Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
Study compares employers with and without anticipating strategic labor force responses.
problem Understanding and optimizing strategic interactions in labor markets.
method Formulation of causal strategic classification, theory, and experiments.
result Performatively optimal hiring policies improve employer and labor outcomes, but can also harm labor force utility.
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.
In this paper we contribute a novel algorithm family, which generalizes many unsupervised techniques including unnormalized and energy models, and allows us to infer different statistical modalities (e.g. data likelihood and ratio between densities) from data samples. The proposed unsupervised technique, named Probabil…
Cointegration helps insurers understand long-range mortality patterns.
problem Insurers struggle to detect long-range dependence in their mortality data.
method Cointegration techniques applied to mixed fractional Brownian motion (mfBm) to capture long-range dependence.
result Cointegration brings long-range dependence information from national mortality data to insurers' models.
Rate GENERIC extends thermodynamics principles to non-equilibrium systems.
problem Understanding non-equilibrium thermodynamics and its relation to equilibrium thermodynamics.
method Developed a geometrical framework for rate GENERIC, extending Onsager's variational principle.
result Rate GENERIC structure provides a new perspective on thermodynamics in non-equilibrium systems.
Proposes linking energy and force uncertainty in deep learning potentials.
problem Uncertainty in predicted energies and forces in machine learning models.
method Introduces a spatially correlated noise process to link energy and force uncertainty.
result Demonstrates the approach on molecular datasets, linking energy and force uncertainties.
CG-BGs combine flow-based models with PMFs to sample large systems efficiently.
problem Sampling equilibrium molecular configurations from the Boltzmann distribution is challenging.
method Coarse-grained Boltzmann Generators (CG-BGs) use flow-based models and learned PMFs for efficient sampling.
result CG-BGs provide a practical route for sampling larger molecular systems efficiently.
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.
Feature normalization prevents collapse in non-contrastive learning dynamics.
problem Non-contrastive learning can collapse into a single point due to lack of repulsive force.
method Extended previous theory based on L2 loss to cosine loss, considering feature normalization.
result Cosine loss induces stable equilibrium, preventing collapse even with insufficient repulsive force.
The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…
The paper classifies and characterizes special surfaces in a 3D space.
problem Understanding surfaces in a vertical force field.
method Analyzing φ-minimal surfaces with specific properties. result A full classification of complete flat embedded φ-minimal surfaces. PenduMAV is a 6-input omnidirectional MAV without internal forces.
problem Designing a MAV without internal forces and structural costs.
method Multibody dynamics derivation, SE(3) control, Lyapunov analysis, Gazebo simulations.
result Asymptotic stabilization of the closed-loop system under parametric uncertainty and actuator noise.
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the f…
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equ…
In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi-Maupertuis metric. This characterization works for the N-body problem with general masses and any 1/rα potential with α>0. We also observe dynamical consequences of these curvature values for relati…
We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17 (2000) 1…
Kernel networks' stability edge linked to Fisher Information singularity.
problem Understanding the stability edge in high-capacity kernel Hopfield networks.
method Statistical manifold analysis and Riemannian geometry.
result The Ridge of Optimization corresponds to the Edge of Stability, revealing a dual equilibrium.
New method reconstructs non-equilibrium stochastic systems from data.
problem Reconstructing non-equilibrium stochastic systems from ensemble measurements.
method Schrödinger bridge problem with multivariate Ornstein-Uhlenbeck process.
result Simulation-free algorithm achieves higher accuracy than competing methods.
A linear and lagged relationship between inflation and labor force change rate, p(t)= A1dLF(t-t1)/LF(t-t1)+A2 was found for developed economies. For the USA, A1=4.0, A2=-0.03075, and t1=2 years. It provides a RMS forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best amon…
This paper generalizes Michell Truss to higher dimensions using geometric measure theory.
problem Finding optimal designs of k-beam structures under equilibrium forces.
method Geometric measure theory and flat chain complex.
result Existence of optimal k-beam structures has been solved completely.
Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
problem Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
method Numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics.
result Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribe…
This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints and found to match real world observations about financi…
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Model calculates optimal trading time for derivatives orders.
problem Balancing execution costs and market risks in large order execution.
method Time Is Money model using Bachelier model and central limit order book.
result Demonstrates a continuous-time Arrival Price framework.
