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 projection techniques reduce the frequency of projections in solving LCPs.
Study on Gauduchon manifolds finds metrics for projectively flat bundles.
In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a techn…
The paper studies knots in projective space using virtual link theory.
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In classification problems there are two general techniques using random projections. T…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is mainly exploited for the task of classification, this paper is developed to study th…
Geometric techniques reveal new insights into Gromov-Witten invariants.
Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic and real data.
The paper presents a practical method for evaluating investment projects using real options.
The paper classifies vector fields on 5D nilpotent Lie groups.
Sinh-acceleration speeds up B-spline option pricing.
We consider the problem of segmenting a large population of customers into non-overlapping groups with similar preferences, using diverse preference observations such as purchases, ratings, clicks, etc. over subsets of items. We focus on the setting where the universe of items is large (ranging from thousands to millio…
Entropy rigidity proven for 3D and higher convex projective manifolds.
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to…
This paper combines two classical theories, namely metric projective differential geometry and superintegrability. We study superintegrable systems on 2-dimensional geometries that share the same geodesics, viewed as unparametrized curves. We give a definition of projective equivalence of such systems, which may be con…
Develops an oblique projection technique to approximate a foliation for non-normal dynamics.
Model projection transfers convolutional network properties to feedforward networks.
In this paper, we explore the limitations of PCA as a dimension reduction technique and study its extension, projection pursuit (PP), which is a broad class of linear dimension reduction methods. We first discuss the relevant concepts and theorems and then apply PCA and PP (with negative standardized Shannon's entropy …
The paper updates SVD of evolving matrices using projection techniques.
A new method sorts projects using Quicksort and Bradley-Terry model for uncertain long-term benefits.
We show that a nonsingular complex projective variety admitting a holomorphic vector field with nonempty isolated zeroes, is rational using a key technique by Harvey-Lawson on finite volume flows. This statement was conjectured by J. Carrell. By the same technique, we obtain a uniform upper bound of Betti numbers of no…
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian as an ordinary differential equation. Our method is based on a moment m…
We determine that the deformation space of convex real projective structures, that is, projectively flat torsion-free connections with the geodesic convexity property on a compact 2-orbifold of negative Euler characteristic is homeomorphic to a cell of certain dimension. The basic techniques are from Thurston's lecture…
Classifies curves up to symplectic isotopy.
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is c…
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curv…
This paper analyzes and improves active learning techniques for real-world projects.
In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms…
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of information about the data. In this paper, we provide a computationally light way to extra…
Quantum cohomology gives a finite dimensional integrable system via the Dubrovin connection. Motivated by Givental's work on mirror symmetry, we use gauge theory techniques and the Frobenius Integrability Theorem to find flat sections for the Dubrovin connection. An explicit calculation is given for projective space.
The paper introduces DP algorithms using random projections and sign random projections for improved privacy in machine learning.
The paper proves a conjecture about the positivity of the Euler characteristic for complex projective manifolds.
Weil-Petersson volumes vary continuously with weighted points on a projective line.
Develops precise expressions for random projections for better machine learning tasks.
Paper solves robust multi-dimensional scaling with accelerated projections.
This work is the first part of a project dealing with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Verona. In particular, we develop an approach mainl…
Fixed points of Minkowski valuations are found in specific ball neighborhoods.
Paper introduces a new project control method using Monte Carlo and statistical learning.
In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing these definitions to depend on the problem / data at hand is a more natural app…
New algorithm reduces adaptive regret without projections.
A novel method reduces dimensionality for filtering SRNs with observed variables.
It is a well known result of Gromov that all manifolds of a given dimension with positive sectional curvature are subject to a universal bound on the sum of their Betti numbers. On the other hand, there is no such bound for manifolds with positive Ricci curvature: indeed, Perelman constructed positive Ricci metrics on …
Tensorized random projections reduce high-dimensional tensor size efficiently.
Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.
We introduce a method to produce bounds for the non secant defectivity of an arbitrary irreducible projective variety, once we know how its osculating spaces behave in families and when the linear projections from them are generically finite. Then we analyze the relative dimension of osculating projections of Grassmann…
Develops optimal low-dimensional approximations to high-dimensional SDEs.
Deployment of emerging technologies and rapid change in industries has created a lot of risk for initiating the new projects. Many techniques and suggestions have been introduced but still lack the gap from various prospective. This paper proposes a reliable project scheduling approach. The objectives of project schedu…