arXiv research

We consider embedded, smooth curves in the plane which are either closed or asymptotic to two lines. We study their behaviour under curve shortening flow with a global forcing term. