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Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…
Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of $N_{k}$ symbols also within the alphabet (with…
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
Source separation is a fundamental task in speech, music, and audio processing, and it also provides cleaner and larger data for training generative models. However, improving separation performance in practice often depends on increasingly…
Source separation problems are ubiquitous in the physical sciences; any situation where signals are superimposed calls for source separation to estimate the original signals. In this tutorial I will discuss the Bayesian approach to the…
A pricing principle is introduced for non-attainable $q$-exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent claim under the ``distorted Radon-Nikodym derivative'' and…
We present a differentiable formalism for learning free energies that is capable of capturing arbitrarily complex model dependencies on coarse-grained coordinates and finite-temperature response to variation of general system parameters.…
In this work we investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or $\alpha$-models. These models describe both nonlocal and local dynamics, with one…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
Real-world time series data are often generated from several sources of variation. Learning representations that capture the factors contributing to this variability enables a better understanding of the data via its underlying generative…
Unsupervised representation learning aims at describing raw data efficiently to solve various downstream tasks. It has been approached with many techniques, such as manifold learning, diffusion maps, or more recently self-supervised…
We propose a new scientific application of unsupervised learning techniques to boost our ability to search for new phenomena in data, by detecting discrepancies between two datasets. These could be, for example, a simulated standard-model…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
In semi-supervised learning (SSL) for enhancing the performance of graph neural networks (GNNs) with unlabeled data, introducing mutually independent decision factors for cross-validation is regarded as an effective strategy to alleviate…
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires…
We propose a statistical mechanics for a general class of stationary and metastable equilibrium states. For this purpose, the Gibbs extremal conditions are slightly modified in order to be applied to a wide class of non-equilibrium states.…
The standard formulation of thermostatistics, being based on the Boltzmann-Gibbs distribution and logarithmic Shannon entropy, describes idealized uncorrelated systems with extensive energies and short-range interactions. In this letter, we…