arXiv research

A simpler edge-based discretization method without dual volumes.

We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partia…

We study non-linear sigma models whose target spaces are the Higgs phases of supersymmetric SO and USp gauge theories by using the Kahler and hyper-Kahler quotient constructions. We obtain the explicit Kahler potentials and develop an expansion formula to make use of the obtained potentials from which we also calculate…

Variance plays a crucial role in risk-sensitive reinforcement learning, and most risk measures can be analyzed via variance. In this paper, we consider two law-invariant risks as examples: mean-variance risk and exponential utility risk. With the aid of the state-augmentation transformation (SAT), we show that, the two…

The method approximates stationary distributions of Markov models by truncating irrelevant states.

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout …

Study optimal periodic dividend strategies for risky businesses with transaction costs.

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. …

Let $Σ$ be a compact Riemann surface and $\h_{d,k}(Σ)$ denote the space of degree $d\geq 1$ holomorphic maps $Σ\ra \CP^k$. In theoretical physics this arises as the moduli space of charge $d$ lumps (or instantons) in the $\CP^k$ model on $Σ$. There is a natural Riemannian metric on this moduli space, called the $L^2$ m…

Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.

An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually directly related to the degree of clustering of large fluctuations within the financial…

The paper introduces a new insurance pricing model based on driving mileage.

Insurance companies often include very long-term guarantees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (G.A.O), the insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rated when the policy matures. Both …

The group SU(2)*SU(2) acts naturally on SL(2,C) by simultaneous right and left multiplication. We study the Kahler metrics invariant under this action using global Kahler potentials. The volume growth and various curvature quantities are then explicitly computable. Examples include metrics of positive, negative and zer…

Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a…

Dataset for rainfall modeling in central Europe from 1981-2011.

Bayesian model updating uses VAEs to approximate likelihood with small data.

Estimates returns for dollar cost averaging using geometric Brownian motion.

Study a continuous-time PA problem with private effort and consumption decisions.

While a user's preference is directly reflected in the interactive choice process between her and the recommender, this wealth of information was not fully exploited for learning recommender models. In particular, existing collaborative filtering (CF) approaches take into account only the binary events of user actions …

This paper examines the optimal annuitization, investment and consumption strategies of a utility-maximizing retiree facing a stochastic time of death under a variety of institutional restrictions. We focus on the impact of aging on the optimal purchase of life annuities which form the basis of most Defined Benefit pen…

Framework for imputing missing heart data to simulate brain-heart interactions.

Optimal healthcare investment timing in a dynamic model with mortality risk.

A machine learning model for PMD compensation in dual-polarization systems.

Researchers develop methods to reduce simulation costs for cardiovascular modeling.

Study optimal liquidation with incomplete trend information and multiplicative price impact.

The paper clarifies long-horizon investment and DCA, showing no risk reduction but different exposure profiles.

Physics-based framework improves building energy forecasting.

Speaker verification (SV) systems using deep neural network embeddings, so-called the x-vector systems, are becoming popular due to its good performance superior to the i-vector systems. The fusion of these systems provides improved performance benefiting both from the discriminatively trained x-vectors and generative …

Paper transforms torse-forming vector fields into simpler forms.

Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the…

New pushforward operation on vector pseudo-bundles creates new examples.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Characterizes spacetimes using doubly torqued vectors.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

Abstract: Generalizes multisymplectic forms to vector-valued versions.

The paper bounds the mean absolute error in DNN vector-to-vector regression.

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields. (ii) Horizontal and vertical vector fields are naturally isomorphic to smooth famil…

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

SVM generalizes well even with many support vectors in high dimensions.

Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.

Classifies equivariant vector bundles over toric manifolds.

We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove that any $n$-fold vector bundle admits a non-canonical isomorphism to a decomposed …