Related papers: Disordered auxetic networks with no re-entrant pol…
Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance,…
Over the past years, inverse problems in partial differential equations have garnered increasing interest among scientists and engineers. However, due to the lack of conventional stability, nonlinearity and non-convexity, these problems are…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
This work demonstrates that, for a simple case of 10 randomly positioned atoms, a neural network can be trained to infer atomic coordinates from Patterson maps. The network was trained entirely on synthetic data. For the training set, the…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
This work introduces a systematic algorithm for generating directed networks with prescribed symmetries by constructing expansions from a given quotient network. The method enables researchers to synthesize realistic network models with…
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…
We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a…
This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…
The Poisson's ratio is a fundamental mechanical property that relates the resulting lateral strain to applied axial strain. While this value can theoretically be negative, it is positive for nearly all materials, though negative values have…
A deep learning approach to blind denoising of images without complete knowledge of the noise statistics is considered. We propose DN-ResNet, which is a deep convolutional neural network (CNN) consisting of several residual blocks…
When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added…
Reconstructing a surface from a point cloud is an underdetermined problem. We use a neural network to study and quantify this reconstruction uncertainty under a Poisson smoothness prior. Our algorithm addresses the main limitations of…
The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamer discharges, since the Poisson solution appears as a source term of the unsteady nonlinear flow…
The competing effect of a periodic pinning potential and random point disorder is studied for arrays of elastic lines or directed polymers. The groundstates are investigated by exact combinatorial optimization. In both two and three…
Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
We introduce a new tensor norm, the average spectrum norm, to study sample complexity of tensor completion problems based on the canonical polyadic decomposition (CPD). Properties of the average spectrum norm and its dual norm are…
In 2020, Cameron et al. introduced the restricted numerical range of a digraph (directed graph) as a tool for characterizing digraphs and studying their algebraic connectivity. In particular, digraphs with a restricted numerical range of a…
We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…