Related papers: The sequence reconstruction problem for permutatio…
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the…
Given a threshold $L$ and a set $\mathcal{R} = \{R_1, \ldots, R_m\}$ of $m$ haplotype sequences, each having length $n$, the minimum segmentation problem for founder reconstruction is to partition the sequences into disjoint segments…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
Computed tomography (CT) has become an essential part of modern science and medicine. A CT scanner consists of an X-ray source that is spun around an object of interest. On the opposite end of the X-ray source, a detector captures X-rays…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…
We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such,…
The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…
Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…
In the problem of blind reconstruction of channel codes, the receiver does not have the knowledge of the channel code used at the transmitter and the aim is to identify this unknown channel code corresponding to the given received sequence.…
The prevalent technique for DNA sequencing consists of two main steps: shotgun sequencing, where many randomly located fragments, called reads, are extracted from the overall sequence, followed by an assembly algorithm that aims to…
To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times…