Let be a compact connected simple Lie group and let $M=G^{\bb{C}}/P=G/K$ be a generalized flag manifold. In this article we focus on an important invariant of , the so called $\fr{t}$-root system $R_{\fr{t}}$, and we introduce the notion of symmetric $\fr{t}$-triples, that is triples of $\fr{t}$-roots $ξ, ζ, η…
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48 results for “Frölicher-Nijenhuis bracket”
We consider in this paper the -deformations of a family of space curves with codimension . Some geometric aspects of a space curve such as flattenings, vertices and twistings points has been studied.
Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Modelsstat.ML
A new method for estimating large-scale linear models with improved precision.
problem Estimating large-scale linear statistical models efficiently.
method Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), integrating Sketch-and-Solve and Iterative-Sketching methods.
result SLSE-FRS produces high-precision estimators, outperforming state-of-the-art methods.
Study shows splitting schemes can approximate WFR flows faster than the exact flow.
problem Improving sampling efficiency in Wasserstein-Fisher-Rao gradient flows.
method Investigates operator splitting techniques to numerically approximate WFR flows.
result A judicious choice of step size and operator ordering can lead to faster convergence of split schemes to the target distribution.
FR-Train improves fair and robust AI training by detecting and reducing poisoned data.
problem Training AI models that are fair and robust in the presence of data bias and poisoning.
method Mutual information-based adversarial training with an additional discriminator.
result FR-Train maintains fairness and accuracy even in the presence of poisoned data.
Proves FR-NGD optimally approximates evolutionary dynamics and continuous Bayesian inference.
problem Optimizing continuous time replicator equations and continuous Bayesian inference.
method Fisher-Rao natural gradient descent (FR-NGD) and its correspondence with evolutionary dynamics.
result FR-NGD optimally approximates continuous time replicator equations and continuous Bayesian inference.
Fuzzy Rough Set selects key features for phishing detection.
problem Efficient feature selection for phishing detection.
method Fuzzy Rough Set (FRS) theory for feature selection.
result Maximum F-measure of 95% using Random Forest.
FR-LUX optimizes portfolio management by learning cost-aware policies robust to market conditions.
problem Transaction costs and regime shifts cause failure in live trading portfolios.
method Integrates three ingredients: microstructure-consistent execution model, trade-space trust region, and explicit regime conditioning.
result Achieves top average Sharpe ratio, maintains flat cost-performance slope, and superior risk-return efficiency.
This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
problem Sampling techniques struggle to traverse between modes in non-convex potential functions.
method Explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.
result The convergence rate to π is independent of the potential function.
Equivalence of a Bridged Link Calculus and Kirby's Calculus on Non-Simply Connected 3-Manifoldsmath.GT
We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are equivalent, and thus describe the same classes of 3-manifolds. This makes the p…
Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometriesmath.DG
Universal construction for Lie algebroids from anchored bundles with connections.
problem Creating a universal framework for Lie algebroids from anchored bundles with connections.
method Adapting Kapranov's construction to anchored bundles with arbitrary connections, showing compatibility with Lie algebroid structure.
result Universal connection on compatible with Lie algebroid structure, turning into a Cartan-Lie algebroid.
We study geodesics of the form , $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces , where is the natural projection. These curves naturally generalise homogeneous geodesics, that is orbits of one-parameter subgroups of (i.e. , $X\in …
Paper proposes FR algorithm to solve minimax optimization locally.
problem Gradient descent fails to find local minimax in minimax optimization.
method Follow-the-Ridge (FR) algorithm, addressing rotational behavior of gradient dynamics.
result FR algorithm provably converges to local minimax.
We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces whose isotropy representation decomposes into a direct sum of three submodules , satisfying the relations $[\fr…
This article follow the article {http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the author characterize the fact of being of finite volume for a convex projective surface. We show here that the moduli space of the convex projective structure on the surface of genius with pun…
A new category generates 1D tangle invariants.
problem Developing a new category for 1D tangles.
method Proving a new -category has universal mapping property.
result The new category generates link invariants.
