The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
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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.
168,657 papers · 148 categories
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48 results for “arbitrary shapes”
In 1998 Smoczyk [Smo98] showed that, among others, the blowup limits at singularities are convex for the mean curvature flow starting from a closed star-shaped surface in . We prove in this paper that this is true for the mean curvature flow of star-shaped hypersurfaces in in arbitrary …
Coarse homotopy theory connects Euclidean cones to shape theory of compact spaces.
problem Establishing connections between coarse homotopy theory and shape theory.
method Using pointed shape invariants and inverse mapping telescopes.
result Proving two compact spaces are strong shape equivalent if their Euclidean cones are coarsely homotopy equivalent.
A hierarchical clustering algorithm for data clouds without structure assumptions.
problem Exploring data clouds without making structure assumptions.
method Hierarchical topological clustering algorithm that infers persistence of outliers and clusters of arbitrary shape from data hierarchy.
result The algorithm can provide meaningful clusters in complex datasets.
The paper classifies affine hypersurfaces with symplectic structures and constraints on their curvature.
problem Characterizing affine hypersurfaces with symplectic structures and curvature constraints.
method Analyzing hypersurfaces with non-degenerate second fundamental forms and almost symplectic structures.
result The rank of the shape operator is at most one under certain conditions on the almost symplectic form.
Paper tackles shape graph registration using neural networks.
problem Constrained registration of shape graphs with varying nodes and edges.
method Shape-Graph Matching Network (SGM-net) with an elastic shape metric loss function.
result State-of-the-art matching performance and reduced computational cost.
New theorem proves convex bodies with specific curvature measures are rescaled Wulff shapes.
problem Characterizing convex bodies based on anisotropic curvature measures.
method Analyzing k-th anisotropic curvature measures and their relation to anisotropic perimeter.
result Arbitrary convex bodies with specific curvature measures are rescaled Wulff shapes.
Paper analyzes shapes of brain arterial networks using statistical methods.
problem Quantifying and comparing shapes of brain arterial networks.
method Mathematical representation of BAN shapes as elastic shape graphs, development of Riemannian metrics and geometrical tools.
result Age has a clear, quantifiable effect on BAN shapes, with increased variance in shapes as age increases.
We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of th…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather than inheriting it from pre-shape space, and using it to formulate a path energ…
Efficiently samples arbitrary compact bodies with polynomial complexity.
problem Uniform sampling from arbitrary compact bodies efficiently.
method Warm start algorithm under isoperimetry and volume growth condition.
result Substantial generalization of known results for convex and star-shaped bodies.
Efficient algorithm for sampling from arbitrary compact bodies.
problem Sampling from arbitrary compact bodies efficiently.
method Warm start algorithm with polynomial complexity.
result Substantial generalization of known results for convex and star-shaped bodies.
Bayesian nonparametric method partitions shapes using curves.
problem Capturing complex shapes in multi-dimensional data.
method Proposes a novel spline partitioning approach using curves.
result Demonstrates improved shape modeling compared to existing methods.
Proves higher regularity for anisotropic inverse mean curvature flow.
problem Higher regularity of solutions to anisotropic inverse mean curvature flow.
method Proves Harnack estimate and constructs smooth solutions from initial sets.
result Smooth solutions become smooth outside a compact set.
New framework classifies high-dimensional shapes using ray intersections, establishing data requirements.
problem Classifying high-dimensional shapes in real-world data.
method Ray-based classification (RBC) framework using intersections of one-dimensional representations (rays) with shape boundaries.
result Established bounds on the number of rays necessary for shape classification, defined by key angular metrics.
The problem of immersing a simply connected surface with a prescribed shape operator is discussed. From classical and more recent work, it is known that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space o…
A partial classification of type I singularities of the mean curvature flow in high codimensionmath.DG
The purpose of this article is to examine the possible shapes of type I singularities that form in the mean curvature flow of submanifolds of arbitrary codimension, assuming that the initial submanifold satisfies a particular curvature pinching condition.
New curvature measures characterize non-convex Wulff shapes in normed spaces.
problem Characterizing non-convex sets with curvature measures.
method Extending curvature measures to non-convex and non-smooth sets in normed spaces.
result Finite unions of disjoint Wulff shapes are the only sets with proportional curvature measures.
Learning Model Reparametrizations: Implicit Variational Inference by Fitting MCMC distributionsstat.ML
We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov chain Monte Carlo operation and a deterministic transformation that can be optimized…
Study shows limits of volume-constrained sets are finite unions of Wulff shapes.
problem Analyzing the behavior of sets with degenerating ellipticity.
method Proving rigidity of -accumulation points of volume-constrained almost-critical sets.
result Limits of volume-constrained sets are finite unions of -Wulff shapes.
The article derives integral formulas for foliated sub-Riemannian manifolds.
problem Integrating geometric concepts in Riemannian manifolds with foliations.
method Deriving integral formulas involving shape operators and curvature tensor.
result Generalizes results for foliated Riemannian manifolds and includes arbitrary functions.
