A space has the maximal number of CKVs if and only if it is conformally flat.
problem Determining the necessity of conformal flatness for maximal CKVs.
method Analyzing properties of conformally flat spaces and CKVs.
result Conformal flatness is a necessary and sufficient condition for maximal CKVs.
We study the hairy graph homology of a cyclic operad; in particular we show how to assemble corresponding hairy graph cohomology classes to form cocycles for ordinary graph homology, as defined by Kontsevich. We identify the part of hairy graph homology coming from graphs with cyclic fundamental group as the dihedral h…
Study finds Hilbert square of real surfaces can be maximal even when the surface has disconnected real locus.
problem Exploring conditions for maximality of Hilbert square of real surfaces.
method Analyzing Hilbert square of maximal real surfaces and examining specific examples.
result Hilbert square can be maximal even for surfaces with disconnected real locus.
Maximal knotless graphs have at least 74% of their vertices' edges.
problem Characterizing maximal knotless graphs and understanding their edge constraints.
method Analyzing edge maximality and constructing graphs to meet constraints.
result There exists an infinite family of maximal knotless graphs with fewer edges than previously thought.
Maximizing margins leads to lossless compression of training data.
problem Generalization in supervised learning.
method Information-theoretic interpretation of margin maximization.
result Margin maximization is a form of lossless maximal compression.
The study classifies area-maximizing hypersurfaces with singularities and exterior domains.
problem Classifying area-maximizing hypersurfaces with singularities and exterior domains.
method Complete classification for entire area maximizing hypersurfaces with isolated singularities. Construction of an example. Partial result on asymptotic behavior for exterior domains. Solvability of exterior Dirichlet problems.
result Complete classification and partial results on asymptotic behavior for area maximizing hypersurfaces.
Maximal acceleration metrics limit spacetime curvature.
problem Bounding spacetime curvature under maximal acceleration.
method Developed a geometric framework for maximal acceleration metrics and associated connections, proving curvature bounds.
result Uniform bounds on curvature components follow from uniform bounds on maximal acceleration.
The paper finds maximal metrics on Euclidean spaces.
problem Finding maximal elements in moduli spaces of Riemannian metrics.
method Defining a preorder on moduli space by isometry groups and identifying maximal elements.
result Constructs many examples of maximal metrics on Euclidean spaces.
Survey on geometry and topology of maximal antipodal sets.
problem Maximal antipodal sets on Riemannian manifolds.
method Comprehensive survey of existing research.
result Relation to various mathematical areas.
New bounds on maximal linkless graphs with improved edge-to-vertex ratios.
problem Finding maximal linklessly embeddable graphs with improved edge-to-vertex ratios.
method Constructing families of graphs and proving necessary and sufficient conditions for clique sums.
result Improved edge-to-vertex ratios for maximal linklessly embeddable graphs.
New maximally linkless graphs found with fewer edges.
problem Finding graphs without any links in 3D space.
method Demonstrated new maximally linkless graphs with improved edge count.
result Found maximally linkless graphs with m≤514n edges. Paper classifies maximal surfaces with planar curvature lines and explores their singularities.
problem Classifying maximal surfaces with specific curvature lines.
method Alternative method to refine classification and investigate singularities.
result Existence of a deformation consisting of all maximal surfaces with planar curvature lines.
Study examines maximal domains of radial harmonic functions across different curvature types.
problem Understanding maximal domains of radial harmonic functions in various curvature settings.
method Analysis of harmonic spaces with positive, zero, and negative curvature.
result Characterization of maximal domains for radial harmonic functions in different curvature contexts.
The paper explores reflection principles for lightlike line segments on maximal surfaces.
problem Reflection property does not hold for lightlike line segments on maximal surfaces.
method Analyzes reflection properties for lightlike line segments connecting shrinking singularities.
result Shows a kind of reflection principle for lightlike line segments on maximal surfaces.
We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.
Study of maximal hypersurfaces in spacetimes, proving uniqueness results.
problem Uniqueness of compact maximal hypersurfaces in stably causal spacetimes.
method Analysis of a distinguished function on maximal hypersurfaces under first order conditions of the spacetime.
result Several uniqueness results on compact maximal hypersurfaces in stably causal spacetimes.
