Synthetic Ricci flows defined for metric measure spaces.
problem Characterizing Ricci flows for non-smooth spaces.
method Heat flow, optimal transport, volume asymptotics.
result Equivalent characterizations of weighted Ricci flow.
On-device research index
arXiv research
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “synthetic spaces”
This survey introduces synthetic timelike Ricci curvature bounds in Lorentzian spaces.
problem Synthetic timelike Ricci curvature bounds in non-smooth Lorentzian spaces.
method Optimal transport and entropy tools.
result Synthetic version of Hawking's singularity theorem and synthetic characterisation of Einstein's vacuum equations.
SyNGLER generates synthetic networks efficiently while preserving key structural properties.
problem Efficiently generating realistic synthetic networks with preserved structural properties.
method SyNGLER uses latent space network models to learn and reconstruct node embeddings, then generates synthetic networks.
result SyNGLER produces synthetic networks that better preserve key network characteristics than existing approaches.
Entropy study on synthetic spaces with curvature bounds.
problem Entropy functional on synthetic spaces with curvature bounds.
method Rigorous justification of entropy formula, monotonicity, and rigidity properties; heat kernel bounds.
result Bounds for heat equation solutions on synthetic spaces.
Develops new synthetic Ricci flow concepts for metric measure spaces.
problem No specific problem stated; focuses on new mathematical concepts.
method Formulated in terms of dynamic convexity and local concavity of entropy, and global/short-time asymptotic transport cost estimates.
result Shows these properties characterise smooth (weighted) Ricci flows.
Unified study of Riemannian and sub-Riemannian geometries with synthetic Ricci curvature bounds.
problem Unified framework for Riemannian and sub-Riemannian geometries.
method Study of gauge metric measure spaces.
result Unified synthetic Ricci curvature lower bounds for both Riemannian and sub-Riemannian structures.
Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.
problem Synthetic curvature bounds for Lorentzian spaces.
method Optimal transport, convexity analysis of entropy functionals.
result Synthetic notion of timelike Ricci curvature lower bounds.
Synthetic construction of 3D complex bases.
problem Creating a complete set of unbiased bases in 3D complex space.
method Synthetic construction using complex projective trigonometry.
result Synthetic construction of mutually unbiased bases in C^3.
Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.
The study proposes conjectures on limit spaces of Riemannian manifolds with Ricci curvature.
problem Understanding the regularity of limit spaces of Riemannian manifolds with Ricci curvature.
method Synthetic treatment of lower bounds on Ricci curvature for metric measure spaces.
result Several conjectures on the regularity of limit spaces.
Synthetic approach to pluripotential theory measures finite energy.
problem Global pluripotential theory on compact Kähler manifolds and projective Berkovich spaces.
method Definition and study of measures of finite energy, introduction of twisted and free energy functionals.
result Coercivity of energy functionals is an open condition with respect to polarization.
Proves a synthetic Lorentzian Cartan-Hadamard theorem.
problem Formulates and proves a theorem for Lorentzian geometry.
method Uses an appropriate notion of local concavity for Lorentzian (pre-)length spaces.
result Establishes existence and uniqueness of timelike geodesics.
Synthetic construction of Hopf fibration in 4D space.
problem Visualizing 4D objects in 3D space.
method Double orthogonal projection method to visualize 4D space.
result Direct synthetic construction of 3-sphere fibers from 2-sphere points.
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize distribution spaces in our study of wave and heat equations.
Molecular Design in Synthetically Accessible Chemical Space via Deep Reinforcement Learningphysics.chem-ph
A new RL framework optimizes drug-like molecules synthetically.
problem Optimizing drug-like molecules for specific criteria.
method Deep Reinforcement Learning framework for chemical space optimization.
result Outperforms existing methods in pharmacological optimization.
Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.
problem Synthetic proof of rigidity for globally hyperbolic Lorentzian spaces.
method Synthetic geometry and warped product analysis.
result Spaces with specific curvature and distance realizer are warped products.
New KD-tree based method for private synthetic data generation.
problem Creating private synthetic data that accurately represents real data.
method KD-trees combined with noise perturbation for differentially private synthetic data generation.
result Our data-dependent approach improves utility over prior work and scales well.
Closing the Gap Between Synthetic and Ground Truth Time Series Distributions via Neural Mappingcs.LG
NM-VQTSG improves synthetic time series fidelity by aligning distributions.
problem Fidelity challenges in VQ-based time series generation.
method Neural mapping model using U-Net to refine synthetic data.
result Significant improvements in FID, IS, and conditional FID metrics.
