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The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
In this paper we explore a new method of analysis of associative algebras.
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…
Genetic algorithms are considered as one of the most efficient search techniques. Although they do not offer an optimal solution, their ability to reach a suitable solution in considerably short time gives them their respectable role in…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
A thesis on some recursive Bayesian filters for data assimilation
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…
We prove several congruences for trinomial coefficients.
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
The main contribution of this paper is the development of a new decision tree algorithm. The proposed approach allows users to guide the algorithm through the data partitioning process. We believe this feature has many applications but in…
The binomial multichannel algorithm is proposed. Some its properties are discussed.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.