arXiv research

This paper classifies instantons with closed reductions and provides examples of non-closed reductions.

Reduces energy for 4D submanifolds in R^n.

In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the torus.

In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in LP_d. We introdu…

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generali…

Algebraic treatment of connection reduction over a special disc.

New method linearizes Darboux transformations of discrete curves.

Introduces generalized moment maps for almost Hermitian settings.

Paper shows spectra can't distinguish naturally reductive manifolds.

The paper proves rigidity theorems for forms on reductive symmetric spaces.

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-com…

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

We prove a generalization of a theorem of Borel-Harish-Chandra on closed orbits of linear actions of reductive groups. Consider a real reductive algebraic group $G$ acting linearly and rationally on a real vector space $V$. $G$ can be viewed as the real points of a complex reductive group $G^\mathbb C$ which acts on $V…

Geometrically reduces Hamiltonian systems using particular integrals.

We describe an action of $U(1)\times Sp(1)$ on $HP^7$ that allows to obtain a $Z_2$-quotient of CAYLEY (the Grassmannian of oriented 4-planes in $R^8$ closed under the three-fold cross product) by quaternionic Kähler reduction.

A new algebraic structure emerges from reductive homogeneous spaces.

Optimizes variance reduction in Heston model using large and moderate deviations.

In this article, we give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of Lie groups defined by T.Robart [13], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem…

We prove the first nontrivial worst-case lower bounds for two closely related problems. First, $Ω(n^{3/2})$ degree-1 reductions, series-parallel reductions, and $Δ$Y transformations are required in the worst case to reduce an $n$-vertex plane graph to a single vertex or edge. The lower bound is achieved by any planar g…

In order to use the technique of dimensional reduction, it is usually necessary for there to be a symmetry coming from a group action. In this paper we consider a situation in which there is no such symmetry, but in which a type of dimensional reduction is nevertheless possible. We obtain a relation between the Coupled…

This work extends reduction processes for nonholonomic discrete mechanical systems.

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space wh…

Study surjectivity of Kirwan map for generalized hyperkähler reduction.

Efficiently reduces rank of non-negative matrices with quadratic time complexity.

A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric…

New algorithm balances spatial data approximation and prediction accuracy.

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where ba…

We find three characterizations for a multidimensional (n+1)-web W possessing a reduct reducible subweb: its closed form equations, the integrability of an invariant distribution associated with W, and the relations between the components of its torsion tensor. In the case of codimension one, the latter criterion estab…

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifol…

For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kaehler space. This notion es…

Paper proposes a tensor data model for incomplete imaging data.

We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…

Improved biclustering algorithm reduces memory usage and runtime.

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptio…

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus \{ 0 \}$ and performing a quantum analogue of Marsden-Weinstein reduction, we ca…

This work examines consistency issues in Gaussian Mixture Model reduction algorithms.

The paper introduces controllable principal connections and estimates distances between bundles and spaces.

New insights into surface energy reduction.

We investigate the Kaluza-Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza-Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza-Klein reductions by classifying the freely-acting spacelike Killing vectors which preserve som…

Drago optimizes DRO problems with faster convergence.

American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European options, the mathematical model involves additional constraints, and a variational in…

Study minimal networks on spheres and balls near standard metrics.

IKD uses eigen-decomposition for nonlinear dimensionality reduction.

Develops a new method for nonlinear dimension reduction using random features.

Unified model for reducing dimensions and clustering high-dimensional data.

We revisit our earlier work on the AKSZ formulation of topological sigma model on generalized complex manifolds, or Hitchin model. We show that the target space geometry geometry implied by the BV master equations is Poisson--quasi--Nijenhuis geometry recently introduced and studied by Stiénon and Xu (in the untwisted …

We present sktime -- a new scikit-learn compatible Python library with a unified interface for machine learning with time series. Time series data gives rise to various distinct but closely related learning tasks, such as forecasting and time series classification, many of which can be solved by reducing them to relate…

Under the Basel II standards, the Operational Risk (OpRisk) advanced measurement approach allows a provision for reduction of capital as a result of insurance mitigation of up to 20%. This paper studies the behaviour of different insurance policies in the context of capital reduction for a range of possible extreme los…