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.
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
A scalable method to learn causal graphs from large data.
Method selects number of communities in weighted networks.
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…
Study designs experiments to identify causal graph structure with cycles and latent confounders.
A goodness-of-fit test for DCSBM improves scalability and power for large sparse networks.
A knot K is called Gordian adjacent to a knot L if there exists an unknotting sequence for L containing K. We provide a sufficient condition for Gordian adjacency of torus knots via the study of knots in the thickened torus. We also completely describe Gordian adjacency for torus knots of index 2 and 3 using Levine-Tri…
Paper determines 2-adjacent knots up to 12 crossings.
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
Adjacency defined for three-manifolds, linking them to the 3-sphere.
The paper introduces an adjacency constraint to improve goal-conditioned HRL.
Graphs represent knot adjacency for n crossings.
A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the un…
For graphs generated from stochastic blockmodels, adjacency spectral embedding is asymptotically consistent. Further, adjacency spectral embedding composed with universally consistent classifiers is universally consistent to achieve the Bayes error. However when the graph contains private or sensitive information, trea…
This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a comp…
A knot is said to be Gordian adjacent to a knot if is an intermediate knot on an unknotting sequence of . We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In additio…
A framework for stable dynamic network embeddings using static methods.
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.
The paper extends hypothesis testing to non-diagonalizable matrices, improving network statistics inference.
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…
Power of network tests degrades when vertices are misaligned.
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
Random projections help in representing sparse graphs efficiently.
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…
A test for comparing networks using stochastic block models.
Study sets limits for detecting a subhypergraph in uniform hypergraphs.
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
Tests if vertices in graphs have the same latent positions.
New matrix reveals cluster info in sparse directed graphs.
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
We propose a method based on deep learning to perform cardiac segmentation on short axis MRI image stacks iteratively from the top slice (around the base) to the bottom slice (around the apex). At each iteration, a novel variant of U-net is applied to propagate the segmentation of a slice to the adjacent slice below it…
New method for freezing sets in arbitrary dimensions.
Fast nonparametric conditional independence testing via two-stage regression
Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of finding communities or clusters in a network has received much attention from statisti…
A knot K is called n-adjacent to another knot K', if K admits a projection containing n generalized crossings such that changing any 0 < m \leq n of them yields a projection of K'. We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to answer th…
New model for network analysis using functional data.
AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.
A graph's winding numbers around two non-adjacent vertices differ by ±1.
It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of "knot adjacency", studied in the paper "Knot adjacency, genus and essential tori" by the authors, can be used to obtain…
New tests detect communities in dense bipartite graphs with high accuracy.
Improved bipartite link prediction using 2-hop paths.
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We…
Two spectral clustering methods for multi-layer networks are analyzed and compared.
Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating rationalization of its output. In the current work, we aim to better understand the ge…
The paper proposes DEA to make graph neural networks fairer in link prediction.
Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This 4-neighbourhood topological simplicity makes the application of convolutional masks straightf…
We study real nonsingular projective cubic fourfolds up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in the middle homology. Moreover, we provide a graph whose vertices represent the equivale…
In this work we propose a method for anatomical data augmentation that is based on using slices of computed tomography (CT) examinations that are adjacent to labeled slices as another resource of labeled data for training the network. The extended labeled data is used to train a U-net network for a pixel-wise classific…