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This is a natural generalization of the previous work by Dan, "Modeling and Simulation of Diffusion Phenomena on Social Networks," to appear in The proceedings of 2011 Third International Conference on Computer Modeling and Simulation. In…
We consider a multitask estimation problem where nodes in a network are divided into several connected clusters, with each cluster performing a least-mean-squares estimation of a different random parameter vector. Inspired by the…
We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…
This doctoral work focuses on three main problems related to social networks: (1) Orchestrating Network Formation: We consider the problem of orchestrating formation of a social network having a certain given topology that may be desirable…
In this paper we study a generalization of distributed conditional gradient method to time-varying network architectures. We theoretically analyze convergence properties of the algorithm and provide numerical experiments. The time-varying…
In this study we present an extension of the replicator equation with diffusion to multiplex graphs. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that…
Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics…
We rigorously calculate the propagation and scattering of electromagnetic waves by rectangular and random arrays of dielectric cylinders in a uniform medium. For regular arrays, the band structures are computed and complete bandgaps are…
Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…
Dynamical systems can be modelled by partial differential equations and numerical computations are used everywhere in science and engineering. In this work, we investigate the performance of recurrent and convolutional deep neural network…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.
In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
We study the excitation spectrum of light and strange mesons in diffractive scattering. We identify different hadron resonances through partial wave analysis, which inherently relies on analysis models. Besides statistical uncertainties,…