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.
New method for robust trajectory classification without parameters.
Estimates multiple means in high dimensions using convex combinations.
In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of Möbius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.
We determine all Chern numbers of smooth complex projective varieties of dimension at least four which are determined up to finite ambiguity by the underlying smooth manifold. We also give an upper bound on the dimension of the space of linear combinations of Chern numbers with that property and prove its optimality in…
In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. We give a complete answer to this question in small dimensions, and also prove partial results without restrictions on the dimension.
Combining Kulpa's proof of the cubical Sperner lemma and a dimension theoretic idea of van Mill we give a very short proof of the invariance of dimension, i.e. the statement that cubes [0,1]^n, [0,1]^m are homeomorphic if and only if n=m. This note is adapted from lecture notes for a course on general topology.
Proves mass theorem up to dimension 19 using symmetrization and singularity techniques.
New approach combines geometric and probabilistic methods to estimate manifold dimension in high-dimensional data.
RMFGP combines multi-fidelity models for efficient uncertainty quantification.
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For dimensional manifolds, our results include the gravitational anomaly cancellation formulas of Alvarez-Gaumé and Witten in dimensions 2, 6 and 10 (\cite{AW}) as special cases. …
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmet…
New algorithm combines new and historical data with different input dimensions for linear regression.
Improves MARS for nonparametric multivariate regression with dimension reduction.
We determine the minimal volume of arithmetic hyperbolic orientable n-dimensional orbifolds (compact and non-compact) for every odd dimension n>3. Combined with the previously known results it solves the minimal volume problem for arithmetic hyperbolic n-orbifolds in all dimensions.
The paper shows how to recover true node positions from a graph or similarity matrix.
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the covariates. The estimated linear combinations include all covariates, making res…
Extends positive mass theorem to arbitrary dimensions using a new inductive scheme.
Quantum codes with optimal distance and dimension for n-dimensional space.
Improved bounds on combining hypothesis classes for binary functions.
We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three we prove that only multiples of the top Chern number, which is the Euler …
In the covariate shift learning scenario, the training and test covariate distributions differ, so that a predictor's average loss over the training and test distributions also differ. In this work, we explore the potential of extreme dimension reduction, i.e. to very low dimensions, in improving the performance of imp…
Proves existence of manifolds with Kervaire invariant one in specific dimensions.
We prove a homological stability theorem for moduli spaces of manifolds of dimension , for attaching handles of index at least , after these manifolds have been stabilised by countably many copies of . Combined with previous work of the authors, we obtain an analogue of the Madsen--Weiss theorem …
The paper studies the dimension of limit sets using variational principles and stationary measures.
New method estimates Gaussian vector functions more efficiently.
It is known that by dualizing the Bochner-Lichnerowicz-Weitzenböck formula, one obtains Poincaré-type inequalities on Riemannian manifolds equipped with a density, which satisfy the Bakry-Émery Curvature-Dimension condition (combining a lower bound on its generalized Ricci curvature and an upper bound on its generalize…
Study confirms equivalence in Heisenberg groups between curvature-dimension conditions and strong Brunn-Minkowski inequalities.
Proposes a neural network for handling multi-sensor time series with varying input dimensions.
New bounds found for vertices of hyperbolic polyhedra in dimensions 5 to 12.
Combines OT and PCA for DR, preserving clusters.
We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of hyperbolic n-space, satisfying a natural condition on their parabolic subgroups, t…
Semi-supervised learning improves classification in high dimensions.
New classification for higher-dimensional shrinking Ricci solitons with positive isotropic curvature.
Consensus dimension reduction combines multiple visualizations to identify shared patterns.
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m_1+m_2-1 in the product X:=X_1^{m_1} times X_2^{m_2} of two Hadamard manifolds X_i^{m_i} of dimension m_i with pinched negative curvature. Combining this result with a Theore…
This paper consists of two parts. In the first part we show that in odd dimension, as well as in even dimension below the critical weight (i.e. half the dimension), the logarithmic singularities of Schwartz kernels and Green kernels of conformal invariant pseudodifferential operators are linear combinations of Weyl con…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimens…
Paper improves differential privacy in sparse Gaussian process models.
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
Researchers prove no unexpected relations between complex manifold numbers.
Generative model combines multi-dimensional annotations for more accurate ground truth estimation.
Variational method for eigenvalues on manifolds.
Training neural networks is hard in fixed dimensions.
The study provides a basis for a 3-manifold's skein module, answering its dimension.
We examine the algebraic and geometric properties of a uni-directional GRU and word embeddings trained end-to-end on a text classification task. A hyperparameter search over word embedding dimension, GRU hidden dimension, and a linear combination of the GRU outputs is performed. We conclude that words naturally embed t…
A new covariance estimator reduces dimensionality in high-dimensional undersized samples.
Neural networks adapt to any input dimensionality.