The paper finds unique equilibrium states for geodesic flows on certain surfaces.
problem Analyzing geodesic flows on surfaces without focal points.
method Proving the existence of unique equilibrium states for specific potentials.
result There are unique equilibrium states for certain potentials, including geometric multiples of scalar less than 1.
Study equilibrium measures on manifolds without conjugate points with visibility covering.
problem Uniqueness and properties of equilibrium measures on manifolds without conjugate points.
method Analysis of geodesic flows, study of equilibrium measures, ergodic properties, and pressure gap.
result Equilibrium measures satisfy a weak pressure gap under certain conditions.
The theorems we proved describe the structure of economic equilibrium in the exchange economy model. We have studied the structure of property vectors under given structure of demand vectors at which given price vector is equilibrium one. On this ground, we describe the general structure of the equilibrium state and gi…
Extends SORTE to multivariate risk functions.
problem Analyzing systemic risk in financial institutions or insurance-reinsurance markets.
method Develops a new framework for multivariate utility functions and applies duality theory.
result Proves existence, uniqueness, and Nash Equilibrium property of Multivariate Systemic Optimal Risk Transfer Equilibrium.
Deep neural network generates molecular structures close to equilibrium.
problem Discovery of atomistic systems with desirable properties.
method Autoregressive, convolutional deep neural network architecture.
result Model generates molecules close to equilibrium for C7O2H10 isomers.
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.
Study equilibrium consumption habits in a large population using mean field games.
problem Equilibrium consumption under external habit formation in a large population.
method Formulated and solved mean field games for linear and multiplicative habit formation preferences, constructed approximate Nash equilibria for large n-player games.
result Characterized mean field equilibrium strategies and derived financial implications.
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the…
We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock written on a default-free dividend process, and a defaultable bond, whose prices are determined via equilibrium. We analyze fi…
Paper improves molecular property prediction using denoising autoencoders.
problem Limited data for molecular property prediction from 3D structures.
method Pre-training via denoising for learning molecular force fields.
result Achieves new state-of-the-art performance on QM9 dataset.
Gradient equilibrium improves online learning performance without requiring sublinear regret.
problem Achieving sublinear regret in online learning.
method Gradient equilibrium: average of gradients converges to zero.
result Gradient equilibrium can be achieved by standard online learning methods.
HomoODE connects DEQs and Neural ODEs via homotopy continuation, improving accuracy and memory efficiency.
problem Connecting DEQs and Neural ODEs for better model performance and efficiency.
method Established a connection between DEQs and Neural ODEs using homotopy continuation, proposing HomoODE.
result HomoODE outperforms existing implicit models in accuracy and memory consumption.
This paper investigates how dataset properties affect GAN training outcomes.
problem GANs often fail to reach equilibrium due to instability or mode collapse.
method Experiments to identify patterns in dataset properties and their effects on GAN training.
result Patterns in dataset properties influence GAN training dynamics and outcomes.
Study on equilibrium points of dynamical systems with multiple integrals.
problem Understanding the equilibrium points of dynamical systems with multiple independent first integrals.
method Analyzes the equilibrium locus as a smooth manifold and fiber bundle with a natural connection.
result Parallel transport exists for the connection and can measure eigenvalue variations.
In this paper we propose a tractable quadratic programming formulation for calculating the equilibrium term structure of electricity prices. We rely on a theoretical model described in [21], but extend it so that it reflects actually traded electricity contracts, transaction costs and liquidity considerations. Our nume…
This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer who engages in order splitting to reach a cumulative trading target and an uncon…
We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is a…
Proposes a new optimization-based method for aggregating sets in neural networks.
problem Limited representational power of existing aggregation methods.
method Equilibrium Aggregation: an optimization-based approach.
result Equilibrium Aggregation outperforms existing methods in various tasks.
A new approach to MV portfolio optimization with jumps and RL.
problem Continuous-time Mean-Variance portfolio optimization with jumps.
method Jump-diffusion process, Reinforcement Learning, time-inconsistent control (TIC), Actor-Critic RL algorithm.
result The proposed RL model is profitable in real-world market data.
Derives equilibrium law for Plateau borders in wet soap films and foams.
problem Equilibrium law for Plateau borders in wet foams and films.
method Rigorous derivation using Gauss' capillarity theory, homotopic spanning condition, and effective compactness theorems.
result Sharp regularity properties of energy minimizers for Plateau borders in wet foams and films.
Study compares cryptocurrency and stock markets using statistical equilibrium models.
problem Comparing the stochastic structure of cryptocurrency and stock markets.
method Applied QRSE model to analyze daily returns of cryptocurrencies and S&P 500 companies.
result Revealed differences in informational efficiency between cryptocurrency and stock markets.
Paper characterizes equilibrium strategies for stochastic control with higher-order moments.
problem Stochastic control problems with higher-order moments.
method Novel characterization of time-consistent control problems, deriving equilibrium conditions via BSDEs.
result Derives sufficient and necessary conditions for an open-loop Nash equilibrium control (ONEC) in a novel way.
The paper studies price impacts in asset liquidation markets.
problem Understanding price impacts in asset liquidation markets.
method Equilibrium formulation and analysis of price impacts.
result Existence and uniqueness of clearing prices for portfolio liquidation.
