Classifies semi-algebraic surfaces up to bi-Lipschitz homeomorphisms.
problem Classifying semi-algebraic surfaces with isolated singularities.
method Bi-Lipschitz homeomorphisms with inner distance.
result Complete classifications for Nash surfaces and complex algebraic curves.
We obtain global extensions of the celebrated Nash-Kuiper theorem for C1,θ isometric immersions of compact manifolds with optimal Hölder exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in 3-space, we show that the Nash-Kuiper non-rigidity prevails upto exponent $θ<1…
Let M and N be Nash manifolds, and f and g Nash maps from M to N. If M and N are compact and if f and g are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, Cinfty R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash…
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
Both analytic and geometric forms of an optimal monotone principle for Lp-integral of the Green function of a simply-connected planar domain Ω with rectifiable simple curve as boundary are established through a sharp one-dimensional power integral estimate of Riemann-Stieltjes type and the Huber analytic and geome…
Machine learning detects NASH patients from medical claims data.
problem Detecting undiagnosed NASH patients for screening and management.
method Gradient-boosted decision trees trained on administrative medical claims data.
result Model precision for NASH detection is significantly higher than NASH incidence.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
problem Optimal geometric estimates for compact Kähler manifolds
method Proving Sobolev-type inequality and local volume noncollapsing with optimal exponents
result Uniformly bounded q-Nash entropy Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types {33,42}, {32,4,3,4}, {6,3,6,3}, {34,6}, {4,82}, {3,122}, {4,6,12}, {6,4,3,4} exist on the torus. In this article we show the e…
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
We explore the practicability of Nash's Embedding Theorem in vision and imaging sciences. In particular, we investigate the relevance of a result of Burago and Zalgaller regarding the existence of isometric embeddings of polyhedral surfaces in R3 and we show that their proof does not extended directly to hi…
Algorithm learns Nash equilibria in stochastic games using entropy-regularized policies.
problem Learning Nash equilibria in zero-sum stochastic games is computationally expensive.
method Entropy-regularized soft policies for Q-function updates.
result Algorithm converges to Nash equilibrium under certain conditions.
The study characterizes Nash maps between semialgebraic sets and their properties.
problem Existence of surjective Nash maps between semialgebraic sets.
method Characterization of semialgebraic subsets and their images under Nash maps.
result Characterization of semialgebraic sets that are Nash images of the unit ball.
A method is provided to resolve Lie algebroids with singularities.
problem Resolving Lie algebroids with singular points.
method Nash-type blow-up construction for Lie algebroids.
result A short exact sequence is established linking the blow-up to Lie algebroids.
In this article we consider the motion of relativistic strings in the Minkowski space R1+n. Those surfaces are known as a timelike minimal surface, and described by a system with n nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the n…
A Nash game theory approach allocates capital requirements among financial institutions.
problem Allocating systemic risk measures among financial institutions.
method Proposes a Nash allocation rule inspired by game theory.
result Provides sufficient conditions for the existence and uniqueness of Nash allocation rules.
In this paper we review our earlier work on quantum computing and the Nash Equilibrium, in particular, tracing the history of the discovery of new Nash Equilibria and then reviewing the ways in which quantum computing may be expected to generate new classes of Nash equilibria. We then extend this work through a substan…
This paper simplifies the Nash Bargaining Solution for use in intellectual property cases.
problem Limited application of Nash Bargaining Solution in assigning intellectual property damages.
method Normalizes the Nash Bargaining Solution and provides a methodology for determining bargaining weight.
result Clarifies the application of Nash Bargaining Solution to specific case facts.
Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.
problem Finding a fair Nash equilibrium in group decision-making.
method Introduces entropy-norm space for geometric selection of strict Nash equilibria.
result The closest entropy-norm pair to the largest entropy-norm pair in rescaled space is the most suitable equilibrium.
Paper refines royalty determination using Bayesian methods.
problem Determining a reasonable royalty with risk and uncertainty.
method Bayesian Cost approach to refine Nash Bargaining Solution.
result Nash Bargaining Solution emerges as more reliable.
A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.
Ancient Ricci flows with bounded Nash entropy have uniform Sobolev inequalities.
problem Bounding Nash entropy in ancient Ricci flows.
method Uniformly bounded Nash entropy implies uniform bounds on the ν-functional, leading to uniform logarithmic and Sobolev inequalities.
result Uniform logarithmic and Sobolev inequalities on ancient Ricci flows with bounded Nash entropy.
We prove that the infinite family of homotopy 4-spheres constructed by Daniel Nash are all diffeomorphic to 4-sphere.
