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.
A framework converts spatial data into embeddings for insurance risk modelling.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exis…
SE-KGE embeds spatial data into KGs for better spatial reasoning.
In this paper we construct some invariants of spatial graphs by disk-summing the constituent knots and show the delta edge-homotopy invariance of them. As an application, we show that there exist infinitely many slice spatial embeddings of a planar graph up to delta edge-homotopy, and there exist infinitely many bounda…
Paper presents a method for geographic ratemaking using spatial embeddings.
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
New method to classify simple Smale flows on .
Two natural generalizations of knot theory are the study of spatially embedded graphs, and Kauffman's theory of virtual knots. In this paper we combine these approaches to begin the study of virtual spatial graphs.
GSNE improves house price predictions by embedding geo-spatial context.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…
Characterizes graphs with leveled embeddings and introduces new graph invariants.
Proves minimal crossing diagrams for specific spatial graphs.
SCNode improves node embeddings for GNNs in both homophilic and heterophilic graphs.
New proof shows no flat embedding for Petersen family graphs.
The paper introduces groupoid racks for spatial surfaces.
A site-specific Gordian distance between two spatial embeddings of an abstract graph is the minimal number of crossing changes from one to another where each crossing change is performed between two previously specified abstract edges of the graph. It is infinite in some cases. We determine the site-specific Gordian di…
New modularity function improves clustering of spatially embedded networks.
In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links' weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what extent metric distances affect relationships (link's weights) in a spatially embedde…
SXL embeds spatial autocorrelation into neural networks for better geographic data learning.
Proposes flexible spatial models for better understanding spatial heterogeneity.
A spatial surface is a compact surface embedded in the 3-sphere. In this paper, we provide several typical examples of spatial surfaces and construct a coloring invariant to distinguish them. The coloring is defined by using a multiple group rack, which is a rack version of a multiple conjugation quandle.
We introduce invariants of spatial graphs related to the Wu invariant and the Simon invariant, and apply them to prove that certain graphs are intrinsically chiral, and to obtain lower bounds for the minimal crossing number of embedded graphs.
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to spatial point processes. While the original embedding is infinite-dimensional a…
We consider the group of isotopy classes of automorphisms of the 3-sphere that preserve a spatial graph or a handlebody-knot embedded in it. We prove that the group is finitely presented for an arbitrary spatial graph or a reducible handlebody-knot of genus two. We also prove that the groups for "most" irreducible genu…
Study on spatial graphs and their constituent knots, linking polynomial invariants.
Extends knotoid theory to include multiple poles and intervals.
We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a nonsplit link due to [1],[2]. Building on this and using the chirality of torus knots and links [3],[4], we prove that nontrivial embeddings of simple 3-…
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
Study limits of quasi-local angular momentum at infinity of gravitating systems.
We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.
A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We show that irreducibility is preserved under certain deformations of embedded graphs…
In this paper, we propose a new pooling method called spatial pyramid encoding (SPE) to generate speaker embeddings for text-independent speaker verification. We first partition the output feature maps from a deep residual network (ResNet) into increasingly fine sub-regions and extract speaker embeddings from each sub-…
We show that all nontrivial embeddings of planar graphs on the torus contain a nontrivial knot or a nonsplit link. This is equivalent to showing that no minimally knotted planar spatial graphs on the torus exist that contain neither a nontrivial knot nor a nonsplit link all of whose components are unknots.
We state and prove a correct version of a theorem presented in an earlier paper.
Study on knot properties, showing relation between unknotting and crossing numbers.
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools. Robust parameter estimation is a challenge for kernel functions that compute suc…
New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.
The paper introduces a test to distinguish spatial graphs based on their knot diagrams.
Spatial understanding is a fundamental problem with wide-reaching real-world applications. The representation of spatial knowledge is often modeled with spatial templates, i.e., regions of acceptability of two objects under an explicit spatial relationship (e.g., "on", "below", etc.). In contrast with prior work that r…
A scalable Bayesian linear regression framework for spatial data.
Road networks are a type of spatial network, where edges may be associated with qualitative information such as road type and speed limit. Unfortunately, such information is often incomplete; for instance, OpenStreetMap only has speed limits for 13% of all Danish road segments. This is problematic for analysis tasks th…
A new method identifies critical transitions in high-dimensional data.
ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.
GraphDINO learns neuronal morphologies from unlabeled data.
DeepKriging uses DNNs to predict spatial data with improved accuracy and scalability.