arXiv research

New Euclidean supersymmetric solutions found for a specific metric.

We prove a conjecture of Crapo and Penne which characterizes isotopy classes of skew configurations with spindle-structure. We use this result in order to define an invariant, spindle-genus, for spindle-configurations. We also slightly simplify the exposition of some known invariants for configurations of skew lines an…

Sharp inequalities found for orbifold metrics.

The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homology was initially suspected to be torsion-free, but we show in this pape…

We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.

New solutions of gravity from branes wrapped on orbifolds.

RED detects sleep EEG events using deep neural networks, outperforming previous methods.

Study efficient geodesics in curve complex using dot graphs.

In manufacture, steel and other metals are mainly cut and shaped during the fabrication process by computer numerical control (CNC) machines. To keep high productivity and efficiency of the fabrication process, engineers need to monitor the real-time process of CNC machines, and the lifetime management of machine tools…

We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices. For every such a structure we define multi-term distributive homology and show some of its properties. The main result is a complete formula for the homology o…

Background: Electroencephalography (EEG) monitors brain activity during sleep and is used to identify sleep disorders. In sleep medicine, clinicians interpret raw EEG signals in so-called sleep stages, which are assigned by experts to every 30s window of signal. For diagnosis, they also rely on shorter prototypical mic…

We prove that the degenerate part of the distributive homology of a multispindle is determined by the normalized homology. In particular, when the multispindle is a quandle $Q$, the degenerate homology of $Q$ is completely determined by the quandle homology of $Q$. For this case (and generally for two term homology of …

We establish a one-to-one correspondence between Finsler structures on the $2$-sphere with constant curvature $1$ and all geodesics closed on the one hand, and Weyl connections on certain spindle orbifolds whose symmetric Ricci curvature is positive definite and all of whose geodesics are closed on the other hand. As a…

Electroencephalography (EEG) during sleep is used by clinicians to evaluate various neurological disorders. In sleep medicine, it is relevant to detect macro-events (> 10s) such as sleep stages, and micro-events (<2s) such as spindles and K-complexes. Annotations of such events require a trained sleep expert, a time co…

In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controll…

Chatter detection has become a prominent subject of interest due to its effect on cutting tool life, surface finish and spindle of machine tool. Most of the existing methods in chatter detection literature are based on signal processing and signal decomposition. In this study, we use topological features of data simula…

The paper confirms a conjecture about convex bodies and their properties.

This thesis surveys various metrics on Riemann surface spaces.

Proves existence and uniqueness of weighted metrics for smooth spaces.

New Finsler metrics constructed from $GDW$-metrics.

In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case $\|β\|_α>1$ is provided, which is similar to the famous Bao-Robles-Shen's result for strongly convex Rand…

We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci metric and the perturbed Ricci metric and prove that the perturbed Ricci metric is a complete Kähler metric with bounded negative holomorphic s…

New metric defined for bounded symmetric domains.

Introduces Finslerian convolution metrics and their properties.

Survey of recent metric geometry in Kähler metrics space.

Study on geodesics of Finsler metrics derived from Riemannian metrics.

We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of Kähler metrics to the space of Riemannian metrics, and we study its geome…

New Kähler metrics generalize Calabi's and relate to Fano manifolds.

We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivati…

New Finsler metrics defined by Riemannian and 1-forms are studied.

Sharp estimates for Finsler metrics in convex domains.

Study on special Finsler metrics with conditions for Riemannian and isotropic properties.

The study examines Lee metrics on groups and their properties.

Survey of spectral, probabilistic, and deep metric learning methods.

Study shows convergence of Lagrangian submanifolds under certain metrics.

In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the classification of Einstein Riemannian metrics.

Defines a new Randers metric based on an existing one.

Study Kähler-Einstein metrics on singular varieties, proving metric completion properties.

Investigates O(n)-invariant metrics on SPD matrices, extending kernel metrics.

The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with general…

Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general $(α,β)$-metrics, which are defined by a Riemannian metric $α=\sqrt{a_{ij}(x)y^iy^j}$ and a $1$-fo…

Proposes a method to select fair performance metrics through metric elicitation.

In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In parti…

In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in $\boldsymbol{R}^3$ are Kossowski metrics, and t…

Study rough Riemannian metrics on manifolds, proving their connectedness and completeness.

Introduces new metric for Riemannian metrics, extending unbalanced optimal transport.

Generalizes Thurston's asymmetric metric to flat metrics.

In this paper, we study generalized Douglas-Weyl $(α, β)$-metrics. Suppose that an regular $(α, β)$-metric $F$ is not of Randers type. We prove that $F$ is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover by ignoring the regularity, if $F$ is not a Berwald met…