In this paper, we define the rectangle condition on the bridge sphere for a -bridge decomposition of a knot whose definition is analogous to the definition of the rectangle condition for Heegaard splittings of -manifolds. We show that the satisfaction of the rectangle condition for a -bridge decomposition can …
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 “Conditional decomposition”
Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to be -manifolds , which generalize characterizations in the codimens…
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
We introduce Fenchel-Nielsen coordinates on Teicmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geom…
The paper explores Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds.
problem Analyzing harmonic forms and Hodge decomposition on almost Kähler manifolds.
method Using Hodge decomposition and the Hard Lefschetz Condition to study almost Kähler manifolds.
result The spaces of harmonic forms have the Hodge decomposition and the Hard Lefschetz Condition is satisfied.
In the present paper, we give a necessary and sufficient condition for a Riemannian manifold to have a reducible action of a hyperbolic analogue of the holonomy group. This condition amounts to a decomposition of as a warped product of a special form, in analogy to the classical de Rham decomposition th…
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 classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warpin…
Estimates CATEs for structured treatments using a new decomposition method.
problem Estimating conditional average treatment effects for complex data types.
method Generalized Robinson decomposition, isolating causal estimand, arbitrary model plugging, quasi-oracle convergence guarantee.
result Demonstrates superior performance in CATE estimation compared to prior work.
Proves hyperbolic 3-manifolds have angle structures under certain conditions.
problem Proving angle structures for non-compact hyperbolic 3-manifolds.
method Subdividing ideal polyhedral decompositions and applying topological conditions.
result Proves existence of ideal triangulations with angle structures.
Study homotopy groups of open books and their pages, pages, and bindings.
problem Homotopy groups of open books and their components.
method Homotopy theoretic conditions on monodromy, integral and rational loop space decompositions.
result Integral and rational loop space decompositions for open books under specific conditions.
Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.
problem Challenges in sensitivity analysis of black-box computer experiments with complex, nonlinear functional outputs.
method Functional-output orthogonal additive Gaussian process (FOAGP) with conditional orthogonality constraint.
result Demonstrates effectiveness in orthogonal effect decomposition and variance decomposition through simulations and real-world application.
The study shows conditions for elliptic surfaces without 1-handles.
problem Finding conditions for elliptic surfaces without 1-handles.
method Analyzing knot surgeries and log-transformations of elliptic surfaces.
result Conditions for elliptic surfaces without 1-handles are established.
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
problem Performing global sensitivity analysis on black-box models with dependent inputs.
method Proposes a novel framework based on probability theory, functional analysis, and combinatorics to handle dependencies.
result Any square-integrable, real-valued function of random elements with mild dependence assumptions can be uniquely additively decomposed.
Study homotopy types of 4-manifolds, finding decompositions and conditions for desuspension.
problem Determine homotopy types of double suspensions of 4-manifolds with 2-torsion.
method Use Postnikov square and analyze homology groups to find decompositions and conditions for desuspension.
result Homotopy decompositions of double suspensions as wedge sums of specific complexes.
New risk decompositions clarify domain adaptation issues.
problem Domain adaptation challenges with different training and test distributions.
method Representation Bayesian Risk Decompositions, hybrid argument.
result Clarifies factors (2) and (3) as reasons for generalization failure.
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.
In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give constructions for kernels. Finally we present e cient means of solving the optimization…
Generalized Robertson-Walker (GRW) spaces constitute a quite important family in Lorentzian geometry, and it is an interesting question to know whether a Lorentzian manifold can be decomposed in such a way. It is well known that the existence of a suitable vector field guaranties the local decomposition of the manifold…
Identifies conditions for multiple invariant probabilities in Markov kernels.
problem Global irreducibility and recurrence do not guarantee uniqueness of invariant probabilities.
method Uses Jordan decomposition of the difference of two invariant probabilities.
result A Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition.
The study examines conditions for completeness and simplicity in hom-Lie superalgebras.
problem Conditions for completeness and simplicity in hom-Lie superalgebras.
method Equivalent conditions and derivations analysis.
result Conditions for completeness and simplicity in hom-Lie superalgebras.
PROD method improves high-dimensional regression by handling strong correlations.
problem Violation of Irrepresentable Condition in LASSO for high-dimensional data.
method PROD procedure based on orthogonal decomposition of design matrix.
result PROD enhances performance of high-dimensional penalized regression.
New algorithms improve tensor CP decomposition under mild conditions.
problem Improving tensor CP decomposition with theoretical guarantees under mild incoherence conditions.
method Composite PCA and Concurrent Orthogonalization algorithms.
result Theoretical guarantees and practical superiority over existing methods.
The Hodge theorem connects cohomology groups on compact Kähler manifolds.
problem Establishing a relationship between cohomology groups on compact Kähler manifolds.
method Proving the Hodge decomposition theorem on compact d-Kähler manifolds.
result Hodge decomposition theorem on compact d-Kähler manifolds.
