Related papers: Successive Spectral Sequences
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
The Hodge-Tate spectral sequence for a proper smooth variety over a p-adic field provides a framework for us to revisit Faltings' approach to p-adic Hodge theory and to fill in many details. The spectral sequence is obtained from the…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
Using methods from random matrix theory researchers have recently calculated the full spectra of random networks with arbitrary degrees and with community structure. Both reveal interesting spectral features, including deviations from the…
We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and boundary length using a spectral curve as initial data for the framework of topological recursion. Based on an earlier result of Chapuy and…
Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of…
Segmental structure is a common pattern in many types of sequences such as phrases in human languages. In this paper, we present a probabilistic model for sequences via their segmentations. The probability of a segmented sequence is…
Scientists aim to extract simplicity from observations of the complex world. An important component of this process is the exploration of data in search of trends. In practice, however, this tends to be more of an art than a science. Among…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
We prove an abstract index formula about Sinnott's symbol between two different lattices. We also develop the theory of the universal distribution and predistribution in a double complex point of view. The theory of spectral sequence is…
Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
This work is about self-similar sequences of growing connected graphs. We explain how to construct such sequences and why they are important. We show for instance that all the connected graphs in a self-similar sequence have not only the…
The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…
Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in…
How do neural networks trained over sequences acquire the ability to perform structured operations, such as arithmetic, geometric, and algorithmic computation? To gain insight into this question, we introduce the sequential group…