The duality principle connects algebraic curvature tensors in pseudo-Euclidean spaces.
problem Understanding algebraic curvature tensors in pseudo-Euclidean spaces.
method Proving equivalence between the Jordan-Osserman condition and the Rakić duality principle.
result The Osserman condition and the duality principle are equivalent in the diagonalisable case.
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric spac…
In the algebraic context, we show that null Osserman, spacelike Osserman, and timelike Osserman are equivalent conditions for a model of signature (2,2). We also classify the null Jordan Osserman models of signature (2,2). In the geometric context, we show that a pseudo-Riemannian manifold of signature (2,2) is null Jo…
Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s,s) for any s (which is at least 2) which are spacelike Jordan …
Let R be an algebraic curvature tensor on a vector space of signature (p,q) defining a spacelike Jordan Osserman Jacobi operator $\JJ_R$. We show that the eigenvalues of $\JJ_R$ are real and that $\JJ_R$ is diagonalizable if p<q.
It is shown that if a compact four-dimensional manifold with metric of neutral signature is Jordan-Osserman, then it is either of constant sectional curvature or Ricci flat.
We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.
The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo (2006).
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher or…
We show the existence of a modified Cliff(1,1) structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds of signature (2,2). We obtain a new characterization of the Weyl curvature tensor of an (anti-)self-dual manifold and we …
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type (r,s) in a vector space of signature (p,q). We then use these examples to establish some results concerning higher order Osserman and highe…
We exhibit a family of generalized plane wave manifolds of signature (2,2). The geodesics in these manifolds extend for infinite time (i.e. they are complete), they are spacelike and timelike Jordan Osserman, and they are spacelike and timelike Jordan Ivanov-Petrova. Some are irreducible symmetric spaces. Some are homo…
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 L∞-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 X given Y. 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.
New risk measures for multivariate data, consistent and decomposable.
problem Developing consistent risk measures for multiple variables.
method Showed strong consistency leads to decomposition into aggregation and univariate risk.
result Multivariate risk measures are conditional certainty equivalents under strong consistency.
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.
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.
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 BQ-condition. method Proof of equivalence between two conditions on primitive elements.
result Primitive stability and Bowditch's BQ-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.
Verifies regularity for conditional expectation operators and embeddings, simplifying validation.
problem Characterizing when conditional expectation operators map between function spaces.
method Establishes a verifiable sufficient condition for bounded and Hilbert-Schmidt mappings based on conditional density regularity.
result Averifiable condition for mapping properties of conditional expectation operators simplifies validation.
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…
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.
Formula for conditional covariance matrices simplified for elliptical distributions.
problem Analytical formula for conditional covariance matrices in elliptical distributions.
method Analytical formula for conditional covariance matrices of elliptically distributed random vectors based on linear combinations of marginal variables.
result Simplified formula for conditional covariance matrices, introducing univariate invariant.
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.
Conditional probabilities modeled using Riemann-Theta Boltzmann Machines.
problem Modeling conditional probabilities in Boltzmann machines.
method Deriving conditional density functions from Riemann-Theta Boltzmann machines.
result Conditional densities can be directly inferred from Riemann-Theta Boltzmann machines.
Study on estimating conditional risk in machine learning.
problem Estimating expected loss of prediction models given input features.
method Analyzed in classification and regression settings, showing equivalence to standard regression. Developed theoretical insights and empirical validation.
result Conditional risk calibration is distinct from existing uncertainty quantification problems.