Efficiently computes quasiconcave envelope with limited data.
problem Approximating unknown quasiconcave function with partial information.
method Solves value problem and interpolation problem with polynomial and logarithmic LPs.
result Efficiently computes quasiconcave envelope with limited data.
Motivated by recent axiomatic developments, we study the risk- and ambiguity-averse investment problem where trading takes place over a fixed finite horizon and terminal payoffs are evaluated according to a criterion defined in terms of a quasiconcave utility functional. We extend to the present setting certain existen…
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of functionals for evaluating financial positions.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of performance evaluation methods.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
We establish a geometric lower bound for the principal curvature of the level surfaces of solutions to F(D2u,Du,u,x)=0 in convex ring domains, under a refined structural condition introduced by Bianchini-Longinetti-Salani in \cite{BLS}. We also prove a constant rank theorem for the second fundamental form of the …
The study finds bounds on metrics with constant curvature in the plane.
problem Bounding metrics with constant positive curvature in the plane.
method Analyzing solutions to a specific partial differential equation.
result The diameter of the plane with a conformal metric is at least 4π/3.
Correct method found for drawing precise envelope of straight lines.
problem Widespread method fails to represent the precise shape of envelope.
method Recently discovered correct method for straight line families in the plane.
result Correct method precisely represents the envelope of straight lines.
Study three discrete envelope types of polygon bisection lines.
problem Understanding different envelope types of polygon bisection lines.
method Examined three distinct notions of discrete envelopes.
result Connected three different notions of discrete envelopes.
Paper solves four problems of pseudo-circle envelopes in Minkowski plane.
problem Four problems of pseudo-circle envelopes in Minkowski plane.
method Solutions to four basic problems.
result Solved four problems of pseudo-circle envelopes in Minkowski plane.
Describes envelopes of Thurston metric on Teichmüller space.
problem Characterizing the shape and properties of envelopes in Teichmüller space.
method Using harmonic stretch lines and topological invariants, the shape and properties of envelopes are described.
result Envelopes are contractible and vary continuously with endpoints.
Improves regression efficiency by separating material and immaterial parts of responses.
problem Improving estimation efficiency in nonlinear multivariate regressions.
method Kernel envelope (KENV) estimator for nonparametric response envelopes in reproducing kernel Hilbert space.
result KENV achieves lower in-sample prediction risk than kernel ridge regression in non-trivial immaterial components.
Study circle families' envelopes and related curves.
problem Understanding relationships between circle families and special curves.
method Investigate envelopes of circle families and their connections to evolutes, pedals, evolutoids, and pedaloids.
result Characterized relationships between circle families and related curves.
Solves four problems related to circle families in the plane.
problem Four basic problems of circle families in the plane.
method Solves all four basic problems of circle families in the plane.
result All four basic problems are solved.
New method for operating envelope identifies key performance indicators without arbitrary binning.
problem Accurate identification of operating envelope for optimal KPIs.
method Regularized GA algorithm with interpretability and implementability constraints.
result Validated through simulations and real-world application in mining.
New Lie group approach for envelope surface computation.
problem Efficient computation of envelope surfaces.
method Interpreting surfaces as curves in Lie group spaces, leveraging Lie group and algebra formalisms.
result Explicit rational parameterization of cone envelope surfaces and solution to trimming problem.
Solves four problems related to sphere families in 3D space.
problem Four basic problems of sphere families in Euclidean 3-space.
method Solves all four basic problems of sphere families in Euclidean 3-space.
result All four basic problems are solved.
The dynamical analysis of American options has motivated the development of robust versions of the classical Snell envelopes. The cost of superhedging an American option is characterized by the upper Snell envelope. The infimum of the arbitrage free prices is characterized by the lower Snell envelope. In this paper we …
This paper explores geometric insights into discrete R-congruences and their envelopes.
problem Understanding the ambiguity in discrete R-congruences and their envelopes.
method Analyzes discrete R-congruences that are enveloped by specific types of surfaces and maps.
result Discovers a 2-parameter family of discrete enveloping surfaces for discrete R-congruences.
Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
problem Finding the minimum of the spectral determinant on isosceles triangles.
method Analyzing the determinant of the Laplacian on Euclidean isosceles triangle envelopes of fixed area.
result Equilateral triangle envelope minimizes the determinant of the Laplacian.
Enhances neural network robustness with polyhedral envelope regularization.
problem Improving neural network robustness against adversarial attacks.
method Introduces polyhedral envelope regularization to bound the robustness region.
result Demonstrates improved robustness guarantees with minimal computational overhead.
This work uses Lasry-Lions envelopes to solve nonconvex optimization problems.
problem Nonconvex and nonsmooth terms in optimization problems.
method Develops a homotopy approach using Lasry-Lions envelopes to approximate and solve the original problem.
result The method can solve composite minimization problems and is more effective than classical alternatives in certain domains.
We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of Cn, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given co…
New geometric mechanism solves four envelope problems.
problem Four basic problems on envelopes created by hyperplane families.
method Simple geometric mechanism of intersections of perpendicular bisectors and normal lines.
result Solves all four basic problems on envelopes at once.
New methods help escape strict saddle points in nonsmooth optimization.
problem Escaping strict saddle points in nonsmooth optimization.
method An inexact stochastically perturbed gradient method applied to the Moreau envelope.
result A variety of algorithms for nonsmooth optimization can efficiently escape strict saddle points of the Moreau envelope.
