Algorithm confirms non-order-preserving braids, proving infinite family not order-preserving.
problem Determining if a braid is non-order-preserving.
method Algorithm that checks non-order-preserving property of braids.
result Infinite family of simple 3-braids are not order-preserving.
Introduces representations of surface groups into Lie groups preserving order.
problem Representations of surface groups into Lie groups that preserve the group order.
method Relates order preserving representations to weakly maximal representations and uses geometric and causal structure.
result Order preserving representations into Lie groups of Hermitian type are faithful with discrete image and form a closed set.
Polytopes A(P) for posets P compactify spaces of order-preserving maps.
problem Compactifying spaces of order-preserving maps for posets.
method Constructing polytopes A(P) and compactifying spaces of order-preserving maps. result Polytopes A(P) correspond to nested collections of subsets of posets. In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with w(X)=τ the map μFX, where F∈{O,OH}, is homeomorphic to trivial Iτ-fibration if and only if X is openly generated χ-homogeneou…
New method calibrates deep networks by preserving top-k predictions.
problem Calibrated confidence scores for multi-class deep networks to avoid rare mistakes.
method Intra order-preserving functions combined with neural network architecture.
result Outperforms state-of-the-art methods in evaluation metrics.
OP-GFNs sample candidates in order-preserving proportion to a learned reward function.
problem Sampling diverse candidates with varying rewards in multi-objective optimization.
method Order-Preserving GFlowNets (OP-GFNs) use a learned reward function consistent with a provided order on candidates.
result Training OP-GFNs sparsifies the reward landscape, focusing on higher-ranked candidates.
Method preserves order in hierarchical clustering of ordered data.
problem Order preserving hierarchical clustering of directed acyclic graphs.
method Combination of classical hierarchical clustering and ultrametric fitting.
result Optimal clustering preserves both cluster quality and order.
We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited only after some other factors are activated. Precedence-ordering arise in appli…
Enhances image classification by integrating semantic hierarchy into CNN models.
problem Limited use of external guidance in image classification.
method Integrates label-hierarchy knowledge into CNN-based classifiers and uses order-preserving embeddings.
result Boosts image classification performance through semantic hierarchy integration.
New set class preserves Fourier series terms for planar ovals, leading to isoperimetric inequalities.
problem Investigate geometric properties of kth Order Preserving Sets and ovals. method Introduce and analyze kth Order Preserving Sets and Midpoint Sets; study geometric properties and isoperimetric inequalities. result Established an isoperimetric-type inequality relating perimeter and area of ovals and their associated sets.
New framework detects directional influence in multivariate time series.
problem Detecting directional influence in multivariate time series.
method Order-constrained spectral non-invariance.
result Unique diagnostic functional for directional influence.
New criterion for bi-ordering free groups under automorphisms.
problem Bi-ordering free groups under automorphisms.
method New criterion for bi-ordering free groups.
result Fundamental group of the magic manifold is bi-orderable.
The paper solves the p-th Kazdan-Warner equation on graphs.
problem Solving the p-th Kazdan-Warner equation on graphs for given h and c.
method Using the discrete p-Laplacian and properties of order-preserving operators.
result The p-th Kazdan-Warner equation has a solution on graphs for any p > 1.
The thesis introduces methods to use semantic hierarchy in image classification.
problem Limited work in training image classifiers with non-conventional external guidance.
method Injects label hierarchy knowledge into arbitrary classifiers and uses order-preserving embeddings for image classification.
result Both embedding-based models and CNN-classifiers with hierarchical information outperform a hierarchy-agnostic model.
MCNet improves uncertainty calibration in online advertising by modeling complex relations and balancing performance.
problem Lack of effective calibration for complex relations and context features in online advertising.
method Introduces MCNet with MCF, order-preserving, and field-balance regularizers.
result Superior performance in generating well-calibrated probability predictions on public and industrial datasets.
Introduces a differentiable approximation to the zero-one loss.
problem Incompatibility of zero-one loss with gradient-based optimization.
method Smooth projection onto hypersimplex through constrained optimization.
result Achieves significant improvements in generalization under large-batch training.
