Related papers: Functions with Diffusive Properties
Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
We prove an inequality for functions on the discrete cube extending the edge-isoperimetric inequality for sets. This inequality turns out to be equivalent to the following claim about random walks on the cube: Subcubes maximize 'mean first…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…
When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by…
The disturbance of the transmission of light through a diffusive medium due to an object hidden in it can be expressed in terms of an effective charge and dipole moment. In the mesoscopic regime, beyond the diffusion approximation, we…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
In this paper we define an internal binary operation between functions called in the text \emph{fractal convolution}, that applies a pair of mappings into a fractal function. This is done by means of a suitable Iterated Function System. We…
The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent DFT Hamiltonian (DeepH) of…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
Deep hashing has shown promising performance in large-scale image retrieval. However, latent codes extracted by Deep Neural Networks (DNNs) will inevitably lose semantic information during the binarization process, which damages the…
Ciphers get their strength from the mathematical functions of confusion and diffusion, also known as substitution and permutation. These were the basics of classical cryptography and they are still the basic part of modern ciphers. In block…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
The lattice dynamics of the metallic tin {\beta} and {\gamma} polymorphs has been studied by a combination of diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. The non-symmorphic space group of the…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…