Study of symplectic trivialization and reduction of bundles with symmetry and connection.
problem Symplectic trivialization and reduction of bundles with symmetry and connection.
method Analysis of the Tulczyjew's triplet with an Ehresmann connection.
result Trivializations and reductions of iterated tangent and cotangent bundles.
Geometrizes second order Lagrangians transformations.
problem No specific problem stated; focuses on geometrization.
method Building a proper Tulczyjew's triplet.
result Symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre transformations.
Taking configuration space as a Lie group, the trivialized Euler-Lagrange and Hamilton's equations are obtained and presented as Lagrangian submanifolds of the trivialized Tulczyjew's symplectic space. Euler-Poincaré and Lie-Poisson equations are presented as Lagrangian submanifolds of the reduced Tulczyjew's symplecti…
The abstract compares two methods in geometric mechanics.
problem No comparison between prolongations and Tulczyjew triples.
method Prolongations vs. Tulczyjew triples in geometric mechanics.
result Prolongations are a more basic approach to geometric mechanics.
Develop contact Tulczyjew formalism for dissipative dynamics on skew algebroids.
problem Dissipative dynamics on skew algebroids
method Contact Tulczyjew formalism
result Intrinsic explanation of contact term and Euler-Lagrange-Herglotz equations
Generalizes Tulczyjew triples for contact manifolds in Hamiltonian and Lagrangian formalisms.
problem Tackles the need for a geometric tool in contact manifolds.
method Introduces a generalized Tulczyjew triple for contact manifolds.
result Contact Hamiltonians and Lagrangians as sections of line bundles determine dynamics on contact phase space.
We propose a geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian mechanics, and concluding with Tulczyjew triples for classical …
We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.
Constructs a triple on an Atiyah algebroid with connection.
problem Dynamics of systems on principal bundles and Atiyah algebroids.
method Constructs a Tulczyjew triple on a principal bundle with connection, then reduces to the Atiyah algebroid.
result Dynamics of systems on principal bundles and Atiyah algebroids are discussed and applied.
In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defini…
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important featu…
Proposes a contact dynamics framework using generalized geometries.
problem Contact dynamics and related geometries.
method Generalizes symplectic and Morse families to contact framework.
result Establishes contact Hamiltonian and Lagrangian Dynamics as Legendrian submanifolds.
The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of th…
Re-examines classical mechanics with superdegrees of freedom.
problem Classical mechanics with both commuting and anticommuting degrees of freedom.
method Defines phase dynamics as an implicit differential equation on supermanifolds.
result Defines phase dynamics on arbitrary supermanifolds.
We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space TM, i.e. the tangent bundle, is replaced with its n-th exterior power, i.e. the bundle of tangent n-vectors. In this framework, which is fully covariant, we geometrically derive pha…
New method samples triplets from data distributions for training Triplet networks.
problem Training robust Triplet networks with discriminative triplets.
method Bayesian updating of multivariate normal distributions for dynamic class embedding sampling.
result Experimental validation on MNIST and histopathology CRC datasets shows effectiveness of the proposed method.
Safe screening reduces the number of triplets in metric learning.
problem Optimizing a metric over many triplets is computationally expensive and impractical.
method Safe triplet screening identifies and removes redundant triplets.
result Safe triplet screening maintains optimality without increasing computational cost.
Develops geometric quantum mechanics in infinite dimensions.
problem Quantum dynamics in infinite-dimensional spaces.
method Tulczyjew triple concept for Lagrangian formalism.
result Self-adjoint operators as Lagrangian submanifolds.
Around mid-1970s W. M. Tulczyjew discovered an approach which brings the two formalisms under a common geometric roof: the dynamics of a particle with configuration space X is determined by a Lagrangian submanifold D of TT∗X (the total tangent space of T∗X), and the description of D by its Hamiltonian H: …
Efficiently augments triplet data for better data analytics.
problem Lack of direct pairwise distance information for data analysis.
method Triplets augmentation to infer hidden information from existing data.
result Improves quality of kernel-based and kernel-free data analytics.
New method accelerates large margin metric learning for nearest neighbor classification.
problem Efficiently learning metrics for nearest neighbor classification.
method Triplet mining and stratified sampling for large margin metric learning.
result Improved efficiency and scalability of optimization.
This paper analyzes the stability and generalization of triplet learning algorithms.
problem Lack of theoretical understanding of triplet learning's generalization performance.
method Stability analysis and high-probability generalization bounds for triplet learning algorithms.
result Established general high-probability generalization bound for triplet learning algorithms.
Paper shows how to use elementary triplets to simplify independence model operations.
problem Simplifying operations with independence models.
method Using elementary triplets to represent conditional independences.
result Elementary triplets help in various operations like finding dominant triplets and computing model unions/intersections.
TripletGAN uses triplet loss to improve generative models, preventing mode collapse.
problem Mode collapse in generative models.
method Substituting discriminator's classification loss with triplet loss.
result TripletGAN helps prevent mode collapse and converges to the given distribution.
Triplet networks improved with GANs for better classification.
problem Improving classification performance of triplet networks.
method Training a triplet network as the discriminator in GANs.
result Significant improvement in classification performance using simple k-nn.
Proposes new kernel functions from similarity triplets.
problem Creating kernel functions from similarity triplets data.
method Defines kernel functions based on high-dimensional embeddings.
result Kernel functions can be used with any kernel method.
