Related papers: A Step towards an Easy Interconversion of Various …
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
System identification has been a major advancement in the evolution of engineering. As it is by default the first step towards a significant set of adaptive control techniques, it is imperative for engineers to apply it in order to practice…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
To represent real $m$-dimensional vectors, a positional vector system given by a non-singular matrix $M \in \mathbb{Z}^{m \times m}$ and a digit set $\mathcal{D} \subset \mathbb{Z}^m$ is used. If $m = 1$, the system coincides with the well…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
In this paper we propose an approach to implement specific relation-ship set between two entities called combinatorial relationship set. For the combinatorial relationship set B between entity sets G and I the mapping cardinality is…
Inspired by the importance of diversity in biological system, we built an heterogeneous system that could achieve this goal. Our architecture could be summarized in two basic steps. First, we generate a diverse set of classification…
Electronic circuits can be separated into two groups, digital and analog circuits. Analog circuits operate on analog quantities that are continuous in value, whereas digital circuits operate on digital quantities that are discrete in value…
Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with…
The decimal digits of $\pi$ are widely believed to behave like as statistically independent random variables taking the values $0, 1, 2, 3, 4, 5$, $6, 7, 8, 9$ with equal probabilities $1/10$. In this article, first, another similar…
Comparison of two numbers in RNS systems is a challenging task. In this paper, a new algorithm to compare the magnitude of two RNS numbers, using a clustering method has been proposed. In the clustering process, each inputted number is…
Orthogonal and quasi-orthogonal matrices have a long history of use in digital image processing, digital and wireless communications, cryptography and many other areas of computer science and coding theory. The practical benefits of using…
Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in…
Computational science is changing to be data intensive. Super-Computers must be balanced systems; not just CPU farms but also petascale IO and networking arrays. Anyone building CyberInfrastructure should allocate resources to support a…
An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A…
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime. The second test is a deterministic polynomial time…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…