group, but with extended symmetry group ({mathbb {Z}}^{d} times H) rtimes P is also provided under a mild assumption on the dimension.

Instantons, symmetries and anomalies in five dimensions

All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

GraphKKE: graph Kernel Koopman embedding for human microbiome analysis

More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.

Reservoir Computing with Random Skyrmion Textures

The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex resistance response exhibited by random magnetic skyrmion textures and using it to demonstrate pattern recognition, we explain how spintronically accessible magnetic systems offer an advantage in the search for an ideal reservoir computer. The low-power properties of compact skyrmion fabrics, coupled with their CMOS integrability operating on similar length and timescales, open the door for their RC employment geared towards industrial application.

General dynamical properties of cosmological models with nonminimal kinetic coupling

We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as η Gμνϕ,μϕ,ν, where η is an arbitrary coupling parameter, and the scalar potential V(ϕ) which assumed to be as general as possible. With an appropriate dimensionless parametrization we represent the field equations as an autonomous dynamical system which contains ultimately only one arbitrary function χ (x)= 8 π | η | V(x/√8 π) with x=√8 πϕ. Then, assuming the rather general properties of χ(x), we analyze stationary points and their stability, as well as all possible asymptotical regimes of the dynamical system. It has been shown that for a broad class of χ(x) there exist attractors representing three accelerated regimes of the Universe evolution, including de Sitter expansion (or late-time inflation), the Little Rip scenario, and the Big Rip scenario. As the specific examples, we consider a power-law potential V(ϕ)=M4(ϕ/ϕ0)σ, Higgs-like potential V(ϕ)=λ/4(ϕ2−ϕ02)2, and exponential potential V(ϕ)=M4 e−ϕ/ϕ0.

Effective Hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems

We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian $H_*$ up to time $\tau_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $t\lesssim \tau_*$, eventually heating up to an infinite-temperature state at times $t\sim \tau_*$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.

History-dependent variability in population dynamics during evidence accumulation in cortex.

We studied how the posterior parietal cortex combined new information with ongoing activity dynamics as mice accumulated evidence during a virtual-navigation task. Using new methods to analyze population activity on single trials, we found that activity transitioned rapidly between different sets of active neurons. Each event in a trial — whether an evidence cue or a behavioral choice — caused seconds-long modifications to the probabilities that govern how one activity pattern transitions to the next, forming a short-term memory. A sequence of evidence cues triggered a chain of these modifications resulting in a signal for accumulated evidence. Multiple distinguishable activity patterns were possible for the same accumulated evidence because representations of ongoing events were influenced by previous within and across trial events. Therefore, evidence accumulation need not require the explicit competition between groups of neurons, as in winner-take-all models, but could instead emerge implicitly from general dynamical properties that instantiate short-term memory.

On some physical and dynamical properties of microplastic particles in marine environment

Simplified physical models and geometrical considerations reveal general physical and dynamical properties of microplastic particles (0.5–5mm) of different density, shape and size in marine environment. Windage of extremely light foamed particles, surface area and fouling rate of slightly positively buoyant microplastic spheres, films and fibres and settling velocities of negatively buoyant particles are analysed. For the Baltic Sea dimensions and under the considered idealised external conditions, (i) only one day is required for a foamed polystyrene particle to cross the sea (ca. 250km); (ii) polyethylene fibres should spend about 6–8months in the euphotic zone before sinking due to bio-fouling, whilst spherical particles can be retained on the surface up to 10–15years; (iii) for heavy microplastic particles, the time of settling through the water column in the central Gotland basin (ca. 250m) is less than 18h. Proper physical setting of the problem of microplastics transport and developing of physically-based parameterisations are seen as applications.

The many sides of RCW 86: a Type Ia supernova remnant evolving in its progenitor's wind bubble

We present the results of a detailed investigation of the Galactic supernova remnant RCW 86 using the XMM-Newton X-ray telescope. RCW 86 is the probable remnant of SN 185 A.D, a supernova that likely exploded inside a wind-blown cavity. We use the XMM-Newton Reflection Grating Spectrometer (RGS) to derive precise temperatures and ionization ages of the plasma, which are an indication of the interaction history of the remnant with the presumed cavity. We find that the spectra are well fitted by two non-equilibrium ionization models, which enables us to constrain the properties of the ejecta and interstellar matter plasma. Furthermore, we performed a principal component analysis on EPIC MOS and pn data to find regions with particular spectral properties. We present evidence that the shocked ejecta, emitting Fe-K and Si line emission, are confined to a shell of approximately 2 pc width with an oblate spheroidal morphology. Using detailed hydrodynamical simulations, we show that general dynamical and emission properties at different portions of the remnant can be well-reproduced by a type Ia supernova that exploded in a non-spherically symmetric wind-blown cavity. We also show that this cavity can be created using general wind properties for a single degenerate system. Our data and simulations provide further evidence that RCW 86 is indeed the remnant of SN 185, and is the likely result of a type Ia explosion of single degenerate origin.

