Paper presents a new triangular form for flat systems.
problem Designing flat systems with two inputs.
method Geometric characterization and static feedback equivalence.
result Sufficient condition for affine input systems to be flat.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “triangular structure”
Paper presents a new flat triangular form for systems.
problem Creating a structurally flat triangular form for systems.
method Developed a new triangular form based on the extended chained form with conditions for static feedback equivalence.
result Provided conditions for affine input systems to be static feedback equivalent to the new triangular form.
The study investigates linearizability of Poisson structures on groupoids.
problem Linearizing Poisson structures on groupoids around the unit section.
method Extending the Lagrangian neighbourhood theorem to cosymplectic Lie algebroids, integrating triangular Lie bialgebras to symplectic LA-groupoids.
result Poisson structures on groupoids are linearizable under certain conditions.
Introduces triangular transport for uncertain data.
problem Uncertainty in complex systems without known probabilistic representations.
method Characterizes and manipulates unknown probability distributions using triangular transport maps.
result Triangular transport guarantees desirable mathematical and computational properties.
Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each \u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson Lie g…
New method uses neural maps to efficiently sample lattice QCD distributions.
problem Challenges in sampling Boltzmann distributions of lattice field theories.
method Sparse triangular transport maps exploiting conditional independence structure of lattice graphs.
result Sparse triangular maps achieve efficient sampling with linear time complexity in lattice size.
Algorithm learns non-Gaussian graphical models via Hessian scores and triangular transport.
problem Learning graph structure from non-Gaussian data.
method Score based on integrated Hessian information, coupled with triangular transport map.
result Algorithm successfully recovers graph structure for non-Gaussian data.
We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold , we show that has a canonical structure of an -bialgebroid. (Higher Koszul brackets on forms introduced earlie…
We find a normal form for two-input flat discrete-time systems.
problem No comparable normal form exists for flat continuous-time systems.
method State- and input transformations to achieve a triangular structure.
result A systematic parameterization of system variables by the flat output and its shifts.
This paper explores the relationship between Leibniz algebras and Nijenhuis operators.
problem Understanding the relationship between Leibniz algebras and Nijenhuis operators.
method Investigation of Nijenhuis operators on Leibniz algebras and classification of Leibniz bialgebras.
result Leibniz algebras are closely related to Nijenhuis operators, and triangular symplectic Leibniz bialgebras possess Nijenhuis operators.
Somewhat unexpectedly, the study of the family of twisted knots revealed a hidden structure behind exclusive Racah matrices , which control non-associativity of the representation product in a peculiar channel . These are simultaneously symmetric and orthogo…
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…
Given a finite collection P of convex n-polytopes in RP^n (n>1), we consider a real projective manifold M which is obtained by gluing together the polytopes in P along their facets in such a way that the union of any two adjacent polytopes sharing a common facet is convex. We prove that the real projective structure on…
Solves problem of describing transformations for upper triangular Toeplitz operators.
problem Describing coordinate transformations preserving upper triangular Toeplitz form of operator fields.
method Implicit formulas involving matrix-valued functions for describing transformations and Nijenhuis operators.
result Formulas for coordinate transformations and Nijenhuis operators in upper triangular Toeplitz form.
We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.
Triangular flows ensure statistical consistency and fast rates in generative modeling.
problem Ensuring statistical consistency and fast rates in generative models.
method Statistical guarantees and sample complexity bounds for triangular flow models using empirical process theory.
result Established statistical consistency and finite sample convergence rates for Kullback-Leibler estimator of Knöthe-Rosenblatt measure coupling.
Contractions of Leibniz algebras and Courant algebroids by means of (1,1)-tensors are introduced and studied. An appropriate version of Nijenhuis tensors leads to natural deformations of Dirac structures and Lie bialgebroids. One recovers presymplectic-Nijenhuis structures, Poisson-Nijenhuis structures, and triangular …
Paper uses GNNs to efficiently detect profitable triangular arbitrage opportunities.
problem Detecting profitable triangular arbitrage opportunities in dynamic markets.
method Formulate the problem as a graph-based optimization task and use a GNN architecture to capture complex relationships.
result GNN-based method achieves higher average yield with reduced computational time compared to traditional methods.
We create a smooth manifold of triangular meshes with a geodesically complete metric.
problem Representing and manipulating 2D shapes as triangular meshes.
method Developed a geodesically complete Riemannian metric for triangular meshes.
result The metric preserves mesh connectivity and avoids mesh degradation.
Smooth resolutions found for quotient of R^2 by infinite discrete groups.
problem Symplectic resolutions of quotient spaces by infinite discrete subgroups.
method Constructing smooth symplectic resolutions for R^2 under infinite discrete subgroups of GL_2(R).
result Minimal resolutions of Du Val singular varieties are symplectic resolutions of R^2/G.
