Related papers: The Kesten-Stigum Reconstruction Bound Is Tight fo…
Our goal in this work is to better understand the relationship between replica symmetry breaking, shattering, and metastability. To this end, we study the static and dynamic behaviour of spherical pure $p$-spin glasses above the replica…
A short survey is presented on spin--glass--like states characteristics in complex nonmagnetic systems. We discuss the interplay of the interaction structure and symmetry with the classification scenarios of the replica symmetry breaking.…
We reconsider a cosmological evolution of domain walls produced by spontaneous breaking of an approxime discrete symmetry. We show, that domain walls may never collapse even if the standard bound on the vacuum energy asymmetry is satisfied.…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…
We examine the supersymmetry of classical D-brane and M-brane configurations and explain the dependence of Killing spinors on coordinates. We find that one half supersymmetry is broken in the bulk and that supersymmetry near the D-brane…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
It has remained an open question for some time whether, given a set of not necessarily binary (i.e. "nonbinary") trees T on a set of taxa X, it is possible to determine in time f(r).poly(m) whether there exists a phylogenetic network that…
The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence.…
Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is…
In this work, we study the metric Steiner Tree problem on graphs focusing on computing lower bounds for the integrality gap of the bi-directed cut (BCR) formulation and introducing a novel formulation, the Complete Metric (CM) model,…
Tomographic reconstruction of a binary image from few projections is considered. A novel {\em heuristic} algorithm is proposed, the central element of which is a nonlinear transformation $\psi(p)=\log(p/(1-p))$ of the probability $p$ that a…
Recent development in the reconstruction of the large-scale structure (LSS) has seen significant improvement in restoring the linear baryonic acoustic oscillation (BAO) from at least the non-linear matter field. This outstanding performance…
We derive a lower limit to the amount of absorptive loss present in passive linear optical devices such as a beam splitter. We choose a particularly simple beam splitter geometry, a single planar slab surrounded by vacuum, which already…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
A systematic investigation is presented of grain boundaries and grain boundary networks in two dimensional flexible membranes with crystalline order. An isolated grain boundary undergoes a buckling transition at a critical value of the…
We review boundary rigidity theorems assessing that, under appropriate conditions, Riemannian manifolds with the same spectrum of boundary geodesics are isometric. We show how to apply these theorems to the problem of reconstructing a $d+1$…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in…