Synthetic theory defines orbifolds as microlinear types with finite identifications.
problem Defining orbifolds in traditional set-level foundations with internal symmetries.
method Synthetic differential cohesive homotopy type theory, microlinearity, finite identifications.
result Proper étale groupoids are orbifolds in synthetic theory.
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from spaces to spacesmath.DG
The study improves harmonic map theory for metric spaces with curvature bounds.
problem Harmonic maps between specific metric spaces with curvature constraints.
method Synthetic geometry, Optimal Transport, Heat Flow, viscosity theory.
result Established Lipschitz continuity and Bochner-Eells-Sampson inequality.
TASC improves synthetic control for time-series data with trends.
problem Inability of existing SC methods to fully utilize temporal structure in time-series data.
method TASC uses a state-space model with a constant trend and Kalman filter for counterfactual inference.
result TASC offers advantages in settings with strong temporal trends and high observation noise.
Generates synthetic ECGs conditioned on clinical statements.
problem Privacy issues with sensitive health data.
method Combines diffusion models and structured state space models.
result SSSD-ECG outperforms GAN-based competitors in synthetic data quality.
Study extends null distance concept to Lorentzian length spaces for spacetime analysis.
problem Understanding spacetime convergence and topology in Lorentzian geometry.
method Extend null distance concept to Lorentzian length spaces, study Gromov-Hausdorff convergence.
result First results on compatibility of null distance with synthetic curvature bounds in warped product Lorentzian length spaces.
Synthetic framework for null hypersurfaces in non-smooth spacetimes.
problem Analyzing null hypersurfaces in non-smooth spacetimes.
method Develops synthetic null hypersurfaces using optimal transport and Lorentzian geometry.
result Synthetic null energy condition stabilizes under convergence and applies to low-regularity spacetimes.
Alexandrov spaces with non negative curvature and displacement convexity of the entropy tensormath.DG
Alexandrov spaces with non-negative curvature are characterized by the matrix displacement convexity of an entropy tensor.
problem Characterizing non-negative curvature in Alexandrov spaces
method Constructing a parallel trivialization of the entropy tensor
result The entropy tensor is matrix displacement convex on Alexandrov spaces
We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in [KS:17]. To this end, we introduce appropriate notions of geodesics and timelike geodesic completeness and prove a general inextendibility result. Our results shed new light on …
Systematization of Knowledge: Synthetic Assets, Derivatives, and On-Chain Portfolio Managementq-fin.GN
This paper systematizes knowledge on synthetic assets in crypto.
problem Disparate academic literature on synthetic assets in crypto.
method Broad perspective, general framework, data-driven analyses.
result Highlights risks and areas of research interest in synthetic assets.
Imbalanced Learning is an important learning algorithm for the classification models, which have enjoyed much popularity on many applications. Typically, imbalanced learning algorithms can be partitioned into two types, i.e., data level approaches and algorithm level approaches. In this paper, the focus is to develop a…
Equivalence found between smooth and synthetic timelike curvature bounds.
problem Understanding timelike sectional curvature bounds in spacetime geometry.
method Established equivalence between sectional curvature bounds on timelike planes and synthetic timelike bounds.
result Equivalence proved for sectional curvature bounds on timelike planes and synthetic timelike bounds on strongly causal spacetimes.
Timelike curvature and Brunn-Minkowski inequality linked in non-smooth spacetimes.
problem Equivalence between timelike Ricci curvature and Brunn-Minkowski inequality in synthetic Lorentzian spaces.
method Introducing strong -timelike Brunn-Minkowski condition and proving equivalence to curvature conditions.
result Timelike curvature dimension condition equivalent to timelike Brunn-Minkowski inequality in specific settings.
New method generates geolocated synthetic populations from real data.
problem Generating synthetic populations with explicit geographic coordinates.
method Mapping coordinates into a latent space using Normalizing Flows (NF), then combining with other features in a Variational Autoencoder (VAE).
result NF+VAE architecture outperforms existing methods in generating geolocated synthetic populations.
We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822
Optimal transport explored on a specific geometric space.
problem Optimal transport problem in sub-Lorentzian Heisenberg group.
method Synthetic metric spacetime structure analysis and sub-Lorentzian version of Brenier's theorem.
result Established sub-Lorentzian version of Brenier's theorem and derived Monge-Ampère equation.
