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Motivated by current interest in understanding statistical properties of random landscapes in high-dimensional spaces, we consider a model of the landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of random wavevectors…
We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling…
In this paper we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the number of observations are fewer than the number of…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
We address the problem of inferring the three-dimensional matter distribution from a sparse set of one-dimensional quasar absorption spectra of the Lyman-$\alpha$ forest. Using a Bayesian forward modelling approach, we focus on extending…
The structure of the B-L MSSM theory--specifically, the relevant mass scales and soft supersymmetric breaking parameters--is discussed. The space of initial soft parameters is explored at the high scale using random statistical sampling…
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
A complete understanding of the precipitous onset of slow dynamics in systems such as supercooled liquids requires making direct connections between dynamics and the underlying potential energy landscape. With the aid of a switch in…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
Recently, it has become clear that neighboring multiple vacua might have interesting consequences for the physics of the early universe. In this paper we investigate the topography of the string landscape corresponding to complex structure…
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…
The integration of heavy scalar fields is discussed in a class of BSM models, containing more that one representation for scalars and with mixing. The interplay between integrating out heavy scalars and the Standard Model decoupling limit…
Nonobservation of superparticles till date, new Higgs mass limits from the CMS and ATLAS experiments, WMAP constraints on relic density, various other low energy data, and the naturalness consideration, all considered simultaneously imply a…
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, for most…
The concept of metastability has caused a lot of interest in recent years. The spectral decomposition of the generator matrix of a stochastic network exposes all of the transition processes in the system. The assumption of the existence of…
The topology of weak lensing fields is studied using the 2-dimensional genus statistic. Simulated fields of the weak lensing convergence are used to focus on the effect of nonlinear gravitional evolution and to model the statistical errors…
Finding the mean of the total number of stationary points for N-dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is…
With significant annotation savings, point supervision has been proven effective for numerous 2D and 3D scene understanding problems. This success is primarily attributed to the structured output space; i.e., samples with high spatial…
In this paper, we propose a Bayesian Graphical LASSO for correlated countable data and apply it to spatial crime data. In the proposed model, we assume a Gaussian Graphical Model for the latent variables which dominate the potential risks…