Study shows most symmetric and 3-symmetric spaces lack solvable Clifford-Klein forms.
problem Existence of compact solvable Clifford-Klein forms in homogeneous spaces.
method Combination of Hirzebruch-Kobayashi-Ono proportionality principle and syndetic hull theory.
result Almost all symmetric and 3-symmetric spaces do not admit solvable compact Clifford-Klein forms.
Completeness theorem for flat pseudo-Riemannian manifolds of signature (2,2).
problem Completeness of closed flat pseudo-Riemannian manifolds of signature (2,2).
method Geometric reduction and semidirect product constructions.
result Only the entire space R2,2 is divisible by a discrete subgroup of isometries. We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We investigate how this construction varies as one changes the family of pseudometrics used…
Optimizes vessel hull forms using PCA and DNN.
problem Designing optimal hull forms for vessel performances.
method PCA compresses hull forms, DNN predicts performances.
result DNN accurately predicts hull form performances.
The paper characterizes sets with infinite hyperbolic convex hull volume.
problem Characterizing sets with infinite hyperbolic convex hull volume.
method Geometric conditions and self-similar sets.
result Characterizes continua and planar self-similar sets with infinite hyperbolic convex hull volume.
Computes algebraic hull of Kontsevich-Zorich cocycle.
problem Finiteness of GL^+_2(R) invariant subvarieties of the Hodge bundle.
method Computes algebraic hull over GL^+_2(R) invariant subvarieties.
result Finiteness results on invariant subvarieties.
The n-th hull of a union of curves in R^3 is the set of points with the property: Any plane passing through the point intersects the curves at least 2n times. The hull number u(L) of a link L is defined as the minimum number of non-empty hulls a representative of L can have. We show that the hull numbers of torus links…
The main result of this paper is a characterization of the minimal surface hull of a compact set K in R3 by sequences of conformal minimal discs whose boundaries converge to K in the measure theoretic sense, and also by 2-dimensional minimal currents which are limits of Green currents supported by conf…
Develops harmonic metrics for Hull-Strominger system stability.
problem Existence of solutions to the Hull-Strominger system with balanced class.
method Uses non-Hermitian Yang-Mills connections and holomorphic Courant algebroids, introduces harmonic metrics.
result Expected existence of a numerical stability condition for generic families of solutions.
Study analyzes correlation structure in two-factor Hull-White model for XVA calculations.
problem Capturing the correlation structure in two-factor Hull-White model for accurate XVA calculations.
method Combination of approximation formula and Monte-Carlo simulation to investigate correlation structure.
result Hull-White model effectively captures de-correlation of the yield curve under specific parameter conditions.
Upper bound found for convex hull volume of 4-vertex curve.
problem Finding upper bound for convex hull volume of 4-vertex curve.
method Elementary parametrization of convex hull as a union of line segments.
result Upper bound for convex hull volume is attained under specific conditions.
Deep learning models generalize by extending decision boundaries outside the convex hull of training data.
problem Understanding how deep learning models generalize beyond their training data.
method Investigation of decision boundaries inside and outside the convex hull of training sets, using various neural network architectures and training regimes.
result Over-parameterization is necessary for deep learning models to extend decision boundaries outside the convex hull of their training data.
Study shows non-compact convex hulls in certain metric spaces.
problem Compactness of convex hulls in weakly non-positive curvature spaces.
method Introduced a conical geodesic bicombing and used it to construct a counterexample.
result Existence of a metric space with a finite subset whose convex hull is not compact.
The paper transforms a convex hull into a concave surface around a point cloud.
problem Creating a concave surface that encloses all points in a point cloud.
method Iterative facet replacement and expansion of the convex hull.
result A method to evolve a convex hull into a concave surface that fits the point cloud.
The integer hull of a polyhedron is the convex hull of the integer points contained in it. We show that the vertices of the integer hulls of a rational family of polyhedra of size O(n) have quasipolynomial coordinates. As a corollary, we show that the stable commutator length of elements in a surgery family is a ratio …
Study characterizes hulls and capacities on Riemannian manifolds, proving isoperimetric inequalities.
problem Characterizing hulls and capacities on Riemannian manifolds.
method Investigates strictly outward minimising hulls and uses p-capacities to recover their areas.
result Sharp isoperimetric inequality on complete noncompact manifolds with nonnegative Ricci curvature.
New proofs given for space curves with totally positive torsion.
problem Description of convex hulls of space curves with totally positive torsion.
method New proofs of parametric representation, surface area, and volume formulas.
result Recovery of formulas for convex hull's surface area and volume.
The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This pro…
We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a generalization of J. Wermer's classical theorem on the hull of a curve in Cn is established in the projective setting. The projective hul…
New solutions found for Hull-Strominger system on torus bundles.
problem Finding solutions to the Hull-Strominger system with torus symmetry.
method Constructing solutions on torus bundles over K3 orbifolds.
result Smooth manifolds with complex structures have solutions to the Hull-Strominger system.
Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.
problem Constructing representations of vertex algebras from non-Kähler solutions of the Hull-Strominger system.
method Embedding the N=2 superconformal vertex algebra in the chiral de Rham complex of a string Courant algebroid, with a condition on the Hermitian-Yang-Mills connection.
result Any solution of the Hull-Strominger system satisfying the Hermitian-Yang-Mills condition has an associated N=2 embedding.
Direct proof of implication between geometric convex hull statements.
problem Deriving one geometric convex hull statement from another.
method Direct proof of implication between statements.
result Direct derivation of one geometric convex hull statement from another.
Estimates convex hulls of smooth function images with error bounds.
problem Estimating the convex hull of the image of a smooth boundary set.
method Using submersion properties and sampling inputs, derive bounds on Hausdorff distance.
result New tighter and more general error bounds for geometric inference.
