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.
An important task in structural design is to quantify the structural performance of an object under the external forces it may experience during its use. The problem proves to be computationally very challenging as the external forces' contact locations and magnitudes may exhibit significant variations. We present an e…
The study of dexterous manipulation has provided important insights in humans sensorimotor control as well as inspiration for manipulation strategies in robotic hands. Previous work focused on experimental environment with restrictions. Here we describe a method using the deformation and color distribution of the finge…
Discusses the tight versus overtwisted dichotomy in 3D contact geometry.
problem Understanding the tight versus overtwisted dichotomy in 3D contact geometry.
method Reviews Eliashberg's seminal work and contributions to the theory.
result Explains the genesis and importance of the tight versus overtwisted dichotomy.
Deep learning predicts adhesive forces in soft viscoelastic contacts quickly and accurately.
problem Predicting the full time-resolved force trajectory of adhesive soft viscoelastic contacts is computationally expensive and impractical.
method Trained a deep learning model to predict the full force evolution from a prescribed displacement history, using FMS representation and various architectures.
result Best-performing model predicts complete force trajectory with low error metrics and fast inference time.
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.
DIGIT is a low-cost tactile sensor for in-hand manipulation.
problem Difficulty in sensing contact forces limits robotic manipulation.
method DIGIT miniaturizes and improves a vision-based tactile sensor.
result DIGIT enables better control of interactions with the environment.
New geometric framework for non-conservative field theories with time-dependent terms.
problem Describing non-conservative field theories with explicit space-time dependence.
method Combining k-cosymplectic and k-contact formulations to develop Hamiltonian and Lagrangian formalisms.
result Illustrated with the nonlinear damped wave equation, demonstrating the new formalism's applicability.
One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric structure and also it defines a "force-free" model of solar physics. By using the symme…
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple. Furtherm…
Introduces GFC for learning complex dynamical systems with geometric constraints.
problem Challenges in accurately modeling and predicting complex dynamical systems with geometric constraints.
method Geometric Contact Flows (GFC) using Riemannian and Contact geometry as inductive biases.
result Ensemble of contactomorphisms adapt the latent contact Hamiltonian model to target dynamics while preserving desirable properties.
Study magnetic Laplacian eigenvalues on contact manifolds.
problem Characterize spectral properties of magnetic fields on contact manifolds.
method Analyze first eigenvalue of magnetic horizontal Laplacian, provide upper bounds, and use topological conditions.
result Equality in upper bounds implies Heisenberg left-invariant nilmanifold structure and unique determination of manifold Chern class.
The study explores rigid constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
problem Investigating constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
method Using a local orthonormal \(\varphi\)-basis, derived the full component form of the almost Ricci-Bourguignon soliton equation.
result For contact metric three-manifolds satisfying \(Qξ=σξ\), a collinear potential field must vanish on the non-Sasakian region whenever \(ξ(σ)=0\).
For humans, the process of grasping an object relies heavily on rich tactile feedback. Most recent robotic grasping work, however, has been based only on visual input, and thus cannot easily benefit from feedback after initiating contact. In this paper, we investigate how a robot can learn to use tactile information to…
A successful grasp requires careful balancing of the contact forces. Deducing whether a particular grasp will be successful from indirect measurements, such as vision, is therefore quite challenging, and direct sensing of contacts through touch sensing provides an appealing avenue toward more successful and consistent …
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.
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.
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…
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.
In this paper we provide a variational derivation of the Euler-Poincaré equations for systems subjected to external forces using an adaptation of the techniques introduced by Galley and others. Moreover, we study in detail the underlying geometry which is related to the notion of Poisson groupoid. Finally, we apply the…
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.
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.
The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of th…
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.
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. 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…
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.
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, Tsang, and Stein [2014]. We show that this construction is useful to…
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
In this paper we study the blow up sequence of mean curvature flow of surfaces in R3 with additional forces. We prove that the blow up limit of a mean curvature flow of smoothly embedded surfaces with additional forces with finite entropy is a smoothly embedded self-shrinker.
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
problem Identification of nonlinear dynamic systems in engineering.
method Modeling the nonlinear restoring force as a Gaussian process, converting it to a state-space model, and inferring internal states and the nonlinear restoring force through filtering and smoothing.
result The approach effectively identifies nonlinear restoring forces in both simulated and experimental datasets.
The forcing relation of braids has been introduced for a 2-dimensional analogue of the Sharkovskii order on periods for maps of the interval. In this paper, by making use of the Nielsen fixed point theory and a representation of braid groups, we deduce a trace formula for the computation of the forcing order.
Study on contact Hamiltonian functions for singular contact structures.
problem Understanding infinitesimal contact transformations on singular contact structures.
method Showed injectivity and provided an explicit local formula for the inverse map.
result Explicit local formula for the inverse map when contact structure has singularities of the first type.
We develop variational integrators from discrete Hamiltonian systems with external forces.
problem Creating accurate discrete models of continuous Hamiltonian systems.
method Constructing discrete Hamiltonian systems with external forces, analyzing symplectic structure, and combining methods to build variational integrators.
result We derive variational integrators that approximate continuous Hamiltonian systems with high accuracy.
The purpose of this article is to study co-dimension 2 iso-contact embeddings of closed contact manifolds. We first show that a closed contact manifold (M2n−1,ξM) iso-contact embeds in a contact manifold (N2n+1,ξN), provided M contact embeds in (N,ξN) with a trivial normal bundle and the contact s…
Curve shortening flow shrinks curves to points under certain conditions.
problem Understanding how curves shrink under curve shortening flow with ambient forces.
method Rescaling and curvature bounds analysis following Gage and Hamilton.
result Curves shrink to round points under certain curvature conditions.
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
The paper defines and studies contact surgery numbers for contact 3-manifolds.
problem Understanding the minimal number of components of a surgery link describing a contact 3-manifold.
method Defined and studied various versions of contact surgery numbers, relating them to other invariants and computing specific cases.
result There exist infinitely many non-isotopic contact structures on certain manifolds that cannot be obtained by a single rational contact surgery from the standard tight contact 3-sphere.
Study bi-harmonic flow with forcing term on smooth curves.
problem Analyzing the evolution of smooth, closed planar curves under bi-harmonic flow with a forcing term.
method Reformulated geometric flow using support function, scalar PDE characterization, Monge Ampére structure analysis.
result Convexity is preserved and steady-state solutions converge over long times under specific conditions.
RPPs improve deep learning models with soft equivariance constraints.
problem Balancing expressiveness and inductive biases in deep learning.
method Introducing Residual Pathway Priors (RPPs) to convert hard constraints into soft priors.
result RPPs enable models to learn structured solutions while retaining flexibility.