New method improves fairness of facial recognition systems.
problem Facial recognition systems exhibit bias across different demographic groups.
method Optimizes centroid-based scores to reduce bias in pre-trained models.
result Demonstrates significant improvement in fairness with minimal loss in accuracy.
This paper introduces a new Urban Point Cloud Dataset for Automatic Segmentation and Classification acquired by Mobile Laser Scanning (MLS). We describe how the dataset is obtained from acquisition to post-processing and labeling. This dataset can be used to learn classification algorithm, however, given that a great a…
We introduce \texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Pytho…
Study reveals centralization in Bitcoin transactions involving retail users.
problem Centralization and bias in Bitcoin transaction data.
method Heuristic classification of Bitcoin users, weekly activity pattern analysis.
result Most real transactions involve Frequent Receivers, centralizing the ecosystem.
We construct examples of finitely generated groups L that have non-trivial actions on -trees but which cannot act, without fixing a vertex, on any simplicial tree. Moreover, any finitely presented group mapping onto L does have a fixed point-free action on some simplicial tree.
This work examines curvature effects on empirical mean in Riemannian and affine manifolds for small samples.
problem Understanding curvature effects on empirical mean in small samples on Riemannian and affine manifolds.
method Established Taylor expansions for the first and second moments of the empirical mean, showing curvature impacts.
result Explicit formulas for bias and modulation of empirical mean's covariance matrix due to curvature.
Improved action recognition in live videos with hybrid FR-DL method.
problem High computational costs and lack of temporal information in conventional action recognition.
method Automated selection of representative frames, feature extraction, background subtraction, HOG, deep neural network, LSTM, Softmax-KNN classifier.
result Significant improvement in accuracy and speed compared to state-of-the-art methods.
Unified framework for discrete diffusion modeling with flexible noising processes.
problem Efficient modeling of large discrete state spaces with arbitrary corruption dynamics.
method Generalized Discrete Diffusion from Snapshots (GDDS) framework that supports uniformization for fast noising and snapshot-based ELBO for reverse process.
result GDDS outperforms existing discrete diffusion methods in training efficiency and generation quality.
Motivation: Prediction of ligands for proteins of known 3D structure is important to understand structure-function relationship, predict molecular function, or design new drugs. Results: We explore a new approach for ligand prediction in which binding pockets are represented by atom clouds. Each target pocket is compar…
New algorithm for multi-armed bandits with delayed, partially observed rewards.
problem Sequential decision-making with delayed feedback.
method Proposed multi-armed bandits with generalized temporally-partitioned rewards, introducing β-spread property.
result Upper bound on performance of TP-UCB-FR-G algorithm improves state of the art.
The paper introduces new geometric methods to analyze radar electromagnetic wave statistics.
problem Analyzing spatio-temporal and polarimetric fluctuations of radar electromagnetic waves.
method Using statistical mechanics and Information Geometry, the paper defines a Fréchet barycentre and maximum entropy density for radar measurements.
result New tools for describing radar electromagnetic wave fluctuations, including a distance on covariance matrices.
In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in …
New bracket unifies nonholonomic dynamics and Hamilton-Jacobi theory.
problem Unified description of nonholonomic dynamics and Hamilton-Jacobi theory.
method Defined and proved coincidence of three nonholonomic brackets.
result Three nonholonomic brackets coincide.
New algorithms improve sampling from complex distributions.
problem Sampling from complex probability distributions efficiently.
method Regime-switching Langevin dynamics and Monte Carlo algorithms.
result Convergence guarantees and iteration complexities provided.
New bracket theory connects three nonholonomic dynamics models.
problem Nonholonomic dynamics and their bracket formulations.
method Definition and proof of equivalence of three nonholonomic brackets.
result Three nonholonomic brackets are equivalent.
Flat connections derived from Poisson brackets on loop spaces.
problem Understanding the structure of Poisson brackets on loop spaces.
method Defined connections by explicit linear combinations of standard connections associated with the Poisson bracket.
result Connections are shown to be flat.
