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We suggest a method for generation of random binary sequences with prescribed correlation properties. It is based on a kind of modification of the widely used convolution method of constructing continuous random processes. Apart from the…
In this thesis, we address the problem of identifying and quantifying variants (alternative splicing and genomic polymorphism) in RNA-seq data when no reference genome is available, without assembling the full transcripts. Based on the…
Sequential model synchronisation is the task of propagating changes from one model to another correlated one to restore consistency. It is challenging to perform this propagation in a least-changing way that avoids unnecessary deletions…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
A balanced generalized de Bruijn sequence with parameters $(n,l,k)$ is a cyclic sequence of $n$ bits such that (a) the number of 0's equals the number of 1's, and (b) each substring of length $l$ occurs at most $k$ times. We determine…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
Sequential recommender systems aims to predict the users' next interaction through user behavior modeling with various operators like RNNs and attentions. However, existing models generally fail to achieve the three golden principles for…
Fitting generative models to sequential data typically involves two recursive computations through time, one forward and one backward. The latter could be a computation of the loss gradient (as in backpropagation through time), or an…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
Statistically sound tests of scalar-tensor gravity theories in the strong-field regime usually involves computationally intensive calculations. In this study, we construct a reduced order surrogate model for the scalar-tensor gravity of…
We study here schedulers for a class of rules that naturally arise in the context of rule-based constraint programming. We systematically derive a scheduler for them from a generic iteration algorithm of Apt [2000]. We apply this study to…
de Bruijn graph-based algorithms are one of the two most widely used approaches for de novo genome assembly. A major limitation of this approach is the large computational memory space requirement to construct the de Bruijn graph, which…
Completely antipersistent binary time series are sequences in which every time that an $N$-bit string $\mu$ appears, the sequence is continued with a different bit than at the last occurrence of $\mu$. This dynamics is phrased in terms of a…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to…
We study a fixed-window counting system in which integers are represented by words of constant length while the alphabet grows as needed. This viewpoint arises from De Bruijn sequences: for fixed order $n$, the reverse prefer-max sequence…
Recurrent neural networks (RNNs) have shown excellent performance in processing sequence data. However, they are both complex and memory intensive due to their recursive nature. These limitations make RNNs difficult to embed on mobile…
We consider linear recurrent neural networks, which have become a key building block of sequence modeling due to their ability for stable and effective long-range modeling. In this paper, we aim at characterizing this ability on a simple…
Regularities in strings are often related to periods and covers, which have extensively been studied, and algorithms for their efficient computation have broad application. In this paper we concentrate on computing cyclic regularities of…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…