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We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models…
Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…
Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
Existing studies indicate that complex system degradation is characterized by degradation of multiple dependent parameters. Capturing the dependencies is crucial for accurate degradation modeling and effective degradation control. This work…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
We determine the critical coupling constant above which dynamical chiral symmetry breaking occurs in a class of QCD motivated models where the gluon propagator has an enhanced infrared behavior. Using methods of bifurcation theory we find…
We examine the critical behaviour of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report (Ferreira et al., Phys. Rev. E 85, 010901 (2012)),…
Gaussian elimination is the most popular technique for solving a dense linear system. Large errors in this procedure can occur in floating point arithmetic when the matrix's growth factor is large. In the study of numerical linear algebra,…
We study the random pinning model, in the case of a Gaussian environment presenting power-law decaying correlations, of exponent decay a>0. We comment on the annealed (i.e. averaged over disorder) model, which is far from being trivial, and…
Nowadays, the need for causal discovery is ubiquitous. A better understanding of not just the stochastic dependencies between parts of a system, but also the actual cause-effect relations, is essential for all parts of science. Thus, the…
The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases…
Granger causality analysis (GCA) provides a powerful tool for uncovering the patterns of brain connectivity mechanism using neuroimaging techniques. Conventional GCA applies two different mathematical theories in a two-stage scheme: (1) the…
This paper studies large deviation principles and weak convergence, both at the level of finite-dimensional distributions and in functional form, for a class of continuous, isotropic, centered Gaussian random fields defined on the unit…
We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus…
The critical Ising model in two dimensions with a defect line is analyzed to deliver the first exact solution with twisted boundary conditions. We derive exact expressions for the eigenvalues of the transfer matrix and obtain analytically…
Inferring the mechanisms underlying physiological and pathological processes in the brain from recorded electrical activity is challenging. Bayesian model selection and dynamic causal modelling aim to identify likely biophysical models to…
In this article, we study concave recursions on trees, which appear widely in information theory through algorithms such as belief propagation, and in statistical mechanics through models on tree-like graphs, including the Ising model,…
We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…