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The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and…
Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do…
We present nested sampling for factor graphs (NSFG), a novel nested sampling approach to approximate inference for posterior distributions expressed over factor-graphs. Performing such inference is a key step in simultaneous localization…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…
We introduce a class of algebras over a field $\mathbb{F}$ related to directed graphs in which all edges are labeled by nonzero elements of the field $\mathbb{F}$. If all labels are different from $1$, these algebras are axial algebras. We…
An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the…
Recent research efforts aiming to bridge the Neural-Symbolic gap for RDFS reasoning proved empirically that deep learning techniques can be used to learn RDFS inference rules. However, one of their main deficiencies compared to rule-based…
Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…
We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…
Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…
In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks.…
Many problems can be presented in an abstract form through a wide range of binary objects and relations which are defined over problem domain. In these problems, graphical demonstration of defined binary objects and solutions is the most…