Generalizes Thurston's asymmetric metric to flat metrics.
problem Defining an asymmetric metric on flat metrics.
method Defined an asymmetric metric on the space of unit-area flat metrics.
result Discussed two different topologies from the asymmetry.
Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.
problem Analysis of geometric properties on asymmetric metric measure spaces.
method Introduction of upper gradients, q-Laplacian, and q-heat flow in asymmetric settings. result Extension of concepts from symmetric to asymmetric metric measure spaces.
New metrics for Anosov representations defined from Thurston's asymmetric metrics.
problem Defining metrics for Anosov representations.
method Generalizing Thurston's asymmetric metric to Anosov representations.
result Provides a (possibly asymmetric) Finsler distance in some cases.
Extends metric to Margulis spacetimes for convex properties.
problem No specific problem stated; extends metric.
method Extends Thurston's asymmetric metric to Margulis spacetimes and proves convex properties.
result Established convex properties of the extended metric.
We highlight several analogies between the Finsler (infinitesimal) properties of Teichmüller's metric and Thurston's asymmetric metric on Teichmüller space. Thurston defined his asymmetric metric in analogy with Teichmüllers' metric, as a solution to an extremal problem, which consists, in the case of the asymmetric me…
This work describes compactifications of metric spaces and vector spaces using asymmetric norms.
problem Compactifying metric spaces and vector spaces using asymmetric norms.
method Nonstandard methods, ultrapowers of the spaces at hand.
result Polyhedral compactifications of vector spaces with stratified structure.
This paper studies gradient flows in asymmetric metric spaces and proves existence results.
problem Investigating gradient flows in asymmetric metric spaces.
method Discrete approximation and natural convexity assumption on potential function.
result Existence of curves of maximal slope in asymmetric metric spaces.
We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.
Paper proves rigidity theorems for geodesically reversible Finsler metrics.
problem Understanding geodesically reversible Finsler metrics in closed manifolds.
method Applied theory of volumes and areas on Finsler spaces to establish rigidity theorems.
result Partial explanation of the scarcity of geodesically reversible Finsler metrics in closed manifolds.
New asymmetric metric on Teichmüller space for surfaces.
problem Defining a new asymmetric weak metric on Teichmüller space.
method Introducing Teichmüller-Randers metric as an asymmetric deformation of the Teichmüller metric.
result Teichmüller geodesics become unique Teichmüller-Randers geodesics under certain conditions.
New separation concepts for Anosov representations help bound Thurston asymmetric metric.
problem Understanding diverging families of Anosov representations.
method Introducing separation concepts and analyzing combinatorial invariants.
result Critical exponent asymptotic to a graph invariant.
In the asymmetric setting, Hilbert's fourth problem asks to construct and study all (non-reversible) projective Finsler metrics: Finsler metrics defined on open, convex subsets of real projective n-space for which geodesics lie on projective lines. While asymmetric norms and Funk metrics provide many examples of esse…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a learning algorithm for quasi-metrics based on sample compression and nearest neighbor…
The paper tackles multi-player information asymmetry bandits in metric spaces.
problem Information asymmetry in rewards, actions, or both in multiplayer bandit problems.
method Adopted CAB and zooming algorithms for information asymmetry in rewards and actions.
result Regret bounds of the same order in all 3 problem settings.
New metrics derived from Hölder distortion on Hitchin components.
problem Deriving metrics on Hitchin components from Hölder distortion.
method Expressing Thurston's metric in terms of Hölder regularity of boundary maps, associating stratified loci, and measuring relative Hölder distortion.
result First known geometrically significant complete metrics on Hitchin components for n>3. New metric on geodesic currents connects different surface genera.
problem Understanding geodesic currents on surfaces of varying genera.
method Introducing a new asymmetric metric on the space of projective filling geodesic currents.
result Metric spaces of projective filling geodesic currents for surfaces of different genera are not isometric.
The paper describes geometric properties of Teichmüller space metrics.
problem Analyzing the geometry of Teichmüller space with weak Finsler metrics.
method Geometric description of unit spheres in weak Finsler metrics.
result Introduced a family of weak Finsler metrics interpolating between Thurston's metric and Teichmüller metric.
A new method uses asymmetric Shapley values to assess gene importance in clinical prediction models.
problem Clinical prediction models struggle with assessing the importance of high-dimensional features like genomics.
method Derive efficient algorithms to compute local and global asymmetric Shapley values for a mixed-dimensional prediction model.
result Asymmetric Shapley values provide a more suitable alternative to quantify feature importance in clinical prediction models.
The paper studies curves in Finsler-like spaces and their properties.
problem Investigating properties of curves in asymmetric metric spaces induced by Finsler structures.
method Analyzes three types of absolutely continuous curves in Finsler-like spaces and establishes the Lisini structure theorem.
result Characterizes the nature of absolutely continuous curves in terms of dynamical transference plans.
We study the action of the elements of the mapping class group of a surface of finite type on the Teichmüller space of that surface equipped with Thurston's asymmetric metric. We classify such actions as elliptic, parabolic, hyperbolic and pseudo-hyperbolic, depending on whether the translation distance of such an elem…
New framework improves differential privacy for asymmetric datasets.
problem Improving differential privacy for asymmetric datasets.
method Adapts inverse sensitivity mechanism with sparse vector technique.
result Efficiently estimates general functions with improved privacy.
Proposes a new OAL algorithm for imbalanced data with limited labels.
problem Handling imbalanced unlabeled datastream with limited query budget.
method Integrates asymmetric losses and queries strategies, uses second-order optimization, and applies sketching technique.
result Demonstrates improved performance and efficiency in class imbalance.
