Related papers: Understanding multifractality: reconstructing imag…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
Multipath effects significantly influence the quality of microwave imaging in highly reflective environments, while the physical measurement aperture size constrains resolution. It is shown that by exploiting multipath reflections, improved…
Dramatic advances in generative models have resulted in near photographic quality for artificially rendered faces, animals and other objects in the natural world. In spite of such advances, a higher level understanding of vision and imagery…
Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal…
Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1x1 convolutions play a key role in existing architectures because they increase…
Image restoration is a class of important tasks that emerges from a wide range of scientific disciplines. It has been noticed that most practical images can be modeled as a composition from a sparse singularity set (edges) where the image…
Scaling and architectural advances have produced strikingly photorealistic image generative models, yet their mechanisms still remain opaque. Rather than advancing scaling, our goal is to strip away complicated engineering tricks and…
Multiple optical scattering occurs when light propagates in a non-uniform medium. During the multiple scattering, images were distorted and the spatial information they carried became scrambled. However, the image information is not lost…
Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches…