Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Pointsmath.DG
We construct non-trapping asymptotically hyperbolic manifolds with boundary conjugate points but no interior conjugate points.
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48 results for “conjugation”
A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical man…
The paper tackles efficient computation of optimal transport by approximating conjugates with amortized optimization.
problem Efficient computation of convex conjugates in optimal transport is challenging and limits the quality of transport maps.
method The approach combines amortized approximations of conjugates with a fine-tuning solver to improve transport map quality.
result The method significantly improves the quality of transport maps for the Wasserstein-2 benchmark and models many 2D couplings and flows.
Estimates geodesics on surfaces without conjugate points.
problem Counting geodesics on surfaces without conjugate points.
method Margulis-type asymptotic estimates.
result Asymptotic estimates for geodesics on surfaces.
We introduce a multiple conjugation biquandle, and show that it is the universal algebra to define a semi-arc coloring invariant for handlebody-links. A multiple conjugation biquandle is a generalization of a multiple conjugation quandle. We extend the notion of -parallel biquandle operations for any integer , an…
The paper studies Jacobi fields and conjugate points in projective sprays.
problem Investigating Jacobi fields and conjugate points in projective sprays.
method Proved that conjugate points are preserved under projective changes and established conditions for the existence of conjugate points.
result Conditions for the existence of conjugate points in projectively deformed sprays.
Paper describes how to extend multiple conjugation quandles using maps.
problem Understanding affine extensions of multiple conjugation quandles.
method Introduces augmented MCQ Alexander pairs for affine extensions.
result Affine extensions of multiple conjugation quandles can be described by quadruples of maps.
For a surface group, a new bound is given for conjugator length function.
problem Finding an explicit bound for the conjugator length function of a surface group.
method Detailed analysis of conjugation reductions.
result An explicit bound for the conjugator length function of a surface group.
The study examines Hopfian properties of conjugation quandles and their underlying groups.
problem Understanding the relationship between Hopfian properties of conjugation quandles and their underlying groups.
method Examined Hopfian and residual finiteness properties of conjugation quandles of specific groups.
result Conjugation quandles of Baumslag-Solitar groups are infinitely generated and not necessarily Hopfian.
Upper bound for conjugate radius in open manifolds with scalar curvature and spectrum constraints.
problem Bounding the conjugate radius of open manifolds with specific curvature and spectrum conditions.
method Established an upper bound using scalar curvature and bottom-of-spectrum constraints.
result For certain conditions, the conjugate radius is no more than π.
We propose automated augmented conjugate inference, a new inference method for non-conjugate Gaussian processes (GP) models. Our method automatically constructs an auxiliary variable augmentation that renders the GP model conditionally conjugate. Building on the conjugate structure of the augmented model, we develop tw…
The questions when two Morse function on closed manifolds are conjugated is investigated. Using the handle decompositions of manifolds the condition of conjugation is formulated. For each Morse function on 3-manifold the ordered generalized Heegaard diagram is built. The criteria of Morse function conjugation are given…
Study conjugate locus in convex 3-manifolds using Jacobi fields.
problem Understanding conjugate points in convex 3-manifolds.
method Use Jacobi fields to define coordinate systems and classify singularities.
result Developed a novel method for determining conjugate points in 3D manifolds.
Paper finds new criteria for conjugate points in fluid flows.
problem Finding conjugate points in steady 2D Euler flows.
method Develops a new sufficient criterion for conjugate points, applies to any rotational cell, and uses a general construction of steady fluid surfaces.
result Improves on existing criteria and captures all known conjugate points in rotational cells.
Study analyzes Lévy process structure on manifolds with conjugate points.
problem Microlocal analysis of Lévy processes on manifolds with conjugate points.
method Microlocal analysis, pseudodifferential operators, Fourier integral operators.
result Generator can be expressed as sum of pseudodifferential and Fourier integral operators.
We study the geodesic X-ray transform on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of and relate it to the con…
In this paper, we establish upper bounds on the length of the shortest conjugator between pairs of infinite order elements in a wide class of groups. We obtain a general result which applies to all hierarchically hyperbolic groups, a class which includes mapping class groups, right-angled Artin groups, Burger--Mozes-ty…
Identifies conjugate points in spherical harmonics solutions of quasi-geostrophic equations.
problem Locating conjugate points in spherical harmonics solutions.
method Utilizing structure constants and quasi-geostrophic equations on the sphere, identifying conjugate points.
result Existence and location of conjugate points along spherical harmonics solutions.
The paper calculates actions of string link operations for 4- and 5-component links.
problem Classifying link-homotopy classes of string links.
method Explicit calculation of actions of partial conjugations and conjugations for 4- and 5-component string links.
result Presentations of link-homotopy classes for 4- and 5-component links.
Study normal operators of double fibration transforms with conjugate points.
problem Normal operators of double fibration transforms with conjugate points.
method Stable conditions on the distribution of conjugate points, splitting into elliptic and Fourier integral operators.
result Normal operator splits into an elliptic pseudodifferential operator and Fourier integral operators.
Researchers compare different gradient methods for ridge regression, finding conjugate gradients have similar performance.
problem Comparing statistical properties of different gradient methods in ridge regression.
method Explicit non-standard error decomposition to bound prediction error of conjugate gradient iterates.
result Conjugate gradient iterates share optimality properties with gradient flow and ridge regression up to a constant factor.
The paper proves estimates and theorems for Kähler manifolds.
problem Curvature conditions on Kähler manifolds.
method Volume comparison and rigidity theorems.
result Conjugate radius estimates for Kähler manifolds.
The study shows conditions for thermostats to have no conjugate points.
problem Conditions for thermostats to have no conjugate points.
method Analyzes smooth functions and properties of thermostats.
result Proves conditions for thermostats to be projectively Anosov and have no conjugate points.
Alexander quandles can be embedded into groups.
problem Embedding Alexander quandles into groups.
method For any twisted conjugate quandle, find a group such that the quandle is embedded into the conjugation quandle of the group.
result Alexander quandles can be embedded into groups.
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
The paper defines Fenchel conjugate and biconjugate on Hadamard manifolds.
problem Defining Fenchel conjugate and biconjugate on curved spaces.
method Introduced a new definition of Fenchel conjugate and biconjugate on Hadamard manifolds based on the tangent bundle.
result Developed a Fenchel-Moreau Theorem for geodesically convex functions on Hadamard manifolds.
Geodesic flows of compact higher genus surfaces without conjugate points have expansive factorsmath.DS
Geodesic flows on certain surfaces are shown to be semi-conjugate to expansive flows.
problem Understanding geodesic flows on compact surfaces without conjugate points.
method Time-preserving semi-conjugation to a continuous expansive flow.
result Geodesic flows on compact surfaces without conjugate points of genus > 1 have a unique measure of maximal entropy.
The paper studies conjugate points on Lie groups with specific metrics.
problem Existence and properties of conjugate points on Lie groups with left-invariant metrics.
method Using reformulated index form in terms of adjoint action, the paper proves sufficient conditions for conjugate points and provides bounds and criteria.
result All geodesics in compact semisimple Lie groups have conjugate points, with upper and lower bounds on conjugate times.
We determine the complete conjugate locus along all geodesics parallel or perpendicular to the center (Theorem 2.3). When the center is 1-dimensional we obtain formulas in all cases (Theorem 2.5), and when a certain operator is also diagonalizable these formulas become completely explicit (Corollary 2.7). These yield s…
We address the challenge of effective exploration while maintaining good performance in policy gradient methods. As a solution, we propose diverse exploration (DE) via conjugate policies. DE learns and deploys a set of conjugate policies which can be conveniently generated as a byproduct of conjugate gradient descent. …
Study natural and conjugate mates of Frenet curves in Lie groups.
problem Characterize Frenet curves and their mates in Lie groups.
method Introduced natural and conjugate mates, derived relationships, analyzed specific curves.
result Obtained results for various Frenet curves in Lie groups.
