Expanded Legendrian knot atlas for 10-arc index knots.
problem Lack of Legendrian knot data for knots with high arc index.
method Created an atlas of Legendrian knots up to arc index 10.
result Legendrian knots of arc index 10 have been cataloged.
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48 results for “atlas”
Identification of Atlas modelsq-fin.MF
Atlas models are systems of Ito processes with parameters that depend on rank. We show that the parameters of a simple Atlas model can be identified by measuring the variance of the top-ranked process for different sampling intervals.
This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.
problem Identifying precise mouse brain microscopy images from the Allen atlas.
method Siamese Networks with contrastive learning to find corresponding atlas plates for partial images.
result Siamese CNNs achieved 25% TOP-1 and 100% TOP-5 accuracy in identifying brain slices from the Allen atlas.
Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest; and positiv…
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Generative models learn manifold structure; new approach uses atlas and geodesic interpolation.
problem Challenges in representing manifolds with topology different from Euclidean space.
method Atlas Generative Models (AGMs) with hybrid latent spaces and geodesic interpolation.
result Geodesic interpolation can be extended to AGMs, improving manifold representation.
ATLAS adapts HMC step size and trajectory length for complex geometries.
problem Sampling complex geometries with constant step size HMC/NUTS.
method Adapts step size and trajectory length using local Hessian and no U-turn condition.
result ATLAS accurately samples complex geometries, outperforming NUTS.
An atlas of Legendrian knotsmath.SG
We present an atlas of Legendrian knots in standard contact three-space. This gives a conjectural Legendrian classification for all knots with arc index at most 9, including alternating knots through 7 crossings and nonalternating knots through 9 crossings. Our method involves a computer search of grid diagrams and app…
New brain atlas method improves classification accuracy.
problem Creating accurate brain atlases from connectomes.
method Connectivity-based hierarchical clustering and consensus aggregation.
result Consensus parcellation outperforms existing atlases in classification tasks.
Study identifies key brain regions and model architectures for ASD diagnosis.
problem Subjective and time-consuming ASD diagnosis by clinicians.
method Comparative analysis of model architectures and atlas granularities.
result High-performing models use 2-4 hidden layers and 16-64 neurons per layer, and cerebellum is predictive of ASD.
Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLASmath.ST
ATLAS separates invariant and transferable latent factors across diverse environments.
problem Transfer learning and robust prediction in heterogeneous environments.
method ATLAS leverages invariance principle to disentangle latent factors and uses auxiliary labels for robust prediction.
result Near-oracle performance and robust transferable prediction in new environments.
Busemann G-spaces with Finsler metrics
problem Admitting a differentiable DC atlas with a continuous Finsler metric
method Comparison geometry
result Generalizes previous work on G-spaces with Riemannian curvature bounds
Hybrid Atlas modelsmath.PR
We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of …
Predict and classify brain image evolution trajectories from a single MRI timepoint.
problem Diagnosing early mild cognitive impairment (eMCI) from a single MRI scan.
method Supervised and unsupervised learning frameworks that predict and label intensity patch evolution trajectories from a baseline MRI.
result Classification accuracy increased by up to 10% points compared to single timepoint-based methods.
ATLAS uses LLMs to adaptively trade by optimizing prompts and coordinating agents.
problem Adapting LLMs for real-time financial decision-making in noisy markets.
method ATLAS integrates structured market data, uses Adaptive-OPRO for prompt optimization, and employs multi-agent coordination.
result Adaptive-OPRO consistently outperforms fixed prompts in financial trading.
Autoencoding topologystat.ML
Generative models use autoencoders to learn manifold structures.
problem Learning a manifold structure on datasets.
method Adversarial/Wasserstein autoencoders for deep neural networks.
result Atlas of a manifold formed from dimensionality reduction and fuzzy clustering.
New HDP-HMM model accurately segments Internet path delays.
problem Automating the statistical analysis of large-scale network delay measurements.
method Infinite Hidden Markov Model (HDP-HMM) for trace segmentation.
result The HDP-HMM model performs as well as human cognition in pattern recognition.
Paper finds essential regularity in singular connections.
problem Determining if singularities in connections are removable or essential.
method Introduces RT-equations and a procedure to lift connections to essential regularity.
result A computable procedure to lift connections to essential regularity.
New method improves Gaussian process regression on complex, sparse point clouds.
problem Traditional Gaussian processes struggle with restricted domains and point clouds.
method Atlas Gaussian Processes (RC-AGPs) combining heat kernel and RBF kernels.
result RC-AGPs outperform existing methods in regression accuracy.
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold of linear subspaces of dimension in which avoids the use of equivalence classes. The set $\mathbb{…
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is …
New coordinates show Toda flow is Morse-Smale.
problem Toda flow on full flags of Lie algebras.
method Introduced atlas and local coordinates.
result Toda flow on full flags is Morse-Smale.
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of companies grows to infinity. Then, we discuss the long-term capital distribution. We r…
Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, which are based on a gravity model predicting the existence of significant trade channel…
SM-netFusion estimates brain network atlas by considering multiple topological measures.
problem Limited BNA estimation methods that overlook topological measures and lack discriminative power.
method Supervised multi-topology network cross-diffusion framework using degree, closeness, and eigenvector centrality measures.
result SM-netFusion produces more centered and representative templates, and improves classification accuracy.