Study on earthquake metric on Teichmüller space, proving properties and new completions.
problem Understanding the earthquake metric on Teichmüller space.
method Proofs of properties, new completions, and interpretation of the metric.
result Coincidence of various completions for the earthquake metric.
On a convex body in a Euclidean space, we introduce a new variational formulation for its Funk metric, a Finsler metric compatible with the tautological Finsler structure of the convex body. We generalize the metric on Teichmuller spaces with the Weil-Petersson distance function. A set of similarities the resulting met…
The arc metric is an asymmetric metric on the Teichm{ü}ller space T(S) of a surface S with nonempty boundary. In this paper we study the relation between Thurston's compactification and the horofunction compactification of T(S) endowed with the arc metric. We prove that there is a natural homeomorphism between the two …
Random walks on free groups reveal asymmetric expansion factors.
problem Understanding expansion factors in free groups.
method Random walks and BGIP on metric spaces.
result Generic outer automorphisms have different forward and backward expansion factors.
The paper defines a metric on Euclidean triangles and polygons, proving properties and completeness.
problem Defining and analyzing a metric space for Euclidean triangles and polygons.
method Introducing and proving properties of a metric on marked Euclidean triangles, extending to polygons and triangulated surfaces.
result The metric is Finsler and complete, providing formulas for its infinitesimal structure.
The aim of this paper is to relate Thurston's metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston's asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorp…
The Teichmüller space T(Σ) of a surface Σ is equipped with Thurston's asymmetric metric. Stretch lines are oriented geodesics for this metric on T(Σ). We give the asymptotic behavior of the lengths of the measured geodesic laminations as one follows a stretch line in the positive direction.
New friction model for geometric locomotion systems.
problem Modeling asymmetric friction in locomotion systems.
method Introducing asymmetric friction into geometric locomotion models using Finsler metrics.
result Generalized motility map for systems with asymmetric friction.
Gradient descent solves asymmetric low-rank matrix sensing without balancing.
problem Recovering asymmetric low-rank matrices from linear measurements.
method Gradient descent with spectral initialization, avoiding balancing term.
result Gradient descent converges linearly without balancing, factors stay balanced.
A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.
problem Inadequate handling of asymmetric error distributions in adaptive filtering.
method Proposes asymmetric correntropy using an asymmetric Gaussian kernel and develops a robust adaptive filtering algorithm.
result The proposed algorithm shows better steady-state convergence performance for asymmetric error distributions.
New insights into currents of Hitchin representations with combinatorial restrictions.
problem Understanding currents associated with Hitchin representations.
method Defining dual spaces and analyzing combinatorial restrictions on self-intersection.
result Dual spaces of discrete boundary currents are polyhedral complexes with dimension at most n-1.
We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichmüller space and strictly convex for generic laminations. We give some consequences of this result in the context of Thurston's asymmetric metric on Teichmüller space.
This study examines asymmetric cross-correlations in cryptocurrency markets using fractal analysis.
problem Exploring asymmetric multifractal cross-correlations in cryptocurrency markets.
method Fractal analysis and MF-ADCCA method to investigate asymmetric volatility dynamics.
result Cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH.
We introduce an asymmetric distance function, which we call the `left Hausdorff distance function', on the space of geodesic laminations on a closed hyperbolic surface of genus at least 2. This distance is an asymmetric version of the Hausdorff distance between compact subsets of a metric space. We prove a rigidity res…
Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
problem Lack of precise theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
method Adapting a finite-time convergence analysis to the asymmetric actor-critic setting with linear function approximators.
result A finite-time bound reveals that the asymmetric critic eliminates aliasing errors in the agent state.
Characterizes isometries between non-reversible Finsler manifolds.
problem Understanding isometries in non-reversible Finsler manifolds.
method Generalization of Myers-Nakai Theorem for Riemannian manifolds, modification of function spaces to accommodate asymmetric structure.
result Functional characterization of isometries between non-reversible Finsler manifolds.
This work presents deep asymmetric networks with a set of node-wise variant activation functions. The nodes' sensitivities are affected by activation function selections such that the nodes with smaller indices become increasingly more sensitive. As a result, features learned by the nodes are sorted by the node indices…
We consider the problem of designing locality sensitive hashes (LSH) for inner product similarity, and of the power of asymmetric hashes in this context. Shrivastava and Li argue that there is no symmetric LSH for the problem and propose an asymmetric LSH based on different mappings for query and database points. Howev…
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
The paper improves asymmetric causality tests by addressing inefficiencies and statistical significance issues.
problem Inefficiencies and statistical significance issues in asymmetric causality tests.
method Improved asymmetric causality tests via partial cumulative sums for positive and negative components, explicitly testing differences between causal parameters.
result Efficiently tested hypotheses on asymmetric causal interaction between financial markets.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
We propose Deep Asymmetric Multitask Feature Learning (Deep-AMTFL) which can learn deep representations shared across multiple tasks while effectively preventing negative transfer that may happen in the feature sharing process. Specifically, we introduce an asymmetric autoencoder term that allows reliable predictors fo…
In this paper we show how the study of asymmetric R&D alliances, that are those between young and small firms and large and MNEs firms for knowledge exploration and/or exploitation, requires the adoption of a coopetitive framework which consider both collaboration and competition. We draw upon the literature on asymmet…
Bayesian VI copula models capture asymmetric intraday equity dependence.
problem Modeling asymmetric and extreme tail dependence in financial data.
method Bayesian variational inference for skew-t copula models in high dimensions.
result The copula captures substantial heterogeneity in asymmetric dependence over equity pairs and time.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.