Researchers from diverse disciplines are increasingly incorporating numeric highorder data, i.e., numeric tensors, within their practice. Just like the matrix-vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and algorithms for arithmetic calculations, e.g., those found in Einstein-like notation, is crucial for the continued adoption of tensors...

The long term goal of this research is the development of a new approach to scientiic computing in which declarative methods derived from constraint logic programming are used to minimize the avoidable errors that can be made when developing scientiic software. The main approach we will pursue is to explore the beneets and challenges of viewing scientiic computing as interval arithmetic constra...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

The main result in [24] on the structure of commutators showed that arithmetic means play an important role in the study of operator ideals. In this survey we present the notions of arithmetic mean ideals and arithmetic mean at infinity ideals. Then we explore their connections with commutator spaces, traces, elementary operators, lattice and sublattice structure of ideals, arithmetic mean idea...

The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information, and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quadratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggregati...

The goal of this paper is to study the dynamics of a genetic algorithm in a more visual, intuitive way than statistical methods do. Rather than modeling the genetic algorithm mathematically, we try to describe how the GA scans through the search space, and how genotypes move through the search space as genetic operators are applied to them. We find that standard genetic operators can be describ...

Future technologies, below 90nm, will present transistors so small that they will be heavily influenced by electromagnetic noise and SEU induced errors. This way, together with process variability, design as known today is likely to change. Since several soft errors may occur in a small period of time, the traditional hypothesis that the behavior of a gate is fixed is no longer valid and a diff...

A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the 0s in a product qubit state do not contribute to the number. They serve only as place holders. The representation is based on the distribution of four types of systems on an integer lattice. The four types, labelled as positive real, negat...

In this work we propose a multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits. The multiplicative depth objective is encountered in the field of homomorphic encryption where ciphertext size depends on the number of consecutive multiplications. The heuristic is based on rewrite operators for multiplicative depth-2 paths. Even if the proposed rewrite operat...