Related papers: Substring Density Estimation from Traces
This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not…
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…
It is demonstrated that an object distribution can be successfully retrieved from its diffraction pattern or hologram, even if some of the measured intensity samples are missing. The maximum allowable number of missing values depends on the…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…
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.…
The $k$-deck problem is concerned with finding the smallest positive integer $S(k)$ such that there exist at least two strings of length $S(k)$ that share the same $k$-deck, i.e., the multiset of subsequences of length $k$. We introduce the…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…
We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is…
Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
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…