Related papers: On The Complexity Of Statistical Models Admitting …
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
Comparisons are made for the amount of agreement of the composite likelihood information criteria and their full likelihood counterparts when making decisions among the fits of different models, and some properties of penalty term for…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
We analyse metastable states in the East model, using a recently-proposed patch-repetition analysis based on time-averaged density profiles. The results reveal a hierarchy of states of varying lifetimes, consistent with previous studies in…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…
The observable outputs of many complex dynamical systems consist in time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions…
In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a ``reference state''. In particular, the evolution of such systems must have a…
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log…