Study constructs totally geodesic submanifolds in skew position.
problem Constructing totally geodesic submanifolds in skew position.
method Used Cartan representations of SO(3), SU(3), and Sp(3) to construct submanifolds. result Constructed totally geodesic submanifolds in complex quadrics, complex 2-Grassmannians, and quaternionic 2-Grassmannians.
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Improves binary classification from positive data with skewed confidence.
problem Skewed confidence in positive data affects the performance of Pconf classifiers.
method Parameterized model of skewed confidence and hyperparameter selection.
result Proposed method effectively cancels out the negative impact of skewed confidence.
There are some statistical anomalies in the Chinese stock market, i.e., positive return skewness, anti-leverage effect (positive returns induce higher volatility than negative returns); and reverse volatility asymmetry (contemporaneous return-volatility correlation is positive). In this paper, we first confirm the exis…
Model predicts jump risk premia influencing cryptocurrency futures and option performance.
problem Capturing asymmetric and time-varying skewness in cryptocurrency returns.
method Bivariate Hawkes process with positive and negative jump premia.
result Inferred jump risk premia predict futures cost of carry and option performance.
New method corrects skewed confidence for PbN classification.
problem Weakly supervised binary classification with biased negative data.
method Corrects skewed confidence in negative data to improve classifier.
result Reduces distortion in posterior probability for PbN classification.
We present extensive evidence that ``risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry,…
This paper analyzes the skewness of momentum trading strategies.
problem Understanding the skewness of momentum trading strategies.
method Examined linear and nonlinear momentum trading strategies, focusing on skewness.
result Skewness is generally positive and has a term structure.
Proposes a method to identify elements in a skewness matrix for multivariate skew-elliptical distributions.
problem Label switching issue in Bayesian estimation of skewness matrix.
method Imposes a positive lower-triangular constraint and uses Bayesian sparse estimation with horseshoe prior.
result Successfully estimates the true structure of skewness dependency.
This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has constant scalar curvature; and if it is …
Counterexample found to estimate for skew-symmetric tensors.
problem Estimate for skew-symmetric tensors was claimed and used for classification results.
method Analysis of the estimate in arXiv:2103.15482.
result Counterexample disproves the estimate for skew-symmetric tensors.
The paper studies geometries with parallel skew-symmetric torsion and their submersions.
problem Understanding geometries with parallel skew-symmetric torsion.
method Analyzing metric connections and submersions.
result Complete local classification of geometries with parallel skew-symmetric torsion in principal bundle cases.
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
Modified Jones-Faddy skew t-distribution captures asymmetry in stock returns.
problem Negative skew and positive mean in stock returns due to broken symmetry of stochastic volatility.
method Modified Jones-Faddy skew t-distribution applied to split gains and losses, using stochastic differential equations for stock returns and volatility.
result The modified distribution effectively captures the asymmetry in daily S&P500 returns, including its tails.
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
Develops a method to study implied volatility of exotic options and VIX skew.
problem Understanding the properties of implied volatility for exotic options and VIX skew.
method Uses Malliavin calculus techniques to describe the properties of at-the-money implied volatility (ATMI).
result Describes the short-term behavior of the ATMI of VIX and realized variance options in terms of the Hurst parameter.
Study of spheres and circles on a manifold with a specific metric structure.
problem Understanding geometric objects on a manifold with a skew-circulant structure.
method Analyzing hyper-spheres, spheres, and circles in a tangent space of a 4D manifold with a skew-circulant tensor structure.
result Characterization of geometric objects under an indefinite metric.
We study n-ary commutative superalgebras and L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their n-ary generalizations, commutative associative and Jordan algebras with an invariant form. We…
We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic to the twistor space of a quaternionic Kaehler manifold with …
Roy's `Safety First' criterion for selecting one risky asset from many is adapted to the case of non-normal returns, via Cornish Fisher expansion. The resulting investment objective is consistent with first order stochastic dominance, and is equal to the Sharpe ratio for the case of normal returns. An investor selectin…
Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.
problem Identifying the skewness in local logarithmic export distributions and its relationship with exporter and destination characteristics.
method Analyzing directed links weighted by the logarithm of export values, studying the skewness of local exports, and formulating quantitative relations.
result Non-zero skewness in local logarithmic export distributions changes with exporter and destination characteristics.
Unified approach to trend-following systems, deriving exact relationships and expected returns.
problem Designing and understanding trend-following systems in financial markets.
method Derive exact relationships, analyze expected returns, and use fractional ARFIMA processes.
result Profitability of trend-following systems depends on positive long-term autocorrelation and excess spectral mass at low frequencies.
Numerous methods for computing conformal mesh paramterizations has been developed due to the vast applications in the field of geometry processing. Spectral conformal parameterization (SCP) is one of these methods to computing a quality conformal parameterization based on the spectral technique. SCP focus on a generali…
New approximations for Value at Risk and Expected Shortfall accounting for kurtosis.
problem Approximating Value at Risk and Expected Shortfall with positive skewness and kurtosis.
method Extensions of the Normal Power Approximation incorporating skewness and kurtosis.
result Improved precision for various loss distributions.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.
problem Examining skewness and kurtosis measures for skew-elliptical distributions.
method Deriving exact expressions for skewness and kurtosis measures for skew-elliptical distributions, constructing test statistics, and comparing measures through simulations and real data analysis.
result Exact expressions and test statistics for skewness and kurtosis measures for various skew-elliptical distributions.
Study infinite Euclidean distance discriminants of algebraic varieties.
problem Understanding the structure of data points with infinitely many critical points in Euclidean distance correspondence.
method Developed computer code to compute discriminants and proved properties of fibers.
result Infinite Euclidean distance discriminants contain all data points with infinitely many critical points for the nearest-point problem.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, p…
Enhances knot counting invariant using skew braces.
problem Counting invariant for virtual knots and links.
method Introduces new invariants using skew brace structures.
result New invariants not determined by the counting invariant.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
Study on simplicity of Lie skew braces, proving new results for compact cases.
problem Simplicity of Lie skew braces, focusing on compact connected cases.
method Reviewing correspondence, investigating ideals and rigidity, proving main result for compact Lie skew braces.
result Compact connected simple Lie skew braces are either trivial or have simple underlying Lie groups.
RényiCL uses Rényi divergence for robust contrastive learning with stronger data augmentations.
problem Learning useful representations from multiple data views with hard augmentations.
method RényiCL employs Rényi divergence for contrastive learning, using a novel variational objective to manage hard negative sampling.
result RényiCL achieves better performance with stronger augmentations compared to other methods.
The study identifies a criterion for when stocks are not good investments, explaining it with a binomial tree model.
problem Determining when stocks are not good investments despite positive expected returns.
method A simple binomial tree model to explain the phenomenon of long-run asymmetry caused by skewed price distributions and volatility.
result The study finds that a certain ratio is a lower bound for when a stock is not a good investment, and empirical properties of this ratio are discussed.
The paper examines smoothness in graded skew Clifford algebras.
problem Smoothness of graded skew Clifford algebras.
method Investigation of differential smoothness.
result Results on the differential smoothness of graded skew Clifford algebras.
Simple method solves Quanto Skew problem.
problem Quanto Skew problem in Equities and FX.
method Analytical method that accommodates Equity and FX volatility skew.
result Highly efficient and fast performance.
Skewness dispersion predicts future stock market returns, especially in months with monetary policy announcements.
problem Predicting future stock market returns using skewness dispersion.
method Cross-sectional analysis of firm-level realized skewness and stock market returns.
result Skewness dispersion is a significant predictor of future stock market returns, robust to various estimation methods.
New topological biquandles created using skew braces.
problem Creating nontrivial topological biquandles.
method Using the concept of skew braces.
result Constructs nontrivial examples of topological biquandles.
Examines differential smoothness in a specific skew PBW extension family.
problem Differential smoothness in skew PBW extensions.
method Investigates a specific family of skew PBW extensions.
result Results on differential smoothness of the family.
New condition ensures submanifolds are skew in small areas.
problem Ensuring submanifolds are skew in Euclidean space.
method Introduces a third-order differential condition.
result Constructs improved totally skew embeddings for Rn. A skew brane is an immersed codimension 2 submanifold in affine space, free from pairs of parallel tangent spaces. Using Morse theory, we prove that a skew brane cannot lie on a quadratic hypersurface. We also prove that there are no skew loops on embedded ruled developable discs in 3-space. The paper extends recent wo…
This paper classifies 4D spin manifolds with skew Killing spinors.
problem Classifying 4D Riemannian spin manifolds with skew Killing spinors.
method Analyzing skew Killing spinors with skew-symmetric endomorphisms A, considering both degenerate and non-degenerate cases.
result In the degenerate case, the manifold is locally isometric to R x N with N having a skew Killing spinor.
Complete classification of quaternionic skew-Hermitian symmetric spaces found.
problem Classifying quaternionic skew-Hermitian symmetric spaces.
method Proving the existence of a torsion-free mSO∗(2n)mSp(1)-structure and showing that any homogeneous space is symmetric. result A complete classification of quaternionic skew-Hermitian symmetric spaces for arbitrary n>1. New RESK distributions improve robust clustering of skewed data.
problem Robustly clustering non-symmetric, heavy-tailed data clusters.
method Proposes RESK distributions and an EM algorithm with robust skew-Huber M-estimator.
result Numerical experiments confirm the effectiveness of the proposed methods.
Study refracted skew Brownian motion, find densities and asymptotics.
problem Modeling and analyzing refracted skew Brownian motion.
method Perturbation approach to find potential densities, transition density, and asymptotic behaviors.
result Expressions and asymptotic behaviors of refracted skew Brownian motion.
Following recent work by Ghomi, Solomon and Tabachnikov, we study geometry and topology of skew branes. A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any pair of distinct points are not parallel. We prove that if an oriented closed manifold has a non-zero Euler characterist…
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
The paper examines differential smoothness in skew PBW extensions over polynomial rings.
problem Differential smoothness in skew PBW extensions over polynomial rings.
method Investigation of skew PBW extensions over commutative polynomial rings.
result Results on differential smoothness for skew PBW extensions over polynomial rings.