Geometric framework for dissipative systems on Lie algebroids.
problem Formulating geometric framework for dissipative systems.
method Herglotz-type variational principle on Lie algebroids.
result Recover classical equations as special cases.
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48 results for “Herglotz condition”
Rigidity of spectral data for spherical manifolds with boundary.
problem Determining the length spectrum of spherically symmetric manifolds with boundary.
method Proving a trace formula and using it to show spectral rigidity.
result The Neumann spectrum uniquely determines the length spectrum for spherically symmetric manifolds with boundary.
Paper derives invariantised Euler-Lagrange equations for Herglotz problems.
problem Nonconservative Herglotz variational problems.
method Invariant calculus of variations and moving frames.
result Derivation of generalised Euler-Lagrange equations and conserved quantities.
Injectivity of geodesic ray transform on specific Finsler manifolds proven.
problem Injectivity of geodesic ray transform on spherically symmetric reversible Finsler manifolds.
method Reduction to invertibility of generalized Abel transforms using angular Fourier series and Taylor expansions of geodesics.
result Injectivity of geodesic ray transform proven on specified Finsler manifolds.
Develops theory of contact systems with nonholonomic constraints.
problem Nonholonomic constraints in contact systems.
method Variational principle and projection of Hamiltonian vector field.
result Nonholonomic dynamics as projection of unconstrained dynamics.
The paper integrates dissipative and curl forces using geometric methods.
problem Incorporating dissipative forces into curl forces for non-conservative systems.
method Geometric metriplectic approach, Herglotz principle, generalized Euler-Lagrange equation, Galley's method.
result Natural formulations for Lagrangian and Hamiltonian dynamics of non-conservative systems.
Paper extends variational problem to spheres using control methods.
problem Extending classical variational problem to spheres.
method Variational and optimal control approaches.
result Established relation between Hamiltonian and Euler-Lagrange equations.
Variational reduction simplifies Lagrangian systems with scaling symmetries.
problem Simplifying Lagrangian systems with scaling symmetries.
method Defining a variational reduction procedure for homogenous Lagrangian systems.
result Reconstructing trajectories from critical points of reduced variational principle.
Reduces equations for contact mechanical systems on Lie groups by exploiting symmetries.
problem Contact mechanical systems on Lie groups with symmetries.
method Reduction process using Lie group actions and symmetries.
result Euler-Poincaré-Herglotz equations on the reduced phase space.
We study ray transforms on spherically symmetric manifolds with a piecewise metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds …
Contact Tulczyjew Geometry for Continuous and Discrete Dissipative Dynamics on Skew Algebroidsmath-ph
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
Research decouples Lie algebroids using bicocycle double cross product theory.
problem Understanding decoupling and coupling phenomena in Lie algebroids.
method Bicocycle double cross product realization method.
result Unified product, double cross product, semi-direct product, and cocycle extension frameworks are instances of the general method.
Suppose M_t is a smooth family of compact connected two dimensional submanifolds of Euclidean space E^3 without boundary varying isometrically in their induced Riemannian metrics. Then we show that the mean curvature integrals over M_t are constant. It is unknown whether there are nontrivial such bendings. The estimate…
The evolution operator connecting the Lagrangian and Hamiltonian formalisms for contact systemsmath-ph
This paper extends the evolution operator to contact mechanics, linking Lagrangian and Hamiltonian formulations.
problem Translating the evolution operator to contact mechanics for mechanical systems with dissipation.
method Using the evolution operator K to connect Lagrangian and Hamiltonian formalisms in contact mechanics.
result The evolution operator provides a geometric description of evolution equations and relates constraints.
Reduces symplectic Hamiltonian systems to contact systems, realizing Poincaré's dream.
problem Scaling symmetries in Hamiltonian systems.
method Contact reduction of symplectic Hamiltonian systems.
result Generically possible reduction to contact Hamiltonian systems, reducing inputs needed.
In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary . We show that the boundary distance function, i.e., , known near a point at which is strictly convex, determines in a suita…
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
The paper classifies Finsler surfaces satisfying the T-condition or σT-condition.
problem Characterizing Finsler surfaces based on specific tensor conditions.
method Analyzing Finsler surfaces in dimensions n≥3, proving conditions equivalence, and solving PDEs.
result All Finsler surfaces satisfying the T-condition or σT-condition are classified.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional -space.
result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
We extend probabilistic programming to handle conditioning on marginal distributions.
problem Conditioning probabilistic programs on marginal distributions of observable variables.
method We define and implement stochastic conditioning, allowing inference in probabilistic programs conditioned on marginal distributions.
result We demonstrate the effectiveness of stochastic conditioning in various real-life scenarios.
Paper constructs solutions to Bogomolny equations with specific boundary and asymptotic conditions.
problem Constructing solutions to Bogomolny equations with given boundary and asymptotic conditions.
method Using generalized Nahm pole boundary condition and real symmetry breaking condition.
result Solutions analogous to instanton solutions, satisfying different asymptotic conditions.
New tests for conditional copulas based on decision trees.
problem Testing constancy of conditional dependence structure given conditioning events.
method Data-driven decision trees to maximize differences in conditional Kendall's tau.
result Asymptotic distributions of test statistics under the null hypothesis.
Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.
problem Logarithmic Minkowski problem in higher dimensions.
method Established a necessary condition through generalization and refinement of previous work.
result Generalizes and refines necessary condition for logarithmic Minkowski problem.
Identifies conditional parity as a general notion of non-discrimination in machine learning.
problem Addressing non-discrimination in machine learning models.
method Identifies conditional parity as a general notion of non-discrimination and studies randomization and a kernel-based test to analyze it.
result Conditional parity is a general notion of non-discrimination and several recent notions of non-discrimination are instances of conditional parity.