Dynamics of Poly(ethylene oxide) around Its Melting Temperature

This study has focused on the ionic conductivity (of impurities) and the changes in relaxation behavior of semicrystalline poly(ethylene oxide) (PEO) around its melting temperature of the crystalline regions. Our main aim was to understand the implications of nucleation and growth of spherulitic structures on the general dynamical properties of the polymer chains and how these dynamical alterations affect the ionic conductivity. Impedance data have been scaled and analyzed under conductivity and modulus formalisms over wide ranges of frequency and temperature. The analysis of the scaled formalisms indicates that both the conductivity and the structural relaxation mechanisms are temperature independent above the melting point of PEO. However, below the melting, point, the slow crystallization of PEO leads to growth of spherulites and also to the formation of interphase regions. These morphological changes result in a hindered long-range dc conductivity, which, in turn, leads to a decoupling of the dc conductivity and the structural relaxation below the melting point of PEO.

SPATIALLY RESOLVED KINEMATICS OF THE CENTRAL REGIONS OF M83: HIDDEN MASS SIGNATURES AND THE ROLE OF SUPERNOVAE

The barred grand-design spiral M83 (NGC 5236) is one of the most studied galaxies given its proximity, orientation, and particular complexity. Nonetheless, many aspects of the central regions remain controversial conveying our limited understanding of the inner gas and stellar kinematics, and ultimately of the nucleus evolution. In this work, we present AO VLT-SINFONI data of its central ~235x140 pc with an unprecedented spatial resolution of ~0.2 arcsec, corresponding to ~4 pc. We have focused our study on the distribution and kinematics of the stars and the ionised and molecular gas by studying in detail the Pa_alpha and Br_gamma emission, the H_2 1-0S(1) line at 2.122 micron and the [FeII] line at 1.644 micron, together with the CO absorption bands at 2.293 micron and 2.323 micron. Our results reveal a complex situation where the gas and stellar kinematics are totally unrelated. Supernova explosions play an important role in shaping the gas kinematics, dominated by shocks and inflows at scales of tens of parsecs that make them unsuitable to derive general dynamical properties. We propose that the location of the nucleus of M83 is unlikely to be related to the off-centre 'optical nucleus'. The study of the stellar kinematics reveals that the optical nucleus is a gravitationally bound massive star cluster with M_dyn = (1.1 \pm 0.4)x10^7 M_sun, formed by a past starburst. The kinematic and photometric analysis of the cluster yield that the stellar content of the cluster is well described by an intermediate age population of log T(yr) = 8.0\pm0.4, with a mass of M \simeq (7.8\pm2.4)x10^6 M_sun.

Dynamical Properties of A Cellular Automaton on A Countable Group

Topological structure of the living space is one of the most important parameters for cellular automata (CA), which can be applied to various scientific areas. In order to study CA in larger extent, we define a new type of cellular automata on countable groups and investigate some general dynamical properties of attractors and periodicity. It is shown that if such cellular automaton on a countable group is transitive, it is either sensitive or composed of a single periodic orbit. By using of the form of attractors, classification of this type of cellular automata is given on countable groups. The set of eventually periodic points of a cellular automaton on a countable residually finite group is proved to be dense.

Modeling the role of IL-2 in the interplay between CD4+ helper and regulatory T cells: Assessing general dynamical properties

Mathematical models accounting for well-known evidences relating to the dynamics of interleukin 2, helper and regulatory T cells are presented. These models extend an existent model (the so-called cross-regulation model of immunity), by assuming IL-2 as the growth factor produced by helper cells, but used by both helper and regulatory cells to proliferate and survive. Two model variants, motivated by current literature, are explored. The first variant assumes that regulatory cells suppress helper cells by limiting IL-2 production and consuming the available IL-2; i.e. they just trigger competition for IL-2. The second model variant adds to the latter competitive mechanism the direct inhibition of helper cells activation by regulatory cells. The extended models retain key dynamical features of the cross-regulation model. But such reasonable behavior depends on parameter constraints, which happen to be realistic and lead to interesting biological discussions. Furthermore, the introduction of IL-2 in these models breaks the local/specific character of interactions, providing new properties to them. In the extended models, but not in the cross-regulation model, the response triggered by an antigen affects the response to other antigens in the same lymph node. The first model variant predicts an unrealistic coupling of the immune reactions to all the antigens in the lymph node. In contrast, the second model variant allows the coexistent of concomitant tolerant and immune responses to different antigens. The IL-2 derived from an ongoing immune reaction reinforces tolerance to other antigens in the same lymph node. Overall the models introduced here are useful extensions of the cross-regulation formalism. In particular, they might allow future studies of the effect of different IL-2 modulation therapies on CD4+ T cell dynamics.