New encoding improves volatility surface generation and risk management.
problem Generating accurate synthetic volatility surfaces from limited data.
method PCA variational auto-encoder model to encode surface descriptors into a latent space.
result Better scenario generation, volatility extrapolation, and direct stock surface inference.
In our [Higher-order preconnections in synthetic differential geometry of jet bundles, Beiträge zur Algebra und Geometrie, 45 (2004), 677-696] we have established the affine bundle theorem in the synthetic approach to jet bundles in terms of infinitesimal spaces Dⁿ's. In our succeeding [Synthetic differential geo…
Study the metric geometry of Cauchy hypersurfaces in spacetimes.
problem Properties of the space of Cauchy hypersurfaces.
method Equipped with a Hausdorff-type metric, studied completeness and local compactness.
result Generalized completeness results for spacetimes.
Bayesian algorithm discovers synthetic routes from target molecules.
problem Identifying synthetic routes from desired products.
method Bayesian inference and combinatorial optimization.
result Algorithm rediscovered 80.3% and 50.0% of known synthetic routes.
New method uses differential equations for better counterfactual analysis.
problem Estimating counterfactual outcomes for policy analysis.
method Continuous-time approach to synthetic controls using controlled differential equations.
result Improves counterfactual estimation for irregularly aligned multivariate time series.
Data Kernel Perspective Space Performance Guarantees for Synthetic Data from Transformer Modelscs.CL
DKPS provides guarantees for synthetic data from Transformer models, improving downstream tasks.
problem Lack of labeled data for building performant AI models.
method Data Kernel Perspective Space (DKPS) for mathematical analysis of synthetic data quality.
result Concrete statistical guarantees for the quality of transformer model outputs.
Extends field theory foundations to infinitesimal spaces, simplifying complex concepts.
problem Develop rigorous foundations for field theory, especially for infinitesimal spaces.
method Formulates local Lagrangian field theory in a new category of thickened smooth sets.
result Establishes a firm foundation for field theory, including tangent bundles and perturbative considerations.
We will study metric measure spaces beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE for which we prove the equivalence with sharp gradient estimates, the class of which will be preserved under…
CorGAN generates synthetic healthcare records while preserving privacy.
problem Generating realistic synthetic healthcare records while maintaining privacy.
method Combining Convolutional Generative Adversarial Networks and Convolutional Autoencoders to capture correlations between medical features.
result CorGAN generates synthetic data with performance similar to real data in various ML settings.
SMEs provide a transparent testbed for RL evaluation.
problem Lack of precise, white-box diagnostics in RL environments.
method Synthetic Monitoring Environments (SMEs) with fully configurable task characteristics and known optimal policies.
result SMEs allow for precise evaluation of RL algorithms, revealing the impact of specific environmental properties.
The paper studies moduli spaces of non-smooth metric structures with non-negative Ricci curvature.
problem Understanding moduli spaces of non-smooth metric structures with non-negative Ricci curvature.
method Relating convergence of RCD(0,N)-structures to their lifts, constructing Albanese and soul maps, proving their continuity, and constructing examples.
result Construction of moduli spaces with non-trivial rational homotopy groups.
Synthetic Petri Dish predicts neural architecture performance faster.
problem Expensive NAS evaluation process with ground-truth data.
method Instantiates motifs in small networks, evaluates with few synthetic samples.
result Significantly higher accuracy in predicting motif performance.
Uniformly Euclidean metrics with isolated singularities on certain manifolds are Ricci flat and have nonnegative synthetic Ricci curvature.
problem Proving the existence of Ricci flat metrics with isolated singularities on specific manifolds.
method Demonstrating nonnegative synthetic Ricci curvature using the RCD(0, n) condition.
result Uniformly Euclidean metrics with isolated singularities on are Ricci flat and extend smoothly over the singularity.
CTSyn generates high-quality synthetic tabular data.
problem Challenges in generating high-quality synthetic tabular data.
method Diffusion-based generative foundation model with autoencoder and conditional latent diffusion.
result CTSyn outperforms existing table synthesizers on standard benchmarks.
New rigidity theorem for sharp spectral gap in nonnegatively curved spaces.
problem Rigidity of sharp spectral gap in nonnegatively curved spaces.
method Mixing Sobolev theory and singular 1D-localization.
result Rigidity of in compact spaces.