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Secret information sharing through image carrier has aroused much research attention in recent years with images' growing domination on the Internet and mobile applications. However, with the booming trend of convolutional neural networks,…
Efficient text embedding is crucial for large-scale natural language processing (NLP) applications, where storage and computational efficiency are key concerns. In this paper, we explore how using binary representations (barcodes) instead…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
This paper proposes a ($k,n$)-threshold secret image sharing scheme that offers flexibility in terms of meeting contrasting demands such as information security and storage efficiency with the help of a randomized kernel (binary matrix)…
Several new estimates for the 2-adic valuations of Stirling numbers of the second kind are proved. These estimates, together with criteria for when they are sharp, lead to improvements in several known theorems and their proofs, as well as…
We study the combinatorial properties of final types, which are certain non-decreasing sequences of integers, together with the partitions naturally associated with them. As a consequence, we obtain an identity expressing the $n$-nacci…
Zernike radial polynomials (ZRP) play a significant role in application areas such as optics design, imaging systems, and image processing systems. Currently, there are two kinds of numerical schemes for computing the ZRP automatically with…
In a recent paper, we generalized a partition identity stated by Siladi\'c in his study of the level one standard module of type $A_2^{(2)}$. The proof used weighted words with an arbitrary number of primary colors and all the secondary…
We propose an alternative way to represent graphs via OBDDs based on the observation that a partition of the graph nodes allows sharing among the employed OBDDs. In the second part of the paper we present a method to compute at the same…
We consider the problem of correcting mass readout errors in information encoded in binary polymer strings. Our work builds on results for string reconstruction problems using composition multisets [Acharya et al., 2015] and the unique…
Recently, binary representation has been proposed as a novel representation that lies between continuous and discrete representations. It exhibits considerable information-preserving capability when being used to replace continuous input…
In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal…
Gravitational wave observations of binary neutron star mergers provide valuable information about neutron star structure and the equation of state of dense nuclear matter. Numerous methods have been proposed to analyze the population of…
This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two…
In the context of Stirling polynomials, Gessel and Stanley introduced the definition of Stirling permutation, which has attracted extensive attention over the past decades. Recently, we introduced Stirling permutation code and provided…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…