Related papers: Blocksequences of k-local Words
Time-series classification has attracted considerable research attention due to the various domains where time-series data are observed, ranging from medicine to econometrics. Traditionally, the focus of time-series classification has been…
In 2017 Day et al. introduced the notion of locality as a structural complexity-measure for patterns in the field of pattern matching established by Angluin in 1980. In 2019 Casel et al. showed that determining the locality of an arbitrary…
In this paper, we consider block languages, namely sets of words having the same length, and we propose a new representation for these languages. In particular, given an alphabet of size $k$ and a length $\ell$, a block language can be…
Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in…
Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…
A locally testable semigroup S is a semigroup with the property that for some nonnegative integer k, called the order or level of local testability, two words u and v in some set of generators for semigroup S are equal in the semigroup if…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
In recent years, the creation of block-structured dictionary has attracted a lot of interest. Learning such dictionaries involve two step process: block formation and dictionary update. Both these steps are important in producing an…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
All poetic forms come from somewhere. Prosodic templates can be copied for generations, altered by individuals, imported from foreign traditions, or fundamentally changed under the pressures of language evolution. Yet these relationships…
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the…
In this paper we provide a new locally consistent decomposition of strings. Each string $x$ is decomposed into blocks that can be described by grammars of size $\widetilde{O}(k)$ (using some amount of randomness). If we take two strings $x$…
Word embedding, which encodes words into vectors, is an important starting point in natural language processing and commonly used in many text-based machine learning tasks. However, in most current word embedding approaches, the similarity…
Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between…
Recent advances in tracking sensors and pose estimation software enable smart systems to use trajectories of skeleton joint locations for supervised learning. We study the problem of accurately recognizing sign language words, which is key…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
This paper develops the notion of \emph{Word Linear Complexity} ($WLC$) of vector valued sequences over finite fields $\ff$ as an extension of Linear Complexity ($LC$) of sequences and their ensembles. This notion of complexity extends the…
Centrality, in some sense, captures the extent to which a vertex controls the flow of information in a network. Here, we propose Local Detour Centrality as a novel centrality-based betweenness measure that captures the extent to which a…
Locality is a fundamental principle used extensively in program and system optimization. It can be measured in many ways. This paper formalizes the metrics of locality into a measurement theory. The new theory includes the precise…