Related papers: An Analytical Representation of the 2d Generalized…
Representing patterns as labeled graphs is becoming increasingly common in the broad field of computational intelligence. Accordingly, a wide repertoire of pattern recognition tools, such as classifiers and knowledge discovery procedures,…
We present a systematic methodology for the reformulation of a broad class of three-dimensional (3D) piezoelectric problems into a two-dimensional (2D) mathematical form. The sole underlying hypothesis is that the system geometry and…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
Probabilistic graphical models are widely used to model complex systems under uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables as they can provide…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…
We use numerical simulations of ray tracing through N-body simulations to investigate weak lensing by large-scale structure. These are needed for testing the analytic predictions of two-point correlators, to set error estimates on them and…
This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…
We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…
In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The…
Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using…
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a…
We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond…
The energy of a vertex $v_i$ in a graph $G$ is defined as $\mathcal{E}_G(v_i) = |A|_{ii}$, where $A$ is the adjacency matrix of $G$, $A^*$ denotes the conjugate transpose of $A$, and $|A| = (AA^*)^{1/2}$. The total energy of the graph,…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…