Model predicts spatial-temporal series with latent dynamical component.
problem Forecasting and discovering spatial-temporal relations in series.
method Recurrent neural network with latent dynamical component and various prior hypotheses.
result Model outperforms baselines in various forecasting tasks.
Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the classical case. Unlike previous attempts at generalizing link homotopy to spatial…
Study on spatial graphs and their constituent knots, linking polynomial invariants.
problem Understanding the polynomial invariants of spatial graphs and their constituent knots.
method Analyzing spatial K4 graphs, constructing band surfaces, and relating polynomials. result Relations between Yamada/Jaeger polynomials and Jones polynomials of constituent knots and associated links.
Defines non-parabolic curves in spatial hybrid space with applications.
problem Defining and analyzing non-parabolic spatial hybrid framed curves.
method Definition and proof of existence and uniqueness theorem for non-parabolic spatial hybrid framed curves.
result Existence and uniqueness theorem for non-parabolic spatial hybrid framed curves.
Graph WaveNet models spatial-temporal graphs by learning hidden dependencies and long sequences.
problem Capturing hidden spatial dependencies and long-range temporal sequences in graphs.
method Graph WaveNet integrates adaptive dependency matrix learning and stacked dilated 1D convolution.
result Graph WaveNet outperforms existing methods on public traffic network datasets.
This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results about symmetries of spatial graphs. In both cases we consider spatial graphs in S3 as well as in other 3-manifolds.
In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbatio…
In a vacuum spacetime equips with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total linear momentum and the Bondi momentum. The relation between the ADM total energy and the Bondi mass in t…
Model predicts severity of traffic accidents using spatial and temporal features.
problem Estimating severity of traffic accidents in aggregated and disaggregated data.
method Gradient Boosting models and Gaussian Processes for inference and feature importance.
result Complexity of road networks and other situational features significantly impact accident severity.
Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
problem Unknottability of spatial graphs by region crossing changes.
method Region crossing changes to switch over/under relations within regions of spatial graph diagrams.
result Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.
Proposes DMVST-Net for taxi demand prediction.
problem Improving taxi demand prediction for smart city resource allocation.
method Deep Multi-View Spatial-Temporal Network (DMVST-Net) combining LSTM, CNN, and semantic views.
result Demonstrates effectiveness over state-of-the-art methods on large-scale taxi demand data.
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the 2-component constituent algebraically split links and show examples…
Formulae for Yamada polynomial of spatial graphs are derived from edge replacements.
problem Computing Yamada polynomial for spatial graphs formed by edge replacements.
method Formulae derived from edge replacements of plane graphs.
result Zeros of Yamada polynomials of certain spatial graphs are dense in a complex plane region.
Spatial graphs are decomposed into planar forests and braids.
problem Understanding the structure of spatial graphs in 3-space.
method Decomposition of spatial graphs into planar forests and braids.
result Every finite spatial graph is a connected sum of a planar graph and a braid.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split li…
SpatialSim benchmarks machine learning in recognizing object spatial configurations.
problem Machine learning in recognizing precise geometrical configurations of groups of objects.
method SpatialSim benchmark with tasks of Identification and Comparison, using Graph Neural Networks (MPGNNs).
result MPGNNs outperform baselines in recognizing spatial configurations, highlighting current limits.
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
problem Understanding the relationship between unknotting numbers and crossing numbers of spatial embeddings of planar graphs.
method Analyzing specific examples of planar graphs and their spatial embeddings to find counterexamples.
result There exist planar graphs and their spatial embeddings where the unknotting number is greater than half the crossing number.
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.
New invariants detect a specific graph in spatial webs.
problem Detecting specific graphs in spatial webs.
method Introduced new invariants and used spectral sequences.
result Proved invariants detect the planar theta graph.
Models learn spatial templates from implicit language, predicting spatial arrangements with high accuracy.
problem Predicting spatial arrangements from implicit spatial language.
method Simple neural-based models leveraging annotated images and structured text.
result Models can predict spatial arrangements from implicit spatial language with high accuracy, even for unseen objects.
Study on crossing numbers of composite knots and graphs.
problem Understanding the minimal crossing number of composite knots and graphs.
method Relating the minimal crossing number of composite knots to the minimal crossing number of spatial graphs, specifically the 2n-theta curve.
result Proved that for large enough n, the crossing number of the 2n-theta curve is n times the sum of the crossing numbers of the prime knots.
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…
Spatial information is not always necessary for spatio-temporal models.
problem The necessity of including spatial information in spatio-temporal models.
method Comparison of spatial agnostic neural networks with state-of-the-art models on ten datasets.
result Spatial information is not always needed in most spatio-temporal models.
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside R×R3≡R4, which forms a triple. We want to define an ambient isotopic equivalence relation on such triples, so that we can obtain equivalence invariant…
Study shows how near crushing singularities, Kasner-like regions can exist.
problem Understanding spatial volume densities near crushing singularities.
method Relates existence of Kasner-like regions to asymptotics of spatial volume densities under scale-invariant curvature bounds.
result Kasner-like regions can exist near crushing singularities under certain curvature conditions.
