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We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
This report considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient…
Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problem,…
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…
Turbulent wall flows offer the most direct means for understanding the effects of boundaries and viscosity on turbulent fluctuations. Available data on mean-square fluctuations in these flows show apparent contradiction with classical…
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…
A new method of estimating some statistical characteristics of TCP flows in the Internet is developed in this paper. For this purpose, a new set of random variables (referred to as observables) is defined. When dealing with sampled traffic,…
In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…
Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context, with a training objective that makes them approximately sample in proportion to a given reward…
How finite-sized material lines stretch in chaotic (mono-scale) and turbulent (multi-scale) flows remains a central but unresolved problem that governs mixing, transport and reaction. We show elongation is controlled by a finite-sampling…
The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
A matching queue is described via a graph $G$ together with a matching policy. Specifically, to each node in the graph there is a corresponding arrival process of items which can either be queued, or matched with queued items in neighboring…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…
In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
We develop a model describing the behavior of two-phase ferrofluid flows using phase field-techniques and present an energy-stable numerical scheme for it. For a simplified, yet physically realistic, version of this model and the…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…