Related papers: The Kesten-Stigum Reconstruction Bound Is Tight fo…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume…
The most established method of reconstructing neural circuits from animals involves slicing tissue very thin, then taking mosaics of electron microscope (EM) images. To trace neurons across different images and through different sections,…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
Recently determined atomistic scale structures of near-two dimensional bilayers of vitreous silica (using scanning probe and electron microscopy) allow us to refine the experimentally determined coordinates to incorporate the known local…
We introduce a new distance-based phylogeny reconstruction technique which provably achieves, at sufficiently short branch lengths, a logarithmic sequence-length requirement---improving significantly over previous polynomial bounds for…
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a discrete de Rham complex that preserves the structure of the…
The broadcasting models on trees arise in many contexts such as discrete mathematics, biology statistical physics and cs. In this work, we consider the colouring model. A basic question here is whether the root's assignment affects the…
We first re-prove with a more complete method that the the minimum standard model, with the inclusion of the CKM-matrix, requires the T-odd/P-odd total cross section of two spin-1/2 particles to vanish in all orders\cite{gxu}. Then we study…
Consider a Markov chain $(\xi_v)_{v \in V} \in [k]^V$ on the infinite $b$-ary tree $T = (V,E)$ with irreducible edge transition matrix $M$, where $b \geq 2$, $k \geq 2$ and $[k] = \{1,...,k\}$. We denote by $L_n$ the level-$n$ vertices of…
The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were…
Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickelbased CMSX-4, cubic symmetry is nevertheless expected. It is…
In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method…
We present numerical results that allow a precise determination of the transition point and of the critical exponents of the 4D Edwards-Anderson Spin Glass with binary quenched random couplings. We show that the low T phase undergoes…
By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.
We investigate static and dynamic properties of gray-scale image restoration (GSIR) by making use of the Q-Ising spin glass model, whose ladder symmetry allows to take in account the distance between two spins. We thus give an explicit…
According to the droplet picture of spin glasses, the low-temperature phase of spin glasses should be replica symmetric. However, analysis of the stability of this state suggested that it was unstable and this instability lends support to…
It is frequently possible to produce new Calabi-Yau threefolds from old ones by a process of allowing the complex structure to degenerate to a singular one, and then performing a resolution of singularities. (Some care is needed to ensure…