arXiv research

Develops a method to identify nonproperness sets in likelihood-equation systems.

New proof classifies homogeneous 3-Sasakian and quaternionic Kähler manifolds.

In this article, relations between the root space decomposition of a Riemannian symmetric space of compact type and the root space decompositions of its totally geodesic submanifolds (symmetric subspaces) are described. These relations provide an approach to the classification of totally geodesic submanifolds in Rieman…

Study differential properties of matrix square roots in specific cases.

Tree++ graph kernel captures similarities at multiple granularities.

Polynomials' roots count tied to surface umbilics.

Automorphisms of Lie algebras and their root systems are fully lifted.

We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential varieties of homogeneous varieties already constructed. Our algorithms make no referenc…

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of compact type. As an application, we verify Sampson's conjecture in all cases for i…

The paper extends ternary algebra concepts using cube roots of unity.

New framework for root-cause analysis in complex CPSs using spatiotemporal graphical modeling.

We classify the systems of $T$-roots of the flag manifolds $M$ of the exceptional compact simple Lie groups with the second Betti number $b_2(M)\ge2$.

A novel method classifies shapes by their square-root velocity function.

Framework classifies urban congestion into recurrent and non-recurrent types.

Classifies G1 structures on flag manifolds using t-roots.

Let $C$ be a curve in a closed orientable surface $F$ of genus $g \geq 2$ that separates $F$ into subsurfaces $\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\widetilde{F_i}$, where $n=\l…

The paper explores feature selection for improving classification accuracy in event logs.

Continuity of roots of hyperbolic polynomials with smooth coefficients.

We introduce a remarkable subset "the stem" of the set of positive roots of a reduced root system. The stem determines several interesting decompositions of the corresponding reductive Lie algebra. It gives also a nice simple three dimensional subalgebra and a "Cayley transform". In the present paper we apply the above…

RAID algorithm detects anomalies in real-time IoT systems.

The paper explores how polynomial roots and operator eigenvalues change with parameters.

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, ω), where \gk is an appropriate regular subalgebra of the complex Lie algebra \gg^{C} associated to G and ωis a closed 2-form on \gk, such t…

This study applies old and new generations of panel unit root tests to test the validity of long-run real interest rate parity (RIP) hypothesis for ten Central and Eastern European Countries (CEECs) with respect to the Euro area and an average of the CEECs' real interest rates, respectively. When the panel unit root te…

Paper tackles anomaly detection and RCA in dynamical systems using ICODE Networks.

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usu…

Geometric models for Lie algebras from simple singularities.

Study of Hitchin map on specific Higgs bundles.

The study examines generalization bounds for regression and classification tasks on adaptive input domains.

Probability calibration trees improve accuracy of probability estimates.

Continuity of polynomial roots shown for varying coefficients.

A new deep metric learning method for defect classification in threaded pipe connections.

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-…

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are provided.

This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Mo…

Two families of $Sp(2,R)$ symmetric $G_2$ structures found in 7D.

Simplifies RCA for anomalies with separable likelihoods.

We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate is based on the interpretation of a suitable signed count of the lines as the Euler number of …

FID misaligns with human judgment due to reliance on ImageNet classes.

Paper establishes a universal growth rate for smooth surrogate losses in classification.

The study confirms that market volatility can be explained by correlated metaorders impacting prices in a square-root fashion.

In this paper, we determine the partial positivity(resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces. From the classifications of abstract root systems and maximal subsystems, we can give the calculations for symmetric spaces both in classical types and in exceptional types.

Logitron combines Perceptron and logistic loss for improved classification.

Anomaly detection aids in labeling fast-running processes for machine learning.

Transforms curves and surfaces for efficient geometric analysis.

Linear classifiers can resist adversarial attacks on Gaussian data.

Compact bilinear pooling approximates covariance features for faster training.

Study on Einstein metrics on specific homogeneous spaces.

We prove a conjecture due to Makanin: if a and b are elements of the Artin braid group B_n such that a^k=b^k for some nonzero integer k, then a and b are conjugate. The proof involves the Nielsen-Thurston classification of braids.