Discretizes Helfrich-type energies on surfaces using triangular complexes.
problem Discretizing curvature energies on surfaces of specific type.
method Asymptotic lower bound combined with recovery sequence of triangulations and edge director fields.
result Valid discrete versions of integral curvature energies on surfaces.
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well known Brun…
Triangular arbitrage as an interaction among foreign exchange ratescond-mat.stat-mech
We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen-dollar rate, the dollar-euro rate and the yen-euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model includes effects of triangular…
New framework for learning KR maps from data, ensuring stable generalization.
problem Learning monotone triangular transport maps efficiently and accurately.
method General framework using invertible transformations of smooth functions, ensuring no spurious local minima.
result Unique global minimizer corresponds to the KR map under certain conditions.
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with la…
New method for conditional sampling using M-GANs, likely-free inference.
problem Conditional sampling of probability measures.
method Developed a novel computational approach called M-GANs based on block triangular transport.
result Accurate sampling of conditional measures in various applications.
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to study cross-correlations. The study is motivated by fundamental questions in compl…
Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.
problem Jordan-Chevalley decomposition for operator fields in small dimensions.
method Tensorial conditions and proof of conjecture for higher order brackets.
result Proves Tempesta-Tondo conjecture for higher order brackets.
We show that for any coboundary Poisson Lie group G, the Poisson structure on G^* is linearizable at the group unit. This strengthens a result of Enriquez-Etingof-Marshall, who had established formal linearizability of G^* for quasi-triangular Poisson Lie groups G. We also prove linearizability properties for the group…
In this paper we look for closed expressions to calculate the number of colourings of prime knots for given linear Alexander quandles. For this purpose the colouring matrices are simplified to a triangular form, when possible. The operations used to perform this triangularization preserve the property that the entries …
Model shows triangular arbitrage key to cross-currency correlations in forex markets.
problem Understanding cross-currency correlations in forex markets.
method Agent-based model of market interactions.
result Triangular arbitrage is primary driver of cross-currency correlations.
For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface element…
New basis confirms Thurston's conjecture and reveals knot configurations.
problem Understanding cluster algebras and their bases from surfaces.
method Topological construction of band basis and comparison with Kazhdan-Lusztig type basis.
result Common triangular basis matches band basis in quantum cluster algebras.
Incremental computation of block triangular matrix exponentials with application to option pricingmath.NA
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting a discretization process pro…
A microscopic model of triangular arbitragephysics.soc-ph
We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the …
New method generates synthetic time series paths with more flexibility.
problem Restrictions in generating synthetic paths using Brownian reference.
method Introduces Triangular-Reference Schrödinger Bridges (TR-SBTS) for time series generation.
result Generates synthetic paths with more flexibility in stochastic volatility and correlated noise.
The paper defines projective structures for Lie bialgebras and Poisson-Lie groups.
problem Defining projective analogues of Lie bialgebras and Poisson-Lie groups.
method Introducing projective tensor products and adapting classical notions to these structures.
result Every quasi-triangular projective r-matrix gives rise to a projective Banach Lie bialgebra.
We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with possibly non locally Lipschitz functions. We characterize the points where this Lip…
The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on the structure of Kähler groups, i.e., the fundamental groups of compact Kahler man…
We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation metho…
In this paper, we classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism. We show how to find each such polyhedron in the upper half-space model by considering lines and circles in the plane. Finally, we give matrix generators in $\mathrm{…
Examines discrete curvature's relation to smooth curvature in 3 spaces.
problem Understanding how discrete curvature relates to smooth curvature in different spaces.
method Using specific triangular tilings of 3 types of spaces to examine curvatures.
result Discrete curvature can sense the smooth curvature of ambient space forms.
Two algorithms create high-quality triangular meshes for surfaces with guaranteed angles.
problem Creating high-quality triangular meshes for surfaces with controlled angles.
method MidNormal and GradNormal algorithms generate meshes with specified angle constraints.
result Meshes converge to surfaces as mesh size decreases, maintaining specified angles.
Develops theory for conditional optimal transport in infinite-dimensional spaces.
problem Bayesian inference with functional parameters in infinite-dimensional spaces.
method Theory of constrained optimal transport for block-triangular maps.
result Regularity estimates on conditioning maps from prior to posterior.
We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular -matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs o…
New model for simulating and inferring from inverse problems.
problem Bayesian inverse problems in conditional sampling.
method Invertible generative model using triangular normalizing flows.
result Training loss for invertible map proposed.
Minimal covolume group found in hyperbolic 3-space.
problem Finding groups with minimal covolume in hyperbolic 3-space.
method Proved existence of a specific group with minimal covolume.
result Minimal covolume group found with covolume equal to Catalan's constant.