Study develops curvature for contact-sequence networks, revealing temporal dynamics.
problem Lack of geometric analysis for temporal network sequences.
method Develops Forman--Ricci curvature on spatiotemporal prism complexes.
result Two curvature variants disagree on 56-67% of temporal edges.
A prism is the product space Δ×I where Δ is a 2-simplex and I is a closed interval. As an analogue of simplicial complexes, we introduce prism complexes and show that every compact 3-manifold has a prism complex structure. We call a prism complex special if each interior horizontal edge lies in four prism…
PRISM integrates diverse rewards in MORL, improving sample efficiency and Pareto coverage.
problem Heterogeneous MORL where dense objectives dominate, leading to poor sample efficiency.
method PRISM uses reflectional symmetry and ReSymNet to reconcile temporal-frequency mismatches and accelerate exploration.
result PRISM consistently outperforms sparse-reward baselines and oracles, achieving significant Pareto gains.
PRISM infers model structures and parameters from simulations, controlling complexity at test time.
problem Choosing among large model families for scientific discovery.
method Simulation-based encoder-decoder that infers model structures and parameters, with test-time complexity control.
result PRISM scales to large model families and performs model selection in biophysical diffusion MRI.
New classification of hyperbolic Coxeter prisms.
problem Classifying hyperbolic Coxeter prisms.
method Determine which prisms are quasi-arithmetic or arithmetic.
result New insights into commensurability and systoles of associated orbifolds.
Hyperbolic knots decompose into prism orbifolds.
problem Understanding hyperbolic knot complements and their geometric properties.
method Analyzing knot complements as quotients of H3 by discrete groups of reflections in polyhedra with triangular prism combinatorial type. result Knot complements decompose into hidden symmetries and contain closed, embedded, totally geodesic surfaces.
Ballinger et al. have determined the list of all prism manifolds that are possibly realizable by Dehn surgeries on knots in S3. In this paper, we explicitly find braid words of primitive/Seifert-fibered knots on which surface slope surgeries yield all the prism manifolds listed above. This completes the solution to …
Bayesian Complementary Kernelized Learning models complex spatiotemporal data.
problem Modeling complex, nonstationary, and nonseparable spatiotemporal data.
method Integrates kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes.
result BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates.
Every prism manifold can be parametrized by a pair of relatively prime integers p>1 and q. In our earlier papers, we determined a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S3 when q<0 or q>p; in the present work, we solve the case when 0<q<p.…
We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers p>1 and q. We determine a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S3 when q>p. The methodology…
Study flat metrics from right prisms, finding non-lattice surfaces with translation coverings.
problem Analyzing flat metrics from right regular prisms.
method Viewing prisms as n-differentials and analyzing unfoldings, proving translation coverings to hyperelliptic surfaces.
result Non-lattice surfaces admit translation coverings to hyperelliptic surfaces, allowing explicit computation of orbit closures and counting problems.
In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.
We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the correspondi…
This paper proposes a geometry-aware active learning framework for spatiotemporal dynamic systems.
problem Challenges in modeling complex dynamic systems with 3D geometries and time evolution.
method Geometry-aware spatiotemporal Gaussian Process (G-ST-GP) and adaptive active learning strategy.
result The proposed framework outperforms traditional methods in predicting high-dimensional dynamic behaviors.
PRISM identifies simplex vertices from noisy data.
problem Identifying vertices of a simplex from noisy data.
method Probabilistic simplex model with maximum likelihood inference.
result Vertices are identifiable under certain assumptions.
The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S3. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every…
Explicitly constructed 5-manifolds tessellated by prisms.
problem Constructing closed arithmetic hyperbolic 5-manifolds.
method Explicit construction and tessellation of manifolds by Coxeter simplicial prisms.
result Explicit construction of 5-manifolds with specified properties.
In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \cite[Chapter 8, §2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimension…
New method learns spatiotemporal dynamics from random point process observations.
problem Challenges in modeling spatiotemporal dynamics from randomly collected data.
method Integration of neural differential equations, neural point processes, implicit neural representations, and amortized variational inference.
result Significant improvements in predictive accuracy and computational efficiency compared to existing methods.
