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The analysis of sequences (e.g., protein, DNA, and SMILES string) is essential for disease diagnosis, biomaterial engineering, genetic engineering, and drug discovery domains. Conventional analytical methods focus on transforming sequences…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. Transformations that depend not only on the sequence elements or…
A linear constraint system is specified by linear equations over the group $\ZZ_d$ of integers modulo $d$. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the…
The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this…
The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the…
Transformer-based entropy models have gained prominence in recent years due to their superior ability to capture long-range dependencies in probability distribution estimation compared to convolution-based methods. However, previous…
In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.
The algebras of Kleinian type are finite dimensional semisimple rational algebras $A$ such that the group of units of an order in $A$ is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
We will introduce the notion of inductive limits of compact quantum groups as $W^*$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit…
We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. Lagrangian cuts can be added to a Benders reformulation, and are derived from solving single scenario integer programming subproblems…
We study the problem of efficient, scalable set-sharing analysis of logic programs. We use the idea of representing sharing information as a pair of abstract substitutions, one of which is a worst-case sharing representation called a clique…
Range-based set reconciliation is a simple approach to efficiently computing the union of two sets over a network, based on recursively partitioning the sets and comparing fingerprints of the partitions to probabilistically detect whether a…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
We compare different notions of limit sets for the action of Kleinian groups on the $n-$dimensional projective space via the irreducible representation $\varrho:PSL(2,\mathbb{C})\to PSL(n+1,\mathbb{C}).$ In particular, we prove that if the…