Professor Forcing improves recurrent network training and sampling quality.
problem Training and sampling quality issues in recurrent networks.
method Adversarial domain adaptation to align training and sampling dynamics.
result Improves test likelihood and sample quality in various tasks.
The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work and also his joint works with Professor T. Nagano and Professor Y. Tazawa of Ja…
Every graph can be represented as a singular set of a special surface.
problem Representing any finite graph as the singular set of a compact 3D surface.
method Constructing a calibrated 3-dimensional homologically area minimizing surface with a special Lagrangian form.
result The singular set of the surface is precisely the given graph.
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus appl…
Survey of recent scalar curvature results on open 3-manifolds.
problem None explicitly stated; focuses on recent results.
method Survey and review of existing research.
result Recent findings on scalar curvature in open 3-manifolds.
The purpose of this paper is to point out that `supremum' in two inequalities of Brooks should be replaced with `infimum'. The results of this paper are already known by Professor Higuci. Hence, I want to delete this paper from this preprint server.
This is a corrected version of my paper "Application of integral geometry to minimal surfaces" appeared in International J. Math. vol. 4 Nr. 1 (1993), 89-111. The correction concerns Proposition 3.5. We discuss this correction in Appendix to the original version of my published paper by reproducing our correspondence w…
In this short Note we would like to bring into the attention of people working in General Relativity a Schwarzschild like metric found by Professor Cleopatra Mociuţchi in sixties. It was obtained by the A. Sommerfeld reasoning from his treatise "Elektrodynamik" but using instead of the energy conserving law from the cl…
Saha seeks physics models to manage income inequality.
problem Minimizing income inequality in society.
method Develops statistical physics models to constrain income distribution entropy.
result Models aim to reduce income inequality.
We have developed a model for a life insurance policy. In this model the net gain is calculated by computer simulation for a particular type of lifetime distribution function. We observed that the net gain becomes maximum for a particular value of upper age of last premium. This paper is dedicated to Professor Dietrich…
Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The given translation was made in 1892 by Dr. M. W. Haskell and transcribed by N. C. Rug…
Survey on extending rigidity theorems to Riemannian manifolds.
problem Extending classical rigidity theorems to Riemannian manifolds.
method Review and extension of existing rigidity theorems.
result Rigidity results for convex hypersurfaces of homogeneous 3-manifolds.
In this expository note, we study the second variation of Perelman's entropy on the space of Kahler metrics at a Kähler-Ricci soliton. We prove that the entropy is stable in the sense of variations. In particular, Perelman's entropy is stable along the Kähler-Ricci flow. The Chinese version of this note has appeared in…
Dedicated to Professor Gromoll: The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by th…
Kempe discusses NTK approach to machine learning problems.
problem Generally unsolvable machine learning problems.
method NTK approach focusing on kernel formulations.
result Practical applications like data distillation and adversarial robustness.
Solla discusses neural processing using statistical physics and Bayesian methods.
problem Understanding neural information processing through statistical physics.
method Bayesian inference, Gibbs description, Generalized Linear Models, dimensionality reduction.
result Connection between neural processing and statistical physics.
This note explores comparison geometry concepts and theorems.
problem Exploring various comparison theorems in geometry.
method Analyzes Rauch and Toponogov theorems and their applications.
result Introduction of Gromov-Hausdorff convergence and Alexandrov Spaces.
In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manifolds. In particular a doubling construction for equatorial spheres in S3(1) is announced. Aspects of the current unde…
Extends results on Futaki invariant for Kaehler metrics on algebraic manifolds.
problem Existence of Kaehler metrics with constant scalar curvature.
method Revisits and extends classical and recent results on Futaki invariant.
result Extensions and applications of Futaki invariant in Kaehler geometry.
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.
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.
Paper computes Stiefel-Whitney classes on real Bott manifolds.
problem Computing Stiefel-Whitney classes on real Bott manifolds.
method Analyzes real Bott manifolds with holonomy group Z2k and diagonal type. result Extends results to compute even and odd Stiefel-Whitney classes.
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.
Derives equations for systems with external forces using variational methods.
problem Deriving equations for systems subjected to external forces.
method Variational derivation of Euler-Poincaré equations using Poisson groupoid geometry.
result Derives variational error for numerical integrators of forced systems.
Paper introduces a PDE-free method for decomposing forces in any dimension.
problem Analyzing non-conservative forces in arbitrary dimensions.
method Geometric decomposition using homotopy operator and Frobenius theorem.
result Decomposes forces into gradient and antiexact components, characterizing curl forces.
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.
