The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show tha…
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48 results for “tetradic action”
The main result of the paper is a new representation of the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that…
algcomparison: Comparing the Performance of Graphical Structure Learning Algorithms with TETRADstat.ML
In this report we describe a tool for comparing the performance of graphical causal structure learning algorithms implemented in the TETRAD freeware suite of causal analysis methods. Currently the tool is available as package in the TETRAD source code (written in Java). Simulations can be done varying the number of run…
Paper extends FOFC algorithm to work with mixed data types.
problem Designing causal discovery algorithms for mixed data types.
method Proves tetrad constraint can be entailed for mixed data types and applies FOFC algorithm.
result FOFC algorithm can work on mixed data types.
Geometric obstructions prevent gravity in high dimensions.
problem Obstacles to realizing gravity in various geometries.
method Analyzing the tetradic Einstein-Hilbert-Palatini action in different geometric settings.
result Gravity is only meaningful in Lorentzian geometry for dimensions .
Study examines how Lorentz transformations affect foliations in spacetime.
problem Understanding foliations and their relation to observers under Lorentz transformations.
method Exploration of kinematic characteristics of timelike congruences (observers) and their relation to foliations.
result Local Lorentz transformations impact the existence of transversal foliations.
The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show tha…
An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Carta-Maxwell-Dirac fields based on "minimal geometric data": all the needed underlying structure is geometrical…
Metric and Gauge Extensorsmath.DG
In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology . We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, g…
The work focuses upon the relativistic and geometric properties of the space--time endowed tentatively with the metric function of the Berwald--Moor type. The zero curvature of indicatrix is a remarkable property of the approach. We demonstrate how the associated geodesic equations can be solved in a transparent way, t…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi-Civita connection. Such deformations and induced…
Study null curves and their motion in 3D flat space-time, leading to integrable hierarchies.
problem Understanding null curves and their motion in 3D flat space-time.
method Analyzing the motion of null curves and their surfaces, deriving integrability conditions and hierarchies.
result Obtained one- and two-soliton surfaces associated with the MKdV equation, showing singularities in finite time.
We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spac…
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjust…
Benchpress streamlines benchmarking structure learning algorithms for probabilistic models.
problem Benchmarking structure learning algorithms for probabilistic graphical models.
method Snakemake workflow for scalable, reproducible benchmarks.
result Demonstrates applicability in five typical data scenarios.
Three RFF-based methods for nonlinear causal discovery in mixed data.
problem Nonlinear causal discovery in mixed data with computational constraints.
method FFML, TRFF, and FFCI methods for score-based, constraint-based, and hybrid causal discovery.
result FFML and TRFF methods provide complementary performance in causal discovery.
Homologically trivial symplectic cyclic actions need not extend to Hamiltonian circle actionsmath.SG
We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies holomorphic methods to extend combinatorial tools developed for circle actions to stu…
Reduces proper actions to simpler core actions for analysis.
problem Understanding properties of proper actions on manifolds.
method Extending Skjelbred and Straume's construction to non-compact groups, focusing on core of actions.
result Properties of proper actions are determined by simpler core actions.
Introduces Conditional Action Trees to simplify RL action spaces.
problem Challenges in RL with large, complex action spaces.
method Structures action spaces and reduces complexity through Conditional Action Trees.
result Demonstrates effectiveness in reducing action space and improving decision making.
Macro Action Reinforcement Learning with Sequence Disentanglement using Variational Autoencodercs.LG
One problem in the application of reinforcement learning to real-world problems is the curse of dimensionality on the action space. Macro actions, a sequence of primitive actions, have been studied to diminish the dimensionality of the action space with regard to the time axis. However, previous studies relied on human…
Study polar actions on Damek-Ricci spaces, proving existence and finding examples.
problem Characterize polar actions on Damek-Ricci spaces.
method Prove criteria for isometric actions to be polar, find examples, and classify actions.
result Non-trivial polar actions exist on all Damek-Ricci spaces.
New RL algorithm tackles complex discrete action spaces.
problem Challenges in applying on-policy RL in high-dimensional discrete action spaces.
method Action-value critic, correlated actions, gradient sparsification.
result Empirically outperforms related on-policy algorithms.
Reduction principles for proper actions on smooth manifolds.
problem Proper actions on smooth manifolds and their properties.
method Exhibit constructions and prove reduction principles for proper actions.
result Reduction principles hold for proper actions, polar actions, and copolarity.
Sections of polar actionsmath.DG
Totally geodesic sections found in polar actions.
problem Understanding sections of polar actions on Riemannian manifolds.
method Elementary proof of a folklore result.
result Sections of polar actions are totally geodesic.
Simplifies large action space bandits by selecting representative actions.
problem Efficiently managing large action spaces with correlated outcomes.
method Random sampling and solving of bandit instances to identify representative actions.
result The algorithm selects a smaller set of representative actions that perform nearly as well as the full action space.
We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual compact symmetric space, which reflects many properties of the original action. F…
Classifies totally geodesic submanifolds and polar actions on Stiefel manifolds.
problem Classifying totally geodesic submanifolds and polar actions on Stiefel manifolds.
method Classification through polar actions and cohomogeneity-one actions.
result Classification of orbits of polar actions on Stiefel manifolds.
