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The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
Conventional ordering transitions, described by the Landau paradigm, are characterized by the symmetries broken at the critical point. Within the constrained manifold occurring at low temperatures in certain frustrated systems,…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
We study a random system of $cn$ linear equations over $n$ variables in GF(2), where each equation contains exactly $r$ variables; this is equivalent to $r$-XORSAT. \cite{ikkm,amxor} determined the clustering threshold, $c^*_r$: if…
Assured AI in unrestricted settings is a critical problem. Our framework addresses AI assurance challenges lying at the intersection of domain adaptation, fairness, and counterfactuals analysis, operating via the discovery and intervention…
We study the pinning transition in a (1+1)-dimensional lattice model of a fluctuating interface interacting with a corrugated impenetrable wall. The interface is modeled as an $N$-step directed one-dimensional random walk on the half-line…
The application of machine learning in the study of phase transitions has achieved remarkable success in both equilibrium and non-equilibrium systems. It is widely recognized that unsupervised learning can retrieve phase transition…
Particulate matter, such as foams, emulsions, and granular materials, attain rigidity in a dense regime: the rigid phase can yield when a threshold force is applied. The rigidity transition in particulate matter exhibits {\it bona fide}…
We study a random system of cn linear equations over n variables in GF(2), where each equation contains exactly r variables; this is equivalent to r-XORSAT. Previous work has established a clustering threshold, c^*_r for this model: if…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
In these proceedings, we first summarize some general properties of phase transitions in the presence of quenched disorder, with emphasis on the following points: the need to distinguish typical and averaged correlations, the possible…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
This study delves into the predictability of atmospheric blocking, zonal, and transition patterns utilizing a simplified coupled model. Initially, we comprehensively scrutinize the model's responses to environmental parameters like solar…
Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show…
We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…