Heegaard Floer homology duality applied to 4D mapping tori.
problem Computing Heegaard Floer invariants of 4D mapping tori.
method Applied Heegaard Floer homology and duality theory.
result Computed invariants of 4D mapping tori using Lefschetz numbers.
Novel framework shows exact recoverability of matrix completion and robust PCA with optimal sample complexity.
problem Efficiently recovering a hidden matrix from limited observations.
method Strong duality and novel analytical framework for non-convex matrix factorization problems.
result Exact recoverability and strong duality hold with nearly-optimal sample complexity guarantees for matrix completion and robust PCA.
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
We show that the self-duality defined in [Trautman, Int.J.Theor.Phys.,{\bf 16},561 (1977)] is equivalent to strong self-duality defined in [Bilge, Dereli and Kocak, Lett.Math.Phys., {\bf 36}, 301-309, (1996)] and we obtain an upper bound on ∫(p2)n, where p2 is the second Pontrjagin class of an SO(N) bund…
Extending previous work that involved D3-branes ending on a fivebrane with θYM=0, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional Chern-Simons theory of a supergroup U(m∣n) or OSp(m∣2n) rather than an ordinary …
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
Researchers develop a pricing method for contingent claims under partial information and short selling constraints.
problem Pricing contingent claims with partial information and short selling restrictions.
method Derive a dual problem using conjugate duality theory and conditions for strong duality.
result Characterization of contingent claim prices involving martingale and super-martingale conditions.
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare v…
Paper relaxes the Lipschitz constraint in WGANs to improve performance.
problem WGANs do not always outperform other GAN variants due to imperfect implementation of the Lipschitz condition.
method Proposes a new dual form of Wasserstein distance (Sobolev duality) that relaxes the Lipschitz constraint but maintains gradient property.
result SWGAN, based on Sobolev duality, outperforms existing methods in experiments.
We solve optimal consumption in a market with bounded risk.
problem Optimal consumption in a semimartingale market with bounded risk.
method Use supermartingale deflators to prove strong duality.
result Strong duality and complete characterisation of optimal consumption.
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched" process consisting of a p…
Study collective pricing and hedging with admissible risk exchanges forming a finitely generated convex cone.
problem Collective pricing and hedging with exchanges forming a finitely generated convex cone.
method Extend collective First Fundamental Theorem of Asset Pricing and pricing-hedging duality.
result No collective arbitrage implies the closedness of the aggregate feasibility cone.
Extended Riemannian geometry aids in DFT formulations.
problem Describing current DFT formulations with clarity.
method Using graded manifolds and extended symmetries.
result Covariant strong section condition and global descriptions.
Study optimizes financial strategies for various options globally.
problem Optimizing financial strategies for different types of options.
method Martingale optimal transport duality for càdlàg processes.
result Existence of robust semi-static superhedging strategies.
The paper explores criteria for positivity of forms and proves their strong positivity in specific cases.
problem Understanding positivity of exterior forms on complex vector spaces.
method Dimensionality reduction and criteria based on Hermitian matrices.
result Strong positivity of certain forms proven by duality.
A new screening rule 'dynamic Sasvi' improves sparse optimization speed.
problem Sparse optimization problem identification.
method Flexible framework based on Fenchel-Rockafellar duality for norm-regularized least squares.
result Dynamic Sasvi can eliminate more features and increase solver speed.
Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.
problem Solving stochastic min-max problems with strong convexity and strong concavity.
method Epoch-wise stochastic gradient descent ascent method (Epoch-GDA) without additional assumptions.
result Achieves the optimal rate of O(1/T) for the duality gap of general SCSC min-max problems. New method reduces over-pessimism in Bayesian control under parameter uncertainty.
problem Over-pessimism in Bayesian control due to misspecified priors.
method Distributionally robust Bayesian control (DRBC) with strong duality and optimization.
result Validated algorithm on synthetic and real data, reducing over-pessimism.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
Deep neural networks with multiple branches are less non-convex, improving performance.
problem Improving neural network performance through multi-branch architectures.
method Quantitative measurement of duality gap for neural networks with multi-branches and various activation functions.
result The duality gap of multi-branch neural networks decreases as the number of branches increases, leading to less non-convex optimization problems.
A new robust Wasserstein distance is proposed to handle outliers in probability distributions.
problem Outliers in probability distributions make Wasserstein distances sensitive and impractical.
method Introduces a new outlier-robust Wasserstein distance Wpε. result Achieves strong robust estimation guarantees under the Huber ε-contamination model. Study stability of contingent claim solutions under probabilistic perturbations.
problem Stability of solutions to discrete-time contingent-claim problems under uncertainty.
method Use Rockafellian perturbations to analyze stability of solutions.
result Establishes convergence of dual problems and shadow prices.
Bundle method solves low rank SDP problems without full matrix construction.
problem Solving semidefinite programming problems with low rank solutions.
method Applying bundle method to randomly sketch matrix optimization problems and using recent results on bundle methods.
result Algorithm produces solutions with low rank representation and convergence rates.
Develops SGH bundles and theories for GC manifolds.
problem No specific problem stated; focuses on new bundle theory.
method Introduces SGH bundles, develops cohomology, and establishes theories.
result Established a Chern-Weil theory and Hodge theory for SGH bundles.
Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher homotopies typically arise when a huge object, e. g. a chain complex defining various …
Extends utility maximization theory for infinite horizons without strong no-arbitrage assumptions.
problem Maximizing lifetime utility from wealth over an infinite horizon.
method Develops a duality theory using deflators and supermartingale properties, extending previous work.
result Establishes a strong duality theorem for infinite horizon utility maximization under minimal no-arbitrage assumptions.
