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The classical pattern matching asks for locating all occurrences of one string, called the pattern, in another, called the text, where a string is simply a sequence of characters. Due to the potential practical applications, it is desirable…
We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…
Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
We show that the size $\gamma(t_n)$ of the smallest string attractor of the $n$th Thue-Morse word $t_n$ is 4 for any $n\geq 4$, disproving the conjecture by Mantaci et al. [ICTCS 2019] that it is $n$. We also show that $\delta(t_n) =…
In geometric measure theory, there is interest in studying the interaction of measures with rectifiable sets. Here, we extend a theorem of Badger and Schul in Euclidean space to characterize rectifiable pointwise doubling measures in…
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are…
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…
Discontinuity in density functions is of economic importance and interest. For instance, in studies on regression discontinuity designs, discontinuity in the density of a running variable suggests violation of the no-manipulation…
The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
A new run length encoding algorithm for lossless data compression that exploits positional redundancy by representing data in a two-dimensional model of concentric circles is presented. This visual transform enables detection of runs (each…
The lack of longitudinal studies of the relationship between the built environment and travel behavior has been widely discussed in the literature. This paper discusses how standard propensity score matching estimators can be extended to…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
A central goal in automatic music transcription is to detect individual note events in music recordings. An important variant is instrument-dependent music transcription where methods can use calibration data for the instruments in use.…
In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
String theory in d dimensions has n+1=11-d parameters that may be thought of as being inherited from the geometry of an n+1 torus which may be used to construct the theory using dimensional reduction from eleven dimensions. We give the…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
There are a number of diverging hypotheses about the neural text degeneration problem, i.e., generating repetitive and dull loops, which makes this problem both interesting and confusing. In this work, we aim to advance our understanding by…