We model notions of computation using algebraic operations and equations. We show that these generate several of the monads of primary interest that have been used to model computational effects, with the striking omission of the continuations monad. We focus on semantics for global and local state, showing that taking operations and equations as primitive yields a mathematical relationship tha...

The amplitude–frequency relationship is an important mathematical property for a nonlinear oscillator. He’s amplitude–frequency formulation and the Max–Min approach are used to handle the conservative nonlinear oscillator ẍ +  1 + ẋ2  x = 0 for the amplitude–frequency relationship. The obtained result is compared with those in the open literature, revealing the effectiveness of the used metho...

This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship can be used to quantify variation among the entities of a system, caused by tolerance, options, specification or implementation errors, independent of noise, impact communications system performance. Means to address these variat...

Insulin receptor substrate (IRS) harbors proteins such as IRS1, IRS2, IRS3, IRS4, IRS5 and IRS6. These key proteins act as vital downstream regulators in the insulin signaling pathway. However, little is known about the evolutionary relationship among the IRS family members. This study explores the potential to depict the evolutionary relationship among the IRS family using bioinformatics, algo...

This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of agents in using the network graph. I show the similarity and relationship between the structural pattern of the network and network utilization.

‖ If we consider the intellectual relationship of the mathematical sciences to philosophy, as they have developed since the time of the Enlightenment, we notice with satisfaction that mathematical thought is now at the point of regaining the powerful influence on philosophical speculation that it had up to Kant’s time, but then suddenly lost completely. That sudden turn from mathematical though...

A recently-developed mathematical semantic theory explains the relationship between knowledge and its representation in connectionist systems. The semantic theory is based upon category theory, the mathematical theory of structure. A product of its explanatory capability is a set of principles to guide the design of future neural architectures and enhancements to existing designs. We claim that...

Although mathematical morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic mathematical morphol...

One of the ultimate goals in plant systems biology is to elucidate the genotype-phenotype relationship in plant cellular systems. Integrated network analysis that combines omics data with mathematical models has received particular attention. Here we focus on the latest cutting-edge computational advances that facilitate their combination. We highlight (1) network visualization tools, (2) pathw...

The present study aims to examine the relationship between cognitive factors and mathematical achievement in primary education. Participants were 103 Portuguese third grade students, aged 8 and 9. All participants completed a battery for working memory (WMTB-C), a test of general intelligence (Raven's Progressive Color Matrices), a selective attention test (d2), and mathematical exercises (arit...