Related papers: Generalized signals on simplicial complexes
The state hidden subgroup problem (StateHSP) is a recent generalization of the hidden subgroup problem. We present an algorithm that solves the non-abelian StateHSP over $N$ copies of the dihedral group of order $8$ (the symmetries of a…
We introduce the notion of "generalized bosons" whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^\dagger]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized…
Neural network models often generalize poorly to mismatched domains or distributions. In NLP, this issue arises in particular when models are expected to generalize compositionally, that is, to novel combinations of familiar words and…
We consider the well-studied problem of decomposing a vector time series signal into components with different characteristics, such as smooth, periodic, nonnegative, or sparse. We describe a simple and general framework in which the…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly to topological data analysis. The…
Graphs are widely used to represent complex information and signal domains with irregular support. Typically, the underlying graph topology is unknown and must be estimated from the available data. Common approaches assume pairwise node…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
We give a decomposition of the Laplace operator (in matrix form) of a covering simplicial complex as a direct sum of several matrices, one of which is the Laplace operator of the base complex. It follows that the spectrum of a covering…
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g.…
Dynamic graphs serve as a generic abstraction and description of the evolutionary behaviors of various complex systems (e.g., social networks and communication networks). Temporal link prediction (TLP) is a classic yet challenging inference…
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…
Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking…
We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding $p$-value. The goal is to make…
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We…
Trivially-acting symmetries in two-dimensional conformal field theory include twist fields of dimension zero which are local topological operators. We investigate the consequences of regarding these operators as part of the global symmetry…
We explore the use of generalized t priors on regression coefficients to help understand the nature of association signal within "hit regions" of genome-wide association studies. The particular generalized t distribution we adopt is a…
We introduce a non-autonomous generalization of spatial-temporal differentiations, and prove results about probabilistically and topologically generic behaviors of certain spatial-temporal differentiations generated by endomorphisms of…