We construct and identify star representations canonically associated with holonomy reducible simple symplectic symmetric spaces. This leads the a non-commutative geometric realization of the correspondence between causal symmetric spaces of Cayley type and Hermitian symmetric spaces of tube type.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “causal symmetric spaces”
Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved.
The article explores causal structures in symmetric spaces and their relation to AQFT.
problem Understanding causal structures in symmetric spaces and their applications in AQFT.
method Classification of reductive causal symmetric spaces using Euler elements and 3-grading.
result Extraction of real Matsuki crowns and description of stabilizer groups of Euler elements.
Study open orbits in causal flag manifolds with applications in AQFT.
problem Understanding open orbits in causal flag manifolds for applications in AQFT.
method Analyzing open orbits of symmetric subgroups on causal flag manifolds, focusing on invariant causal structures and modular flows.
result Determine the positivity regions of modular flows and their global hyperbolicity for different types of open orbits.
Symmetric observations don't necessarily imply symmetric causal explanations.
problem Inferring causal models from observed correlations is challenging and computationally intensive.
method An explicit example using a tripartite probability distribution over binary events.
result Symmetries in observations cannot be used to reduce the hypothesis space of causal models.
Study modular geodesics and wedge domains in non-compactly causal symmetric spaces.
problem Understanding the geometric implementation of modular group in symmetric spaces.
method Analyzing the flow generated by Euler elements and their geometric properties.
result The wedge region W is connected and coincides with the observer domain under certain conditions.
Rigidity of causal mapsmath.DG
We show that order-invariant injective maps on the noncompactly causal symmetric space belong to .
Using symmetric space techniques, we show that closed orbits of the Iwasawa subgroups of naturally define singularities of a black hole causal structure in anti-de Sitter spaces in dimensions. In particular, we recover for the non-rotating massive BTZ black hole. The method presented here i…
The abstract discusses a new causal structure on manifolds using paths and points.
problem Constructing a causal structure on manifolds using paths and points.
method Constructing a four-manifold from pairs of points and paths, and a seven-dimensional manifold from pairs of points and conics.
result The causal structure corresponds to a conformal structure only when the underlying surface is a real projective plane.
Characterizes stably elliptic elements in Lie groups and their properties.
problem Understanding stably elliptic elements in Lie groups and their geometric and algebraic properties.
method Characterization through fixed point algebra and Weyl group action; relates to maximal invariant cones and compactness of order intervals.
result Connected components of stably elliptic elements can be described using Weyl group action on a compactly embedded Cartan subalgebra.
Geometric Causal Modelsstat.ML
Develops geometric causal models for causal inference from dependent data.
problem Causal inference from structured, dependent data (e.g., spatial, network, molecular).
method Geometric causal models (GCMs) exploiting symmetries of data generating process, combining group theory, ergodic theory, and Bayesian inference.
result Establishes identification and estimation of causal effects from dependent data.
In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property…
Novel criterion identifies heteroscedastic noise in causal discovery.
problem Heteroscedastic noise violates equal-variance assumption in causal discovery.
method Skewness-based criterion for identifying HSNMs.
result Skewness-based criterion distinguishes causal from anticausal directions.
Study uncovers new phase transitions in asymmetric causal inference scenarios.
problem Understanding typical phase transitions in asymmetric causal inference.
method Combining Causal inference (C-inf) and Low-rank recovery (LRR) with Random duality - Free probability theory (RDT-FPT).
result Discovering a doubling low-rankness phenomenon in asymmetric scenarios.
This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert--Schmidt norm of the cross-covariance operator) and transfer entrop…
A rank-n tensor on a Lorentzian manifold V whose contraction with n arbitrary causal future directed vectors is non-negative is said to have the dominant property. These tensors, up to sign, are called causal tensors, and we determine their general properties in dimension N. We prove that rank-2 tensors which map the n…
The paper explores conjugate points in Lorentzian spaces, comparing different definitions and proving related theorems.
problem Understanding conjugate points in Lorentzian geometry.
method Introducing and comparing different definitions of conjugate points in synthetic Lorentzian length spaces.
result All defined notions of conjugate points are compatible with the smooth spacetime setting.
New exact spherically symmetric vacuum solutions found in Finsler gravity.
problem Finding exact vacuum solutions in Finsler gravity.
method Spherically symmetric, asymptotically flat Berwald spacetimes solved for Finsler gravity vacuum equation.
result Only one class of spherically symmetric Berwald spacetimes is compatible with asymptotic flatness and a well-defined causal structure.
The paper constructs a Poisson algebra bundle for multilocal observables.
problem Representing multilocal observables in classical field theory.
method Working with unordered configuration spaces and using symmetric algebras with respect to two tensor products.
result Obtained a Poisson 2-algebra bundle mimicking Peierls bracket.
The most likely common causephysics.data-an
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
SkewD robustly discovers causal relationships in skewed noise models.
problem Distinguishing cause from effect in skewed noise models.
method SkewD extends normal-distribution framework to skew-normal setting for reliable inference.
result SkewD remains robust under high skewness, improving reliability.
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of th…
Study subgroups preserving proper domains in flag manifolds.
problem Identify subgroups preserving proper domains in flag manifolds.
method Establish necessary conditions and introduce causal convexity in Shilov boundary.
result Transverse subgroups with geometric properties in Shilov boundary.
