The paper proves a global geometric formula for volume holonomy in gauge theory.
problem Describing higher parallel transport in classical principal bundle theory.
method Global geometric approach to parallel transport on surfaces and volumes.
result Global formula for volume holonomy and gauge invariance.
Proposes Fusion Recurrent Neural Network for sequence data.
problem Improving sequence learning for practical applications.
method Fusion module and Transport module for sequence data.
result Fusion RNN performs comparably to state-of-the-art RNNs.
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard do…
Transport functions for principal bundles and Morse homology with differential graded coefficients
problem Transport functions for principal bundles
method Constructing transport functions as maps from broken gradient flow lines to a topological group
result Recovering the principal bundle from the transport function
ZegOT uses optimal transport to zero-shot segment images with text prompts.
problem Zero-shot semantic segmentation with limited image-text alignment knowledge.
method ZegOT uses optimal transport to match multiple text prompts with frozen image embeddings.
result ZegOT achieves state-of-the-art performance in zero-shot semantic segmentation.
Polestar optimizes public transportation routes for efficiency and user satisfaction.
problem Difficulty in finding optimal public transportation routes due to complex networks and dynamic situations.
method Developed a Public Transportation Graph (PTG) and a route search algorithm with station binding and ranking modules.
result Demonstrated superior efficiency and user satisfaction compared to existing systems.
Increasing urban concentration raises operational challenges that can benefit from integrated monitoring and decision support. Such complex systems need to leverage the full stack of analytical methods, from state estimation using multi-sensor fusion for situational awareness, to prediction and computation of optimal r…
Assemblies of modular subsystems are being pressed into service to perform sensing, reasoning, and decision making in high-stakes, time-critical tasks in such areas as transportation, healthcare, and industrial automation. We address the opportunity to maximize the utility of an overall computing system by employing re…
Concept modulation models unify identifiability and extrapolation in conditional latent variable models.
problem Reliable generalization in conditional latent variable models
method Concept modulation models (CMMs) with structure AoΛoCoX result Lifts identifiability to conditional settings and controls extrapolation through attribute potentials.
Optimal transport embedding learns feature sets efficiently.
problem Learning on sets of features with long-range dependencies and few labeled data.
method Parametrized fixed-size embedding that aggregates features according to optimal transport plan.
result Achieves state-of-the-art results on protein fold recognition and chromatin profiles.
MOT uses RL with OT to adapt to different market conditions for algorithmic trading.
problem Adapting to varying market conditions in algorithmic trading.
method MOT uses multiple actors with disentangled representation learning and Optimal Transport to model different market patterns.
result MOT outperforms in real futures market data with excellent profit capabilities and risk balancing.
We provide explicit spinor representations for Clifford algebras.
problem Building explicit representations of Clifford algebras.
method Explicit construction of spinor modules and parallel spinor fields.
result Explicit spinor representations for all mixed signature Clifford algebras.
PSTN improves traffic condition forecasting with deep neural networks.
problem Challenges in accurately forecasting traffic conditions due to complex spatiotemporal correlations.
method Proposes PSTN with three modules: graph convolutional network, temporal convolutional network, and gated recurrent unit framework.
result Significantly outperforms state-of-the-art benchmarks in short-term traffic conditions forecasting.
Improved neural framework for scaling entropic MOT with significant computational gains.
problem High computational overhead in multimarginal optimal transport.
method Neural Entropic MOT (NEMOT) using mini-batch training to reduce complexity.
result Significant speedups and feasibility improvements for multimarginal data.
GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
problem Understanding plasma turbulence in fusion reactors, which impairs confinement and limits reactor design.
method Introduces GyroSwin, a scalable 5D neural surrogate that approximates 5D nonlinear gyrokinetic simulations.
result GyroSwin outperforms reduced models in heat flux prediction and captures turbulent energy cascade.
A new framework for generative modeling using controlled vector fields.
problem Expressive modeling with limited parameters.
method Continuous-time modeling with modulated fixed vector fields and learned scalar controls.
result Expressive transport achieved with a small number of learned control channels.
ScoreGrad predicts multivariate time series with energy-based models, achieving state-of-the-art results.
problem Predicting multivariate time series with generative models while considering noise and distribution.
method ScoreGrad uses continuous energy-based generative models with a feature extraction and score matching module.
result ScoreGrad achieves state-of-the-art results on six real-world datasets.
Short-term road traffic prediction (STTP) is one of the most important modules in Intelligent Transportation Systems (ITS). However, network-level STTP still remains challenging due to the difficulties both in modeling the diverse traffic patterns and tacking high-dimensional time series with low latency. Therefore, a …
Paper proposes TRA to learn multiple stock trading patterns.
problem Inconsistent i.i.d. assumption limits stock prediction performance.
method TRA architecture with Optimal Transport for pattern assignment.
result Improves information coefficient (IC) by 0.04-0.06 compared to baselines.