A scalable Bayesian linear regression framework for spatial data.
problem Scalable methodologies for analyzing large spatial datasets.
method Conjugate Bayesian linear regression framework.
result Exact sampling from joint posterior distribution without iterative algorithms.
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…
New approach uses graphs for sign language recognition.
problem Challenges in recognizing sign language for deaf individuals.
method Spatial-Temporal Graph Convolutional Network.
result Improved sign language recognition using human skeletal movements.
Develops BASGCN for graph classification with improved feature learning.
problem Graph classification with information loss and imprecise representation.
method Transforms graphs into grid structures and defines a new spatial graph convolution operation.
result Reduces information loss and improves feature representation compared to existing models.
Language models trained on chess board states outperform those on moves, even with causal masking.
problem Applying causal masking to spatial data for training unimodal language models.
method Trained bidirectional and causal self-attention models on both spatial (board-based) and sequential (move-based) chess data.
result Models trained on spatial board states achieve stronger playing strength than those trained on sequential data, even with causal masking.
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
A new framework combines CNN and GRU for better structural damage detection.
problem Improving damage detection in structural engineering using machine learning.
method Hierarchical CNN and Gated Recurrent Unit (GRU) framework to model spatial and temporal relations.
result The proposed HCG framework significantly outperforms existing methods for structural damage detection.
We extend the theory of combinatorial link Floer homology to a class of oriented spatial graphs called transverse spatial graphs. To do this, we define the notion of a grid diagram representing a transverse spatial graph, which we call a graph grid diagram. We prove that two graph grid diagrams representing the same tr…
STOIC improves energy demand forecasting with reliable uncertainty estimates.
problem Accurate point forecasts alone are insufficient for energy systems; reliable uncertainty estimates are needed.
method Integrates graph-based forecasting with tabular foundation models for zero-shot calibration of spatial-temporal residuals.
result STOIC delivers more reliable and robust uncertainty estimates for complex graph-structured energy time series.
Study on knot properties, showing relation between unknotting and crossing numbers.
problem Relations between unknotting and crossing numbers of spatial embeddings.
method Analyzes handcuff-graphs and theta curves, extends known results to handlebody-knots.
result Characterizes handlebody-knots satisfying the equality between unknotting and crossing numbers.
Minimal moves for surfaces in 4D discovered, linking planar and spatial moves.
problem Finding the minimal set of moves for surfaces in 4D.
method Derived minimal generating set of spatial moves, translated into planar moves.
result Minimal generating set of spatial moves for surfaces in 4D.
Current image captioning systems miss spatial location details.
problem Capturing spatial location information in image captions.
method Evaluation of image captioning systems from literature.
result Language models alone are insufficient for capturing spatial location in image captions.
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential well. Complicated non-linear relations including inter-band positive correlatio…
The study applies spatial density models to mobile node movements using Möbius distributions.
problem Modeling the steady-state density of mobile nodes on a 2D terrain.
method Used mixture density networks with Möbius distributions to describe node density over a disk.
result Möbius distributions are more suitable for capturing radial changes in node density compared to Gaussian distributions.
This work relates the framework of model-based clustering for spatial functional data where the data are surfaces. We first introduce a Bayesian spatial spline regression model with mixed-effects (BSSR) for modeling spatial function data. The BSSR model is based on Nodal basis functions for spatial regression and accom…
A new method classifies hyperspectral images using dynamic graph convolutional networks.
problem Complex spatial context in HSI classification leads to inaccurate results.
method Develops a GCN-based method that captures long-range contextual relations and refines graph edges.
result Significant improvement in HSI classification performance compared to state-of-the-art methods.
Study quantifies risk of extreme wind events using spatial risk measures.
problem Assessing risk of impacts from extreme wind events.
method Spatial risk measure axioms, Brown-Resnick max-stable random fields, powers of max-stable random fields.
result Spatial risk measures associated with extreme wind speeds satisfy risk measure axioms.
Paper proposes a neural network to improve traffic flow forecasting.
problem Forecasting future traffic flow distribution in an area.
method Position-aware convolutional neural network integrating data features and position information.
result Our approach outperforms previous methods even with fewer data sources.
Proposes flexible dilation networks for better time series analysis.
problem Fixed dilation limits flexibility in time series analysis.
method End-to-end learnable dilation layers and independent kernels.
result Improves efficiency and flexibility in training.
Researchers calculate quasi-local mass on unit spheres at infinity.
problem Computing quasi-local mass on unit spheres at spatial infinity.
method Developed new techniques to evaluate quasi-local mass.
result Leading order term of quasi-local mass recovers stress-energy tensor for vacuum spacetime.
SE-KGE embeds spatial data into KGs for better spatial reasoning.
problem Spatially explicit KG embeddings for geographic tasks.
method Location-aware KG embedding model SE-KGE.
result SE-KGE outperforms baselines on DBGeo dataset.
Extends knotoid theory to include multiple poles and intervals.
problem No new problem introduced.
method Definition of generalized knotoids and graphs, exploration of invariants.
result Theory subsumes various topological objects and introduces new cases.