1,720,976 research outputs found
Coexistence of Stable Limit Cycles in a Generalized Curie–Weiss Model with Dissipation
Full text linkIn this paper, we modify the Langevin dynamics associated to the generalized Curie–Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples
On a class of time-Fractional continuous-State branching processes
Full text linkWe propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton – Watson processes. The class includes as specific cases the classical continuous-state branching processes and Markov branching processes. Several results such as the expressions of moments and the branching inequality governing the evolution of the process are presented and commented. The generalized Feller branching diffusion and the fractional Yule process are analyzed in detail as special cases of the general model
McKean–Vlasov limit for interacting systems with simultaneous jumps
Full text linkMotivated by several applications, including neuronal models, we consider the McKean–Vlasov limit for a general class of mean-field systems of interacting diffusions characterized by an interaction via simultaneous jumps. We focus our interest on systems where the rate of the jumps is unbounded, which are rarely treated in the mean-field literature, and we prove well-posedness of the McKean–Vlasov limit together with propagation of chaos via a coupling technique. To highlight the role of simultaneous jumps, we introduce an intermediate process which is close to the original particle system but does not display simultaneous jumps. This shows in particular that the simultaneous jumps contribute to the overall rate of convergence of the N-particle empirical measures by a term of order 1/√N
A large-deviations principle for all the cluster sizes of a sparse Erdős–Rényi graph
Full text linkLet (Formula presented.) be the Erdős–Rényi graph with connection probability (Formula presented.) as N → ∞ for a fixed t ∈ (0, ∞). We derive a large-deviations principle for the empirical measure of the sizes of all the connected components of (Formula presented.), registered according to microscopic sizes (i.e., of finite order), macroscopic ones (i.e., of order N), and mesoscopic ones (everything in between). The rate function explicitly describes the microscopic and macroscopic components and the fraction of vertices in components of mesoscopic sizes. Moreover, it clearly captures the well known phase transition at t = 1 as part of a comprehensive picture. The proofs rely on elementary combinatorics and on known estimates and asymptotics for the probability that subgraphs are connected. We also draw conclusions for the strongly related model of the multiplicative coalescent, the Marcus–Lushnikov coagulation model with monodisperse initial condition, and its gelation phase transition
Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model
Full text linkWe consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution
Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model
No full textWe consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution
Noise-induced periodicity in a frustrated network of interacting diffusions
Full text linkWe investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population interactions are positive; each particle wants to conform to the average position of the particles in its own community. On the other hand, inter-population interactions have different signs: the particles of one population want to conform to the average position of the particles of the other community, while the particles in the latter want to do the opposite. We show that this system features the phenomenon of noise-induced periodicity: in the infinite volume limit, in a certain range of interaction strengths, although the system has no periodic behavior in the zero-noise limit, a moderate amount of noise may generate an attractive periodic law
A large-deviations principle for all the components in a sparse inhomogeneous random graph
Full text linkWe study an inhomogeneous sparse random graph, G(N), on [N] = {1, . . . , N} as introduced in a seminal paper by Bollobas et al. (Random Struct Algorithms 31(1):3-122, 2007): vertices have a type (here in a compact metric space S), and edges between different vertices occur randomly and independently over all vertex pairs, with a probability depending on the two vertex types. In the limit N -> infinity, we consider the sparse regime, where the average degree is O (1). We prove a large-deviations principle with explicit rate function for the statistics of the collection of all the connected components, registered according to their vertex type sets, and distinguished according to being microscopic (of finite size) or macroscopic (of size asymptotic to N). In doing so, we derive explicit logarithmic asymptotics for the probability that G(N) is connected. We present a full analysis of the rate function including its minimizers. From this analysis we deduce a number of limit laws, conditional and unconditional, which provide comprehensive information about all the microscopic and macroscopic components of G(N). In particular, we recover the criterion for the existence of the phase transition given in Bollobas et al
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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