It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predatorprey system, we show that the solution curve of the limit cycle exhibits temporal patterns of a relaxation oscillator, or a Heaviside function, when certain parameter is small.

The existence of a mean-square continuous strong solution is established for vectorvalued Itô stochastic differential equations with a discontinuous drift coefficient, which is an increasing function, and with a Lipschitz continuous diffusion coefficient. A scalar stochastic differential equation with the Heaviside function as its drift coefficient is considered as an example. Upper and lower s...

In this paper the superheating of electron plasma by femtosecond laser pulses is investigated. With Heaviside thermal equation (Lasers in Engineering, 12, (2002), p. 17) the generation of superhot electrons is described. It is shown that in hot electron plasma (i.e. with electron energies > 5 MeV) the thermal shock waves can be generated.

Today, mobile devices have become an integral part of their possessor’s life. Learning using mobile devices has the advantage of receiving educational content at the moment when it is actually needed, or when the learner feels like s/he is able to study. Moreover, mobile devices used in education can augment the learning experience by delivering further information to the learner, depending on ...

Unlike device-centric monitoring, task-centric tracing enables an operator to causally trace the complete execution of a networked system across the boundaries of applications, protocols, and administrative domains. In this paper, we argue that causal, end-to-end tracing should be an integral part of network services. Moreover, it is not fundamentally difficult to achieve, given a primitive tha...

This paper presents two new analytical equations, the Two Exponent Phenomenological Percolation Equation (TEPPE) and Single (SEPPE) which, for proper choice of parameters, approximate widely used Heaviside Step Function. The plots equations presented in figures this show some, but by no means all, step, ramp, delta, differentiable activation functions that can be obtained using percolation equa...

Abstract Understanding causal relationships is one of the most important goals modern science. So far, inference literature has focused almost exclusively on outcomes coming from Euclidean space Rp. However, it increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework effects for Wasserstein cumulative distribut...