Related papers: On the generation of periodic discrete structures …
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…
Generative modeling over discrete structures underpins applications across deep learning, from biological sequence design and code generation to large language models, yet generation often remains sequential, relying on autoregressive…
Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Crystal structure design is important for the discovery of new highly functional materials because crystal structure strongly influences material properties. Crystal structures are composed of space-filling polyhedra, which affect material…
Complex periodic structures inherit spectral properties from the constituent parts of their unit cells, chiefly their spectral band gaps. Exploiting this intuitive principle, which is made precise in this work, means spectral features of…
Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $\mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple…
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples,…
In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
We train a generative diffusion model (DM) to simulate ultra-relativistic heavy-ion collisions from end to end. The model takes initial entropy density profiles as input and produces two-dimensional final particle spectra, successfully…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
We present Diffusion Structures, a family of resilient shell structures from the eigenfunctions of a pair of novel diffusion operators. This approach is based on Michell's theorem but avoids expensive non-linear optimization with…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…