arXiv research

Survey of open problems in finite-dimensional integrable systems.

Survey of recent results on homogeneous finite-dimensional spaces.

Solves classical problem with Kähler-Einstein metrics in complex projective spaces.

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…

We show that a continuous local semiflow of $C^k$-maps on a finite-dimensional $C^k$-manifold M can be embedded into a local $C^k$-flow on M under some weak (necessary) assumptions. This result is applied to an open problem in [fil/tei:01]. We prove that finite-dimensional realizations for interest rate models are high…

The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.

We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of futures price curve models wh…

Infinite-dimensional polynomial diffusions preserve tractability of finite-dimensional counterparts.

The purpose of this paper is to study finite dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite dimensional equivariant moduli problem. In addition, we define a coindex for a G-vector bundle which is determined by t…

The paper extends lossy coding to nonlinear latent representations.

Researchers find a list of non-isometric toric para-Kaehler-Einstein manifolds.

This paper solves nonparametric estimation of continuous DPPs using kernel methods.

Separates estimation and control in risk-sensitive investment problems with partial observation.

Study improves learning algorithms for convex polyhedra in Hilbert spaces.

Study bounds financial path expectations using martingale distributions.

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…

Develops a finite construction for self-duality and related moduli spaces over Riemann surfaces.

Study local properties of homogeneous ANR-spaces, proving dimension full-valuedness.

New result on finite gerbes simplifies classification of certain bundles.

Paper finds conditions for finite-dimensional vector spaces of cross-sections.

The paper extends LDDMM framework to include Lie group actions in large deformation shape registration.

Classifies connections on central extensions and finds vanishing obstruction classes.

We prove that there is no faithful finite-dimensional representation by skew-hermitian matrices of a ``basic algebra of observables'' B on a noncompact symplectic manifold M. Consequently there exists no finite-dimensional quantization of any Lie subalgebra of the Poisson algebra C^\infty(M) containing B.

Finite-dimensional spaces of biharmonic functions on manifolds are explored.

Constructs blowup solutions for wave maps with specific symmetry.

We approximate the Sobolev discrepancy for finite dimensional kernels from samples.

Paper develops a finite dimensional approximation scheme for Riemannian manifolds.

Finite spaces can be or not coproducts of subspaces.

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.

The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.

Minimal Gaussian surface area is achieved by cones over a regular simplex for $m>3$ sets partitioning $R^n$.

Continuous selections for optimal portfolios under convex risk measures fail in finite-dimensional settings.

Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.

We study the problem asking if one can embed manifolds into finite dimensional Euclidean spaces by taking finite number of eigenvector fields of the connection Laplacian. This problem is essential for the dimension reduction problem in massive data analysis. Singer-Wu proposed the vector diffusion map which embeds mani…

We prove that any finite dimensional Alexandrov space with a lower curvature bound is locally Lipschitz contractible. As applications, we obtain a sufficient condition for solving the Plateau problem in an Alexandrov space considered by Mese and Zulkowski.

In this paper we study the problem of approximation of the $L^2$-topological invariants by their finite dimensional analogues. We obtain generalizations of the theorem of Lück, dealing with towers of finitely sheeted normal coverings. We prove approximation theorems, establishing relations between the homological invar…

We solve a linear equation on affine manifolds, finding finite-dimensional solutions.

We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asympt…

In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computa…

A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.

In this paper, we refine the notion of Z-boundaries of groups introduced by Bestvina and further developed by Dranishnikov. We then show that the standard assumption of finite-dimensionality can be omitted as the result follows from the other assumptions.

The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - μ(t_j))^2 + λ\int_a^b [μ"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The minimization is taken over an infinite-dimensional function space, the space of all functions wi…

New bounds for adaptive control in high dimensions without fixed state space.

We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of measures of entanglement.

In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian.

We show that groups satisfying Kazhdan's property (T) have no unbounded actions on finite dimensional CAT(0) cube complexes, and deduce that there is a locally CAT(-1) Riemannian manifold which is not homotopy equivalent to any finite dimensional, locally CAT(0) cube complex.

This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.

Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of…