Elliptic Chern characters and Atiyah-Witten formula generalized to double loop spaces.
problem Generalizing classical Atiyah-Witten formula to double loop spaces.
method Constructing elliptic Chern and Bismut-Chern characters, defining elliptic holonomy, and using equivariant twisted parallel transport.
result Established elliptic Atiyah-Witten formula on double loop space.
Taxi demand prediction has recently attracted increasing research interest due to its huge potential application in large-scale intelligent transportation systems. However, most of the previous methods only considered the taxi demand prediction in origin regions, but neglected the modeling of the specific situation of …
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order connectivity patterns captured by small subgraphs, also called network motifs, de…
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
We describe an A∞-quasi-equivalence of dg-categories between the first authors' PA ---the category of category of prefect A0-modules with flat Z-connection, corresponding to the de Rham dga A of a compact manifold M--- and the dg-category of \emph{infinity-local syst…
Introduces statistical optimal transport for probabilistic lectures.
problem No specific problem stated; focuses on introduction.
method Lecture-based introduction to statistical optimal transport.
result Provides an introduction to statistical optimal transport.
Study shows how optimal transport behaves in higher dimensions.
problem Characterizing optimal transport in higher dimensions with Euclidean distance.
method Investigates the small regularization limit of entropic optimal transport.
result The limiting transport plan is supported on transport rays and uniquely minimizes a relative entropy functional.
A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…
Classifies modules of surface-knots in terms of their properties.
problem Characterizing modules of surface-knots in terms of their properties.
method Using homology and covering spaces, the reduced first module is characterized.
result The reduced first module for every genus g is characterized in terms of properties of a finitely generated module.
The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "conn…
New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans π1,π2,… converges weakly to a transport plan π, then π is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…
NOT learns optimal transport plans, kernel costs improve performance.
problem NOT algorithm learns non-optimal plans with weak quadratic costs.
method Introduced kernel weak quadratic costs to improve NOT's performance.
result Kernel costs provide improved theoretical and practical guarantees.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the former.
Curvature defined for Hilbert modules and Kasparov modules.
problem Defining and studying curvature in Hilbert modules and Kasparov modules.
method Introduced curvature for densely defined universal connections on Hilbert C∗-modules relative to spectral triples. result Curvature only depends on the represented form of the universal connection modulo junk forms.
New metric for probability measures connects physics and geometry.
problem Developing a new metric for probability measures.
method Transport Hessian metric, formulated dynamical systems.
result Connections to physics equations and mathematical models.
Using McCann's transportation map, we establish a transport inequality on compact manifolds with positive Ricci curvature. This inequality contains the sharp spectral comparison estimates.
A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.
problem Statistical analysis of shape data, especially in time series and optimization.
method Pole ladder algorithm for parallel transport on Kendall shape spaces, compared to integration methods.
result The pole ladder algorithm is a more efficient method for parallel transport.
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
Extends optimal transport to dynamic and martingale settings.
problem Dynamic and martingale relaxation of optimal transport problems.
method Extends Benamou-Brenier formula to weak optimal transport and introduces barycentric optimal transport.
result Relates barycentric optimal transport to martingale Benamou-Brenier formula.
Defines super projective modules and explores their properties.
problem Exploring the geometric-algebraic link in super geometry.
method Defined and explored super projective modules over supersmooth functions.
result Module of vector fields over a supersphere is a super projective module.
Review of modern computational optimal transport methods for biomedical applications.
problem Efficient computation of optimal transport for big data.
method Regularization-based and projection-based computational methods.
result Advancements in computational optimal transport methods for biomedical research.
Paper relaxes optimal transport using convex functions for data science.
problem Optimal transport problem on finite spaces.
method Relaxation via strictly convex functions (Kullback-Leibler divergence, Bregman divergences). Gradient descent iterative process.
result Mathematical foundations and iterative process for the relaxed optimal transport problem.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
problem Regularity of transport map and potential on simplex boundary.
method Boundary regularity results for optimal transport maps, exploiting simplex symmetries.
result Regularity properties of transport map and its convex potential.
Bayesian approach to optimal transport with stochastic costs.
problem Inferring optimal transport plans with uncertain costs.
method Bayesian framework and Hamiltonian Monte Carlo (HMC) sampling.
result Inference of optimal transport plans under stochastic cost functions.
This paper generalizes Sinkhorn algorithm for unbalanced optimal transport.
problem Handling distributions with different total mass and robustness to outliers.
method Alternates between standard Sinkhorn updates and pointwise application of a contractive function.
result Defines Sinkhorn divergences that are differentiable, positive, definite, convex, and robust.
A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is …
We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.