Conditions for reducing quasi-actions to tree actions and group properties.
problem Conditions for reducing quasi-actions to tree actions.
method Reduction to cobounded isometric actions on trees.
result Groups with quasi-orbits quasi-isometric to trees are virtually free.
The study proves conditions for symplectic torus actions on manifolds with non-contractible orbits.
problem Conditions for symplectic torus actions with non-contractible orbits.
method Analyzes symplectic torus actions on manifolds, proving conditions for Hamiltonian actions and orbit properties.
result Symplectic actions with non-contractible orbits are not Hamiltonian unless the orbits are contractible.
We identify action representations from video data, proving their statistical benefits.
problem Identifying latent action policies from video data.
method Entropy-regularized LAPO objective, formalizing desiderata for action representations.
result Entropy-regularized LAPO identifies action representations satisfying desiderata under suitable conditions.
Study properties of orbits of Hermann actions without commutability assumptions.
problem Investigate geometric properties of orbits of Hermann actions.
method Compute the second fundamental form and provide conditions for weak reflection and aridity.
result Sufficient conditions for weak reflection and aridity of orbits of Hermann action.
We classify the polar actions on the complex hyperbolic plane up to orbit equivalence. Apart from the trivial and transitive polar actions, there are five polar actions of cohomogeneity one and four polar actions of cohomogeneity two.
A new method learns action representations for reinforcement learning.
problem Efficient action-value estimation in reinforcement learning.
method Action hypergraph networks framework for learning action representations.
result Hypergraph Q-networks show effectiveness on various domains.
The paper studies curvatures and austere properties of orbits in symmetric spaces.
problem Analyzing curvatures and austere properties of orbits in symmetric spaces.
method Using Hermann actions and hyperpolar properties, the paper derives explicit formulas for principal curvatures and conditions for orbits to be austere.
result The paper provides conditions for orbits to be austere and extends previous results to a larger class of infinite-dimensional submanifolds.
New reinforcement learning framework for adapting to new actions.
problem Making reinforcement learning agents adaptable to new actions without retraining.
method Two-stage framework: infer action representations first, then train a flexible policy.
result Agents can make decisions from new action sets without retraining.
AQL uses amortized inference to handle high-dimensional action spaces in Q-learning.
problem Difficulty in maximizing over large action spaces in Q-learning.
method Replace expensive maximization over all actions with a maximization over a small subset sampled from a learned proposal distribution.
result AQL outperforms existing methods on continuous control tasks with up to 21 dimensional actions.
Defines and computes a generalized spectral action for Lorentz warped products.
problem Computing spectral actions for Lorentz warped products.
method Defines and computes the bimetric spectral Einstein-Hilbert action for Lorentz warped products.
result Derives a Kastler-Kalau-Walze type theorem for Lorentz warped products.
The paper studies acylindrical actions on trees and proves acylindrical hyperbolicity of Baumslag-Solitar groups.
problem Exploring acylindrical actions on trees and their properties.
method Demonstrates criteria for preserving acylindrical hyperbolicity and analyzes the outer automorphism group of Baumsligar-Solitar groups.
result Proves acylindrical hyperbolicity of non-solvable Baumsligar-Solitar groups.
UTE improves reinforcement learning by measuring action uncertainty, enhancing policy learning efficiency.
problem Degrading performance of action repetition in reinforcement learning, especially with sub-optimal actions.
method UTE uses ensemble methods to measure uncertainty during action extension, allowing strategic exploration or certainty.
result UTE outperforms existing action repetition algorithms, significantly enhancing policy learning efficiency.
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
Proper actions on bornological spaces are characterized with compatible coarse structures.
problem Characterizing proper actions on bornological spaces.
method Proving the existence of compatible coarse structures for proper actions.
result Bornological spaces admit compatible coarse structures for proper actions.
Learning how to act when there are many available actions in each state is a challenging task for Reinforcement Learning (RL) agents, especially when many of the actions are redundant or irrelevant. In such cases, it is sometimes easier to learn which actions not to take. In this work, we propose the Action-Elimination…
We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…
The study examines how perturbations of lattice actions on group boundaries behave.
problem Understanding how perturbations of lattice actions on group boundaries affect semi-conjugacy.
method Analyzes continuous factorization of perturbed actions onto original actions by semi-conjugacy.
result Perturbations of lattice actions on group boundaries can be semi-conjugate or not.
Non-proper surface group action on product of trees found.
problem Proper surface group action on product of trees proposed, but not proper.
method Demonstrated non-properness of the surface group action.
result Surface group action on product of trees is not proper.
We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a …
Study of symplectomorphisms on ruled surfaces under circle actions.
problem Homotopy type of equivariant symplectomorphisms on rational ruled surfaces.
method Analysis of action on compatible and invariant almost complex structures, use of Delzant's and Karshon's classifications.
result Equivariant symplectomorphisms are homotopy equivalent to tori or their pushout.
Study free circle actions on specific 7-manifolds with positive Ricci curvature.
problem Classify and construct metrics on manifolds with a specific cohomology ring.
method Classify manifolds, construct free circle actions, and find positive Ricci curvature metrics.
result Almost all manifolds admit infinitely many non-equivalent free circle actions with positive Ricci curvature.