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A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…
Stress transmission in planar open-cell cellular solids is analysed using a recent theory developed for marginally rigid granular assemblies. This is made possible by constructing a one-to-one mapping between the two systems. General…
The paper is devoted to the problem of resonances in one-dimensional disordered systems. Some of the previous results are reviewed and a number of new ones is presented. These results pertain to different models (continuous as well as…
Multi-phase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring…
Intrinsically disordered proteins and regions are increasingly appreciated for their abundance in the proteome and the many functional roles they play in the cell. In this short review, we describe a variety of approaches used to obtain…
Polaron defects are ubiquitous in materials and play an important role in many processes involving carrier mobility, charge transfer and surface reactivity. Determining the spatial distribution of small polarons is essential to understand…
The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in these data that is not directly visible by standard tools and…
We study the propagation of waves in a set of absorbing subwavelength scatterers positioned on a stealth hyperuniform point pattern. We show that spatial correlations in the disorder substantially enhance absorption compared to a fully…
Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of the Bin Packing Problem in which each item has a size and a color and the goal is to minimize the sum of the number of bins containing items of each color. In this…
The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…
We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main…
We introduce a perturbation expansion for athermal systems that allows an exact determination of displacement fields away from the crystalline state as a response to disorder. We show that the displacement fields in energy minimized…
This paper proposes a simple method to distill and detect backdoor patterns within an image: \emph{Cognitive Distillation} (CD). The idea is to extract the "minimal essence" from an input image responsible for the model's prediction. CD…
Predicting the densest random disc packing fraction is an unsolved paradigm problem relevant to a number of disciplines and technologies. One difficulty is that it is ill-defined without setting a criterion for the disorder. Another is that…
It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the…
Compressive Sensing (CS) theory asserts that sparse signal reconstruction is possible from a small number of linear measurements. Although CS enables low-cost linear sampling, it requires non-linear and costly reconstruction. Recent…
Among the remarkable scattering properties of correlated disordered materials, the origin of pseudo-gaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves…