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A competitive learning model was introduced in Ref. 1 (A. Mehta and J. M. Luck, Phys. Rev. E 60, 5, 1999), in which the learning is outcome-related. Every individual chooses between a pair of existing strategies or types, guided by a combination of two factors: tendency to conform to the local majority, \em{and} a pre... |
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two complementary approaches to modeling evolution of player populations. |
We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. |
Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. |
The study in [Phys. Rev. Lett. 117, 014102 (2016)] discovered a novel type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another novel form of chimera, which we refer to ... |
We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer. The nonlocality in the interaction among the dyn... |
Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. |
We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. |
It is delightful to observe the emergence of synchronization in the blinking of fireflies to attract partners and preys. Other charming examples of synchronization can also be found in a wide range of phenomena such as, e.g., neurons firing, lasers cascades, chemical reactions, and opinion formation. |
A generalization of Kermack-McKendick model of epidemics to the case of inhomogeneous susceptibility of population is proposed. Some quantitative and qualitative features of epidemic process development in this situation are established. |
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. |
Basing on a paper which explores the adoption of a whole system approach to a more sustainable and innovative design, the present paper wants to apply the same approach to a real case, inside of a famous Italian sportscar factory. A case study in this factory was developed and decodified gaining improved understanding... |
Intelligent agents collect and process information from their dynamically evolving neighbourhood to efficiently navigate through it. However, agent-level intelligence does not guarantee that at the level of a collective; a common example is the jamming we observe in traffic flows. |
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make the strong assumption that the dynamics resides exclusively on the nodes. |
The concept of neutral evolutionary networks being a significant factor in evolutionary dynamics was first proposed by Huynen {\em et al. } about 7 years ago. |
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective reproduction rate fluctuates close to the critical value one, as observed for di... |
The spin market model [S. Bornholdt, <a href="http://Int.J.Mod.Phys" rel="external noopener nofollow" class="link-external link-http">this http URL</a>. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings betwee... |
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a living, technological or social than fully random Kauffman networks. |
After presenting possible motives for fighting against the second law of thermodynamics, several attempts to beat this law are analyzed. The second law wins, but an interesting interpretation of it emerges. |
With the increasing inclusion of regenerative resources in the energy mix, their intermittent character challenges power grid stability. Hence it is essential to determine which input fluctuations power grids are particularly vulnerable to. |
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying ... |
Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous formulation [K. Nagai et al., Phys. Rev. E 71, 036217 (2005)], dynamics of the circ... |
A future goal of robot teams and agent-based models (ABMs) is to field organizations and systems based on first principles derived from human counterparts. Forestalling that opportunity, the failure of traditional organizational theory has at the same time opened the way to innovative theories of organizations and cha... |
It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested numerically. |
A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. |
We comprehensively studied the morphology of the self-organized effective network structures that form in simple coupled maps with interelement synchronization-dependent connection changes. Based on the parameter values, the spontaneous formation of four types of directional hierarchical networks, named pair-driven ne... |
Dissipative environments are ubiquitous in nature, from microscopic swimmers in low-Reynolds-number fluids to macroscopic animals in frictional media. In this study, motivated by various behaviours of {\it Caenorhabditis elegans} during swimming and crawling locomotion, we consider a mathematical model of a slender el... |
Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. |
Simulating a cellular automaton (CA) for t time-steps into the future requires t^2 serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed ``linear'' because they obey a principle of superposition. |
Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different types of nontrivial dynamics. |
We present a new tierra-inspired artificial life system with local interactions and two-dimensional geometry, based on an update mechanism akin to that of 2D cellular automata. We find that the spatial geometry is conducive to the development of diversity and thus improves adaptive capabilities. |
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to those obtained using multiscale asymptotic techniques and, remarkably, remains eff... |
We investigate the effect of time-correlated noise on the phase fluctuations of nonlinear oscillators. The analysis is based on a methodology that transforms a system subject to colored noise, modeled as an Ornstein-Uhlenbeck process, into an equivalent system subject to white Gaussian noise. |
We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical point. More precisely, SOC is shown to result from the tuning of... |
It is high time to openly and without finalism define the dangerous but needed term 'purposeful information', whose quantity is an Eigen information value. Using the term 'biological information' in its stead forces one into an uncomfortable detour. |
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states. |
Researchers have proposed that the distinction between so-called "simple" and "complex" societies can be expressed by an increase in the number of levels at which functional organization, interaction, and thus selection, operate. In spite of the obvious links between this suggestion and research into c... |
The existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport are deduced from the criticality scenario giving rise to ratchet universality, and confirmed by numerical experiments in the context of a driven overdamped Brownian particle subjected to a vibrat... |
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. |
Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree $k$ is proportional to $k^{-\gamma}$. However, the motivatio... |
We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of ... |
Chimera states, which consist of coexisting domains of coherent and incoherent parts, have been observed in a variety of systems. Most of previous works on chimera states have taken into account specific form of interaction between oscillators, for example sinusoidal coupling or diffusive coupling. |
We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady-state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration ... |
We propose a robust universal approach to identify multiple dynamical states, including stationary and travelling chimera states based on an adaptive coherence measure. Our approach allows automatic disambiguation of synchronized clusters, travelling waves, chimera states, and asynchronous regimes. |
In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well, our understanding of large-scale networked resilience is limited. |
Inspired by our recent work that relates bus bunching as a phenomenon of synchronisation of phase oscillators, we construct a model of Kuramoto oscillators that follows an analogous interaction mechanism of local unidirectional coupling. In the bus loop system, we can introduce a no-boarding policy as a form of kickin... |
We will introduce two evolving models that characterize weighted complex networks. Though the microscopic dynamics are different, these models are found to bear a similar mathematical framework, and hence exhibit some common behaviors, for example, the power-law distributions and evolution of degree, weight and streng... |
Although much political capital has been made regarding the war on terrorism, and while appropriations have gotten underway, there has been a dearth of deep work on counter-terrorism, and despite massive efforts by the federal government, most cities and states do not have a robust response system. In fact, most do no... |
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a certain value. We focus on Kuramoto oscillators with peaked, bimodal distribution o... |
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: |
Given any subvariety of a complex torus defined over $\mathbb{Z}$ and any positive integer $k$, we construct a finite CW complex $X$ such that the $k$-th cohomology jump locus of $X$ is equal to the chosen subvariety, and the $i$-th cohomology jump loci of $X$ are trivial for $i<k$. |
Moduli spaces for Galois covers of p-adic Mumford curves by Mumford curves are constructed using Herrlich's Teichmuller spaces, Andre's orbifold fundamental groups, and Kato's graphs of groups encoding ramification data of charts for Mumford orbifolds. |
We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. |
We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional sheaves on $\mathbb{P}^2$ of any degree. We obtain a minimal set of tautological generators, which implies an optimal generation result for both the cohomology and the Chow ring of the moduli space. |
We provide two different proofs of an irreducibility criterion for the preimages of a transverse subvariety of a product of elliptic curves under a diagonal endomorphism of sufficiently large <a href="http://degree.For" rel="external noopener nofollow" class="link-external link-http">this http URL</a> curves, we presen... |
In this paper we study the geometric structure of affine Deligne-Lusztig varieties for $GL_n$ and $b$ basic. We introduce a new condition on $\lambda$. |
In \cite{Valette}, Guillaume and Anna Valette associate singular varieties $V_F$ to a polynomial mapping $F: \C^n \to \C^n$. In the case $F: \C^2 \to \C^2$, if the set $K_0(F)$ of critical values of $F$ is empty, then $F$ is not proper if and only if the 2-dimensional homology or intersection homology (with any perver... |
Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can take on an infinite number of values and yet yield the same input-output data. |
We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. |
In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety. |
The usual language of algebraic geometry is not appropriate for Arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace rings by the collection of "vectors" or by bi-operads and another based on "matrices" or props. |
We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated categories, this means that the derived category of perfect complexes embeds as an admis... |
Affine rotation surfaces are a generalization of the well-known surfaces of revolution. Affine rotation surfaces arise naturally within the framework of affine differential geometry, a field started by Blaschke in the first decades of the past century. |
In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for which these cones are finitely generated. |
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and the decorations are required to satisfy certain conditions. |
We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$, extending the invariant defined by Saito in the case of hypersurfaces. Our definition is in terms of the Kashiwara-Malgrange $V$-filtration associated to $Z$. |
For a reaction network with species set $\mathscr{S}$, a log-parametrized (LP) set is a non-empty set of the form $E(P, x^*) = \{x \in \mathbb{R}^\mathscr{S}_> \mid \log x - \log x^* \in P^\perp\}$ where $P$ (called the LP set's flux subspace) is a subspace of $\mathbb{R}^\mathscr{S}$, $x^*$ (called the LP set&#... |
Let $G$ be a finite group. The Bogomolov multiplier $B_0(G)$ is constructed as an obstruction to the rationality of $\bm{C}(V)^G$ where $G\to GL(V)$ is a faithful representation over $\bm{C}$. |
We establish first parts of a tropical intersection theory. Namely, we define cycles, Cartier divisors and intersection products between these two (without passing to rational equivalence) and discuss push-forward and pull-back. |
We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus $\Sigma$, and moreover determine the ranks of the nontrivial homology groups. |
In this paper, we seek an appropriate definition for a Shimura curve of Hodge type in positive characteristics, i.e. a characterization of curves in positive characteristics which are reduction of Shimura curve over the complex field. Specifically, we study the liftablity of a curve in moduli space of principally pola... |