This paper generalizes the envelope of mid-lines to intermediate lines for a plane curve.
problem Understanding the envelope of intermediate lines for a plane curve.
method Using singularity theory techniques to analyze the local behavior of the envelope of intermediate lines.
result The envelope of intermediate lines (EIL) is formed by three disconnected sets: AEIL, the curve itself, and IPTL. The paper proves boundedness of envelopes in complex manifolds.
problem Regularity of envelopes in complex manifolds.
method Analyzes bounded functions and their envelopes in the context of cohomology classes and Laplacians.
result The α-psh envelope P(f) is locally bounded with locally bounded Laplacian on the ample locus of {α}. We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid. We prove that the category of torsors is equivalent to that of pregroupoids. Hence we also get enveloping groupoids for torsors, and for pri…
We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the curve itself, its inflectional geodesics and its tangential caustics (formed by the conjugate points to those of the initial curve along th…
By using the support function on the xy-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.
We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus new conformal surfaces. Applying these constructions to Willmore surfaces, we show…
Smooth convergence to an enveloping cylinder proved for mean curvature flow of complete graphical hypersurfaces.
problem Proving smooth convergence of mean curvature flow to an enveloping cylinder.
method Analyzing mean curvature flow of complete graphical hypersurfaces over domains Ωt, proving convergence under certain circumstances. result Smooth convergence of Mt−hen+1 to the enveloping cylinder under specific conditions. We study the geometry of Outer Space CVn in regard of the asymmetric Lipschitz metric via envelopes, that is the set of all geodesics between two points. In the simplicial structure of CVn the envelopes are polytopes. We construct a piecewise unique geodesic between any two points in CVn by concatenating edges…
Defines a calculus for integrating Moreau envelopes in differentiable programming.
problem Lack of a mathematical framework for applying Moreau envelopes to deep networks and machine learning systems.
method Develops a compositional calculus adapted to Moreau envelopes and integrates it into differentiable programming.
result Integrates Moreau envelopes into differentiable programming, enabling new gradient back-propagation methods.
We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the $\A$-normal form of these families, their envelopes and local patterns near the cusp. We obtain a new codimension 2 singularity…
Given any smooth plane curve α(s)representing a mirror that reflects light the usual way and any radiant light source at a point in the plane, the reflected light will produce a caustic envelope. For such an envelope, we show that there is an associated curve \b{eta}(s) and a family of circles C(s) that roll on \b{eta}…
A spacetime can be embedded in an enveloping space with all its extensions.
problem Existence and uniqueness of C0-maximal extensions in globally hyperbolic conformally flat spacetimes.
method Proving conformal embedding into an enveloping space containing all extensions.
result Existence and uniqueness of C0-maximal extensions proven.
The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve, together with the entire affine tangent line at each inflexion of C. In this paper, we consider plane curves without inflexions. We use some techniques of singulari…
The paper extends a theorem to Lie-Rinehart algebras and provides new decompositions of universal enveloping algebras.
problem Understanding universal enveloping algebras of Lie-Rinehart algebras.
method Extending a theorem to left Hopf algebroids and applying it to universal enveloping algebras of Lie-Rinehart algebras.
result Provides a crossed product decomposition of universal enveloping algebras for curved and flat connections.
In this paper, we further study the forward-backward envelope first introduced in [28] and [30] for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the origin…
Enhances LLM quantization with MDBF, improving perplexity and accuracy.
problem Limited performance of Double Binary Factorization in extreme quantization.
method Introduces Multi-envelope DBF, retaining sign matrices and replacing single envelope with rank-l envelope. result Improves perplexity and zero-shot accuracy over previous binary formats.
We shall use the classical Perron envelope method to show a general existence theorem to degenerate complex Monge-Ampère type equations on compact Kähler manifolds.
Paper presents a method for identifying isotope envelopes in MALDI-ToF data.
problem Deisotoping of isotopic peaks in MALDI-ToF molecular imaging data.
method Uses Mamdani-Assilan fuzzy system and spatial maps of molecular distribution to identify isotope envelopes.
result Proposed method detects overlapping envelopes and analyzes large data sets.
Study of complex Hessian equations using subharmonic functions and geodesics.
problem Understanding geodesics within complex Hessian equations.
method Perron envelope construction, comparison principle, rooftop equality, Kiselman minimum principle.
result Established criterion for geodesic connectivity among m-subharmonic functions. Designing deterministic denominators for SGLD stabilizes large drifts.
problem Stabilizing large drifts in SGLD
method Using state-dependent envelopes and empirical quantiles for activation thresholds
result Proxy-quantile denominators are close to oracle-score behavior and improve deterministic taming choices
The paper generalizes envelope constructions for chords in circles, revealing complex singularities.
problem Understanding envelopes of chords in circles with varying parameters and configurations.
method Generalizing the embroidery method to rational and concentric circles, breaking symmetry to reveal higher singularities.
result Higher singularities like swallowtails and butterflies can be unfolded, revealing their structure.
Study confirms geodesic connectivity and rooftop envelopes in complex Monge-Ampère equation domains.
problem Confirming geodesic connectivity and rooftop envelopes in complex Monge-Ampère equation domains.
method Examined geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains.
result Affirmative answer to a longstanding open question about geodesic connectivity and rooftop envelopes.
Characterizes surfaces enveloped by rotating cones for CNC machining.
problem Characterizing surfaces enveloped by rotating cones for CNC machining.
method Derives higher-order nonlinear PDEs for enveloping surfaces, including local approximations.
result Characterizations generalize previous work on developable and ruled surfaces.
The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a compact complex manifold. We prove that the complex Hessian forms of these envelopes …