DQN outperforms static policies in a dynamic fee environment for automated market makers.
problem How automated market makers (AMMs) perform under dynamic fees is unknown.
method Constructed a closed-loop simulator with dynamic fees, noise flow, and arbitrage.
result A small DQN policy outperforms static policies in a dynamic fee environment.
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
We develop a model to study the role of rationality in economics and biology. The model's agents differ continuously in their ability to make rational choices. The agents' objective is to ensure their individual survival over time or, equivalently, to maximize profits. In equilibrium, however, rational agents who maxim…
A linear and lagged relationship between inflation, unemployment and labor force change rate, p(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+ A2, where A0, A1, and A2 are empirical country-specific coefficients, was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=…
Model predicts asset prices from initial shocks using neural networks.
problem Missing data on actual asset liquidations limits model calibration.
method Dual neural network structure, first stage maps shocks to liquidations, second stage uses liquidations to predict prices.
result Model accurately predicts equilibrium prices from initial shocks without liquidation data.
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
Model shows PoS networks can be captured by external finance, leading to centralization.
problem Long-term centralization of PoS networks under external finance pressures.
method Heterogeneous macroeconomic model with two actor classes: investors and consumers.
result External finance forces PoS networks to centralize, leading to zero internal staking yield.
Geometric approach solves maximum likelihood for Cauchy-like distributions.
problem Estimating center and scatter robustly from heavy-tailed data.
method Geodesic convexity and symmetry spaces of noncompact type.
result Efficient numerical solution for robust estimates of location and spread.
Despite the growing interest in generative adversarial networks (GANs), training GANs remains a challenging problem, both from a theoretical and a practical standpoint. To address this challenge, in this paper, we propose a novel way to exploit the unique geometry of the real data, especially the manifold information. …
Volume-preserving neural networks prevent gradient issues.
problem Vanishing and exploding gradients in deep neural networks.
method A new neural network architecture with volume-preserving sublayers.
result Volume-preserving neural networks maintain gradient stability.
Understanding how funding and 4H context regulate crypto markets.
problem Analyzing the chaotic appearance of financial markets.
method Observing interactions between market context and capital conditions in the 4H timeframe.
result Ranges in crypto markets are strategic positioning by informed participants, not indecision.
GGFPS improves model performance by sampling molecules more efficiently.
problem Improving model performance and reducing data costs in chemistry problems.
method Gradient-Guided Furthest Point Sampling (GGFPS) that leverages molecular force norms.
result GGFPS leads to superior data efficiency and model robustness compared to other sampling methods.
We explore a model of the interaction between banks and outside investors in which the ability of banks to issue inside money (short-term liabilities believed to be convertible into currency at par) can generate a collapse in asset prices and widespread bank insolvency. The banks and investors share a common belief abo…
LNK improves uncertainty estimation for molecular dynamics, reducing errors by up to 2.5 times.
problem Uncertainty estimation for molecular force fields to improve model reliability.
method LNK: Gaussian Process-based extension to GNNs addressing six desiderata.
result LNK reduces out-of-equilibrium detection errors by up to 2.5 times compared to existing methods.
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
problem Lack of reference atomistic forces makes force matching infeasible for MLCG force fields.
method Introduces noise-based kernels adapted to low-data regimes using normalizing flows.
result Flow-based kernels reduce local distortions while preserving global accuracy.
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium…
New algorithm efficiently trains machine learning models to atomic forces data.
problem Efficiently training machine learning models to large amounts of force data.
method Developed an efficient algorithm for training machine learning models to all available force data.
result Training to all available force data is only a few times more expensive than training to energies alone.
The paper integrates dissipative and curl forces using geometric methods.
problem Incorporating dissipative forces into curl forces for non-conservative systems.
method Geometric metriplectic approach, Herglotz principle, generalized Euler-Lagrange equation, Galley's method.
result Natural formulations for Lagrangian and Hamiltonian dynamics of non-conservative systems.
Diffusion models simulate molecular dynamics with adjustable accuracy.
problem Simulating molecular dynamics with high accuracy and efficiency.
method Diffusion models as Euler-Maruyama integrators for Langevin dynamics, learning forces from static snapshots.
result Diffusion models generate molecular trajectories with temporal correlations similar to MD simulations.
Improved CG force-field learning from all-atom data.
problem Training accurate coarse-grained models from all-atom simulations is challenging.
method Optimized force mapping to improve statistical efficiency of force-field learning.
result Substantially improved CG force-fields can be learned from the same simulation data.
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.