The paper maps two types of hyperkähler manifolds and identifies their symplectic structures.
problem Mapping and identifying symplectic structures of two types of hyperkähler manifolds.
method Produced a map from star-shaped quiver varieties to Higgs bundle moduli spaces, verified stability, and showed it is a homeomorphism.
result Identified natural holomorphic symplectic structures on the two spaces.
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
New algorithms detect outliers in high-dimensional data with arbitrary shapes.
problem Challenges of high dimensionality and varying cluster shapes in traditional outlier detection methods.
method Cluster Catch Digraphs (CCDs) and their variants (U-MCCD, UN-MCCD, SU-MCCD, SUN-MCCD).
result U-MCCD efficiently identifies outliers with high true negative rates, and SU-MCCD improves handling of non-uniform clusters.
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…
Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape under the above restrictions. We prove that flexible polyhedral surfa…
Over-parameterized CNNs show U-shaped test risk with depth increase.
problem Understanding the impact of depth on test risk in over-parameterized CNNs.
method Empirical image classification experiments and linear regression framework.
result Test risk is U-shaped with increasing depth in over-parameterized CNNs.
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched t…
We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We sho…
We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrin…
Paper proposes MMC to avoid high-density bias in clustering.
problem High-density bias in density-based clustering.
method Introduces mass distribution as a better foundation for clustering, proposing mass-maximization clustering (MMC).
result MMC avoids high-density bias and discovers clusters of arbitrary shapes, sizes, and densities.
Napoleon in isolationmath.GT
Napoleon's theorem in elementary geometry describes how certain linear operations on plane polygons of arbitrary shape always produce regular polygons. More generally, certain triangulations of a polygon that tiles R^2 admit deformations which keep fixed the symmetry group of the tiling. This gives rise to isolation ph…
Study curvature-adapted submanifolds in semi-Riemannian Lie groups.
problem Understanding curvature-adapted submanifolds in semi-Riemannian Lie groups.
method Analyzing normal Jacobi operators and shape operators in terms of Lie bracket and bi-invariant metrics.
result Established a geometric interpretation of curvature adaptation in terms of left translations.
Weierstrass representation is a classical parameterization of minimal surfaces. However, two functions should be specified to construct the parametric form in Weierestrass representation. In this paper, we propose an explicit parametric form for a class of parametric polynomial minimal surfaces of arbitrary degree. It …
Paper uses VAEs to control IVS features for financial modeling.
problem Generating realistic IVSs with desired characteristics.
method Variational autoencoder architecture with controllable latent variables.
result Controlled generation of IVSs with specified features.
Introduces a new stationary GE-process for gold price analysis.
problem Analyzing gold price data with a flexible stationary process.
method Developed a new stationary GE-process with three parameters. Analyzed synthetic and real gold price data.
result Maximum likelihood estimators can be obtained for the unknown parameters.
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
problem Covariance estimation for random objects on Riemannian manifolds.
method Defines covariance and correlation via parallel transport.
result Proposed covariance is independent of coordinate choices.
We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However, precisely throwing arbitrary objects in unstructured settings presents many challenges:…
We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study of the geometry of G and a generalization of P. Pansu's thesis. In particular, we show that any such G is weakly commensurable to some simply connected solvable Lie group S, the Lie …
New algorithm broadens BART models applicability.
problem Limited applicability of Bayesian additive regression trees (BART) models due to conditional conjugacy.
method Introduces a reversible jump Markov chain Monte Carlo algorithm for generalized BART models.
result Extends BART models to arbitrary generalized BART models without conditional conjugacy.
A new distributed clustering framework using distributional kernel.
problem Clustering in distributed networks with arbitrary shapes, sizes, and densities.
method Distributed Clustering based on Distributional Kernel (KDC) using similarity of distributions.
result KDC guarantees equivalent clustering outcomes to centralized methods, reduces runtime, and discovers arbitrary clusters.
We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset in the sphere. One of the problems is the uniqueness of the tangent plane that minimizes the area for an arbitrary fixed subset. The other …
T-Basis represents neural network tensors with fewer parameters.
problem Efficiently representing neural network tensors with fewer parameters.
method T-Basis uses Tensor Rings to represent tensors in a neural network, parameterizing them with a small number of coefficients.
result T-Basis achieves high compression rates with minimal performance loss.
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitr…
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals. Optimal rates of detection are established for the three cases and rate-optimal detectors are constructe…
Stability of hypersurface immersions in Riemannian manifolds proved for perturbations.
problem Stability of isometric immersions of hypersurfaces in Riemannian manifolds under perturbations of their fundamental forms.
method Young measure approach, relaxation of energy, regularity result for immersions.
result Sequence of immersions converges to an isometric immersion with the reference shape operator.
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…
For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…