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Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed…
Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…
Background: Models describing nuclear fragmentation and fragmentation-fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data…
Traditional neuron models use analog values for information representation and computation, while all-or-nothing spikes are employed in the spiking ones. With a more brain-like processing paradigm, spiking neurons are more promising for…
We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class…
Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to…
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either…
Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial for real applications…
Recent studies have demonstrated the advantages of fractional-order calculus tools for probing the viscoelastic properties of collagenous tissue, characterizing the arterial blood flow and red cell membrane mechanics, and modeling the…
Fractional excitations in fracton models exhibit novel features not present in conventional topological phases: their mobility is constrained, there are an infinitude of types, and they bear an exotic sense of 'braiding'. Hence, they…
The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the…
In this report the authors examine the possibility of using the Fractal Attrition Equation as a metamodel to describe outcomes of cellular automaton combat models. This Fractal Attrition Equation has been proposed as a replacement for the…
The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be…
Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit non-uniform convergence in certain singular…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
Nonadiabatic effects in chemical reaction at metal surfaces, due to excitation of electron-hole pairs, stand at the frontier of the studies of gas-surface reaction dynamics. However, the first principles description of electronic excitation…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
A simple threshold model of neuron firing (with the neuron membrane electrochemical potential governed by the chaotic Rossler attractor) has been analyzed by mapping the generated irregular spiking time-series into telegraph signals. In…
We demonstrate the existence of a fundamentally new type of excitation, fractonic lines, which are line-like excitations with the restricted mobility properties of fractons. These excitations, described using an amalgamation of higher-form…
Neurons are connected to other neurons by axons and dendrites that conduct signals with finite velocities, resulting in delays between the firing of a neuron and the arrival of the resultant impulse at other neurons. Since delays greatly…