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A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
Characterizing the connection between material design decisions/parameters and their effective properties allows for accelerated materials development and optimization. We present a global sensitivity analysis of woven composite…
Neural Collapse refers to the curious phenomenon in the end of training of a neural network, where feature vectors and classification weights converge to a very simple geometrical arrangement (a simplex). While it has been observed…
The last decade has witnessed the success of the traditional feature-based method on exploiting the discrete structures such as words or lexical patterns to extract relations from text. Recently, convolutional and recurrent neural networks…
The comprehension of the mechanisms at the basis of the functioning of complexly interconnected networks represents one of the main goals of neuroscience. In this work, we investigate how the structure of recurrent connectivity influences…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
We present results on thermodynamic quantities, resistivity and optical conductivity for the Hubbard model on a simple hypercubic lattice in infinite dimensions. Our results for the paramagnetic phase display the features expected from an…
Assembly-based tools provide a powerful modeling paradigm for non-expert shape designers. However, choosing a component from a large shape repository and aligning it to a partial assembly can become a daunting task. In this paper we…
In this paper, we conjecture that if the permutation invariance of neural networks is taken into account, SGD solutions will likely have no barrier in the linear interpolation between them. Although it is a bold conjecture, we show how…
Motivated by the finding of nearly isotropic superconductivity in $\mathrm{(Ba,K)Fe_2As_2}$, we use renormalized mean field theory to investigated the $t$-$J$ model on three-dimensional simple cubic lattice. A tunable anisotropic parameter…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
The Hubbard model is the simplest model that is believed to exhibit superconductivity arising from purely repulsive interactions, and has been extensively applied to explore a variety of unconventional superconducting systems. Here we study…
Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity)…
We construct the theta-exact covariant noncommutative (NC) model and obtain various closed constraints on the NC scale (Lambda_NC) from inelastic neutrino-nucleon scatterings (nu N -> nu+X), from plasmon decay into neutrino pair (gamma_pl…
The all-to-all momentum coupling of the Hubbard interaction makes interacting lattice models generically unsolvable. In many settings, however, from Peierls instabilities to Moir\'e superlattice physics, the low-energy behavior is dominated…
Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive…
We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…
We study metric versions of transitivity, mixing, and hypercyclicity for continuous maps, based on intersections of the form \( f^{n}(U)\cap B_{\delta}(V)\neq\varnothing. \) We introduce $\delta$-topological transitivity,…