A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.
CT improves neural network performance on cell complex data.
Novel framework predicts cell responses to perturbations using GRNs.
A new framework for knowledge graph embedding using sheaves.
Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy pol…
Wavelets model complex interactions in spatial transcriptomics.
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier work of Looijenga.
We compare two combinatorial models for the moduli space of two-dimensional cobordisms: Bödigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. We also discuss natural compactifications of these two models, the unilevel harmoni…
CW Networks leverage cell complexes to enhance GNNs, achieving state-of-the-art results on molecular datasets.
In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are re…
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application of two forms of cellular homology is given in terms of the persistence of shape…
The study classifies cellular pseudomanifolds and their properties.
Research shows finiteness in triangulations with girth constraints.
Quantum cellular automata form a homology theory.
This survey paper begins with the description of the duality between arc systems and ribbon graphs embedded in a punctured surface. Then we explain how to cellularize the moduli space of curves in two different ways: using Jenkins-Strebel differentials and using hyperbolic geometry. We also briefly discuss how these tw…
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect…
Optimizes natural frequencies of cellular composites with various microstructures.
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, González, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that the classifying space (order complex) of the face poset of a totally …
Study immersions of punctured 4-manifolds for quantum automata applications.
A deep learning model for traffic forecasting in telecommunication networks.
Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of critical points of a Morse function with given boundary condition.
New architectures improve topological deep learning's ability to capture complex data features.
In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.
ChemCPA predicts cellular responses to novel drugs using transfer learning.
Partial recovery of node mappings between correlated graphs is possible under specific conditions.
Machine learning algorithms can be fooled by small well-designed adversarial perturbations. This is reminiscent of cellular decision-making where ligands (called antagonists) prevent correct signalling, like in early immune recognition. We draw a formal analogy between neural networks used in machine learning and model…
New findings on hyperbolicity of augmented links in thickened surfaces.
Consider a planar, bounded, -connected region , and let $\bordΩ$ be its boundary. Let be a cellular decomposition of $Ω\cup\bordΩ$, where each 2-cell is either a triangle or a quadrilateral. From these data and a conductance function we construct a canonical pair where is a genus …
CURIE uses cellular automata to detect concept drift in data streams.
Deep learning identifies transcriptomic patterns and cell types associated with SARS-CoV-2 infection and COVID-19 severity.
FC-GAGA forecasts traffic using a novel gating mechanism.
Electron Cryo-Tomography (ECT) allows 3D visualization of subcellular structures at the submolecular resolution in close to the native state. However, due to the high degree of structural complexity and imaging limits, the automatic segmentation of cellular components from ECT images is very difficult. To complement an…
Classifies fake surfaces up to complexity 5.
Polynomials derived from Heegaard diagrams for 3-manifolds.
The paper optimizes UAV path and power for QoS in cellular networks.
Proposes GFMMD for comparing signals on graphs.
Motivation: Understanding functions of proteins in specific human tissues is essential for insights into disease diagnostics and therapeutics, yet prediction of tissue-specific cellular function remains a critical challenge for biomedicine. Results: Here we present OhmNet, a hierarchy-aware unsupervised node feature le…
We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the -finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular complex such that the stabilizers are open and compact and the restriction of the act…
We analyze oversquashing in topological message-passing using relational structures.
New method enhances graph neural networks using contractions and hourglass persistence.
We study the problem of computing the homology of the configuration spaces of a finite cell complex . We proceed by viewing , together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we …
This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.
Proposes CXNs for neural network computations on cell complexes.
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This approach has been highly successful owing to the theory, methodology and software that …
In this brief sequel to a previous article, we recall the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by cou…