Related papers: The Kesten-Stigum Reconstruction Bound Is Tight fo…
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal…
In this thesis we analyze the problem of symmetry breaking in models with extra dimensions compactified on orbifolds. In the first chapter we briefly review the main symmetry breaking mechanisms peculiar of extra dimensions such as the…
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
Reconstructing evolutionary trees from molecular sequence data is a fundamental problem in computational biology. Stochastic models of sequence evolution are closely related to spin systems that have been extensively studied in statistical…
We explore physics of unstable particles when mother particle mass is around the sum of its daughter particle masses. In this case, the conventional wave function renormalization factor is ill-defined. We propose a simple resolution of the…
We study robust community detection in the context of node-corrupted stochastic block model, where an adversary can arbitrarily modify all the edges incident to a fraction of the $n$ vertices. We present the first polynomial-time algorithm…
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a…
Understanding the large-scale physics is crucial for the spin foam approach to quantum gravity. We tackle this challenge from a statistical physics perspective using simplified, yet feature-rich models. In particular, this allows us to…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…
This paper concerns the reconstruction of a complex-valued anisotropic tensor $\gamma=\sigma+\i\omega\varepsilon$ from knowledge of several internal magnetic fields $H$, where $H$ satisfies the anisotropic Maxwell system on a bounded domain…
Simulations of pure-gauge SU(2) lattice gauge theory are performed in the minimal Coulomb gauge. This leaves a residual or remnant gauge symmetry still active which is global in three directions but still local in one. Using averaged…
Spectral enhancement near the 2m_{\pi} threshold in the I=J=0 channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with the possible detection of 2\pi^{0} and…
We establish thresholds for the feasibility of random multi-graph alignment in two models. In the Gaussian model, we demonstrate an "all-or-nothing" phenomenon: above a critical threshold, exact alignment is achievable with high…
Unrolled neural networks have recently achieved state-of-the-art accelerated MRI reconstruction. These networks unroll iterative optimization algorithms by alternating between physics-based consistency and neural-network based…
This paper introduces constNJ, the first algorithm for phylogenetic reconstruction of sets of trees with constrained pairwise rooted subtree-prune regraft (rSPR) distance. We are motivated by the problem of constructing sets of trees which…
The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random an\-iso\-tropy but without…
We review constraints on the minimal supersymmetric extension of the Standard Model (MSSM) coming from direct searches at accelerators such as LEP, indirect measurements such as b -> s gamma decay and the anomalous magnetic moment of the…
The reconstruction of fundamental parameters in supersymmetric theories requires the evolution to high scales, where the characteristic regularities in mechanisms of supersymmetry breaking become manifest. We have studied a set of…