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We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the unregularised case, we show that unbalanced optimal…
Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterized by Wardrop conditions. However, it is well known that equilibria are inefficient in…
These lecture notes were prepared for the 2018 Summer School on `Active Matter and Non-equilibrium Statistical Physics' at l'\'{E}cole de Physique des Houches. They survey metabolic activity across a wide range of living organisms, and…
In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Crowd dynamics and many large biological systems can be described as populations of agents or particles, which can only be observed on aggregate population level. Identifying the dynamics of agents is crucial for understanding these large…
The recent surge in the network modeling of complex systems has set the stage for a new era in the study of fundamental and applied aspects of optimization in collective behavior. This Focus Issue presents an extended view of the state of…
We study optimal transport for stationary stochastic processes taking values in finite spaces. In order to reflect the stationarity of the underlying processes, we restrict attention to stationary couplings, also known as joinings. The…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
Since its early beginnings, mankind has put to test many different society forms, and this fact raises a complex of interesting questions. The objective of this paper is to present a general population model which takes essential features…
We present an overview of our recent work on implementable solutions to the Schroedinger bridge problem and their potential application to optimal transport and various generalizations.
This paper presents a model addressing welfare optimal policies of demand responsive transportation service, where passengers cause external travel time costs for other passengers due to the route changes. Optimal pricing and trip…
In this paper we investigate numerically the model for pedestrian traffic proposed in [B.Andreianov, C.Donadello, M.D.Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods…
Urban transportation is a complex phenomenon. Since many agents are constantly interacting in parallel, it is difficult to predict the future state of a transportation system. Because of this, optimization techniques tend to give obsolete…
Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules,…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…