Study uncovers new phase transitions in asymmetric causal inference scenarios.
problem Understanding typical phase transitions in asymmetric causal inference.
method Combining Causal inference (C-inf) and Low-rank recovery (LRR) with Random duality - Free probability theory (RDT-FPT).
result Discovering a doubling low-rankness phenomenon in asymmetric scenarios.
Recently the authors showed that there is a robust potential theory attached to any calibrated manifold (X,φ). In particular, on X there exist φ-plurisubharmonic functions, φ-convex domains, φ-convex boundaries, etc., all inter-related and having a number of good properties. In this paper we show that, in a strong sens…
Investigates geometric aspects of double field theory and its membrane sigma-model formulation.
problem Capturing geometric and non-geometric flux backgrounds in DFT.
method Determines a splitting and projection of the Courant algebroid, constructs a membrane sigma-model, and analyzes gauge invariance.
result Unified description of geometric and non-geometric flux backgrounds in DFT.
Develops algorithms for multi-class Neyman-Pearson classification with cost sensitivity.
problem Asymmetric misclassification costs in multi-class classification problems.
method Establishes connection with cost-sensitive learning, proposes two algorithms, extends NP oracle properties.
result Proposes algorithms with theoretical guarantees for multi-class Neyman-Pearson classification.
A manifold (M,I,J,K) is called hypercomplex if I,J,K are complex structures satisfying quaternionic relations. A quaternionic Hermitian metric is called HKT (hyperkaehler with torsion) if IdωI=JdωJ=KdωK, where ωI,ωJ,ωK are Hermitian forms associated with I, J, K. A Hermitian metric ω on a complex manifo…
Paper analyzes complexity of PSGLA for sampling log-concave distributions.
problem Sampling from log-concave distributions with composite potentials.
method Uses primal-dual interpretation and duality gap to analyze PSGLA complexity.
result Complexity of PSGLA is O(1/ε2) for strongly convex potentials. New graph feedback model for bandits with improved regret bounds.
problem Understanding how graph structure affects regret in bandit problems.
method Introduced fractional weak domination number and k-packing independence number to capture upper and lower bounds on regret. Used strong duality theorem to derive upper and lower bounds. result Proved general upper and lower bounds on regret for various graph structures, showing tightness up to a logarithmic factor.
The twist construction is a geometric T-duality that produces new manifolds from old, works well with for example hypercomplex structures and is easily inverted. It tends to destroy properties such as the hyperKähler condition. On the other hand modifications preserve the hyperKähler property, but do not have an obviou…
Proves Poincaré duality for Hopf algebroids with bijective antipode.
problem Proving Poincaré duality for Hopf algebroids.
method Using twisted Poincaré duality and bijective antipode properties.
result Recovering and extending known Poincaré dualities for Hopf algebroids.
Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological n-manifolds whose coefficient systems are n-disk algebras or n-disk stacks. In this work we prove a precise formulation of this idea, giving an axiomatic characterization of fa…
Given an n-manifold M and an n-category C, we define a chain complex (the "blob complex") B_*(M;C). The blob complex can be thought of as a derived category analogue of the Hilbert space of a TQFT, and as a generalization of Hochschild homology to n-categories and n-manifolds. It enjoys a number of nice formal properti…
New proof of chain duality for simplicial complexes.
problem Proving the existence of chain duality for chain complexes over simplicial complexes.
method Geometric and conceptual treatment of chain duality.
result Fundamental for Ranicki's surgery exact sequence.
The paper establishes general results in Lorentzian optimal transport theory.
problem Establishing strong duality and optimality conditions in Lorentzian optimal transport.
method Providing non-trivial assumptions on measures, characterizing optimality, and proving regularity results.
result Regularity results for c-convex functions and (weak) Kantorovich potentials do not extend to the Lorentzian setting, but under suitable assumptions, they are locally semconvex. Revisits shallow neural networks using Lipschitz norms and measures.
problem Existence and compactness of minimizers in neural network formulations.
method Mean field parametrization, signed measures, duality pairings, Kantorovich-Rubinstein norms.
result Compactness results and uniform large data limits for empirical risk minimization.
Introduces Kähler duality between domains in complex space.
problem None explicitly stated; focuses on concept introduction.
method None explicitly stated; focuses on concept introduction.
result Introduces Kähler duality between domains in complex space.
Research on dualities in geometric stereotypes.
problem Understanding dualities in geometric stereotypes.
method Continuation of previous research on stereotype spaces and algebras.
result New insights into geometric stereotype dualities.
Geometric framework for CFMMs simplifies many results.
problem Understanding the behavior of CFMMs without strong conditions.
method Developed a geometric framework encompassing known results.
result CFMMs have a canonical trading function with specific properties.
Duality restored in gauge theory, gravity, and string theory models.
problem Restoring duality invariance in theories coupled to matter.
method Extending phase space to allow for violations of the algebraic Bianchi identity and considering the axion as the duality current.
result Duality current in NS-NS gravity is the divergence of the axion.
Unified proof of four Bavard dualities and new results on quasimorphisms.
problem Comparing stable commutator length and quasimorphisms on groups.
method Expository account and new strengthening of Bavard duality, providing complete proofs.
result Generalized mixed Bavard duality, recovering all previous dualities.
In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each natural n…
Study T-duality on nilmanifolds using Lie algebras.
problem Finding symplectic structures on 2-step nilpotent Lie algebras.
method Construct generalized complex structures and use Infinitesimal T-duality. result Criteria for the integrability of infinitesimal T-duality to topological T-duality. Optimal transport with scalar martingales defined over multiple periods.
problem Finding optimal transport plans with specific properties over multiple time periods.
method Introducing left-monotone transports and characterizing them through various properties.
result Left-monotone transports are unique under certain conditions and have specific order properties.