This paper introduces a neural operator for probabilistic conditioning.
problem Probabilistic conditioning of random variables given .
method Develops a single operator that maps any joint density to its conditional, approximated by neural operators.
result Neural operators can approximate the conditioning operator to arbitrary accuracy.
CSI method learns conditional distributions by estimating flow equations.
problem Learning conditional distributions in generative models.
method Estimates probability flow equations to transport reference to target distribution.
result Derives explicit expressions for conditional drift and score functions.
New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
A new method for learning conditional distributions using ODEs and neural networks.
problem Learning conditional distributions efficiently and accurately.
method Conditional Föllmer Flow, discretized with Euler's method, using nonparametric velocity estimation.
result Effective approximation of target conditional distributions, with convergence results for Wasserstein-2 distance.
Sharp statistical theory for conditional diffusion models.
problem Lack of theoretical foundation for conditional diffusion models.
method Sharp statistical theory with approximation of conditional score function.
result Sample complexity bound that adapts to data distribution smoothness.
An analysis is made of reality conditions within the context of noncommutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule is equivalent to the reality condition. We show also that the matrix which determines the reality condition must satisfy the Yang-…
The Bakry-Émery condition is satisfied for glued spaces of Riemannian manifolds.
problem Conditions for metric measure spaces to satisfy the Bakry-Émery condition.
method Sufficient and necessary conditions for the Bakry-Émery condition on glued spaces of Riemannian manifolds.
result The Bakry-Émery condition is strictly weaker than the RCD condition and the local dimension is not constant.
Sufficient conditions for the absence of relaxation gaps in state-constrained optimal controlmath.OC
New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
Kernel conditional exponential family generalizes conditional distributions.
problem Modeling conditional distributions with flexibility and consistency.
method Introduces a nonparametric family using RKHS and functional parameters, with an algorithm for learning the natural parameter.
result Consistency of the estimator in well-specified cases, and superior performance in experiments.
Develops a rigorous theory for conditional mean embeddings.
problem Efficient conditioning of probability distributions in RKHSs.
method Mathematical theory for both centred and uncentred covariance operators.
result Significantly weakens conditions for applicability of CMEs.
We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…
Proposes a new method for interpreting feature importance and effects in dependent feature models.
problem Challenges in interpreting feature importance when features are dependent and interactions are present.
method Conditional Subgroup Approach
result Conditional PFI and PDP estimates based on this approach often outperform existing methods.
This paper investigates how policy conditioning affects reinforcement learning stability.
problem Improving stability and generalization of reinforcement learning agents.
method The authors study Jacobian conditioning behavior during policy optimization and propose a conditioning regularization algorithm.
result The proposed conditioning regularization algorithm enhances reinforcement learning agent generalization.
Two conditions on primitive elements are shown to be equivalent.
problem Equivalence of primitive stability and Bowditch's -condition.
method Proof of equivalence between two conditions on primitive elements.
result Primitive stability and Bowditch's -condition are equivalent.
New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.
problem Understanding non-local boundary conditions for Dirac operators on spacetimes.
method Define and analyze a class of Lorentzian boundary conditions that are local in time and non-local in spatial directions.
result Well-posed Cauchy problem for the Dirac operator is established under these conditions.
A method for estimating conditional mode using multiple quantile regressions.
problem Estimation of conditional mode with high-dimensional conditioning variables.
method Estimate conditional density by solving multiple quantile regressions, then find the maximum of the estimated density.
result The proposed method is computationally stable and statistically efficient with a fast convergence rate.
We extend CS divergence to conditional distributions and show its advantages in time series data and sequential decision making.
problem Quantifying the closeness between conditional distributions.
method Developed and estimated a conditional Cauchy-Schwarz divergence using kernel density estimation.
result Conditional CS divergence outperforms previous methods in time series clustering and sequential decision making.
Improves conditional image generation quality on ImageNet dataset.
problem Improving conditional image generation quality on ImageNet dataset.
method Projection-based discriminator modification in GANs.
result Significantly improved image generation quality on ILSVRC2012 dataset.
Paper addresses Heston model under violated Feller condition, deriving new change of measure conditions.
problem Investigates Heston model under Feller condition violation.
method Derives sufficient conditions for equivalent martingale measure and true martingale stock price process.
result New conditions for change of measure and martingale properties in Heston model are established.
The Samuelson condition is not satisfied by tangent lines of quadratic curves.
problem Area condition for Lagrangian 2-web
method Show that the Samuelson condition is not satisfied
result The Samuelson condition is not satisfied by tangent lines of quadratic curves.
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…
From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Mapsstat.ML
A new method tests conditional independence by transforming it into an unconditional problem using transport maps.
problem Testing conditional independence between two random vectors given a third.
method Constructing transport maps to transform conditional independence into unconditional independence, estimating these maps from data using conditional continuous normalizing flow models.
result The proposed method is validated through simulations and real-data analysis, demonstrating practical effectiveness.
DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
problem DG algorithms fail to consistently outperform ERM in limited domains.
method Examined necessary and sufficient conditions for DG, proposing a subspace alignment method.
result DG methods focus on sufficient conditions, often neglecting necessary conditions, leading to generalization failures.
Generalizes moment-matching for exponential families with conditioning or hidden data.
problem Generalizing moment-matching conditions for exponential families with conditioning or hidden data.
method First-principles explanation and self-contained derivation of generalized moment-matching conditions.
result Derives generalized moment-matching conditions for conditional exponential families and hidden data.