arXiv research

The paper explores the geometry of level lines of quasiperiodic functions with many periods.

The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimization problems for functions of one variable over finite intervals. One of the main ideas in this paper is to use…

The paper optimizes insurance strategies for two collaborating business lines.

Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

This paper shows how path spaces on two-level manifolds can be Hilbert manifold structures.

We prove a result of Chern-Weil type for canonically metrized line bundles on one-parameter families of smooth complex curves. Our result generalizes a result due to J.I. Burgos Gil, J. Kramer and U. Kühn that deals with a line bundle of Jacobi forms on the universal elliptic curve over the modular curve with full leve…

I propose and briefly define the concept of Urban Isobenefit Lines by using functions as easy as efficient, whose results can offer a rich tool to use into spatial equilibrium analysis involving cities. They are line joining urban points with equal level of positional advantage from city amenities. The results which on…

The paper optimizes insurer's decisions on dividends, reinsurance, and capital injection under model uncertainty.

The paper optimizes insurer's dividend, reinsurance, and capital injection strategies for two collaborating business lines.

Any surface can be foliated into equipotential hypersurfaces of the level sets. A current result is that the contours are the progressing wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The lev…

Lorentzian distances to Cauchy surfaces fail to be locally equi-Lipschitz.

Accurately predicting drug responses to cancer is an important problem hindering oncologists' efforts to find the most effective drugs to treat cancer, which is a core goal in precision medicine. The scientific community has focused on improving this prediction based on genomic, epigenomic, and proteomic datasets measu…

We give a direct proof of a cancellation formula raised in [7] on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among these cancellation formulas are discussed.

We give a one parameter family of exceptional planar 5-webs. Each web is formed by four pencils of lines and by a foliation defined by the level curves of a function sn_k(x)sn_k(y) where sn_k denotes a Jacobi's elliptic function.

For $4 \nmid L$ and $g$ large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level $L$ structures. In particular, we determine the divisibility properties of the standard line bundles over these moduli spaces and we calculate the second integral …

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each …

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…

The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.

In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, decay to a linearize…

Low-cost water-level tracking using LTE power metrics and wavelet analysis.

The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…

This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including Gradient Descent, L-BFGS, Stochastic Gradient Descent, Conjugate Gradient, etc.), …

During a stock market peak the price of a given stock ($i$) jumps from an initial level $p_1(i)$ to a peak level $p_2(i)$ before falling back to a bottom level $p_3(i)$. The ratios $A(i) = p_2(i)/p_1(i)$ and $B(i)= p_3(i)/p_1(i)$ are referred to as the peak- and bottom-amplitude respectively. The paper show…

In this paper we analyze, evaluate, and improve the performance of training generalized linear models on modern CPUs. We start with a state-of-the-art asynchronous parallel training algorithm, identify system-level performance bottlenecks, and apply optimizations that improve data parallelism, cache line locality, and …

Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X. This establishes part of the Homological Mirror Conjecture for toric var…

Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.

The paper studies the metric and algebraic structures on section rings of projective manifolds.

Exploratory cancer drug studies test multiple tumor cell lines against multiple candidate drugs. The goal in each paired (cell line, drug) experiment is to map out the dose-response curve of the cell line as the dose level of the drug increases. We propose Bayesian Tensor Filtering (BTF), a hierarchical Bayesian model …

The paper introduces mortgage-rate-adjusted home prices to help buyers and adjust housing indices.

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of trapped, umbilical and extremal surfaces, which split into several different cla…

Motivated by a question of Rubel, we consider the problem of characterizing which noncompact hypersurfaces in $\RR^n$ can be regular level sets of a harmonic function modulo a $C^\infty$ diffeomorphism, as well as certain generalizations to other PDEs. We prove a versatile sufficient condition that shows, in particular…

New findings on hypersurfaces in Euclidean space that are both maximal and minimal.

Let $X$ be a compact connected orientable CR manifold with the action of a connected compact Lie group $G$. Under natural pseudoconvexity assumptions we show that the CR Guillemin-Strernberg map is Fredholm at the level of Sobolev spaces of CR functions. As application we study this map for holomorphic line bundles whi…

The paper constructs quantizations for symplectic manifolds with specific Laplacian properties.

The paper analyzes systemic risk in an insurance model with multiple business lines and heterogeneous claims.

Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.

The paper explores a B-field transform of complex structures on complex tori.

We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural requirements which we encode as algebraic constraints in a linear program. Our cluste…

Paper uses ML to predict insulator flashover risk.

The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid state physics, as a partial (nongeneric) case of Hamiltonian foliations of Fermi s…

Historical documents present many challenges for offline handwriting recognition systems, among them, the segmentation and labeling steps. Carefully annotated textlines are needed to train an HTR system. In some scenarios, transcripts are only available at the paragraph level with no text-line information. In this work…

Study helical motions of lines in 3D spaces, solving control problems.

Recent work has shown that Field-Programmable Gate Arrays (FPGAs) play an important role in the acceleration of Machine Learning applications. Initial specification of machine learning applications are often done using a high-level Python-oriented framework such as Tensorflow, followed by a manual translation to either…

A surface diffeo reversing orientation is isotopic to identity.

Unified benchmark for GLAD and GLOD methods across 35 datasets.

The study proves manifolds with specific curvature and volume properties always split off a line at infinity.

Holomorphic vector fields and anti-canonical divisors on complex manifolds are studied.