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.
New method reduces spatial graphs while preserving their topological features.
New framework for 3D spatial topology enumeration and identification.
Study reveals how dengue spread patterns vary across different years in Recife, Brazil.
Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.
Spatial graphs can be unknotted with region crossing changes.
Graphoids are topological invariants of virtual graph diagrams.
This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian -graphs.
Algorithm determines spatial graph isomorphism with vertex, edge colorings and orientations.
New cosmological spacetimes without CMC Cauchy surfaces found.
Classical knot theory can be generalized to virtual knot theory and spatial graph theory. In 2007, Fleming and Mellor combined virtual knot theory and spatial graph theory to form, combinatorially, virtual spatial graph theory. In this paper, we introduce a topological definition of virtual spatial graphs that is simil…
The Gannon-Lee singularity theorems give well-known restrictions on the spatial topology of singularity-free (i.e., nonspacelike geodesically complete), globally hyperbolic spacetimes. In this paper, we revisit these classic results in the light of recent developments, especially the failure in higher dimensions of a c…
Proposes a method to forecast spatial-temporal data with limited training data.
This paper identifies all topological symmetry groups for Heawood family graphs.
We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus then proving that this algebra injects into the Kauffman bracket …
Extends knotoid theory to include multiple poles and intervals.
The study explores spacetimes with changing spatial curvature, leading to topological transitions.
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.
Spatial and time-dependent data is of interest in many applications. This task is difficult due to its complex spatial dependency, long-range temporal dependency, data non-stationarity, and data heterogeneity. To address these challenges, we propose Forecaster, a graph Transformer architecture. Specifically, we start b…
The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial graphs and singular knots, that is obtained by replacing unknown crossings or ve…
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered () model for interaction events fal…
Study on future stability of FLRW spacetime solutions with decelerated expansion.
We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.
New vacuum spacetimes without CMC Cauchy surfaces found.
New topological quantum gravity theories linked to Ricci flow.
Paper presents voxel graph operators for vector data models.
In order to apply quantum topology methods to nonplanar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. These \emph{virtual graphs} are a categorical interpretation of ribbon graphs. We describe an extension of the flow polynomial to virtual graphs, t…
We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in 5 dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean in which spatial cross-sections at infinity have lens space topology, or asymptotically Kaluza-Klein so t…
Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical work suggests that the concept of space can be grounded by capturing invariants induced by the structure of space in an ag…
Machine learning classifies topological phases in leaky photonic lattices.
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruen…
DNNs improve SIMP method but not spatially invariant, study shows.
Proposes deep graph persistence to address neural persistence issues in deep learning.
Accurate and real-time traffic forecasting plays an important role in the Intelligent Traffic System and is of great significance for urban traffic planning, traffic management, and traffic control. However, traffic forecasting has always been considered an open scientific issue, owing to the constraints of urban road …
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and pro…
The 2008 financial crisis revealed banking consolidation paradoxically increased systemic fragility and global financial contagion with negligible spatial decay.
We consider the vacuum Einstein flow with a positive cosmological constant on spatial manifolds of product form. In spatial dimension at least four we show the existence of continuous families of recollapsing models whenever at least one of the factors or admits a Riemannian Einstein metric with positive Einstein const…
Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical works suggest that the Euclidean structure of space induces invariants in an agent's raw sensorimotor experience. We hypot…
Local index formula for Lorentzian Dirac operators on spacetimes.
A3T-GCN improves traffic forecasting by capturing spatial and temporal dependencies.
The universe's shape and size are determined in general cosmological models.
We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice of such a structure, but not on a choice of metric and in this sense, it is topo…
New framework for diffusion geometry simplifies complex calculations.
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
Study on embeddings and their topological properties in R^d.
Develops a new neural spike train decoding framework using topological data.
Researchers prove a special case of Borde-Sorkin's conjecture about topology change in spacetimes.
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability fo…