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study symmetries in the systems with gyroscopic forces to find out when these systems admi…
Efficiently predicts worst-case force configurations for structural analysis.
problem Computational challenges in determining critical force locations with uncertainty.
method Experimental design method to select force locations, simple regression model, post-processing step.
result Significant improvements over existing methods and brute force approaches.
Dedicated to Professor K. Shiohama on the occasion of his seventieth birthday: This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold M. In the first series [arXiv:0901.4010], we showed that all Busemann functions on an M which is not less curved than a vo…
Study of surfaces' flow with additional forces, proving limit behavior.
problem Understanding the behavior of surfaces under mean curvature flow with external forces.
method Analysis of blow-up sequences and entropy.
result Blow-up limit of surfaces with additional forces is a self-shrinker.
Derives equations for forced systems using variational methods.
problem Designing high-order integrators for forced Lagrangian systems.
method Duplicating variables and applying variational order to forced systems.
result Characterization of method order using variational order of duplicated system.
The paper analyzes errors in mechanical systems with external forces.
problem Error analysis of mechanical systems with external forces.
method Analysis of variational integrators with contact order r for discrete mechanical systems. result The contact order of the integrator is the same as the contact order of the original systems.
Study curve flows with global forcing terms using a distance comparison principle.
problem Analyse the behavior of curves under curve flows with global forcing terms.
method Prove a distance comparison principle for curve shortening flow with arbitrary global forcing terms.
result Established a distance comparison principle for curve flows with global forcing terms.
The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.
problem Determining planar curves for constant-speed motion under specific force conditions.
method Analyzing the motion of a particle under friction and a central force field.
result Every solution to the constant-speed motion problem approaches either a circle or a logarithmic spiral.
We show that under suitable non-degeneracy conditions, complete gradient flow lines of the scalar curvature functional of a riemannian manifold perturb into eternal forced mean curvature flows with large forcing term.
Study curve flows with a global forcing term, proving distance comparison and convexity.
problem Analyzing the behavior of curves under curve shortening flow with a global forcing term.
method Distance comparison principle, finite time exclusion of singularities, convexity and convergence analysis.
result Convexity and smooth exponential convergence to a circle for closed curves.
Study on evolving singular hypersurfaces using mean curvature flow with driving force.
problem Evolving singular initial hypersurfaces under mean curvature flow with driving force.
method Level set method to analyze fattening or non-fattening interface evolution.
result Criteria to judge the evolution of singular initial hypersurfaces.
Proposes a new model to price options considering market forces beyond Black-Scholes.
problem Tackles the limitations of the Black-Scholes model in capturing unexpected market behaviors.
method Uses the analogy between quantum harmonic oscillator and financial market dynamics to propose a new market force-driven model.
result Shows how various market forces can be incorporated to modify option pricing, providing practical applications.
Proves uniqueness of blowups for forced mean curvature flow.
problem Proving uniqueness of blowups for forced mean curvature flow.
method Adapting methods from Euclidean space mean curvature flow to handle forcing term and blow-up limits.
result Uniqueness of tangent cones for forced mean curvature flow at self-shrinkers and cylindrical self-shrinkers.
The paper simplifies complex mechanical systems with external forces.
problem Analyzing symmetric discrete mechanical systems with external forces.
method Lagrangian reduction and reconstruction for principal bundles.
result Evolution of momentum maps and Poisson structures under different conditions.
Enhances dynamic system modeling with multiplicative latent forces.
problem Handling sparse data and complex models in dynamic systems.
method Extends latent force models to include multiplicative interactions and introduces an approximation method for inference.
result Improved control over trajectory geometry through multiplicative interactions.
New insights into Hessian structure of neural networks reveal two forces.
problem Understanding the Hessian structure of neural networks.
method Analyzing the static and dynamic forces, comparing limit distributions using random matrix theory.
result The Hessian structure arises from a combination of static and dynamic forces, with C being a primary driver. This work tackles force control for contact-rich manipulation tasks with rigid robots using RL.
problem Challenges in working with real robotic hardware, especially position-controlled robots.
method Combines RL with traditional force control techniques, implementing parallel position/force control and admittance control.
result Validated methods on both simulation and real robot (UR3 e-series) for force control.
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
Paper uses black-box inference to estimate non-linear latent force models.
problem Estimating posterior state and forcing term in non-linear systems with unknown forcing terms.
method Black-box variational inference with local inverse autoregressive flows.
result Demonstrates effectiveness of approximation on known posterior systems and non-linear dynamics.
In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and expand to infinity if the forcing term is large enough. The flow can also conver…
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.