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Given a sequence $s_1$ of $n$ letters drawn i.i.d. from an alphabet of size $\sigma$ and a mutated substring $s_2$ of length $m < n$, we often want to recover the mutation history that generated $s_2$ from $s_1$. Modern sequence aligners…
We study the problem of reconstructing an unknown point in $\mathbb{R}^d$ from approximate linear queries. This setting arises naturally in applications ranging from low-dimensional remote sensing and signal recovery to high-dimensional…
Let $G$ be a $3$-connected ordered graph with $n$ vertices and $m$ edges. Let $\mathbf{p}$ be a randomly chosen mapping of these $n$ vertices to the integer range $\{1, 2,3, \ldots, 2^b\}$ for $b\ge m^2$. Let $\ell$ be the vector of $m$…
The problem of how many trajectories of a random walker in a potential are needed to reconstruct the values of this potential is studied. We show that this problem can be solved by calculating the probability of survival of an abstract…
Given a pattern string $P$ of length $n$ consisting of $\delta$ distinct characters and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet $\Sigma$ of size $\Delta$, the {\em exact string…
Stroke order and velocity are helpful features in the fields of signature verification, handwriting recognition, and handwriting synthesis. Recovering these features from offline handwritten text is a challenging and well-studied problem.…
Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…
Search is a key service within constraint programming systems, and it demands the restoration of previously accessed states during the exploration of a search tree. Restoration proceeds either bottom-up within the tree to roll back…
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…
The problem of recovering (count and sum) range queries over multidimensional data only on the basis of aggregate information on such data is addressed. This problem can be formalized as follows. Suppose that a transformation T producing a…
The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
Given a random binary picture $P_n$ of size $n$, i.e., an $n\times n$ grid filled with zeros and ones uniformly at random, when is it possible to reconstruct $P_n$ from its $k$-deck, i.e., the multiset of all its $k\times k$ subgrids? We…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
When a network is reconstructed from data, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the vertex degree distribution of the true underlying network is…
In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e. attractor reconstruction. The process has focused primarily on heuristic and empirical…
We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of…
We consider the problem of computing a $k$-sparse approximation to the Fourier transform of a length $N$ signal. Our main result is a randomized algorithm for computing such an approximation (i.e. achieving the $\ell_2/\ell_2$ sparse…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
Motivated by the problem of routing reliably and scalably in a graph, we introduce the notion of a splicer, the union of spanning trees of a graph. We prove that for any bounded-degree n-vertex graph, the union of two random spanning trees…