arXiv research

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

New result on finite gerbes simplifies classification of certain bundles.

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

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…

Survey of recent results on homogeneous finite-dimensional spaces.

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

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.

Categorifies Stokes coefficients in Chern-Simons theory models.

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…

We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical for…

Paper develops a finite dimensional approximation scheme for Riemannian manifolds.

Finite spaces can be or not coproducts of subspaces.

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

Upper bound for Hausdorff distance between hyperbolic space and its medianization.

Paper introduces FNM framework for learning finite-dimensional parametrized models.

Extends SGM to functional spaces for multimodal data.

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.

Infinite dimensional measure-valued processes modeled as polynomial diffusions.

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 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 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.

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…

Study minimal networks on spheres and balls near standard metrics.

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.

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…

We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues of exponential family distributions and their canonical conjugate priors. This c…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…

In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of c…

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

Simplified Ricci curvature for spherical fluid dynamics models.

Lie's third theorem proven for Lie ∞-algebras.

The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference "Finite-dimensional Integrable Systems, FDIS 2017" held at CRM, Barcelona in July 2017.

The paper explores mapping class groups and their quantum field theory representations.

The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.

The study connects Kato bounds to finite-dimensional RCD spaces.

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(ν_q)}$, that is known to linearize the Wasserstein $W_2$ distance and plays a fundamental role in the dynamic formulation of…

In this paper we consider the complex vector spaces of holomorphic cross-sections of homogeneous holomorphic vector bundles over elliptic adjoint orbits, and provide a sufficient condition for the vector spaces to be finite dimensional in view of root systems.

Study shows Roller compactification's median graph has limited asymptotic dimension.

We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero et al. (2012) and Filipovic and Larsson (2016) is transferred to this infinite …

We introduce a class of regularisable infinite dimensional principal fibre bundles which includes fibre bundles arising in gauge field theories like Yang-Mills and string theory and which generalise finite dimensional Riemannian principal fibre bundles induced by an isometric action. We show that the orbits of regulari…

Unified formula for higher traces of linear maps on finite-dimensional normed spaces.

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

The paper solves integrable systems of PDEs, including famous equations.

Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep network is expressed using a highly non-convex finite-dimensional model, and thus th…

Classifies vector field algebras in complex space.