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The basic underlying assumption of machine learning (ML) models is that the training and test data are sampled from the same distribution. However, in daily practice, this assumption is often broken, i.e. the distribution of the test data…
We review several models of glassy systems where the randomness is self generated, i.e. already an infinitesimal amount of disorder is sufficient to cause a transition to a non-ergodic, glassy state. We discuss the application of the…
A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d=3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated.…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (modes) for posterior distributions arising from model-specific…
We introduce a spectral approach to characterizing the three-dimensional Edwards-Anderson spin glass. By analyzing the eigenvalue statistics of overlap matrices constructed from two-dimensional cross-sections, we identify a crossover from…
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical…
We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution…
We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely…
Diffusion models have made significant advances recently in high-quality image synthesis and related tasks. However, diffusion models trained on real-world datasets, which often follow long-tailed distributions, yield inferior fidelity for…
We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…
In the paradigm of multi-task learning, mul- tiple related prediction tasks are learned jointly, sharing information across the tasks. We propose a framework for multi-task learn- ing that enables one to selectively share the information…
Broken-symmetry-induced order parameters account for many phenomena in condensed matter physics. For spin glasses, such a framework dictates its theoretical construction, whereas experiments have only established dynamical behaviors such as…
We present a new field theoretic approach for finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. We analyze this field…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…