We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, test…
In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…
We find necessary and sufficient conditions for existence of a locally isometric embedding of a vacuum space-time into a conformally-flat 5-space. We explicitly construct such embeddings for any spherically symmetric Lorentzian metric in dimensions as a hypersurface in . For the Schwarzschild metric the…
A new measure of causal influence quantifies intrinsic contributions in DAGs.
problem Quantifying intrinsic causal contributions in Directed Acyclic Graphs (DAGs).
method Recursive decomposition of node contributions, structure-preserving interventions, Shapley symmetrization.
result A measure of intrinsic causal contribution that is invariant to node relabeling.
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction and it takes its maximal value at the cen…
Study gluing of Lorentzian length spaces and their causal ladder properties.
problem Compatibility of Lorentzian amalgamation with length space properties.
method Conditions for gluing Lorentzian length spaces and criteria for causal ladder preservation.
result Gluing of Lorentzian length spaces yields again a Lorentzian length space under certain conditions.
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causality violations, which Bonnor and Steadman identified even in solutions to the Einstein equation referring to ordinary laboratory situations, are not necessarily undesirab…
We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on and Randers metrics on . In particular, for stationary spacetimes, we give a simple characterization of when they are causally conti…
Study on symmetric hyperbolic systems with nonlocal potentials, proving well-posedness and existence of solutions.
problem Initial value problem for symmetric hyperbolic systems with nonlocal potentials.
method Analysis on globally hyperbolic Lorentzian manifolds, proving existence, uniqueness, and regularity of solutions.
result Established well-posedness of the Cauchy problem for symmetric hyperbolic systems with nonlocal potentials.
Study causal structure of warped spacetimes using novel pre-length spaces.
problem Understanding the causal structure of warped spacetimes.
method Novel notion of Lorentzian pre-length spaces and proof of causal completion as globally hyperbolic pre-length space.
result Causal completion of GRW spacetime is a globally hyperbolic pre-length space under Hausdorff chronological topology.
Study on metrizability and Ricci-flatness of Finsler spaces with Kropina metrics.
problem Investigating metrizability and Ricci-flatness of Finsler spaces with specific metrics.
method Analyzing the Levi-Civita connection, covariant derivative of 1-forms, and using cohomology groups.
result Explicitly obtained all Ricci-flat, locally metrizable m-Kropina metrics in (3+1)D.
Study defines new products for Lorentzian spaces and analyzes causal diamonds.
problem Understanding causal diamonds in Lorentzian spaces.
method Introduced taxicab and uniform products for Lorentzian pre-length spaces. Defined space and analyzed its properties.
result The space is geodesic and globally hyperbolic for complete .
CASPER improves DAG structure learning by integrating graph structure into score function.
problem Discovering suboptimal DAGs and model vulnerabilities in causal discovery.
method CASPER integrates graph structure into the score function as a new measure in the causal space, enhancing DAG structure learning via adaptive attention to DAG-ness.
result CASPER outperforms state-of-the-art methods in terms of accuracy and robustness.
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study c…
Complete classification of quaternionic skew-Hermitian symmetric spaces found.
problem Classifying quaternionic skew-Hermitian symmetric spaces.
method Proving the existence of a torsion-free -structure and showing that any homogeneous space is symmetric.
result A complete classification of quaternionic skew-Hermitian symmetric spaces for arbitrary .
Compactness theorem for timed-metric spaces established.
problem Compactness of timed-metric spaces and causality.
method Timed-Gromov--Hausdorff distance and intrinsic timed-Hausdorff distance.
result Induces same notion of convergence as intrinsic timed-Hausdorff distance.
This research tackles intervention-centric causal reasoning in learning agents by using meta-learning.
problem Learning agents lack the concept of interventions, making causal learning challenging.
method A meta-reinforcement learning algorithm is used to learn causal relationships from observational data.
result The approach enables agents to learn and manipulate the environment effectively.
Method infers causal structure from system behaviors using RKHS and kernel -machines.
problem Discovering causal structure in systems with varying external and measurement noise.
method Combines causal states and RKHS for efficient representation and inference of causal structure.
result Robustly estimates causal structure in high-dimensional data with varying noise.
New proof for symmetric spaces with rectangular lattices.
problem Characterizing symmetric spaces with rectangular unit lattices.
method Explicit construction of isometric embeddings and analysis of root systems.
result Symmetric spaces with rectangular unit lattices are symmetric R-spaces.
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
problem Determining inextendibility of spacetimes near singularities.
method Asymptotic analysis of volume-distance-ratio (VDR) to prove inextendibility criteria.
result Failure of VDR convergence to the Minkowski value implies inextendibility of spacetime.
New model learns causal world dynamics from state space models.
problem Lack of causal world models in neural world modeling.
method State Space Models (SSM) with attention mechanisms.
result SSM can learn causal models of environments with equivalent performance.
Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.
problem Characterize para-Sasakian φ-symmetric spaces.
method Use Boothby-Wang fibration to construct and provide examples.
result Explicit construction and example of para-Sasakian φ-symmetric spaces.
M-CaStLe discovers causal structures in multivariate space-time data.
problem Challenges in causal graph discovery for high-dimensional gridded data.
method Generalizes CaStLe to multivariate analyses, using local embeddings and pooling spatial replicates.
result More accurately recovers multivariate causal structure and identifies physical dynamics.
Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite dimensional generalization: Affine Kac-Moody symmetric spaces. Affine Kac-Moody …