Related papers: Random sampling vs. exact enumeration of attractor…
We investigate the attractor of spin density in relativistic spin hydrodynamics using Zubarev's non-equilibrium statistical operator formalism in the spin probe limit. We derive the (0+1)D Bjorken flow equations and the associated attractor…
Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of…
A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having attracted attention…
We introduce $\varepsilon$-projectors, using which we can sample from limiting distributions of continuous-time quantum walks. The standard algorithm for sampling from a distribution that is close to the limiting distribution of a given…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
Power law potentials dictate interactions across scales and matter, controlling the structure and dynamics of inanimate, and living systems. Though the equilibrium distributions of particles with a power law repulsion were extensively…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
The density of states for a chaotic billiard with randomly distributed point-like scatterers is calculated, doubly averaged over the positions of the impurities and the shape of the billiard. Truncating the billiard Hamiltonian to a N x N…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence.…
In this paper, we apply the implicit Euler scheme to discretize the (random) Burgers-Huxley equation and prove the existence of a numerical attractor for the discrete Burgers-Huxley system. We establish upper semi-convergence of the…
We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
In our previous work, we introduced the random $k$-cut number for rooted graphs. In this paper, we show that the distribution of the $k$-cut number in complete binary trees of size $n$, after rescaling, is asymptotically a periodic function…
We study the structural and dynamical behaviors of a diblock copolymer chain in a bath of active Brownian particles (ABPs) by extensive Brownian dynamics simulation in a two-dimensional model system. Specifically, the A block of chain is…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…
We investigated the scaling and topology of engineered urban drainage networks (UDNs) in two cities, and further examined UDN evolution over decades. UDN scaling was analyzed using two power-law characteristics widely employed for river…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…