Related papers: de Finetti Style Theorems With Applications to Net…

Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…

One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…

We prove several de Finetti theorems for the unitary dual group, also called the Brown algebra. Firstly, we provide a finite de Finetti theorem characterizing $R$-diagonal elements with an identical distribution. This is surprising, since…

We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…

The fundamental decomposition of a chemical reaction network (also called its "$\mathscr{F}$-decomposition") is the set of subnetworks generated by the partition of its set of reactions into the "fundamental classes" introduced by Ji and…

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

Zeckendorf's theorem states every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. This result has been generalized to many sequences $\{a_n\}$ arising from an integer positive linear recurrence, each…

By Zeckendorf's theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every positive number can be written uniquely as a sum of non-adjacent…

We present a new deep unfolding network for analysis-sparsity-based Compressed Sensing. The proposed network coined Decoding Network (DECONET) jointly learns a decoder that reconstructs vectors from their incomplete, noisy measurements and…

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.…

We propose an approach that connects recurrent networks with different orders of hidden interaction with regular grammars of different levels of complexity. We argue that the correspondence between recurrent networks and formal…

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of…

Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains…

We propose the Decomposer Networks (DecompNet), a semantic autoencoder that factorizes an input into multiple interpretable components. Unlike classical autoencoders that compress an input into a single latent representation, the Decomposer…

In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the…

In this paper Moussouris' algorithm for the decomposition of spin networks is reviewed and the implicit assumptions made in the Decomposition Theorem relating a spin network with its state sum are examined. It is found that the theorem in…

A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present our conclusions about the generalization of…

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…