On the dynamics of cellular automata induced from a prefix code

In this paper we study some general dynamical properties of the class of one-dimensional permutation cellular automata induced by maximal finite prefix codes defined on the one-sided full shift A N . Then we define families of codes every member of which induces an onto permutation cellular automaton F, and we investigate some properties of the (topological) dynamical system ( A N , F ) such as positive expansiveness, entropy and periodic points. We also define and study a special case of permutation cellular automata, namely, elector automata, which are canonically constructed from codes, and provide classes of cellular automata which attain their limit sets in finite time, and other families without that property.

Lyapunov exponents from unstable periodic orbits

We propose a method that allows us to analytically compute the largest Lyapunov exponent of a Hamiltonian chaotic system from the knowledge of a few unstable periodic orbits (UPOs). In the framework of a recently developed theory for Hamiltonian chaos, by computing the time averages of the metric tensor curvature and of its fluctuations along analytically known UPOs, we have re-derived the analytic value of the largest Lyapunov exponent for the Fermi-Pasta-Ulam-beta (FPU-beta) model. The agreement between our results and the Lyapunov exponents obtained by means of standard numerical simulations confirms the point of view which attributes to UPOs the special role of efficient probes of general dynamical properties, among them chaotic instability.

Three-dimensional chaotic flows with discrete symmetries.

There are a number of well-known three-dimensional flows with quadratic nonlinearities, which demonstrate a chaotic behavior. The most popular among them are Lorenz and Rössler systems. Using an exhaustive computer search, J. Sprott found 19 examples of chaotic flows with either five terms and two quadratic nonlinearities or six terms and one nonlinearity [Phys. Rev. E 50, R647 (1994)]. In contrast to this approach, we use symmetry-related considerations to construct types of chaotic flows with an arbitrary dimension. The discussion is based on our previous work devoted to nonlinear dynamics of the physical systems with discrete symmetries [see Physica D 117, 43 (1998), etc.]. Here, we present all possible chaotic flows with quadratic nonlinearities which are invariant under the action of 32 point groups of crystallographic symmetry. These systems demonstrate a typical chaotic behavior as well as general dynamical properties of nonlinear systems with discrete symmetries. In particular, we found a dynamical system with the point symmetry group D2 which seems to be more simple and more elegant than those by Lorenz and Rössler.

Hierarchical Dynamical Information Systems With a Focus on Biology

A system of a number of relatively stable units that can combine more or less freely to form somewhat less stable structures has a capacity to carry information in a more or less arbitrary way. I call such a system a physical information system if its properties are dynamically specified. All physical information systems have certain general dynamical properties. DNA can form such a system, but so can, to a lesser degree, RNA, proteins, cells and cellular subsystems, various immune system elements, organisms in populations and in ecosystems, as well as other higher-level phenomena. These systems are hierarchical structures with respect to the expression of lower level information at higher levels. This allows a distinction between macro and microstates within the system, with resulting statistical (entropy driven) dynamics, including the possibility of self-organization, system bifurcation, and the formation of higher levels of information expression. Although lower-level information is expressed in an information hierarchy, this in itself is not sufficient for reference, function, or meaning. Nonetheless, the expression of information is central to the realization of all of these. 'Biological information' is thus ambiguous between syntactic information in a hierarchical modular system, and functional information. However, the dynamics of hierarchical physical information systems is of interest to the study of how functional information might be embodied physically. I will address 1) how to tighten the relative terms in the characterizations of 'information system' and 'informational hierarchy' above, 2) how to distinguish between components of an information system combining to form more complex informational modules and the expression of information, 3) some aspects of the dynamics of such systems that are of biological interest, 4) why information expression in such systems is not sufficient for functional information, and 5) what further might be required for functional information.

Hysteresis in vibrated granular media

Some general dynamical properties of models for compaction of granular media based on master equations are analyzed. In particular, a one-dimensional lattice model with short-ranged dynamical constraints is considered. The stationary state is consistent with Edward's theory of powders. The system is submitted to processes in which the tapping strength is monotonically increased and decreased. In such processes the behavior of the model resembles the reversible–irreversible branches which have been recently observed in experiments. This behavior is understood in terms of the general dynamical properties of the model, and related to the hysteresis cycles exhibited by structural glasses in thermal cycles. The existence of a “normal” solution, i.e., a special solution of the master equation which is monotonically approached by all the other solutions, plays a fundamental role in the understanding of the hysteresis effects.

Stability in systems with moving contact lines

An energy stability theory is formulated for systems having moving contact lines. The method derives from criteria obtained from the integral mechanical-energy balance manipulated to reflect general material and dynamical properties of moving-contact-line regions. The method yields conditions for both stability and instability and is applied to the two-dimensional Rayleigh-Taylor problem in a vertical slot.