Paper uses DMD to embed time in spatiotemporal forecasting.
problem Forecasting long-range seasonal dependencies in spatiotemporal data.
method Dynamic Mode Decomposition (DMD) for time representation.
result DMD-based embedding improves long-horizon forecasting accuracy.
Asymmetry PRISM outperforms CPU and GPU solvers for institutional rebalancing.
problem Institutional rebalancing with deadline constraints
method Asymmetry PRISM
result Asymmetry PRISM-CPU is 4.5x to 24.1x faster than the fastest completed reference row in the same lane.
New unsupervised transfer learning method for spatiotemporal tasks.
problem Transfer knowledge from unsupervised models to new predictive tasks.
method Differentiable framework with Transferable Memory Unit (TMU).
result Significant improvements on spatiotemporal prediction benchmarks.
We prove the following comparison theorem for metrics with nonnegative scalar curvature, also known as the dihedral rigidity conjecture by Gromov: for n≤7, if an n-dimensional prism has nonnegative scalar curvature and weakly mean convex faces, then its dihedral angle cannot be everywhere not larger than its Euc…
GATGPT uses LLMs with graph attention for spatiotemporal data imputation.
problem Missing values in spatiotemporal data due to sensor malfunctions and data transmission errors.
method Integrates pre-trained large language models with graph attention mechanisms.
result GATGPT achieves comparable results to deep learning benchmarks on real-world datasets.
ProGen improves spatiotemporal forecasting with SDEs and diffusion models.
problem Complex spatial and temporal dependencies in spatiotemporal data.
method ProGen uses Stochastic Differential Equations and diffusion-based generative models.
result ProGen outperforms state-of-the-art models on traffic datasets.
New model fills in missing traffic data efficiently.
problem Missing data in large-scale spatiotemporal traffic data.
method Developed scalable tensor learning model LSTC-Tubal for imputation.
result LSTC-Tubal achieves high accuracy with lower computational cost.
PRISM-FCP improves federated prediction robustness against Byzantine attacks.
problem Byzantine attacks in federated learning.
method Partial model sharing and distance-based maliciousness scores.
result Maintains nominal coverage guarantees under Byzantine attacks.
This paper explores how deep learning models can fit data exactly and why this is important.
problem Understanding why deep learning models can fit data exactly and generalize well.
method Interpolation and over-parameterization as key themes to understand deep learning.
result Interpolation and over-parameterization are crucial for deep learning models to fit data exactly and generalize well.
A novel method for efficiently integrating spatiotemporal point processes.
problem Challenges in integrating spatiotemporal neural point processes, especially for flexible intensity functions.
method AutoSTPP (Automatic Integration for Spatiotemporal Neural Point Processes) extends a dual network approach to 3D STPP using ProdNet for decomposable parametrization of the integral network.
result AutoSTPP effectively sidesteps computational complexities and shows significant advantage in recovering complex intensity functions.
INP accelerates stochastic simulations using deep Bayesian active learning.
problem Computational expense of stochastic simulations at fine-grained resolution.
method Interactive Neural Process (INP) framework combining spatiotemporal surrogate model and active learning acquisition function.
result STNP outperforms baselines in accelerating stochastic simulations and LIG achieves state-of-the-art for Bayesian active learning.
Person re-identification (re-id), an emerging problem in visual surveillance, deals with maintaining entities of individuals whilst they traverse various locations surveilled by a camera network. From a visual perspective re-id is challenging due to significant changes in visual appearance of individuals in cameras wit…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framew…
TK-GCN forecasts spatiotemporal dynamics using Koopman-enhanced graph convolutional networks.
problem Forecasting complex spatiotemporal dynamics over irregular domains.
method Two-stage framework: Koopman-enhanced Graph Convolutional Network (K-GCN) for spatial encoding and Transformer for temporal modeling.
result TK-GCN outperforms state-of-the-art methods in spatiotemporal cardiac dynamics forecasting.
