In this letter, the genesis of spike-wave activity a hallmark of many generalized epileptic seizures is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from r...

Zipf’s law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language communication systems emerge at an abrupt phase transition in the fidelity of mappings between symbols and objects. Since the phase transition approximates the Heavis...

in Gaussian units and in spherical coordinates where a(t) is the radius of the shell, Q is the total surface charge, and H(x, x0) = ∫ x −∞ δ(x ′ − x0) dx′ is the Heaviside step function. However, magnetic charges do not exist, so we cannot have a radial magnetic field of the form (1). That is, the magnetic field is zero, B = 0 everywhere, no matter what is the time dependence a(t) of the radius...

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With the progress of society and diversification transportation modes, people are faced with more complicated travel choices, thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years. A number traffic network equilibrium been proposed, but most them do not involve data uncertainty nor computational methods. This paper focuses on methods for solvin...

It is known that some predator-prey system can possess a unique limit cycle which is globally asymptotically stable. For a prototypical predator-prey 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. MSC 2000: 34C26, 34C15, 34C07, 92D25

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.

In this paper we study the one-sided Hausdorff distance between the Heaviside function and some transmuted activation functions. Precise upper and lower bounds for the Hausdorff distance have been obtained. Numerical examples are presented throughout the paper using the computer algebra system MATHEMATICA. The results can be successfully used in the field of applied insurance mathematics.

A connection is investigated between integral formulas and neural networks based on the Heaviside function. The integral formula developed by Kůrková, Kainen and Kreinovich is derived in a new way for odd dimensions and extended to even dimensions. In particular, it is shown that well-behaved functions of d variables can be represented by integral combinations of Heavisides with weights dependi...