New maximal surfaces solve Bernstein problems.
problem Bernstein problems in centroaffine geometry.
method Calabi affine maximal surfaces and orthonormal frame fields.
result Complete centroaffine extremal hypersurfaces solve all Bernstein problems.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
problem Difficulties in studying optimal portfolio strategies due to discontinuity and time inconsistency in maximizing median and quantile returns.
method Used intra-personal equilibrium approach to analyze portfolio selection under median and quantile maximization.
result Median maximization is the only viable strategy, with no investment in risky assets for other quantiles.
This work explores maximal symmetry in unimodular solvmanifolds.
problem Finding metrics with maximal symmetry in unimodular solvmanifolds.
method Analyzing unimodular solvable Lie groups and proving the existence of metrics with maximal symmetry.
result There is always a metric with maximal symmetry in unimodular solvmanifolds.
Study on dual surfaces of rotational minimal and maximal in Euclidean and Lorentz-Minkowski spaces.
problem Investigating the duality between minimal and maximal surfaces in different spaces.
method Analysis of rotational surfaces and use of one-parameter group of rotations.
result Family of Bonnet minimal and maximal surfaces emerge in the duality process.
This paper surveys AUC maximization for big data and AI.
problem Assessing classifier performance for imbalanced data.
method Maximizing AUC score directly.
result No comprehensive survey of AUC maximization exists.
Classifies maximal antipodal sets in symmetric spaces.
problem Identifying maximal antipodal sets in symmetric spaces.
method Explicit classification for most irreducible compact symmetric spaces.
result Classification of maximal antipodal sets in most symmetric spaces.
Study of large group actions on surfaces, focusing on Hurwitz and handlebody groups.
problem Characterizing and understanding group actions on surfaces, especially maximal handlebody and Hurwitz groups.
method Analyzing various group actions, comparing Hurwitz and handlebody groups, and examining bounding actions.
result Relationship between Hurwitz groups and maximal handlebody groups, and insights into geometric bounding actions.
New guarantees for adaptive combinatorial maximization with various objectives.
problem Maximizing under cardinality constraints and minimum cost coverage in adaptive settings.
method Bayesian approach with comprehensive approximation guarantees for various utility functions.
result Maximal gain ratio is a new parameter that provides stronger approximation guarantees than greedy policies.
We study homologically maximizing timelike geodesics in conformally flat tori. A causal geodesic γ in such a torus is said to be homologically maximizing if one (hence every) lift of γ to the universal cover is arclength maximizing. First we prove a compactness result for homologically maximizing timelike geodesics…
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. The ball maximizes the first biharmonic Steklov eigenvalue.
problem Maximizing the first biharmonic Steklov eigenvalue for bounded domains.
method Comparing domains with fixed measure to find the maximum eigenvalue.
result The ball maximizes the first positive biharmonic Steklov eigenvalue.
Study on maximal surfaces with high genus in Lorentz-Minkowski space.
problem Existence of nonorientable maximal surfaces with high genus.
method Existence results for nonorientable maximal surfaces with high genus and one end.
result Existence of maximal surfaces with high genus in Lorentz-Minkowski space.
We show that a positive braid knot has maximal topological 4-genus exactly if it has maximal signature invariant. As an application, we determine all positive braid knots with maximal topological 4-genus and compute the topological 4-genus for all positive braid knots with up to 12 crossings.
New manifolds found with near-maximal entropy.
problem Finding manifolds with near-maximal entropy.
method Proving existence of non-hyperbolic manifolds with near-maximal entropy.
result Existence of manifolds with near-maximal entropy that are not hyperbolic.
Maximal representations in symplectic lattices proven for most cases.
problem Understanding maximal representations in symplectic lattices.
method Analyzing mapping class group orbits and continuous deformations of maximal diagonal representations.
result Proof of maximal representations in most lattices of Sp(2n,R).
