Related papers: Shotgun identification on groups
We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…
We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which…
We study a class of finite state machines, called \defi{$w$-matching machines}, which yield to simulate the behavior of pattern matching algorithms while searching for a pattern $w$. They can be used to compute the asymptotic speed, i.e.…
We study coverage processes in which each draw reveals a subset of $[n]$, and the goal is to determine the expected number of draws until all items are seen at least once. A classical example is the Coupon Collector's Problem, where each…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…
We consider the problem of reconstructing graphs or labeled graphs from neighborhoods of a given radius r. Special instances of this problem include the well known: DNA shotgun assembly; the lesser-known: neural network reconstruction; and…
Most DNA sequencing technologies are based on the shotgun paradigm: many short reads are obtained from random unknown locations in the DNA sequence. A fundamental question, studied in arXiv:1203.6233, is what read length and coverage depth…
In this work we consider the task of relaxing the i.i.d assumption in pattern recognition (or classification), aiming to make existing learning algorithms applicable to a wider range of tasks. Pattern recognition is guessing a discrete…
Genome sequencing is the basis for many modern biological and medicinal studies. With recent technological advances, metagenomics has become a problem of interest. This problem entails the analysis and reconstruction of multiple DNA…
A popular way to define or characterize graph classes is via forbidden subgraphs or forbidden minors. These characterizations play a key role in graph theory, but they rarely lead to efficient algorithms to recognize these classes. In…
A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyze the minimum-error protocol…
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic…
We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…
Camera model identification refers to the problem of linking a picture to the camera model used to shoot it. As this might be an enabling factor in different forensic applications to single out possible suspects (e.g., detecting the author…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
The prime graph of a finite group $G$ is the labelled graph $\Gamma(G)$ with vertices the prime divisors of $|G|$ and edges the pairs $\{p,q\}$ for which $G$ contains an element of order $pq$. A group $G$ is recognisable by its prime graph…
The probabilistic Waring problem for finite simple groups asks whether every word of the form $w_1w_2$, where $w_1$ and $w_2$ are non-trivial words in disjoint sets of variables, induces almost uniform distribution on finite simple groups…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
Shotgun proteomics is a high-throughput technology used to identify unknown proteins in a complex mixture. At the heart of this process is a prediction task, the spectrum identification problem, in which each fragmentation spectrum produced…
In this paper, we address the problem of identifying the Pareto Set under feasibility constraints in a multivariate bandit setting. Specifically, given a $K$-armed bandit with unknown means $\mu_1, \dots, \mu_K \in \mathbb{R}^d$, the goal…