arXiv research

Open books constructed from Morse functions and divides are shown to be isotopic.

Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.

We consider a two-dimensional optimal dividend problem in the context of two branches of an insurance company with compound Poisson surplus processes dividing claims and premia in some specified proportions. We solve the stochastic control problem of maximizing expected cumulative discounted dividend payments (among al…

The paper finds local minimizers for obstacle avoidance on curved spaces.

QATS efficiently decodes HMMs with polylogarithmic complexity.

Four geometries govern sequential and distribution-free inference.

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the exp…

The paper proves Mabuchi solitons and constants on Fano admissible manifolds.

Paper provides criteria to detect non-admissible quandles via coloring.

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

New divide with gleams method simplifies symmetric link representation.

The paper characterizes links in 3D from divides with cusps.

Investigates admissible metrics on compact Kähler varieties and their stability.

New examples show deletion type admissible pairs can be rigid under rational saturation.

Topological obstructions to admissibility in $σ_k$-Loewner--Nirenberg problem

The paper proves Liouville rigidity for Hessian equations, characterizing geometric conditions for constant solutions.

This paper reveals hidden hyperbolic structures in divide links.

We give a method for constructing a shadowed polyhedron from a divide. The 4-manifold reconstructed from a shadowed polyhedron admits the structure of a Lefschetz fibration if it satisfies a certain property, which we call the LF-property. We will show that the shadowed polyhedron constructed from a divide satisfies th…

Starting from a divide, i.e. a generic immersion of finitely many copies of the interval [0,1] in the disk, we construct a classical link in the 3-sphere. We prove that the link's complement fibers over the circle, if the divide is connected. Moreover, we compute the monodromy diffeomorphism from the combinatorics of t…

New method to encode Weinstein 4-manifolds using multisections with divides.

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so-called fat graph, which we call the systolic graph. We study which fat graphs are systolic graphs for some surface (we call these admissible). There is a natural necessary condition on such grap…

Study on pre-Lie structures for semisimple Lie algebras over C.

Construct divide knots with specific genus properties.

I present a formula for the Casson invariant of knots associated with divides. The formula is written in terms of Arnold's invariants of pieces of the divide. Various corollaries are discussed.

Statistical tests for fairness in admissions data reveal hidden patterns.

Model predicts wound and episode-level readmission risk and time to re-admit.

Introduces admissible skein modules for non-semisimple categories.

The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this question has been a focus of considerable attention over the last twenty years. We…

Divides help construct fibered links from singularities.

The paper characterizes curves in pseudo-Galilean 4-space.

Divide-and-conquer method splits large data sets for efficient analysis.

In the present paper we determine the Thurston-Bennequin invariant of graph divide links, which include all closed positive braids, all divide links and certain negative twist knots. As a corollary of this and a result of P. Lisca and A.I. Stipsicz, we prove that the 3-manifold obtained from the 3-sphere by Dehn surger…

This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …

Innovative contact invariant derived from Heegaard Floer homology.

We prove that a potential $q$ can be reconstructed from the Dirichlet-to-Neumann map for the Schrodinger operator $-Δ_g + q$ in a fixed admissible 3-dimensional Riemannian manifold $(M,g)$. We also show that an admissible metric $g$ in a fixed conformal class can be constructed from the Dirichlet-to-Neumann map for $Δ_…

This paper classifies all admissible quotients of a surface braid group up to order 127.

We study the existence of weighted extremal Kähler metrics in the sense of Apostolov-Calderbank-Gauduchon-Legendre and Lahdili on the total space of an admissible projective bundle over a Hodge Kähler manifold of constant scalar curvature. Admissible projective bundles have been defined by Apostolov-Calderbank-Gauducho…

Combining forecasts of 16 ED causes improves accuracy and stability.

Deep network clusters hospital patients' vital signs.

Symmetric spaces' connections form Lie admissible triple algebras.

The study describes handle decompositions and Kirby diagrams for line arrangements.

In this paper we study the local behaviour of admissible metrics in the k-Yamabe problem on compact Riemannian manifolds $(M, g_0)$ of dimension $n\ge 3$. For $n/2 <k<n$, we prove a sharp Harnack inequality for admissible metrics when $(M,g_0)$ is not conformally equivalent to the unit sphere $S^n$ and that the set of …

In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space $G_3^1$. Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relatio…

We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible G-covers. This formula can be interp…

The article discusses extensions of Harish-Chandra's admissibility theorem.

We produce the first examples of closed, tight contact 3-manifolds which become overtwisted after performing admissible transverse surgeries. Along the way, we clarify the relationship between admissible transverse surgery and Legendrian surgery. We use this clarification to study a new invariant of transverse knots - …

This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.