New contractions found between hyperbolic orbifolds.
problem Finding strict contractions between hyperbolic orbifolds.
method Elementary construction and use of Gueritaud-Kassel and Tholozan's work.
result Exotic quotients of SO_0(d,1) determined.
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48 results for “strict contractions”
We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …
The paper revisits a claim about a principal bundle over a contractible base and finds it non-trivial.
problem Investigating the properties of a specific quotient space construction over a smoothly contractible base.
method Revisiting a previous claim and using the concept of vector pseudo-bundles to redefine the structure as a non-trivial principal pseudo-bundle.
result The projection fails to satisfy the strict condition of local triviality, but the structure remains rich with a smooth, free, and fiber-transitive group action.
Proposes a new generalization bound for Bayesian deep nets without strict assumptions.
problem Lack of generalization bounds for Bayesian deep nets without strict assumptions.
method Exploits contractivity of Log-Sobolev inequalities to add a loss-gradient norm term to the generalization bound.
result Introduces a new generalization bound for Bayesian deep nets that avoids strict assumptions.
Refines d'Alembertian for signed Lorentz distance functions in metric measure spacetimes.
problem Exact representation and bounds of d'Alembertian for signed Lorentz distance functions.
method Metric geometry techniques, localization, Sobolev calculus.
result Distributional d'Alembertian is a signed measure with integration by parts formula.
Operational theory for 2-bundles defines connections and gauge transformations.
problem Defining connections and gauge transformations for 2-bundles.
method Operational framework based on derived Lie group.
result Original formulation of 2-connections and gauge transformations.
The paper computes torsion invariants for groups acting on complexes.
problem Computing torsion invariants for groups acting on complexes.
method Analyzes residually finite groups acting cocompactly on contractible complexes with specific stabilizers.
result Torsion limits to the torsion of the boundary subcomplex, independent of the chain of subgroups.
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the be…
In this article, we study the relationship between the weak limit of a sequence of integral currents in a metric space and the possible Hausdorff limit of the sequence of supports. Due to cancellation, the weak limit is in general supported in a strict subset of the Hausdorff limit. We exhibit sufficient conditions in …
Operational theory for 2-bundles defined via group actions and derivations.
problem Formalizing the geometry of 2-bundles using group actions and derivations.
method Constructing an operational total space theory for strict principal 2-bundles using a crossed module and derived Lie group.
result A new operational framework for 2-connections and gauge transformations.
The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
Proposes a new metric space example showing non-constant topological dimension.
problem Non-constant topological dimension in metric measure spaces.
method Refines Ketterer and Rajala's example to satisfy CD(0,∞) condition.
result Shows non-constancy of topological dimension for CD spaces.
We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold for model prices and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a chan…
Optimal maps exist in very strict spaces despite plan uniqueness issues.
problem Existence of optimal transport maps in very strict spaces.
method Introduced a more restrictive condition and showed existence of optimal maps.
result Existence of optimal maps in very strict spaces.
The paper studies strict equivalence in multi-virtual linkoids with new invariants.
problem Understanding strict equivalence in multi-virtual linkoids.
method Utilizing multi-virtual knot theory, defining strict virtual linkoids, and studying invariants.
result New invariants for strict virtual linkoids are defined.
Geometric derivation of quantum dynamics from Lie group actions.
problem Deriving quantum dynamics from geometric principles.
method Euler-Poincaré reduction on adjoint-coupled semidirect products.
result Reproduces the Lindblad equation from geometric reduction.
Improves SGM convergence bounds in W2-distance without strict assumptions.
problem Convergence bounds for SGMs in W2-distance require stringent assumptions.
method Novel framework using the OU process and PDE analysis.
result Log-concavity evolves from weak to strong over time.
Study strict stability of cones with isolated singularities.
problem Stability of cones with isolated singularities.
method Analyzes special Lagrangian and coassociative cones, provides examples for the complex case.
result Proves strict stability for special Lagrangian and coassociative cones.
Maps Lie 2-groups to Weil algebras, showing cohomology isomorphisms.
problem Cohomology of strict Lie 2-groups.
method Constructs van Est map using double complex and Weil algebra.
result Induces isomorphisms in cohomology under connectedness.
Proves integrability of strict Lie 2-algebras using cohomological methods.
problem Integrability of strict Lie 2-algebras.
method Van Est theorems relating cohomologies of Lie 2-groups and algebras.
result Proves integrability of Lie 2-algebras.
We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer. We show that strict local martingales arise whenever there is a consistent family of change of measures where the two measures are not equivalent to one another. Several old and new strict local martingales are i…
Abstract shows entropy and convexity definitions of very strict spaces are equivalent.
problem Equivalence of definitions of very strict spaces.
method Showed equivalence of definitions using entropy functionals and full displacement convexity class.
result Equivalence of definitions of very strict spaces.
The paper proves strict convexity of the Mabuchi functional for geodesics connecting energy minimizers.
problem Proving strict convexity of the Mabuchi functional for geodesics.
method Explicit formula for the complex Hessian of the weighted log-Bergman kernel, and proof by showing geodesics must be non-degenerate and smooth.
result Strict convexity of the Mabuchi functional along geodesics connecting energy minimizers.
