Paper relaxes identifiability conditions for causal models with latent variables.
problem Challenges in identifying causal graphical models with latent variables.
method Proposes a double triangular graphical condition for nonparametric measurement models with binary latent variables.
result Guarantees identifiability of the entire causal graphical model under relaxed conditions.
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.
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.
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.
If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et …
Extends Lie bialgebroids for string and M theories with new calculus framework.
problem Formalize calculus on algebroids for string and M theories.
method Reinterpret matched pairs of Leibniz algebroids, examine algebroid axioms, construct double on direct sum.
result Construct Drinfel'd double of Lie bialgebroids for general algebroids.
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.
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.
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.
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.…
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.
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.
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 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.
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R-matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that c…
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.
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.
Paper studies simplified trisections and their equivalence classes.
problem Understanding right-left equivalence of simplified (2,0)-trisections. method Analyzes simplified trisection diagrams and upper-triangular handle-slides.
result At least two simplified (2,0)-trisections can be right-left equivalent without being related by automorphisms or handle-slides. 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…
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.
Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional density estimation, by specifying one-dimensional transformations (equivalently co…
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…
Sharp large deviations and Gibbs conditioning for portfolio credit risk models.
problem Analyzing the risk of default in financial portfolios with dependent factors.
method Sharp large deviation estimates and conditional Bahadur-Rao estimates for threshold models with diverging latent factors.
result Conditioned on a large exceedance event, default indicators become asymptotically i.i.d., and loss-given-default is exponentially tilted.
A simple proof is given of the necessary and sufficient condition on a triple of positive numbers A,B,C for the existence of a conformal metric of constant positive curvature on the sphere, with three conic singularities of total angles A,B,C. The same condition is necessary and sufficient for the triple A,B,C to be in…
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…
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.
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 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.
We elaborate on the recent observation that evolution for twist knots simplifies when described in terms of triangular evolution matrix B, not just its eigenvalues Λ, and provide a universal formula for B, applicable to arbitrary rectangular representation R=[rs]. This expression is in terms of s…
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 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…
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 …
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…
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…
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.
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.
Paper finds conditions for special geometric structures on certain spaces.
problem Existence of specific geometric structures on double disk bundles.
method Derives a sufficient condition involving geometric data from principal orbits.
result Sufficient condition for the existence of cohomogeneity one Einstein metrics.
The paper explores conditions for positive scalar curvature on manifolds with boundaries and their doubles.
problem Conditions for positive scalar curvature on manifolds with boundaries and their doubles.
method Analyzes the relationship between boundary conditions and positive scalar curvature metrics on manifolds and their doubles.
result Provides conditions for positive scalar curvature metrics on manifolds with boundaries and their doubles.
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.