We give geometrical conditions under which there exist extremal functions for the sharp L2-Nash inequality.
The study examines Nash equilibria in utility maximization games with multiplicative performance criteria.
problem Existence and uniqueness of Nash equilibria in multiplicative performance criteria games.
method General characterization of Nash equilibria for a large class of utility functions.
result Existence and uniqueness of Nash equilibria for arbitrary initial wealth vectors.
Kuranishi's proof of complex deformation theory revisited
problem Existence of complex deformations on compact complex manifolds
method Hamilton-Nash-Moser implicit function theorem
result Revisits classical proof with modern tools
Study Nash equilibrium between broker and trader in a lit exchange with price impact.
problem Optimizing trading strategies between informed and uninformed traders with broker's inventory penalties.
method Characterized Nash equilibrium through FBSDEs, solved explicitly.
result Explicit solution to trading strategies of broker and informed trader.
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for ε-mixed Nash equilibrium. Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
This research uses reinforcement learning to find optimal emission offsets in greenhouse gas markets.
problem Finding optimal emission offsets in greenhouse gas markets to control excess emissions.
method Utilized reinforcement learning, specifically Nash-DQN, to estimate market Nash equilibria.
result Emitting firms can achieve significant financial savings by abiding by the Nash equilibria found in the market.
Study shows how multiple traders can trade together without excessive price impact.
problem Coordination issues in trading to exploit a common signal.
method Closed-loop Nash competition model for stochastic differential games.
result Excessive trading reduced but not significantly for practical parameters.
Study Nash equilibrium in mean field portfolio games with random market parameters.
problem Modeling wealth and relative performance in competitive financial markets.
method Martingale optimality principle approach to characterize Nash equilibrium in mean field FBSDE.
result Unique Nash equilibrium found under weak interaction assumption and market parameters independence.
A new algorithm reduces memory and computational needs for reinforcement learning.
problem Memory and computational inefficiency in model-free reinforcement learning.
method Memory-Efficient Nash Q-Learning (ME-Nash-QL) for two-player zero-sum games.
result Proves ME-Nash-QL reduces space and sample complexity for tabular and long-horizon cases.
We introduce a new loss function for evaluating forecasts and estimate models using it.
problem Lack of a decision-theoretic foundation for evaluating forecasts using the Nash-Sutcliffe efficiency.
method We introduce and analyze the Nash-Sutcliffe loss function and its application in estimating models.
result Nash-Sutcliffe loss provides a decision-theoretic foundation for evaluating and estimating models.
We prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied, then it is diffeomorphic to Rnl.
The paper proves inequalities on Finsler manifolds under Ricci curvature bounds.
problem Proving (p,q)-Sobolev and Nash inequalities on Finsler metric measure manifolds. method Global p-Poincaré inequality, (p,q)-Sobolev inequality, Nash inequality derivation. result Established global optimal (p,q)-Sobolev inequality with a sharp constant. This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
Study Nash competition among dealers quoting prices to clients with unknown trading motives.
problem Adverse selection and inventory costs in dealer-client interactions.
method Analyzes one-shot Nash competition with unknown client type and inventory constraints.
result Unique symmetric Nash equilibrium exists and can be characterized by a nonlinear ODE.
Solves open problem on simple surfaces with novel twistor correspondence.
problem Existence of nontrivial holomorphic vector bundles on simple surfaces.
method Novel twistor correspondence, Nash-Moser inverse function theorem, and microlocal analysis.
result Simple surface twistor space supports no nontrivial holomorphic vector bundles.
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
Given a multifunction from X to the k−fold symmetric product Symk(X), we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…
In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity…
We prove that, given a C2 Riemannian metric g on the 2-dimensional disk D2, any short C1 immersion of (D2,g) into R3 can be uniformly approximated with C1,α isometric immersions for any α<51. This statement improves previous results by Yu.F. Borisov and of a joint paper of th…
The paper analyzes game theory in convertible contracts during liquidity events.
problem Optimizing payments in convertible contracts during liquidity events.
method Defined a general model for games, showed non-existence of pure strategy Nash equilibria, developed algorithms for computing equilibria.
result Optimum pure strategy Nash equilibria exist when all contracts are of the same type (SAFE).
Nash integrates covariate-specific side info into sparse regression via neural networks.
problem Sparse linear regression struggles with covariates exhibiting structure or coming from heterogeneous sources.
method Neural Adaptive Shrinkage (Nash) framework that integrates side information into sparse regression via neural networks. Uses split variational empirical Bayes algorithm.
result Nash improves accuracy and adaptability over existing methods in real data experiments.