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.
In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do \textbf{not} belong to. Let Y and Yˉ be the true and complementary labels, respectively. We first model the annotati…
In this note we study the Seifert rational homology spheres with two complementary legs, i.e. with a pair of invariants whose fractions add up to one. We give a complete classification of the Seifert manifolds with 3 exceptional fibers and two complementary legs which bound rational homology balls. The result translate…
Collecting labeled data is costly and thus a critical bottleneck in real-world classification tasks. To mitigate this problem, we propose a novel setting, namely learning from complementary labels for multi-class classification. A complementary label specifies a class that a pattern does not belong to. Collecting compl…
Complementary products recommendation is an important problem in e-commerce. Such recommendations increase the average order price and the number of products in baskets. Complementary products are typically inferred from basket data. In this study, we propose the BB2vec model. The BB2vec model learns vector representat…
Study relationships between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds.
problem Find a relationship between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds isometrically immersed in another Riemannian manifold.
method Establish an optimal inequality involving mixed scalar curvature and square of mean curvature.
result Optimal inequality that includes mixed scalar curvature and square of mean curvature.
Study on quaternionic contact structures with integrable complementary distribution.
problem Characterize quaternionic contact structures with integrable complementary distributions.
method Analyze positive definite quaternionic contact (4n+3)-manifolds, focusing on the integrable complementary distribution and its relationship with Sasaki and 3-Sasaki structures.
result Identify a new class of quaternionic contact structures with integrable complementary distributions that are not isomorphic to su(2).
We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.
Feature selection has attracted significant attention in data mining and machine learning in the past decades. Many existing feature selection methods eliminate redundancy by measuring pairwise inter-correlation of features, whereas the complementariness of features and higher inter-correlation among more than two feat…
In contrast to the standard classification paradigm where the true class is given to each training pattern, complementary-label learning only uses training patterns each equipped with a complementary label, which only specifies one of the classes that the pattern does not belong to. The goal of this paper is to derive …
The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to (M,L) and the corresponding objects associated to (M,L~), L=eσ(x)L being the Finsl…
This paper investigates the relationship between private and public investment in R&D, while taking into account the effect of several instruments policies such as subsidies and taxes. We design a new look of knowledge spillovers and R&D cooperation to explain the contribution of public and private R&D on growth. We pr…
The International Trade Network (ITN) is the network formed by trade relationships between world countries. The complex structure of the ITN impacts important economic processes such as globalization, competitiveness, and the propagation of instabilities. Modeling the structure of the ITN in terms of simple macroeconom…
This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in their utility. For simplicity, a model is presented with two first-price auctions …
Theorem converse to Jordan's curve theorem says that {\it if a compact set K has two complementary domains in R2, from each of which it is at every point accessible, it is a simple closed curve}. We show that the requirement of this theorem that {\it all} points of K were accessible from {\it both} complementa…
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…
An increasing sequence of integers is said to be universal for knots and links if every knot and link has a projection to the sphere such that the number of edges of each complementary face of the projection comes from the given sequence. This paper is an investigation into which sequences, either finite or infinite, a…
This paper studies the relationship between the classification performed by deep neural networks (DNNs) and the decision of various classical classifiers, namely k-nearest neighbours (k-NN), support vector machines (SVM) and logistic regression (LR), at various layers of the network. This comparison provides us with ne…
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior…