Paper proves Penrose inequality with a weaker late-time condition.
problem Penrose's inequality under the black hole final state conjecture.
method Developed a new late-time condition called quasi final state hypothesis and proved the inequality.
result Proved the spacetime Penrose inequality under the quasi final state hypothesis.
Reduces nonlinear electromechanical dynamics through quasi-steady state hypothesis.
problem Nonlinear dynamics of electromechanical systems.
method Quasi-steady state hypothesis, non-dimensionalization, scaling.
result Physical justification and characteristic time scales of dynamics.
A test for neural networks identifies genetic associations.
problem Testing complex associations in neural networks.
method Sieve quasi-likelihood ratio test for neural networks with one hidden layer.
result The test statistic has an asymptotic chi-squared distribution.
Study new involutivity theorems for Poisson quasi-Nijenhuis manifolds.
problem Understanding involutivity in Poisson quasi-Nijenhuis geometry.
method Present new versions of deformation and involutivity theorems under specific factorization hypotheses.
result New versions of involutivity theorems for Poisson quasi-Nijenhuis manifolds.
New class of manifolds studied with special properties.
problem Characterizing and studying a new class of almost contact metric manifolds.
method Introducing anti-quasi-Sasakian manifolds and analyzing their properties.
result Anti-quasi-Sasakian manifolds with constant curvature are flat and cokähler.
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in F(R)-gravity.
problem Characterizing spacetimes with quasi-constant sectional curvature.
method Investigation through examples, proofs, and analysis of energy conditions.
result A spacetime of quasi-constant sectional curvature can represent a Robertson Walker spacetime or a static spacetime.
The Schatten-p quasi-norm (0<p<1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may…
Study deformations of compact Calabi-Yau conifolds with singularities.
problem Understanding deformations of compact Calabi-Yau conifolds with singularities.
method Analyzes the obstructions and local triviality of deformations under specific topological and geometric hypotheses.
result Obstruction to deformations concentrates at singularities, generalizing previous results.
Quantum machine learning classification depends on mutual informations between state and parameter spaces.
problem Generalization in quantum machine learning models.
method Link between quantum machine learning and quantum hypothesis testing, using mutual informations.
result Quantum classifier accuracy and generalization depend on mutual informations between state and parameter spaces.
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…
The paper establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
problem Learning Latent Markov Decision Processes (LMDPs) with separated components.
method The paper considers various notions of separation and establishes a nearly-sharp statistical threshold for efficient learning. It also presents a quasi-polynomial algorithm with time complexity scaling in terms of the statistical threshold under a weaker assumption of separability under the optimal policy, and a near-matching time complexity lower bound under the exponential time hypothesis.
result Establishes a nearly-sharp statistical threshold for efficient learning in Latent MDPs with separated components.
The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with general…
Momentum-based acceleration of stochastic gradient descent (SGD) is widely used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM) as an extremely simple alteration of momentum SGD, averaging a plain SGD step with a momentum step. We describe numerous connections to and identities with other alg…
Deforms Poisson quasi-Nijenhuis manifolds using closed 2-forms.
problem Deforming Poisson quasi-Nijenhuis manifolds.
method Using quasi-Lie bialgebroids and twisting.
result Interprets deformation in terms of quasi-Lie bialgebroids and Courant algebroids.
The paper introduces a new volatility model for state heterogeneous financial markets using high-frequency data.
problem State heterogeneity in financial volatility processes.
method Developed a state heterogeneous GARCH-Ito (SG-Ito) model based on continuous Ito diffusion process.
result Empirical studies reveal various state heterogeneities in S&P 500 index volatility.
New findings on leafwise quasi-geodesic foliations in 3-manifolds.
problem Understanding leafwise quasi-geodesic foliations in 3-manifolds.
method Analyzing intersections of transverse foliations in 3-manifolds with Gromov hyperbolic leaves.
result Hausdorff leafspace condition for leafwise quasi-geodesic foliations.
The paper studies quasi-X-convex functions and their applications in optimization.
problem Optimization problems with quasi-X-convex functions. method Definition and study of X-convex, quasi-X-convex, and related functions. result Applications of quasi-X-convex functions in optimization problems. Study of groups and their quasi-isometrically embedded subgroups.
problem Understanding the structure and properties of groups and their subgroups.
method Abstracting the notion of A/QI triples and using methods from geometric group theory.
result Stability of quasi-isometrically embedded subgroups in finitely generated groups.
Study identifies transitions between traffic modes on Cologne motorways.
problem Understanding transitions between different traffic modes.
method Constructed state transition network, identified dominant states using PageRank algorithm.
result Identified seasonal dependence in traffic modes.
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated Courant algebroid is obtained. We introduce the notion of a morphism of quasi-Lie…
The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.
problem Understanding quasi-isometry in almost contact metric manifolds.
method Definition and study of quasi-isometry for almost contact metric manifolds.
result Established a relation between scalar curvature and quasi-isometric constants.
New algorithm for planning in observable POMDPs in quasi-polynomial time.
problem Planning in POMDPs is computationally hard.
method Assumption of well-separated distributions on states and observations leads to quasi-succinct descriptions of near-optimal policies.
result Quasipolynomial-time algorithm for planning in observable POMDPs.
Optimal subset selection for hypothesis testing with penalties.
problem Optimal subset selection of information sources for hypothesis testing with misclassification penalties.
method Proposes a misclassification penalty framework and studies two variants of subset selection problems under centralized Bayesian learning.
result Proves the submodularity of the objective and constraints of the subset selection problems and establishes performance guarantees for greedy algorithms.