We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.
Atlas dataset categorizes clothing products with high accuracy.
problem Lack of real-world datasets for e-commerce clothing product categorization.
method Collected and labeled a dataset of 186,150 images, established a benchmark for image classification and sequence models.
result Benchmark model achieved a micro f-score of 0.92.
Robust RL with learned optimal adversary improves agent performance under adversarial state observations.
problem Ensuring reinforcement learning agents' robustness against adversarial perturbations of state observations.
method Proposed a framework of alternating training with learned adversaries (ATLA) to find optimal adversarial policies and enhance agent robustness.
result ATLA achieves state-of-the-art performance under strong adversaries in continuous control environments.
New method defines Gysin maps for stratified spaces, preserving signatures.
problem Defining and preserving signatures in stratified spaces.
method Smooth atlas stratified spaces, fiber bundles, Gysin maps, KK-theory.
result Gysin maps preserve analytic signature classes of Witt spaces.
We generalize geometric prequantization of symplectic manifolds to differentiable stacks. Our approach is atlas-independent and provides a bijection between isomorphism classes of principal circle bundles (with or without connections) and second cohomology groups of certain chain complexes.
An (flat) affine -manifold is a -manifold with an atlas of charts to an affine space with transition maps in the affine transformation group . Equivalently an affine -manifold is a -manifold with a flat torsion-free affine connection. We show that a closed affine -mani…
Conjectures on the Khovanov Homology of Torus Knots, Twist Knots, and Legendrian Simple Knotsmath.GT
The paper conjectures Khovanov homology can distinguish torus and twist knots.
problem Detecting and distinguishing knots using Khovanov homology.
method Examining all prime knots with up to 20 crossings, conjecturing Legendrian simplicity.
result Numerical evidence supports Khovanov homology distinguishing torus and twist knots.
A new framework enhances generative modeling by learning local flows over complex manifolds.
problem Limited expressivity of current normalizing flows for low-dimensional manifolds.
method Vector quantized local normalizing flows (VQ-Flows) using a VQ-AE atlas and conditional flows.
result Enhanced modeling of complex data distributions over manifolds.
In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth st…
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms. Graded bundles are graded manifolds in the sense that we can choose an atlas whose…
Diagonalizes metrics of 3D Lorentzian manifolds.
problem Diagonalizing metrics of 3D Lorentzian manifolds.
method Applying the technique of moving frames.
result Every smooth Lorentzian 3-manifold admits an atlas with a diagonal metric.
For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geomet…
Generalizes soft noncommutative schemes to flag varieties.
problem Applying soft noncommutative schemes to flag varieties.
method Generalization via toric geometry and distinguished affine charts.
result Soft noncommutative schemes can be applied to flag varieties.
Spark complexes defined on good effective orbifold atlases.
problem Constructing a structured representation for effective orbifolds.
method Defining good atlases and constructing spark complexes categorically.
result Spark character 2-functor factors through the constructed 2-functor.
We consider (local) parametrizations of Teichmuller space (of genus hyperbolic surfaces with boundary components) by lengths of geodesics. We find a large family of suitable sets of geodesics, each set forming a special structure called "admissible double pants decomposition". For …
New GPU-based algorithm for fast optimal transport on brain tractograms.
problem Efficiently comparing and transferring labels in brain tractograms.
method Multiscale algorithm using Sinkhorn divergences on GPU.
result Smooth assignments for label transfer in tractograms.
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on varying geometrical supports. Analysing variability of fshapes' ensembles requir…
New bridge between diffeology and noncommutative geometry.
problem Connecting diffeology and noncommutative geometry.
method Embedding quasifolds into diffeology and associating C*-algebras.
result Morita classes of C*-algebras associated with diffeomorphic quasifolds.
New method clusters disease subtypes from model explanations.
problem Discovering disease subtypes in noisy, high-dimensional data.
method Train classifier, extract explanations, cluster in explanation space.
result Cluster analysis on model explanations outperforms classical methods.
Axel Seeliger tabulated ribbon knots and found non-symmetric examples.
problem Identifying non-symmetric ribbon knots.
method Tabulated symmetric union presentations and band diagrams for ribbon knots.
result Found non-symmetric ribbon knots with 11 and 12 crossings.
We consider the question of which virtual knots have finite fundamental medial bikei. We describe and implement an algorithm for completing a presentation matrix of a medial bikei to an operation table, determining both the cardinality and isomorphism class of the fundamental medial bikei, each of which are link invari…
Proves embedding theorem for definable manifolds.
problem Embedding abstract-definable manifolds into Euclidean space.
method Proves Whitney embedding theorem for definable manifolds.
result Abstract-definable manifolds are embedded into .
Let be an even-dimensional pseudo-Finsler manifold. We construct an almost hypercomplex structure on any chart domain of a certain atlas of by using a considered non-linear connection. Then by using the almost hypercomplex structure we define two new families of Finsler connections. Also w…