Framework analyzes neural network dynamics for better understanding and optimization.
problem Understanding the fundamental mechanisms of deep neural networks.
method Dynamical systems theory, transformation units, attraction basins.
result Different transformation modes lead to distinct learning phases and network performance.
A new method estimates rare events using tensor trains.
problem Estimating rare event probabilities in high-dimensional problems.
method Approximating optimal importance distribution via tensor-train decompositions and compositions.
result Better variance reduction and efficient computation of rare event probabilities.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
problem Undesirable effects of current Nasdaq-100 index rebalancing.
method A simple rebalancing strategy that avoids undesirable effects.
result Preserves the order of index weights and prevents maximum weight increase.
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
Proposes a novel framework for multi-label text classification.
problem Lack of coherent consideration of non-consecutive and long-distance semantics and hierarchical relations among labels.
method Hierarchical taxonomy-aware and attentional graph capsule recurrent CNNs framework.
result Significantly improves multi-label text classification performance.
Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish tha…
Study on braids and their impact on hyperbolic 3-manifolds' orderability.
problem Investigating the relationship between braids and the orderability of hyperbolic 3-manifolds.
method Examined faithful representations of braid groups on automorphism groups of free groups, focusing on bi-orderability.
result Found that the bi-orderability of hyperbolic 3-manifolds' fundamental groups is linked to the braids used.
A lot of attention has been devoted to multimedia indexing over the past few years. In the literature, we often consider two kinds of fusion schemes: The early fusion and the late fusion. In this paper we focus on late classifier fusion, where one combines the scores of each modality at the decision level. To tackle th…
In the past few years, a lot of attention has been devoted to multimedia indexing by fusing multimodal informations. Two kinds of fusion schemes are generally considered: The early fusion and the late fusion. We focus on late classifier fusion, where one combines the scores of each modality at the decision level. To ta…
Paper finds formulas for mutual information and MMSE in matrix tensor product problems.
problem High-dimensional inference problems involving matrix tensor products.
method Single-letter formulas for mutual information and MMSE, using new techniques.
result Analytical formulas describe leading order terms in mutual information and MMSE.
Efficiently learns and transports posterior densities for real-time inference.
problem High computational cost of Bayesian inference for complex posterior densities.
method Tensor-train (TT) format for offline learning, conditional transport for online inference.
result Significant improvement in inference performance for high-dimensional problems.
Paper generalizes tensor-train approximation for complex random variables.
problem Characterizing intractable high-dimensional random variables.
method Extends inverse Rosenblatt transform to general reference measures and integrates into deep variable transformation framework.
result Deep inverse Rosenblatt transport significantly expands tensor approximations for complex random variables.
A new framework separates classifier calibration and discrimination.
problem Combining reliability and resolution in probabilistic predictions.
method Manokhin Probability Matrix separates reliability and resolution using Spiegelhalter Z-statistic and AUC-ROC.
result Classifiers are categorized into four archetypes: Eagle, Bull, Sloth, and Mole.
TMTF improves time series visualization by separating dynamic regimes.
problem Misleading global transition matrix in time series analysis.
method Temporal chunking, local transition matrices, and image assembly.
result Temporal segmentation reveals distinct transition dynamics.
Improved change point detection using matched filters for non-parametric tests.
problem False positives and localization ambiguity in non-parametric two-sample tests.
method Derived and applied matched filters for various two-sample tests.
result Matched filters reduce false positives and improve test precision.
Develops a new nonparametric trace regression model for high-dimensional data.
problem Violation of known functional form and global low-rank structure assumptions in trace regression.
method Structured sign series representations for nonparametric trace regression models.
result Establishes excess risk bounds and sample complexities for the proposed model.
The paper develops a Galois theory for cluster algebras and Riemann surfaces.
problem Building a correspondence between cluster subalgebras and automorphism groups.
method Introducing Galois-like extensions and automorphism groups for cluster algebras.
result Conditions for Galois-like extensions and properties of cluster automorphism groups.
