Related papers: Anomalous diffusion in nonlinear transformations o…
The conventional voter model is modified so that an agent's switching rate depends on the `age' of the agent, that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes…
This paper investigates the performance of diffusion models for video anomaly detection (VAD) within the most challenging but also the most operational scenario in which the data annotations are not used. As being sparse, diverse,…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
We study the behavior of Range Voting and Normalized Range Voting with respect to electoral control. Electoral control encompasses attempts from an election chair to alter the structure of an election in order to change the outcome. We show…
We propose two nonlinear random walk models which are suitable for the analysis of both chemotaxis and anomalous transport. We derive the balance equations for the population density for the case when the transition rate for a random walk…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, \textit{et al.} Phys. Rev. Lett. \textbf{87}, 045701 (2001)], we show that they behave differently from…
We investigate dynamical scaling properties of the 1D tight-binding Anderson model with a weak diagonal disorder, by means of the spreading of a wave packet. In the absence of disorder, and more generally in the ballistic regime, the…
Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time…
When recording the movement of individual animals, cells or molecules one will often observe changes in their diffusive behaviour at certain points in time along their trajectory. In order to capture the different diffusive modes assembled…
In recent studies of political decision-making, apparently anomalous behavior has been observed on the part of voters, in which negative information about a candidate strengthens, rather than weakens, a prior positive opinion about the…
It is experimentally known that virus exhibits stochastic motion in cytoplasm of a living cell in the free form as well as the form being contained in the endosome and the exponent of anomalous diffusion of the virus fluctuates depending on…
We experimentally study anomalous diffusion of ultra-cold atoms in a one dimensional polarization optical lattice. The atomic spatial distribution is recorded at different times and its dynamics and shape are analyzed. We find that the…