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.
Unified understanding of neural representation similarity measures.
A new method matches similar regions in non-rigid shapes using spectra of differential operators.
New method uses Riemannian geometry to quantify molecular shapes.
New method uses Riemannian geometry to describe molecular shapes.
Coarse homotopy theory connects Euclidean cones to shape theory of compact spaces.
We show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. A similar result holds for tunnel number n manifolds. As a consequence, for fixed n, there are infinitely many hyperbolic tunnel number n manifolds with at most one exceptional Dehn filling. Thi…
Optimizes shapes of curves using Möbius energy gradients.
The study proves uniqueness and symmetry of self-similar solutions in warped product spaces.
Reward shaping is one of the most effective methods to tackle the crucial yet challenging problem of credit assignment in Reinforcement Learning (RL). However, designing shaping functions usually requires much expert knowledge and hand-engineering, and the difficulties are further exacerbated given multiple similar tas…
This paper proposes the adaptation of Support Vector Data Description (SVDD) to the multiple kernel case (MK-SVDD), based on SimpleMKL. It also introduces a variant called Slim-MK-SVDD that is able to produce a tighter frontier around the data. For the sake of comparison, the equivalent methods are also developed for O…
Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The formula is based on the fact that the space of similarity classes of triangles …
This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.
Left atrium shape has been shown to be an independent predictor of recurrence after atrial fibrillation (AF) ablation. Shape-based representation is imperative to such an estimation process, where correspondence-based representation offers the most flexibility and ease-of-computation for population-level shape statisti…
Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal transport can be used to model shapes in ways similar as with contours, while the Kanto…
Paper proves rigidity of certain 2D Lagrangian shapes in 4D space.
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
Proposes DILATE and STRIPE++ for precise time series forecasting.
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …
A horospherical torus about a cusp of a hyperbolic manifold inherits a Euclidean similarity structure, called a cusp shape. We bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp. The bounds are in terms of the change in structure in a neighb…
New framework classifies high-dimensional shapes using ray intersections, establishing data requirements.
This work is an extension of a result given by Kuttler and Sigillito (SIAM Rev :, ) on a star-shaped bounded domain in . Let be a star-shaped bounded domain in a hypersurface of revolution, having smooth boundary. In this article, we obtain a sharp lower bound for all Steklov eigenv…
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…
The paper proposes a new method for modeling and quantifying uncertainty in multiple closed curves.
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then, these invariants expressed by focal curvatures of the curve. And then, we give t…
The paper explores a new type of kernel using Wasserstein distance for better classification of shapes.
BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.
In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. We consider these curves in the framework of the similarity geometry and characterize them as invariant curves under the integrable flow on plane curves which is gov…
Rapid overlay of chemical structures (ROCS) is a standard tool for the calculation of 3D shape and chemical ("color") similarity. ROCS uses unweighted sums to combine many aspects of similarity, yielding parameter-free models for virtual screening. In this report, we decompose the ROCS color force field into "color com…
Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and -means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure b…
New measures link neural representation geometry to decoding ability.
New method estimates shape distance in neural representations with limited data.
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat -manifold , we show that the set of similarity classes of flat metrics on which occur as a cusp cross-section of a hyperbolic -orbifold is dense in the space of similarity classes of flat metri…
Improves functional linear regression with shape transfer learning.
Inner product-based convolution has been the founding stone of convolutional neural networks (CNNs), enabling end-to-end learning of visual representation. By generalizing inner product with a bilinear matrix, we propose the neural similarity which serves as a learnable parametric similarity measure for CNNs. Neural si…
New findings connect shaped and unshaped neural networks using differential equations.
TLRS improves predictive power of mined formulaic alpha factors.
We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds. Our method relies on studying the lower-star filtration induced by the eigenfunctions of the Laplacian. This gives us a shape descriptor that inherits the rich information encoded in the eigen…
Spaces with similar long paths have similar shapes.
New connection found between shape reconstruction methods and persistent homology.
New method groups similar functional covariates for better modeling.
New disks found with similar outer shapes.
This study improves sentence embeddings from BERT models.
I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…
This monograph describes a Riemannian geometric reduction approach to the three-body problem. The fundamental theorems are presented in the introductory part, whereas their proofs are provided in later chapters where specific topics are analyzed in more detail. The basic idea is to reduce the kinematic and dynamics of …
Chirality affects the curvature of molecular networks, influencing their shape and stability.
METASET selects diverse unit cells for efficient data-driven metamaterial design.
An anisotropic surface energy is the integral of an energy density that depends on the normal at each point over the considered surface, and it is a generalization of surface area. The minimizer of such an energy among all closed surfaces enclosing the same volume is unique and it is (up to rescaling) so-called the Wul…
A novel method compares 3D point clouds using information geometry.