In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic line arrangements of degree $7$ with certain fixed combinatorics and determine the number of connected components. |
We show that an $n$-dimensional compact Kähler manifold $X$ admitting a non-degenerate meromorphic map $f:{\bf C}^n\to X$ of order $\rho_f<2$ is rationally connected. |
Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up to isometry, as dual divisors to such rational curves. |
We establish a relative version of the abstract "affine representability" theorem in ${\mathbb A}^1$--homotopy theory from Part I of this paper. We then prove some ${\mathbb A}^1$--invariance statements for generically trivial torsors under isotropic reductive groups over infinite fields analogous to the Bass--... |
We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as for complexes of mixed Hodge modules. |
Let $C$ be a curve of genus $g \geq 11$ such that $g-1$ is a composite number. Suppose $C$ is on a K3 surface whose Picard group is generated by the curve class $[C]$. |
We prove the following form of the Clemens conjecture in low degree. Let $d\le9$, and let $F$ be a general quintic threefold in $\IP^4$. |
We study the cohomological properties of the fixed locus $X^G$ of an automorphism group $G$ of prime order $p$ acting on a variety $X$ whose integral cohomology is torsion-free. We obtain an precise relation between the mod $p$ cohomology of $X^G$ and natural invariants for the action of $G$ on the integral cohomology... |
$\frak g$-endomorphism algebras form an interesting class of associative algebras related to the adjoint representation of a semisimple Lie algebra $\frak g$. These algebras were recently introduced by <a href="http://A.Kirillov" rel="external noopener nofollow" class="link-external link-http">this http URL</a>, who u... |
We explain how the Riemann-Roch theorem for divisors on an abelian variety $A$ is related to the reduced norms of the Wedderburn components of $\operatorname{End}^0(A)$ the $\mathbb{Q}$-endomorphism algebra of $A$. We then describe consequences and examples. |
This is a survey of the classical geometry of the Hesse configuration of 12 lines in the projective plane related to inflection points of a plane cubic curve. We also study two K3 surfaces with Picard number 20 which arise naturally in connection with the configuration. |
Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed closed point. In order to establish this correspondence, they have to show that des... |
Given $X$ a smooth projective toric variety, we construct a morphism from a closed substack of the moduli space of stable maps to $X$ to the moduli space of quasimaps to $X$. If $X$ is Fano, we show that this morphism is surjective. |
We study graded rings associated to big divisors on LC pairs whose difference with the log-canonical divisor is nef. For divisors that are positive enough at the LC centers of the pair, we prove the finite generation of such rings if the pair is DLT or the dimension is low, given that a Zariski decomposition exists. |
In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$, which is the intersection of a quartic and three general quadratics in $\mathbb{P}^5$. We thus prove a stronger Bogomolov-Gieseker inequality for characters of stable vector bundles and stable objects on $X_{2,4}$. |
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component. |
The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group $G$. To achieve this, we introduce the moduli functor $\mathsf{M}^G_h$ of $G$-marked Gorenstein canonical models with Hilbert polynomial $h$, and ... |
We obtain a combinatorial proof that the number of points of the space $\overline{{\mathcal M}_{0,n}}({\mathbb F}_q)$ satisfies the recurrent formula for Poincare polynomials of the space $\overline{{\mathcal M}_{0,n}}({\mathbb C})$. |
We present an enhanced algorithm for exploring mirror symmetry for elliptic curves through the correspondence of algebraic and tropical geometry, focusing on Gromov-Witten invariants of elliptic curves and, in particular, Hurwitz numbers. We present a new highly efficient algorithm for computing generating series for ... |
We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli of stable pointed curves. These generalize Verlinde bundles or vector bundles of conformal blocks defined using affine Lie algebras studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work of ... |
By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X\times D\cup F\times X$, for some divisor $D$ a... |
We propose a construction of separated quotient space and apply this construction for simple description of Study-Semple-Satake-Furstenberg-De Concini-Procesi-Oshima boundary of symmetric space |
We study the Chow ring with rational coefficients of the moduli space $\mathcal F_{2}$ of quasi-polarized $K3$ surfaces of degree $2$. We find generators, relations, and calculate the Chow Betti numbers. |
In this paper we describe the unramified Langlands correspondence for two-dimensional local fields, we construct a categorical analogue of the unramified principal series representations and study its properties. The main tool for this description is the construction of a central extension. |
In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The formula can be easily implemented for computations and it is in agreement with t... |
For unramified reductive groups, we determine the connected components of affine Deligne-Lusztig varieties in the partial affine flag varieties. Based on the work of Hamacher-Kim and Zhou, this result allows us to verify, in the unramified group case, the He-Rapoport axioms, the ``almost product structure" of Newt... |
We prove that a vector bundle $E$ over a smooth complex projective variety $M$ is étale trivial if and only if $E$ is semiample and $c_1(E) \in H^2(M, {\mathbb Q})$ vanishes. Also, a vector bundle $E$ over a smooth complex projective curve is semiample if and only if it is virtually globally generated. |
We give the Castelnuovo-Mumford regularity of arrangements of (n-2)-planes in P^n whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen-Macaulay. |
An orbifold version of Bogomolov decomposition theorem is established for compact Kähler spaces with quotient singularities and first Chern class <a href="http://zero.The" rel="external noopener nofollow" class="link-external link-http">this http URL</a> proof is a direct adaptation of the classical smooth case, using ... |
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