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery (S3d), decides which physical terms are necessary and which can be removed (because they are physically n…
The study examines the systole of 3-manifolds with positive scalar curvature.
problem Analyzing the systole of 3-manifolds with positive scalar curvature.
method Local-to-global approach using capillary prisms and Coxeter gluing.
result Estimates the systole of 3-manifolds with positive scalar curvature.
Enformer and GEnformer use Transformers with stochastic learning to forecast multivariate and spatiotemporal data with uncertainty.
problem Uncertainty quantification in multivariate time series and spatiotemporal forecasting.
method Synthesizing Transformer's expressive power with stochastic learning to model conditional distributions directly.
result Enformer and GEnformer yield calibrated probabilistic forecasts and outperform state-of-the-art baselines.
Deep models forecast epidemics with uncertainty quantification.
problem Accurate probabilistic forecasting of epidemics is challenging due to nonlinear temporal dependencies and spatial interactions.
method Deep spatiotemporal engression methods with geometric ergodicity and asymptotic stationarity.
result Proposed methods outperform benchmarks in point and probabilistic forecasting.
Predicts financial asset dependencies using spatiotemporal patterns.
problem Complex dependency structures in financial assets for risk mitigation.
method Proposes Asset Dependency Matrix (ADM) and Asset Dependency Neural Network (ADNN) with ConvLSTM for spatiotemporal asset dependency prediction.
result ADNN outperforms baselines in predicting asset dependencies and their applications.
SPACY discovers causal graphs from spatiotemporal data using variational inference.
problem Inferring causal relationships from high-dimensional spatiotemporal data with complex correlations.
method SPACY uses variational inference to model latent time series and their causal relationships, incorporating spatial factors to aggregate correlated data.
result SPACY outperforms state-of-the-art methods on synthetic and real-world data, identifying key causal phenomena.
In this paper, we classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism. We show how to find each such polyhedron in the upper half-space model by considering lines and circles in the plane. Finally, we give matrix generators in $\mathrm{…
This study improves weather forecasting accuracy with spatiotemporal models.
problem Complexity and resource-intensive nature of weather forecasting.
method Spatiotemporal forecasting models integrating machine learning and deep neural networks.
result Spatiotemporal models reduce computational costs and improve accuracy.
In arxiv:1205.1274 Rieck and Yamashita defined the link volume of 3-manifolds and studied some of its basic properties. Many of these properties are similar to the corresponding properties of the hyperbolic volume. In this paper we calculate the link volume of an infinite family of prism manifolds. As a corollary, we s…
Unified inference framework for spatiotemporal data.
problem Challenges in extracting mechanistic insights from complex spatiotemporal data.
method Vision transformer-driven variational encoding and likelihood-free Bayesian approach.
result Unified inference framework for identifying spatial and temporal patterns.
DeepRV accelerates spatiotemporal inference using neural priors.
problem Intractable scaling of Gaussian Processes for large datasets.
method Neural-network surrogate replacing GP prior sampling with O(N2) complexity. result DeepRV achieves highest fidelity to exact GPs while significantly speeding up inference.
This paper reviews spatial and spatiotemporal volatility models.
problem Capturing spatial dependence in volatility of spatial and spatiotemporal data.
method Review of time series volatility models and their extensions.
result Comparison and practical recommendations for spatial and spatiotemporal volatility models.
Building spatiotemporal activity models for people's activities in urban spaces is important for understanding the ever-increasing complexity of urban dynamics. With the emergence of Geo-Tagged Social Media (GTSM) records, previous studies demonstrate the potential of GTSM records for spatiotemporal activity modeling. …
DYffusion improves diffusion models for spatiotemporal forecasting.
problem Challenges in generating stable and accurate forecasts for dynamic data.
method Leverages temporal dynamics in data, directly coupling it with diffusion steps.
result Improves computational efficiency and performs competitively on complex dynamics.
We classify n-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if n>3, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the 3-dimensional case by showing that such a manifold is either a lens space or a prism mani…