arXiv research

RAM extends attention-based mechanism for existence determination.

Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.

We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperb…

The paper establishes conditions for optimal sampling configurations on complex manifolds.

Study on 4-manifolds for special Kähler metrics with constant Ricci determinant.

New Gram determinant from Möbius band connects to annulus case.

The paper proves a generalized Kauffman-Harary conjecture for prime determinant links.

New examples show transverse knots are determined by their branched covers.

Calibrating a trading rule using a historical simulation (also called backtest) contributes to backtest overfitting, which in turn leads to underperformance. In this paper we propose a procedure for determining the optimal trading rule (OTR) without running alternative model configurations through a backtest engine. We…

Identifies special Lagrangian submanifolds in non-Kähler Calabi-Yau manifolds.

We consider the relations $\ge$ and $\ge_p$ on the collection of all knots, where $k \ge k'$ (respectively, $k \ge_p k'$) if there exists an epimorphism $πk \to πk'$ of knot groups (respectively, preserving peripheral systems). When $k$ is a torus knot, the relations coincide and $k'$ must also be a torus knot; we dete…

Proves existence and uniqueness of solutions to a complex equation with gradient term.

Conformally equivariant quantization is a peculiar map between symbols of real weight $δ$ and differential operators acting on tensor densities, whose real weights are designed by $λ$ and $λ+δ$. The existence and uniqueness of such a map has been proved by Duval, Lecomte and Ovsienko for a generic weight $δ$. Later, Si…

Study of complex structures on specific solvmanifolds, proving existence and non-existence results.

A semi-regular tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons surrounding the vertex. We determine combinatorial criteria for the existence, …

This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2…

The conformal anomalies and functional determinants of the Branson--GJMS operators, P_{2k}, on the d-dimensional sphere are evaluated in explicit terms for any d and k such that k < d/2+1 (if d is even). The determinants are given in terms of multiple gamma functions and a rational multiplicative anomaly, which vanishe…

Compact Lie group actions with a free point are determined by two vector fields.

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…

As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its Levi-Civita connection? It is shown that for a generic…

This paper presents results on the extent to which mean curvature data can be used to determine a surface in space or its shape. The emphasis is on Bonnet's problem: classify and study the surface immersions in $\R^3$ whose shape is not uniquely determined by the first fundamental form and the mean curvature function. …

Accounting frameworks follow stipulations of existing Accounting Theories. This exploratory research sets out to trace the evolution of accounting theories of Charge and Discharge Syndrome and the Corollary of Double Entry. Furthermore, it dives into the theories of Income Determination, garnishing it with areas of div…

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

Investigates special metrics in hypercomplex geometry.

A graph is apex if it can be made planar by deleting a vertex, that is, $\exists v$ such that $G-v$ is planar. We define the related notions of edge apex, $\exists e$ such that $G-e$ is planar, and contraction apex, $\exists e$ such that $G/e$ is planar, as well as the analogues with a universal quantifier: $\forall v$…

For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-trivial p-coloring with any number of colors, from the minimum to the maximum number of colors. Furthermore, for any rational link, we prove …

We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition proba…

Procedure groups nonparametric regression curves automatically.

We provide a short proof for the theorem that two compact Riemannian manifolds are isomorphic if and only there exists an order isomorphism which intertwines between the heat semigroups on the manifolds.

It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an arbitrary flat bundle E over the manifold (E is not required to be unimodular). The construction of this metric (called Poincare …

The study examines averages of Laplacian determinants over large genus moduli spaces.

In this paper we show how the existence of a certain stable cylinder determines (locally) the ambient manifold where it is immersed. This cylinder has to verify a {\it bifurcation phenomena}, we make this explicit in the introduction. In particular, the existence of such a stable cylinder implies that the ambient manif…

In this paper we examine the relationship between the length spectrum and the geometric genus spectrum of an arithmetic hyperbolic 3-orbifold M. In particular we analyze the extent to which the geometry of M is determined by the closed geodesics coming from finite area totally geodesic surfaces. Using a variety of tech…

Proves existence of Yamabe metrics on conical manifolds with conical points and links.

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.

We propose a robust risk measurement approach that minimizes the expectation of overestimation plus underestimation costs. We consider uncertainty by taking the supremum over a collection of probability measures, relating our approach to dual sets in the representation of coherent risk measures. We provide results that…

For any given number of crossings $c$, there exists a formula to determine the number of 2-bridge knots of $c$ crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and …

New approach to $Z$-stability and critical metrics on Kähler manifolds.

We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Herm…

Minimal normal curvature immersions in the unit ball studied.

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformall…

Improved bounds on volume-det inequality for links with many twists.

We investigate the Lawson genus $2$ surface by methods from integrable system theory. We prove that the associated family of flat connections comes from a family of flat connections on a $4-$punctured sphere. We describe the symmetries of the holonomy and show that it is already determined by the holonomy around one of…

A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in presence of a very restricted topology. We show that a warped product metric is formal if and only if the warping function is c…

Study ruled surfaces in 3D Riemannian manifolds, determining curvature and striction curves.

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms …

Two critical questions about intergenerational outcomes are: one, whether significant barriers or traps exist between different social or economic strata; and two, the extent to which intergenerational outcomes do (or can be used to) affect individual investment and consumption decisions. We develop a model to explicit…

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional nilmanifolds carrying an invariant half-flat structure.