Related papers: Exploring Stochastic Mean Curvature Flow on Networ…
Stochastic linear modelling proposed in Tissot, M\'emin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the…
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge…
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…
Motivated by recent development of mean-field systems with common noise, this paper establishes Ito's formula for flows of conditional probability measures under a common filtration associated with general semimartingales. This generalizes…
Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for…
Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge…
Variety of machine learning problems can be formulated as an optimization task for some (surrogate) loss function. Calculation of loss function can be viewed in terms of stochastic computation graphs (SCG). We use this formalism to analyze…
Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance…
The large-scale integration of intermittent renewable energy has brought serious challenges to the frequency security of power systems. In this paper, a novel nonparametric stochastic analysis method of system dynamic frequency is proposed…
The stochastic network calculus (SNC) holds promise as a versatile and uniform framework to calculate probabilistic performance bounds in networks of queues. A great challenge to accurate bounds and efficient calculations are stochastic…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural…
There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model…
The macroscopic fundamental diagram (MFD) is a powerful and popular tool that describes a network scale traffic operational state and serve as the plant model of perimeter control. As both the supply and the demand suffer from random…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with application in IT and neurogeometry (see Citti-Franceschiello-Sanguinetti-Sarti, 2016). Unfortunately this equation…