Study finds knots with ideal length need not have smallest volume.
problem Tackles the conjecture that ideal knot length equals smallest volume.
method Measures convex hull volume of knots during length annealing.
result Identifies knots with non-ideal global minimum volume.
Study Hull-Strominger system and Anomaly flow on specific solvmanifolds.
problem Characterize invariant solutions to Hull-Strominger system and investigate flow of invariant metrics.
method Characterization of invariant solutions using Gauduchon connections, investigation of Anomaly flow, and proof of flow immortality under certain conditions.
result Anomaly flow reduces to a special form and always converges to a Kähler metric when slope parameter is zero.
New solutions found for complex structures on specific manifolds.
problem Constructing smooth solutions to the Hull-Strominger system.
method Using fibrations over K3 orbisurfaces.
result Proved existence of solutions for certain manifolds.
Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.
problem Understanding properties of convex hulls of coadjoint orbits of compact groups.
method Introduce partial convex hulls and use them to define numerical invariants.
result Orbits with new invariants form rational convex polyhedral cones related to Littlewood-Richardson cones.
Proposes a faster algorithm for machine learning problems.
problem General minimum conical hull problems in machine learning.
method Sublinear classical algorithm for general minimum conical hull problems.
result Achieves exponential speedup over existing methods.
For a convex curve in an even-dimensional affine space we introduce a series of convex domains (called Young hulls), describe their structure and give a formulas fo the volume of the biggest of these domains. This paper is an attempt to generalize the classical isoperimetric inequality for the volume of the convex hull…
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel…
Optimal algorithm finds if point is in convex hull of distributions.
problem Determining if a point is inside the convex hull of means of multiple distributions.
method Thompson-CHM algorithm with modular design of stopping and sampling rules.
result First asymptotically optimal algorithm for CHM problem in one dimension.
New flow defined to solve Hull-Strominger system, with estimates and convergence results.
problem Constructing solutions to the Hull-Strominger system of equations.
method Introducing a natural extension of pluriclosed flow and using string algebroids and higher gauge theory.
result Proves global existence and convergence of the flow on special backgrounds.
Optimum in Convex Hulls (OCH) generalizes clinical trial results to broader populations.
problem Clinical trials exclude confounding but limit recruitment; observational data are more inclusive but suffer from confounding.
method OCH uses convex hulls of conditional expectations or densities to approximate the true treatment effect from both observational and trial data.
result OCH estimates the treatment effect with state-of-the-art accuracy in terms of both expectations and densities.
New solutions found for complex geometry problem.
problem Solving the Hull-Strominger system on non-Kähler manifolds.
method Constructing solutions with a specific connection ansatz and using moduli spaces of sheaves.
result First T-dual solutions on compact non-Kähler manifolds with different topology.
We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced functio…
Estimate collapsibility of causal effects in CPDAGs via strong d-convex hulls.
problem Estimate causal effects in CPDAGs.
method Use strong d-convex hulls to characterize minimal collapsible sets.
result Efficient algorithm for obtaining collapsible sets in DAGs and CPDAGs.
Automorphisms and subdivisions of Helly graphs are studied, leading to explicit models and rational translation lengths.
problem Understanding automorphisms and subdivisions of Helly graphs.
method Simple fine simplicial subdivisions and explicit simplicial models of the injective hull.
result Any automorphism of a Helly graph is either elliptic or hyperbolic, with rational translation lengths.
Study the Hull-White model with volatility uncertainty, finding an arbitrage-free term structure.
problem Finding an arbitrage-free term structure in the Hull-White model with volatility uncertainty.
method Representing volatility uncertainty with sublinear expectation and G-Brownian motion; adjusting the model to find an arbitrage-free term structure.
result The resulting term structure is affine with respect to the short rate and the adjustment factor, consistent with the traditional Hull-White model after fitting the yield curve.
We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.
New obstruction found for Hull-Strominger system solutions.
problem Existence of solutions to the Hull-Strominger system.
method Construction of Hermitian-Einstein metric on string algebroid.
result Definition of Futaki invariants obstructing solutions.
Sketching algorithm finds closest point on convex hull efficiently.
problem Finding the closest point on a convex hull of large datasets.
method Sketching procedure to exploit data structure, gradient project method.
result Faster solution than standard optimization algorithms.
GraphHull models networks with clear multi-scale explanations of community structure.
problem Lack of self-explainable models in graph machine learning.
method Two-level convex hulls with global archetypes and local prototypes.
result GraphHull models networks with clear multi-scale explanations.
Study shows Nelson-Siegel curves fit well with Ho-Lee and Hull-White models.
problem Fitting observed interest rate term structures with interest rate models.
method Examined Nelson-Siegel curves in the context of Ho-Lee and Hull-White models.
result Extended Nelson-Siegel curves emerge from the forward curve process of the models.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
A curve of minimum length to enclose a unit sphere in 3D is at least 4π.
problem Finding the shortest closed curve that encloses a unit sphere within its convex hull.
method Analyzing the geometric properties and using convex hull concepts.
result The minimum length of such a curve is 4π in 3D, with equality in a specific case.
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
Characterizes extreme points in polygon limit sets.
problem Identifying boundary points in polygon limit sets.
method Characterization through affine dilations and polygon vertices.
result Characterizes which points lie on the boundary of convex hull.
Study on curvature bounds for specific hypersurfaces in Anti-de Sitter space.
problem Bounding principal curvatures of constant mean curvature hypersurfaces.
method Generalized convex hull concept and quantitative estimates based on width.
result Explicit bounds on sectional curvature and quasiconformal dilatation.