Characterizes optimal-speed quantum state evolution Hamiltonians.
problem Optimal-speed unitary time evolution of pure and quasi-pure quantum states.
method Construction of the manifold of pure states and isometry with flag manifold, characterization of equigeodesic vectors.
result Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of the flag manifold.
The aim of this note is to give an explicit description of quasi-Einstein metrics on Hn×R. We shall construct two examples of quasi-Einstein metrics on this manifold and then we shall prove the uniqueness of these examples. Finally, we shall describe the closed relation between quasi-Einstein met…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be approximated by stochastic oracles. The proposed method combines general stochastic …
We provide a direct proof for the positivity of Chen-Nester-Tung quasi-local energy with analytic reference in spherical symmetry. A hoop-type theorem for this energy is also established. Finally, the relation between Chen-Nester-Tung and Brown-York quasi-local energies will be discussed.
The study characterizes and proves properties of 3D Poisson quasi-Nijenhuis manifolds.
problem Characterizing and understanding 3D Poisson quasi-Nijenhuis manifolds.
method Characterization through deformation and application of Haantjes structures.
result Every 3D Poisson quasi-Nijenhuis manifold is a Haantjes manifold.
Enhances RL agents with predictive internal representations.
problem Improving model-free reinforcement learning agents.
method Introduces Deep InfoMax (DIM) objective to train predictive internal representations.
result Successfully learned predictive representations in synthetic settings.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
Characterizes quasi-isometric embeddings in coarsely Lipschitz category.
problem Understanding quasi-isometric embeddings in geometric terms.
method Formalizes quasi-isometric embeddings as regular monomorphisms in coarsely Lipschitz category.
result Quasi-isometric embeddings are equivalently characterised as effective, strong, or extremal monomorphisms.
In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of L. Polterovich and M. Schwarz, we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our…
We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we see that these manifolds admit a unique metric connection that is compatible wi…
Study quasi-isometry invariants of square complexes and their applications.
problem Classifying quasi-isometry types of 2D right-angled Artin groups and graph 2-braid groups.
method Define and analyze intersection complexes for universal covers of weakly special square complexes.
result Discover new quasi-isometric relationships between graph 2-braid groups and right-angled Artin groups.
Defines new types of preinvex functions for optimization.
problem Optimization problems with new types of preinvex functions.
method Definition and analysis of w-invex functions.
result New types of preinvex functions solve optimization problems.
The paper characterizes a class of almost Kenmotsu manifolds with quasi Yamabe solitons.
problem Characterizing almost Kenmotsu manifolds with quasi Yamabe solitons.
method Analyzing the properties of quasi Yamabe solitons on (k,μ)′-almost Kenmotsu manifolds. result If a (k,μ)′-almost Kenmotsu manifold admits a quasi Yamabe soliton, then V is a constant multiple of ξ, V is a strict infinitesimal contact transformation, and (£Vh′)X=0 for any vector field X. Paper solves tracking control for (x,u)-flat systems using classical states.
problem Tracking control for (x,u)-flat systems. method Quasi-static feedback of classical states.
result Achieves linear, decoupled and asymptotically stable tracking error dynamics.
With any non necessarily orientable unpunctured marked surface (S,M) we associate a commutative algebra, called quasi-cluster algebra, equipped with a distinguished set of generators, called quasi-cluster variables, in bijection with the set of arcs and one-sided simple closed curves in (S,M). Quasi-cluster variables a…
This paper puts the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, Toën, Vaquié and Vezzosi. We compute the symplectic structures on mapping stacks and show how the AKSZ topological field theory defined by Calaque allows one to neatly package the constructio…
Cellular Electron CryoTomography (CECT) is a 3D imaging technique that captures information about the structure and spatial organization of macromolecular complexes within single cells, in near-native state and at sub-molecular resolution. Although template matching is often used to locate macromolecules in a CECT imag…
Classifies certain graph 2-braid groups up to quasi-isometry.
problem Classifying 2-braid groups over graphs up to quasi-isometry.
method Using intersection complexes and right-angled Artin groups.
result Classifies 2-braid groups over graphs with circumference ≤ 1 up to quasi-isometry.
The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.
problem Exploring new types of spacetimes in general relativity.
method Mathematical analysis of geometric and physical properties of comprehensive quasi-Einstein manifolds.
result Existence of comprehensive quasi-Einstein spacetimes and their properties.
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
problem Characterizing and classifying manifolds with specific geometric properties.
method Analyzing warped products, contact manifolds, and semi-Riemannian manifolds.
result Characterizations and classifications of weakly conformally flat and quasi-Einstein manifolds.
The paper studies m-quasi Einstein manifolds with convex potential and finds constant scalar curvature.
problem Investigating m-quasi Einstein manifolds with a convex potential function. method Analyzing integral conditions and properties of the potential vector field.
result An m-quasi Einstein manifold with a convex potential function has constant scalar curvature. Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
New lower bound shows RL with linear approximations is computationally hard.
problem Computational hardness in reinforcement learning with linear function approximation.
method Reduction from Unique-Sat to MDPs with linear optimal value functions.
result No randomized polynomial time algorithm exists for RL with linear function approximation unless NP=RP.
Extended Thistlethwaite's result on Jones polynomials of quasi-alternating links.
problem Characterizing Jones polynomials of quasi-alternating links.
method Analyzing structure and properties of Jones polynomials for quasi-alternating links.
result Jones polynomials of prime quasi-alternating links have no gaps.