Related papers: Robustness via Diffractal Architectures
The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…
Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically…
When multimode optical fibers are perturbed, the data that is transmitted through them is scrambled. This presents a major difficulty for many possible applications, such as multimode fiber-based telecommunication and endoscopy. To overcome…
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…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
Precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and photonics. These advances around the engineering of materials with new functionalities have also opened up exciting avenues for…
Fractals are self-similar recursive structures that have been used in modeling several real world processes. In this work we study how "fractal-like" processes arise in a prediction game where an adversary is generating a sequence of bits…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
Including information from additional spectral bands (e.g., near-infrared) can improve deep learning model performance for many vision-oriented tasks. There are many possible ways to incorporate this additional information into a deep…
This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing…
In this paper, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical…
Reconstructing transparent objects from a set of multi-view images is a challenging task due to the complicated nature and indeterminate behavior of light propagation. Typical methods are primarily tailored to specific scenarios, such as…
We report a broadband diffractive optical neural network design that simultaneously processes a continuum of wavelengths generated by a temporally-incoherent broadband source to all-optically perform a specific task learned using deep…
Despite their unmatched performance, deep neural networks remain susceptible to targeted attacks by nearly imperceptible levels of adversarial noise. While the underlying cause of this sensitivity is not well understood, theoretical…
We introduce a comprehensive statistical characterization of the multipath wireless channel built as a superposition of a number of scattered waves with random phases. We consider an arbitrary number $N$ of specular (dominant) components…
We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi,…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…