Modeling trading behavior with information signals and limit order books, showing market impact and equilibrium properties.
problem Analyzing the impact of information signals on trading behavior and market equilibrium in limit order books.
method Static equilibrium model with profit-maximizing investors and competitive dealers, using iterative algorithms and asymptotic analysis.
result The market impact of large trades follows a power law with fat tails and a logarithmic law with lighter tails, and the order book flattens as noise trading increases.
New method for studying t-dependent Hamilton equations on cosymplectic manifolds.
problem Existence and stability of solutions of t-dependent Hamilton equations. method Develops a cosymplectic energy-momentum method for Hamilton equations with more types of symmetries.
result Provides a more general framework for studying t-dependent Hamilton equations. Model analyzes competitive pricing strategies in large markets of perishable products.
problem Maximizing profits in a competitive market of perishable products.
method Mean-field competition model, Hamilton-Jacobi-Bellman equation, iterative numerical algorithm.
result Properties of equilibrium pricing strategies and market dynamics.
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property)…
The paper characterizes equilibrium strategies under random risk aversion, showing unique solutions based on risk aversion distribution.
problem Characterizing equilibrium strategies in a continuous-time portfolio selection problem under random risk aversion.
method Provided a complete characterization of all deterministic equilibrium strategies in closed form, analyzing the structure of the solution based on the distribution of random risk aversion.
result The equilibrium is unique (if exists) when the expectation of random risk aversion is finite, but infinite expectation leads to either infinitely many equilibria or a unique trivial one.
We consider n risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions f…
Study of pursuit-evasion game on sphere and its relation to planar Apollonius circle.
problem Analyzing pursuit-evasion game on a sphere and its properties.
method Extending classical planar pursuit-evasion game to spherical geometry, studying equilibrium intercept points and their relation to Apollonius domain.
result Condition for intercept point to belong to Apollonius domain on sphere, analogous to planar game.
Improved sampling for gauge theory with SNFs.
problem Sampling from target probability distributions in gauge theory.
method Stochastic Normalizing Flows (SNFs) for SU(3) lattice gauge theory. result Promising scaling properties of SNFs with degrees of freedom.
Enhanced diffusion sampling improves rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular systems.
method Quantitative steering protocols to generate biased ensembles and exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties.
Enhanced diffusion sampling tackles rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular simulations.
method Quantitative steering protocols to generate biased ensembles, followed by exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties for folding free energies.
We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the …
Gradient descent dynamics studied for DEQs in linear and single-index models.
problem Understanding gradient descent dynamics for DEQs.
method Rigorously studied gradient descent dynamics for DEQs in linear and single-index models.
result Gradient descent converges to a global minimizer for linear DEQs and single-index models.
Extends inf-convolution to countable risk measures for risk sharing.
problem Limited inf-convolution theory to finite sets of risk measures.
method Extends inf-convolution to countable sets, investigates properties and results.
result Generalizes known properties and results to countable case.
Graph dynamics link combinatorics to geometry, revealing manifold intersections and stability.
problem Understanding the geometry of graph dynamical systems with odd interactions.
method Proved geometry and stability of manifolds governed by graph homology and coverings.
result Derived upper and lower bounds on the dimension of the equilibrium set.
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach becomes increasingly problematic as network size increases. In the context of curre…
Introduces strong equilibrium for time-inconsistent stopping problems in continuous time.
problem Time-inconsistent stopping problems in continuous time.
method Introduces strong equilibrium, compares with existing mild and weak equilibria, and provides an iteration method to construct optimal mild equilibria.
result Optimal mild equilibria are always strong equilibria under certain conditions.
Economic integration, globalization and financial crises represent examples of processes whose understanding requires the analysis of the underlying network structure. Of particular interest is establishing whether a real economic network is in a state of (quasi)stationary equilibrium, i.e. characterized by smooth stru…
Various multi-agent models of wealth distributions defined by microscopic laws regulating the trades, with or without a saving criterion, are reviewed. We discuss and clarify the equilibrium properties of the model with constant global saving propensity, resulting in Gamma distributions, and their equivalence to the Ma…
New algorithm finds optimal sample complexity for pure exploration with multiple good answers.
problem Determining the optimal number of samples needed to explore multiple good answers in a bandit problem.
method Derive lower bound using game equilibrium, extend Track-and-Stop algorithm to multiple answers.
result New algorithm has asymptotic sample complexity matching the derived lower bound.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Two-cycle GEILA equilibria are OLG equilibria and vice versa, with applications to indeterminacy and bubbles.
problem Relationship between GEILA and OLG models.
method Proof of equilibrium equivalence and application to indeterminacy and bubbles.
result GEILA and OLG models are equivalent under certain conditions.
We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity.…
Paper presents a GMFG framework for large stochastic games.
problem Learning Nash Equilibrium in large stochastic games.
method Value-based and policy-based reinforcement learning algorithms with smoothed policies.
result Proposed algorithms GMF-V and GMF-P are efficient and robust in GMFG setting.
A new method relaxes molecules without needing non-equilibrium data.
problem Molecular relaxation requires understanding non-equilibrium structures.
method MoreRed: molecular relaxation by reverse diffusion with time step prediction.
result MoreRed learns a simpler pseudo potential energy surface.
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…