Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the "critical order" 2-s andâ€¦ (More)

We define new functional spaces designed to measure the fine local regularity of functions. In contrast with classical approaches based on, e. g., Littlewoodâ€“Paley or wavelet analysis, these spacesâ€¦ (More)

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physicalâ€¦ (More)

We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to aâ€¦ (More)

The diffusive motion of Brownian particles near irregular interfaces plays a crucial role in various transport phenomena in nature and industry. Most diffusion-reaction processes in confiningâ€¦ (More)

Quansheng Ren, Kiran M. Kolwankar, 2 Areejit Samal, 3 and JÃ¼rgen Jost 4 Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany Department of Physics, Ramniranjanâ€¦ (More)

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals,â€¦ (More)

We study the interplay of topology and dynamics in a neural network connected with spike-timing-dependent plasticity (STDP) synapses. Stimulated with periodic spike trains, the STDP-driven networkâ€¦ (More)

We study the effect of learning dynamics on network topology. Firstly, a network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve accordingâ€¦ (More)