Strongly-cyclic branched coverings of knots are studied by using their (g,1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups admit geometric g-words cyclic presentations.
We formalize the concept of a family of metric spaces satisfying a coarse property uniformly and we generalize finite decomposition complexity of Erik Guentner, Romain Tessera, and Guoliang Yu. Of particular interest are results determining sufficient conditions for a metric space to satisfy Property A of Guoliang Yu.
Let $G=\C^{n}\ltimes_φ \C^{m}$ with a semi-simple action $φ: \C^{n}\to GL_{m}(\C)$ (not necessarily holomorphic). Suppose has a lattice . Then we show that in some conditions on and , admits a Hermitian metric such that the space of harmonic forms satisfies the Hodge symmetry and decomposition. By t…
We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We…
In this paper we use 3-manifold techniques to illuminate the structure of the string link monoid. In particular, we give a prime decomposition theorem for string links on two components as well as give necessary conditions for string links to commute under the stacking operation.
Despite the wide application of Graph Convolutional Network (GCN), one major limitation is that it does not benefit from the increasing depth and suffers from the oversmoothing problem. In this work, we first characterize this phenomenon from the information-theoretic perspective and show that under certain conditions,…
We compute the Dolbeault cohomology of geodesically convex domains contained in Cousin groups which satisfy a strong dispersiveness condition. As a consequence we obtain a description of the Dolbeault cohomology of Oeljeklaus-Toma manifolds and in particular the fact that the Hodge decomposition holds for their cohomol…
A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.
problem Capturing nonlinear predictability in financial return dynamics.
method Decomposes returns into sign and magnitude components, using a joint distribution model.
result Significantly outperforms traditional linear models in forecasting U.S. stock market returns.
Analysis of DPPs and k-DPPs via spectral decomposition reveals identifiable parameters and non-identifiability gaps.
problem Identifying parameters of DPPs and k-DPPs through spectral decomposition.
method Spectral decomposition of the covariance matrix, analysis of invariances, and counting arguments.
result Identifiability of parameters changes fundamentally for k-DPPs, with specific invariances and non-identifiability gaps.
Extends geometric decompositions to arbitrary meshes and forms.
problem Constructing local bases for finite element spaces on arbitrary meshes.
method Generalizes extension operators to arbitrary meshes and forms, showing they yield geometric decompositions.
result Extension operators yield geometric decompositions for arbitrary meshes and forms.
We study properties concerning decomposition in cohomology by means of generalized-complex structures. This notion includes the -pure-and-fullness introduced by Li and Zhang in the complex case and the Hard Lefschetz Condition in the symplectic case. Explicit examples on the moduli space of the Iwas…
We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.
problem Invariants for 3-manifolds with toral boundaries and non-degenerate Thurston norm.
method Constructing an invariant called guts and proving its invariance under sutured decompositions.
result The guts of different homology classes are related by sutured decompositions.
We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…
New method preserves topology in Hodge decomposition for scalar and vector fields.
problem Topology-preserving Hodge decomposition on manifolds with boundaries.
method Comprehensive 5-component decomposition in Eulerian representation.
result Effective numerical experiments validate the method's accuracy and orthogonality.
Klartag recently gave a beautiful alternative proof of the isoperimetric inequalities of Levy-Gromov, Bakry-Ledoux, Bayle and E. Milman on weighted Riemannian manifolds. Klartag's approach is based on a generalization of the localization method (so-called needle decompositions) in convex geometry, inspired also by opti…
Overcomplete latent representations have been very popular for unsupervised feature learning in recent years. In this paper, we specify which overcomplete models can be identified given observable moments of a certain order. We consider probabilistic admixture or topic models in the overcomplete regime, where the numbe…
A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in the empty ball condition are replaced by other families of regions bou…
The paper derives upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
problem Finding upper bounds on eigenvalues of Laplace-Beltrami operator on hyperbolic surfaces.
method Using spectral decompositions and consistency conditions derived from quadruple overlap integrals in terms of triple overlap integrals.
result Derives upper bounds on eigenvalues, nearly saturated by the Bolza surface.
Variational Autoencoders (VAEs) are a popular generative model, but one in which conditional inference can be challenging. If the decomposition into query and evidence variables is fixed, conditional VAEs provide an attractive solution. To support arbitrary queries, one is generally reduced to Markov Chain Monte Carlo …
We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly warped product up to a zero measure subset formed by an union of leaves. We also…
Tensor Decompositions Meet Control Theory: Learning General Mixtures of Linear Dynamical Systemscs.LG
New approach learns mixtures of linear dynamical systems without separation conditions.
problem Learning mixtures of linear dynamical systems with better fit or understanding.
method Tensor decompositions to learn mixtures of linear dynamical systems.
result Algorithm succeeds without strong separation conditions and can compete with Bayes optimal clustering.
In this paper we first establish the relation between the zeta-determinant of a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary condition on a cylinder. Using this result and the gluing formula of the zeta-determinant given by Burghelea, Friedlander and Kappeler with some assumptions, we prov…