Related papers: Multiple pattern matching: A Markov chain approach
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
The problem of generalized function matching can be defined as follows: given a pattern $p=p_1 \cdots p_m$ and a text $t=t_1 \cdots t_n$, find a mapping $f:\Sigma_p\rightarrow\Sigma_t^{*}$ and all text locations $i$ such that $f(p_1) f(p_2)…
In this paper, we present a new kind of learning implementation to recognize the patterns using the concept of Mirroring Neural Network (MNN) which can extract information from distinct sensory input patterns and perform pattern recognition…
Since data is often stored in different sources, it needs to be integrated to gather a global view that is required in order to create value and derive knowledge from it. A critical step in data integration is schema matching which aims to…
Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…
Despite impressive capabilities, LLMs' successes often rely on pattern-matching behaviors, yet these are also linked to OOD generalization failures in compositional tasks. However, behavioral studies commonly employ task setups that allow…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the…
In runtime verification, pattern matching, which searches for occurrences of a specific pattern within a word, provides more information than a simple violation detection of the monitored property, by locating concrete evidence of the…
This paper introduces a high-order Markov chain task to investigate how transformers learn to integrate information from multiple past positions with varying statistical significance. We demonstrate that transformers learn this task…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
Causal discovery, the task of inferring causal structure from data, has the potential to uncover mechanistic insights from biological experiments, especially those involving perturbations. However, causal discovery algorithms over larger…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
RNA 3D motifs are recurrent substructures, modelled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and…
Recognizing shallow linguistic patterns, such as basic syntactic relationships between words, is a common task in applied natural language and text processing. The common practice for approaching this task is by tedious manual definition of…
This work proposes a markovian memoryless model for the DNA that simplifies enormously the complexity of it. We encode nucleotide sequences into symbolic sequences, called words, from which we establish meaningful length of words and group…