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A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…

Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…

In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…

We introduce the method of stochastic lists to deal with a multi-variable positive function, defined by a self-consistent equation, typical for certain problems in physics and mathematics. In this approach, the function's properties are…

Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions…

This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…

Predicting human mobility patterns has many practical applications in urban planning, traffic engineering, infectious disease epidemiology, emergency management and location-based services. Developing a universal model capable of accurately…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a…

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…

Studies using massive, passively data collected from communication technologies have revealed many ubiquitous aspects of social networks, helping us understand and model social media, information diffusion, and organizational dynamics. More…

Generalization methods offer a powerful solution to one of the key drawbacks of randomized controlled trials (RCTs): their limited representativeness. By enabling the transport of treatment effect estimates to target populations subject to…

We propose a novel method for numerical modeling of spatially inhomogeneous moment dynamics of populations with nonlocal dispersal and competition in continuous space. It is based on analytically solvable decompositions of the time…

We propose a metric which can be used to compute the amount of heritable variation enabled by a given dynamical system. A distribution of selection pressures is used such that each pressure selects a particular fixed point via competitive…

We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of…

Human motion prediction is essential for the safe and smooth operation of mobile service robots and intelligent vehicles around people. Commonly used neural network-based approaches often require large amounts of complete trajectories to…