VBTA learns across domains using triplet information.
problem Learning across different domains using limited data.
method Variational Bi-domain Triplet Autoencoder (VBTA) with triplet constraints.
result Improved performance on various tasks.
Enhances DNN robustness with adversarial training and triplet loss.
problem Vulnerability of DNNs to adversarial examples.
method Adversarial Training with Triplet Loss (AT2L) incorporating triplet loss into adversarial training framework. result Significantly improves DNN robustness without accuracy loss.
Novel method decorrelates batches of triplets for active metric learning.
problem Correlation among triplets degrades active learning performance.
method Proposes a novel method to decorrelate batches of triplets, balancing informativeness and diversity.
result Method outperforms state-of-the-art in active metric learning.
Personalized activity recognition improves performance for diverse users.
problem Poor performance of impersonal algorithms for individual users.
method Personalized activity recognition using deep embeddings from a fully convolutional neural network with triplet loss.
result Novel subject triplet loss provides the best performance overall.
TripletBoost learns classifiers from noisy triplet comparisons.
problem Learning from comparison-based data.
method Aggregate weak classifiers from weakly learned triplets, then boost.
result Theoretical guarantees and empirical competitiveness.
The paper introduces uncertainty estimates for embedding objects based on noisy triplet comparisons.
problem Learning from ordinal data without a distance metric.
method Bootstrap and Bayesian approaches to estimate uncertainty for embedding algorithms.
result Empirical uncertainty estimates are well-calibrated and useful for selecting parameters or quantifying uncertainty.
Paper proposes an unbiased classifier from triplet comparison data.
problem Learning a classifier from triplet comparison data.
method Empirical risk minimization framework with an unbiased estimator.
result The proposed method achieves better performance than baseline methods.
Paper proposes semi-supervised learning with triplet Markov chains.
problem Lack of labels in training data.
method Variational Bayesian inference for semi-supervised learning.
result Derives semi-supervised algorithms for various sequential models.
Visualization tools show how embeddings generalize beyond validation data.
problem Understanding how learned embeddings generalize to new data.
method Visualization tools and triplet selection strategies for metric learning.
result Best performance in metric learning comes from selecting a few well-considered triplets.
TristouNet improves speaker comparison using neural networks and triplet loss.
problem Speaker comparison and change detection in short speech turns.
method Triplet loss for training neural network to project speech sequences into fixed-dimensional space.
result Significant improvements over state-of-the-art techniques for speaker comparison and change detection.
This paper shows how optimizing with hard negative examples improves image retrieval.
problem Training with hard negative examples leads to poor training behavior.
method Characterize the space of triplets, derive why hard negatives fail, and offer a fix to the loss function.
result Optimizing with hard negative examples leads to more generalizable features and better image retrieval.
Alternative approach to regularize time-dependent singular Lagrangian systems.
problem Regularizing time-dependent singular Lagrangian systems.
method Employing the coisotropic embedding theorem and the Tulczyjew isomorphism.
result Uniqueness of the Lagrangian regularization to first order.
TVAE integrates deep metric learning into VAE for better latent embedding.
problem Lack of fine-grained data representation in traditional VAE.
method TVAE combines deep metric learning with VAE, optimizing a triplet loss on VAE's mean vectors.
result TVAE achieves higher triplet accuracy (95.60%) compared to traditional VAE (75.08%).
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.
problem Understanding the behavior of the semi-hard triplet loss function.
method Developed a higher-order asymptotic analysis using the Edgeworth expansion.
result Derived explicit Edgeworth expansions revealing first-order corrections in terms of the third cumulant.
Paper introduces new loss functions for Siamese networks using FDA.
problem Training Siamese networks with improved loss functions.
method Proposes Fisher Discriminant Triplet (FDT) and Fisher Discriminant Contrastive (FDC) loss functions based on FDA.
result Shows effectiveness of FDT and FDC on MNIST and histopathology datasets.
A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hami…
Develops optimal trading strategy for illiquid currency pairs.
problem Maximizes revenues for a broker liquidating an illiquid currency pair.
method Uses a currency triplet strategy, considering model ambiguity, and employs simulations.
result Mean P&L increases and standard deviation decreases as ambiguity aversion increases.
End-to-end deep triplet ranking network for one-shot learning.
problem Efficiently classifying new classes with only one labeled instance.
method Triplet ranking loss for embedding learning and incorporating one-shot instances.
result Improved performance on one-shot learning datasets.
A new method uses triplet embeddings to improve human annotation for hidden constructs.
problem Improving human annotation for hidden constructs in machine learning.
method Proposes a novel annotation approach using triplet embeddings to lift absolute annotations to relative comparisons.
result Successfully represents synthetic hidden constructs in time under noisy sampling conditions.
The static of smooth maps from the two-dimensional disc to a smooth manifold can be regarded as a simplified version of the Classical Field Theory. In this paper we construct the Tulczyjew triple for the problem and describe the Lagrangian and Hamiltonian formalism. We outline also natural generalizations of this appro…
PerceptNet learns haptic signal similarity using human data.
problem Designing haptic icons requires accurate perceptual similarity estimation.
method Deep neural network projecting signals to an embedding space with a triplet loss.
result Our method effectively models perceptual dissimilarity compared to alternatives.