Related papers: On sampling and modeling complex systems
Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
The representations of conditional entropy and conditional mutual information are significant in explaining the unique effects among variables. While previous studies based on conditional contrastive sampling have effectively removed…
We successfully model the behavior of two-spin systems using neural networks known as conditional Restricted Boltzmann Machines (cRBMs) which encode physical information in the properties of a thermal ensemble akin to an Ising model. The…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
A scientific model need not be a passive and static descriptor of its subject. If the subject is affected by the model, the model must be updated to explain its affected subject. In this study, two models regarding the dynamics of model…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
Large-scale electrophysiological recordings now allow simultaneous monitoring of thousands of neurons across multiple brain regions, revealing structured variability in neural population activity. Understanding how these collective patterns…
Choice models, which capture popular preferences over objects of interest, play a key role in making decisions whose eventual outcome is impacted by human choice behavior. In most scenarios, the choice model, which can effectively be viewed…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
The development of enhanced sampling methods has greatly extended the scope of atomistic simulations, allowing long-time phenomena to be studied with accessible computational resources. Many such methods rely on the identification of an…
We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a…
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…
It is discussed how the superstatistical formulation of effective Boltzmann factors can be related to the concept of Kolmogorov complexity, generating an infinite set of complexity measures (CMs) for quantifying information. At this level,…