Extends PoS proof-of-stake transaction fee mechanism with miner utility model.
problem Designing a transaction fee mechanism for PoS protocol that incorporates miner utility.
method Introduced a new mechanism (BSP(θ)) incorporating a parameter θ to ensure user and miner incentives.
result The new mechanism (BSP(θ)) satisfies user and miner incentives and contract proofness.
Proximal methods avoid local minima in weakly convex problems.
problem Weakly convex optimization problems with strict saddle properties.
method Proximal methods on nonsmooth functions with strict saddle guarantees.
result Proximal methods converge to local minimizers only, when initialized randomly.
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
problem Generalization bounds with strict assumptions like uniformly bounded loss.
method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.
result Proposes a new generalization bound with a surrogate of model complexity.
Study complex hyperbolic lattices and their relation to strict hyperbolization.
problem Understanding the relationship between complex hyperbolic lattices and strict hyperbolization.
method Analyzing the fundamental groups of complex hyperbolic manifolds and spaces arising from strict hyperbolization.
result Uniform lattices in PU(n,1) cannot be fundamental groups of Charney-Davis strict hyperbolizations when n ≥ 2.
Study on implied volatility in strict local martingale models, showing how to detect price bubbles.
problem Detecting price bubbles in financial models with strict local martingale behavior.
method Asymptotic expansion and duality method based on absolutely continuous measure change.
result Strict local martingale property can be determined from the asymptotic expansion of implied volatility.
New algorithms improve robust reinforcement learning under uncertainty.
problem Robust reinforcement learning in MDPs with contamination.
method Non-asymptotic convergence analysis of -learning and actor-critic methods.
result Efficient algorithms learn robust policies with minimal samples.
This paper defines new categories and functors related to Morse theory.
problem Defining new categories and functors for Morse theory.
method Constructing new almost strict -categories and defining functors.
result Functors and from to and .
Investors with high risk aversion always invest during financial bubbles.
problem Optimal investment in a financial bubble model.
method Modeling financial bubbles using strict local martingales and Johansen-Ledoit-Sornette (JLS) model relaxations.
result Investors with high relative risk aversion always invest during financial bubbles.
In this paper, we initiate the study of a parametrised version of Rieffel's strict deformation quantization. We apply it to give a classification of noncommutative principal torus bundles, in terms of parametrised strict deformation quantization of ordinary principal torus bundles. The paper also contains a putative de…
Active learning framework for strict partial orders from concept prerequisite relations.
problem Lack of large-scale labels for mining strict partial order relations.
method Active learning framework incorporating relational reasoning.
result Framework improves classification performance with same query budget.
New insights into matrix factorization show strict saddles have bounded eigenvalues.
problem Understanding the nature of critical points in matrix factorization.
method Analyzing orbits of critical points under the general linear group and identifying canonical points.
result Minimum eigenvalue of strict saddles is not uniformly bounded below zero.
Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costsq-fin.MF
Paper introduces prospective strict no-arbitrage for markets with transaction costs.
problem No-arbitrage condition in markets with transaction costs.
method Introduces prospective strict no-arbitrage, proves closedness of attainable portfolios.
result Prospective strict no-arbitrage implies closed attainable portfolios, equivalent to consistent price system.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
In this paper, we use the parametrised strict deformation quantization of C*-bundles obtained in a previous paper, and give more examples and applications of this theory. In particular, it is used here to classify H_3-twisted noncommutative torus bundles over a locally compact space. This is extended to the case of gen…
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraintmath.DG
Proves strict inequality for minimizers of Willmore energy under isoperimetric constraints.
problem Minimizing the Willmore energy under isoperimetric constraints.
method Connected sum approach, building on previous work by Keller-Mondino-Rivière.
result Existence of minimizers for the isoperimetric constrained Willmore problem in every genus.
Study on Kähler manifolds sharing submanifolds, proving projective implies relative.
problem Understanding Kähler manifolds sharing submanifolds.
method Proving properties of weak and strict relatives Kähler manifolds.
result If one Kähler manifold is projective and shares a submanifold with another, they are relatives.
We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equat…
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.
Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b in H_1(\partial M, Z). We demonstrate that either X has exactly two associated strict boundary slopes \pm t, or else there are strict bound…
Strict type-II blowup in harmonic map flow is proven to have Hölder continuous body map.
problem Finite-time singularity of harmonic map flow.
method Analysis of outer energy scale and Hölder continuity proof.
result Strictly type-II blowup body map is Hölder continuous.
We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SU(1,n). This answers a question raised by Rieffel.
The curvature-dimension condition fails in sub-Finsler geometry, extending previous results in sub-Riemannian geometry.
problem The failure of the curvature-dimension condition in sub-Finsler geometry.
method Non-trivial adaptation of Juillet's work, introduction of new tools and ideas.
result The condition does not hold in sub-Finsler geometry for various norms and measures.
A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of "naturally occurring" strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a p…
The paper explores coalescent contractions in contractible spaces, providing criteria and examples.
problem Existence and absence of coalescent contractions in contractible spaces.
method Analysis of contractible finite simplicial complexes and criteria for coalescent contractions.
result Criteria for contractible finite simplicial complexes that ensure no coalescent contractions.
We prove that two links related by a surgery along a connected, strict graph clasper of degree n are C_n-equivalent, i.e, related by a sequence of surgeries along strict tree claspers of degree n.