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Membranes are of great technological and biological as well as theoretical interest. Two main classes of membranes can be distinguished: Fluid membranes and polymerized, tethered membranes. Here, we review progress in the theoretical…
By a "covering" we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models,…
We present a simple four-dimensional model in which anomaly mediated supersymmetry breaking naturally dominates. The central ingredient is that the hidden sector is near a strongly-coupled infrared fixed-point for several decades of energy…
We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an…
Let X(t) be a Gaussian random field R d $\rightarrow$ R. Using the notion of (d -- 1)-integral geometric measures, we establish a relation between (a) the volume of the level set (b) the number of crossings of the restriction of the random…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…
Masked discrete diffusion models (MDMs) are a promising new approach to generative modelling, offering the ability for parallel token generation and therefore greater efficiency than autoregressive counterparts. However, achieving an…
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-colors nodes. The interaction is local and described through…
In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact that nonlocal operators…
A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to considerably simplify the proofs. The solutions of the quenched…
We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on $\mathbb{R}^{\Lambda_N}$, $\Lambda_N=[-N, N]^d\cap \mathbb{Z}^d$ with Hamiltonian $H_N(\phi)=…
We establish finite sample bounds for the error of standard and waste-free SMC samplers. Our results cover estimates of both expectations and normalising constants of the target distributions. We consider first an arbitrary sequence of…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
This paper proposes a new model called \emph{spatial continuum asymmetric channels} to study the channel capacity region of asymmetric scenarios in which either one source transmits to a spatial density of receivers or a density of…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
We show that intermediate scales in supersymmetric grand unified theories may exist naturally. Their origin is traced to the violation of the survival principle: in supersymmetry internal symmetries often forbid cubic couplings in the…