Probabilistic descent on manifolds using triangular sets and embedding theorems.
problem Descent over manifolds defined by polynomials.
method Triangularization, embedding theorem, numerical continuation.
result Effective numerical method for probabilistic descent.
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.…
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.
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.
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.
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…
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.
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…
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.
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.
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.
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…
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…
Study uses multifractal detrended cross-correlation to detect Forex arbitrage opportunities.
problem Detecting arbitrage opportunities in Forex markets.
method Multifractal detrended cross-correlation analysis applied to Forex time series.
result Strong cross-correlations found between exchange rates involved in triangular relations, including AUD and NZD.
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…
The paper classifies and describes five-sided hyperbolic polyhedra with one ideal vertex.
problem Classifying five-sided hyperbolic polyhedra with one ideal vertex.
method Using lines and circles in the plane to find each polyhedron in the upper half-space model, and generating matrix generators for the reflection groups.
result Matrix generators for the orientation-preserving subgroup of each corresponding reflection group.
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.
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.
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.
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
problem Discrete representation of continuous vector-valued environmental data.
method Develops discrete intrinsic Gaussian processes for vector-valued data on triangular meshes using discrete differential operators.
result Models can capture harmonic flows, incorporate boundary conditions, and model non-stationary data.
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.
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.
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 …
Generalizes Lie bialgebroids to supermanifolds with homotopy Poisson structures.
problem Relating Lie bialgebroids to homotopy Poisson structures on supermanifolds.
method Introduces L-infinity bialgebroids and higher Koszul brackets to connect these structures.
result Shows that (TM,T∗M) has an L-infinity bialgebroid structure for homotopy Poisson structures. The paper extends character varieties to marked surfaces and discovers their triangular decompositions.
problem Character varieties on marked surfaces and their properties.
method Triangulations of marked surfaces and cohomological groups.
result Stated character varieties admit triangular decompositions.
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…
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.
We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle M×G by the so-called gauge equivalence. We consider the case when M is a compact Kähler manifold and G is a solv…
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.
Study on flow-based methods for capturing tail properties in densities.
problem Flow-based methods struggle with capturing non-Gaussian tails.
method Characterize and adapt triangular maps to capture tail properties.
result Flow models lack the ability to capture non-Gaussian tails.
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.
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.
HINT improves invertible neural networks for better density estimation and Bayesian inference.
problem Sparse Jacobians limit expressiveness in invertible neural architectures.
method Recursive hierarchical coupling within subsets of variables leads to dense, triangular Jacobian.
result HINT allows efficient sampling from joint and posterior distributions using a single network.
Sum-of-Squares flow improves autoregressive and flow-based density estimation.
problem Density estimation in high dimensions with limitations of existing methods.
method Proposes a Sum-of-Squares (SOS) flow framework based on triangular maps.
result SOS flow achieves competitive results in simulations and real-world datasets.
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.
New combinatorial type helps distinguish plane curve topologies.
problem Distinguishing the topology of plane curves.
method Introducing G-combinatorial type using modified plumbing graphs.
result Invariant of G-combinatorial type under certain homeomorphisms.
STM maps improve terrain perception for autonomous robots.
problem Perception of terrain for autonomous robots in general environments.
method Stochastic triangular mesh (STM) technique for 2.5-D surface mapping.
result STM maps are more accurate than standard elevation maps.
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.
A new neural network for efficient density estimation.
problem Efficient density estimation for high-dimensional data.
method Triangular neural network implementation of neural autoregressive flow (NAF).
result Achieves state-of-the-art bits-per-dimension indices on MNIST and CIFAR-10.
It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular 2x2 matrices. In this work, we propose to generalize this result by considering the representations…
Researchers compute the cohomology ring of a foliation defined by a group action.
problem Computing the cohomology ring of a specific foliation defined by a group action.
method Non-abelian harmonic analysis on G to compute the leafwise cohomology ring. result Computed the leafwise cohomology ring H∗(FP).