Maximal index vanishes for certain spin manifolds with positive scalar curvature.
problem Maximal index vanishing for spin manifolds with positive scalar curvature.
method Functional calculus for Dirac operator in maximal equivariant uniform Roe algebra.
result Maximal higher index vanishes in K-theory of maximal equivariant Roe algebra.
In the present paper we study two-dimensional maximal surfaces with harmonic level-sets. As a corollary we obtain a new class of one-periodic maximal surfaces.
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Moebius strips and maximal Klei…
Study utility maximization with costs, proving convergence and strategies.
problem Utility maximization with proportional transaction costs.
method Extended weak convergence theory and Meyer--Zheng topology.
result Prove convergence of utility maximization problems and optimal trading strategies.
Maximal metric spheres found, related to Sobolev-to-Lipschitz property.
problem Finding maximal metric spheres.
method Characterizing maximal spheres by Sobolev-to-Lipschitz property.
result Maximal spheres uniquely characterized by Sobolev-to-Lipschitz property.
We consider trading in a financial market with proportional transaction costs. In the frictionless case, claims are maximal if and only if they are priced by a consistent price process--the equivalent of an equivalent martingale measure. This result fails in the presence of transaction costs. A properly maximal claim i…
Maximal causal curves for Lipschitz metrics are either lightlike or timelike.
problem Characterizing maximal causal curves for Lipschitz metrics.
method Analyzing the parametrization and geodesic equation for maximal causal curves in terms of Filippov solutions.
result Maximal causal curves for Lipschitz metrics are either everywhere lightlike or everywhere timelike.
We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
The study finds a metric that maximizes the second eigenvalue of the Conformal Laplacian.
problem Maximizing the second eigenvalue of the Conformal Laplacian over conformal metrics.
method Analyzes properties of the Conformal Laplacian and constructs metrics to maximize eigenvalues.
result Existence of a metric that maximizes the second eigenvalue of the Conformal Laplacian.
Maximal and Borel Anosov representations in Sp(4,R) are proven to be Hitchin.
problem Characterizing representations of surface groups into Sp(4,R) that are Borel Anosov and maximal. method Proving representations are Hitchin if they have maximal Toledo invariant and are Borel Anosov.
result Maximal and Borel Anosov representations in Sp(4,R) are Hitchin. Construct Schottky subgroups for maximal representations in symmetric spaces.
problem Maximal representations of surface groups into Sp(2n, R).
method Construction of Schottky type subgroups of automorphism groups.
result Schottky subgroups correspond to maximal representations of surface groups.
Maximal dilatation found on nonorientable surfaces.
problem Finding maximal dilatation on nonorientable surfaces.
method Proving irreducibility of a polynomial to show maximal dilatation.
result Maximal dilatation is achieved by the Liechti-Strenner polynomial.
Unique maximal curve systems found for up to 5 punctures.
problem Finding unique maximal curve systems in punctured projective planes.
method Analyzing mapping class group action on maximal 1-systems of loops. result Maximal 1-system is unique for up to 5 punctures. Study exterior maximal surfaces with precise asymptotic behavior.
problem Maximal surfaces in exterior domains with prescribed asymptotic behavior.
method Analyze the maximal surface equation and prove the exterior Dirichlet problem's uniqueness.
result Uniquely solvable exterior Dirichlet problem with given asymptotic behavior.
Local equivalence found between maximally symmetric rolling and flat Cartan distributions.
problem Establishing local equivalence between maximally symmetric rolling and flat Cartan distributions.
method Using complex parametrisation of su(2), a change of coordinates maps the maximally symmetric rolling (2,3,5)-distribution to the flat Cartan distribution. result Local equivalence between maximally symmetric rolling and flat Cartan distributions established.
This paper improves tail dependence analysis by introducing a path-based approach.
problem The classical tail dependence coefficient fails to capture non-exchangeable features of tail dependence.
method The paper introduces a path-based maximal tail dependence approach to capture the most pronounced feature of dependence over all possible paths.
result The paper proves the existence and provides an explicit characterization of the path-based maximal TDC, improving analytical and computational tractability.