The paper constructs arbitrary order conformally invariant operators in higher spin spaces.
problem Classifying and constructing conformally invariant differential operators in higher spin spaces.
method Explicit expressions and convolution type operators, intertwining operators, and representation theory.
result Explicit expressions and properties of conformally invariant differential operators in higher spin spaces.
New operators for Paneitz energy on manifolds with boundary.
problem Energy functional for Paneitz operator on compact manifolds with boundary.
method Conformally covariant boundary operators associated to Paneitz operator.
result Agreement with fractional GJMS operators in Poincaré-Einstein manifolds.
New boundary operators for sixth-order GJMS operator on manifolds.
problem Developing boundary operators for sixth-order GJMS operator.
method Conformally covariant boundary operators and fractional GJMS operators.
result New realization of fractional GJMS operators and Sobolev trace inequalities.
The paper connects eigenvalue problems for various operators and establishes inequalities and asymptotic formulas for heat traces.
problem Eigenvalue problems and heat trace asymptotics for different operators.
method Establishes connections and inequalities for eigenvalues and heat traces.
result Eigenvalue inequalities and three-term asymptotic formulas for heat traces of various operators.
Introduces a new elliptic operator with positive eigenvalue.
problem None explicitly stated in the abstract.
method Introduces a new elliptic operator called the two-radical Laplace operator.
result The eigenvalue of the new operator is the positive square root of the Laplace operator's eigenvalue.
Proves Kato inequalities for various conformal operators.
problem Proving inequalities for differential operators.
method Analyzes a class of first order differential operators, including Dirac and Penrose twistor operators.
result Derives Kato inequalities that interpolate between classical and refined versions.
Study higher order fermionic and bosonic operators on cylinders and Hopf manifolds.
problem Understanding higher order higher spin operators on specific manifolds.
method Analysis of higher order operators on cylinders and Hopf manifolds.
result Construction of kernels for these operators on the studied manifolds.
Study on biharmonic hypersurfaces with specific recurrent operators in Euclidean space.
problem Characterizing biharmonic hypersurfaces with recurrent operators.
method Analysis of various recurrent operators and their impact on biharmonic hypersurfaces.
result Some well-known recurrent operators play a significant role in making biharmonic hypersurfaces minimal.
The k-Dirac operator is defined with initial conditions.
problem Defining the k-Dirac operator with initial conditions.
method Adapting Cartan-Kahler theorem to weighted differential operators.
result Initial conditions for the k-Dirac operator established.
Study the heat operator of a transversally elliptic operator on Lie groups.
problem Spectral properties and convergence of a heat operator on Lie groups.
method Review spectral properties, define character, estimate heat operator convergence.
result Estimate of fα(t) determines convergence of the character. Local index theorem for chiral geometric operators proved using heat kernel.
problem Proving a local index theorem for geometric first-order differential operators.
method Using Gilkey's invariance theory and heat kernel techniques.
result Supertrace of heat kernel converges to Chern-Weil form.
Study estimates eigenvalues for concave Hessian operators on convex domains.
problem Estimating eigenvalues for concave elliptic Hessian operators.
method Investigates Dirichlet eigenvalue problem for a broad class of concave elliptic Hessian operators.
result Existence and properties of the first nonzero eigenvalue and eigenfunction.
The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.
problem Spaces of unbounded Fredholm operators and their properties.
method Analyzing the spaces and proving homotopy equivalences.
result Natural maps between four spaces of unbounded Fredholm operators are homotopy equivalences.
Characterizes operations on contact manifold differential forms.
problem Understanding natural operations on contact manifold differential forms.
method Introduces algebraic operators and the exterior derivative to characterize operations.
result All natural operations are built from introduced algebraic operators and the exterior derivative.
Standard Laplace operator extends Hodge and Casimir operators to broader geometric contexts.
problem Extending Laplace operator to vector bundles and Riemannian manifolds.
method Functorial approach, showing commutation with homomorphisms and differential operators.
result Standard Laplace operator commutes with a wide range of differential operators.