In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's construction of pseudo-Anosov mapping classes. As a consequence, …
Study on conjugate points in a -algebra's Grassmann manifold.
problem Characterizing conjugate points in a -algebra's Grassmann manifold.
method Analyzes connections and geodesics in the Riemannian metric induced by the Killing form.
result Points that are tangent conjugate in the classical setting may not be conjugate in a -algebra's Grassmann manifold.
Proves robust transitivity for geodesic flows from metrics with conjugate points.
problem Transitivity of geodesic flows from metrics with conjugate points.
method General criterion for robust transitivity of partially hyperbolic geodesic flows.
result First example of a open set of Riemannian metrics with conjugate points and transitive geodesic flow.
Existence of a conjugate point in the incompressible Euler flow on a three-dimensional ellipsoidmath.DG
Existence of a conjugate point proven on 3D ellipsoid.
problem Existence of conjugate points in incompressible Euler flow on 3D ellipsoid.
method Volume-preserving diffeomorphism group, Misiolek curvature criterion.
result Existence of a conjugate point on 3D ellipsoid.
The paper generalizes a mean value theorem for solutions of the ultrahyperbolic equation.
problem Establishing a mean value property for solutions of the ultrahyperbolic equation.
method Using conformal maps of the pseudo-Euclidean space of signature 2+2, the paper extends Asgeirsson's theorem to a more general class of pairs of curves.
result The mean value property is proven for non-degenerate conjugate conics, including conjugate circles, hyperbolae, parabolae, and line-empty pairs.
Nonlinear Fenchel Conjugatesmath.FA
Generalizes Fenchel conjugation to nonlinear functions on arbitrary sets.
problem Extending Fenchel conjugation to functions on arbitrary sets without structure.
method Replacing linear test functions with nonlinear ones, investigating properties including biconjugation.
result Derived further results on smooth manifolds and Lie groups, relating to convexity.
Relations between conjugate connections with respect to the pair of Norden metrics and to the almost complex structure on almost Norden manifolds are studied. Conjugate connections of the Levi-Civita connections induced by the Norden metrics are obtained. Statistical structures on almost Norden manifolds are considered…
Characterizes bi-Perron numbers with specific Galois conjugates.
problem Understanding bi-Perron numbers with real or unimodular conjugates.
method Characterization through power properties and spectral radii of transformations.
result Bi-Perron numbers with real or unimodular conjugates admit a power as stretch factors or spectral radii.
We define a functor from the category of multiple conjugation biquandles to that of multiple conjugation quandles. We show that for any multiple conjugation biquandle , there is a one-to-one correspondence between the set of -colorings and that of -colorings diagrammatically for any …
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial differential equations controlling the functions of three variables that admit a c…
Conjugate Projective Limitsmath.ST
We characterize conjugate nonparametric Bayesian models as projective limits of conjugate, finite-dimensional Bayesian models. In particular, we identify a large class of nonparametric models representable as infinite-dimensional analogues of exponential family distributions and their canonical conjugate priors. This c…
The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.
problem Understanding the properties and behavior of Ricci solitons.
method Analytical proofs and estimates for various types of Ricci solitons.
result Upper bounds and estimates for conjugate radius of Ricci solitons.
The paper counts geodesic loops on surfaces without conjugate points.
problem Counting geodesic loops on surfaces of genus at least 2 without conjugate points.
method Proves asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points.
result Generalizes classical counting results and sector theorems for surfaces of strictly negative curvature.
We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case we prove a strengthened Price inequality. We employ these inequalit…
Study finds conjugate points in geodesics of Kolmogorov flows on torus.
problem Characterizing pairs of integers (m,n) for which geodesics have conjugate points.
method Analysis of geodesics in the group of volume-preserving diffeomorphisms of a torus using stream functions.
result Existence of conjugate points for all pairs of strictly positive integers (m,n).
This note investigates a conjugate class for the Dirichlet distribution class in the exponential family.
The study identifies conjugate and cut points in ideal fluid motion configurations.
problem Understanding stability and re-convergence of fluid configurations.
method Existence and non-existence of conjugate points in specific fluid configurations, using geometric and physical analysis.
result Existence of conjugate points in Kolmogorov flows and non-existence in Arnold steady states.