It is shown that two definitions for an exterior differential in superspace, giving the same exterior calculus, yet lead to different results when applied to the Poisson bracket. A prescription for the transition with the help of these exterior differentials from the given Poisson bracket of definite Grassmann parity t…
New method to calculate 3-manifold invariants via skew-racks.
problem Calculating invariants of 3-manifolds.
method Introducing skew-racks with good involution and Property FR, defining cocycle invariants.
result Established new approach to obtain 3-manifold invariants via Dehn surgery.
The paper constructs compatible Poisson brackets on gl(N).
problem Constructing compatible Poisson brackets on gl(N).
method Using constant tensors and Schouten brackets, the paper explicitly constructs quadratic Poisson brackets compatible with the standard Lie-Poisson bracket.
result Explicit construction of quadratic Poisson brackets compatible with the standard Lie-Poisson bracket on gl(N).
Derived bracketsmath.DG
We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp…
Researchers attempt to categorify biquandle brackets using Khovanov homology methods.
problem Categorify biquandle brackets using Khovanov homology methods.
method Outline a Khovanov homology-style construction for biquandle brackets.
result A canonical biquandle 2-cocycle is defined, but not a true categorification of biquandle brackets.
Explains biquandle brackets and quivers for a topology talk.
problem None explicitly stated; focuses on background information.
method Review of biquandle concepts and related structures.
result Clarifies understanding of biquandle bracket quivers.
An inclusive curvature-like framework for describing dissipation: metriplectic 4-bracket dynamicsmath-ph
A new framework describes dissipation using a metriplectic 4-bracket.
problem Describing dissipation in a way that preserves energy and entropy.
method Using a metriplectic 4-bracket, a quantity like the Poisson bracket with symmetries motivated by Riemannian curvature.
result The metriplectic 4-bracket dynamics includes all known previous binary bracket theories for dissipation.
New biquandle bracket invariants are linked to biquandle 2-cocycles.
problem Quantum enhancements and biquandle colored links.
method Proving biquandle bracket invariants are pointwise products of other invariants and biquandle 2-cocycles.
result New biquandle bracket invariants are equivalent to the Jones polynomial on knots.
New geometric definition of Lie bracket for undirected curves.
problem Understanding the Lie bracket of undirected curves on a surface.
method Local geometric definition and proof of three results.
result The TWG bracket counts intersection and suggests disjoint representatives.
New examples show non-trivial parity-biquandle bracket.
problem Constructing non-trivial parity-biquandle bracket examples.
method Slightly changed notation and constructed examples of knots and links.
result Minimality theorem: graphs appear as link invariants.
Abstract: Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
problem Relationship between Fenchel-Nielsen coordinates and shear coordinates on Riemann surfaces.
method Explicitly showed the Poisson bracket on shear coordinates induces the Fenchel-Nielsen bracket on gluing parameters.
result Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In th…
Enhances quantum invariants using tribracket brackets.
problem Quantum invariants of tribracket-colored knots and links.
method Introduces tribracket brackets as skein invariants.
result Provides new quantum invariants and examples.
The paper defines symmetric brackets for skew-symmetric algebroids with totally skew-symmetric torsion.
problem Defining symmetric brackets for skew-symmetric algebroids.
method Using connections with totally skew-symmetric torsion and pseudo-Riemannian metrics.
result Explicit formula for the Levi-Civita connection and symmetric brackets on almost Hermitian manifolds.
In this note we prove that, for a vector bundle over a manifold , a Dorfman bracket on anchored by and with a vector bundle over , is equivalent to a lift from to linear sections of , that intertwines the given Dorfman bracket w…
Introduces a new bracket for multicontact geometry and applies it to field theories.
problem Developing a new mathematical structure for multicontact geometry.
method Introducing a graded Jacobi bracket and multisymplectization.
result Established a new bracket that extends contact geometry concepts.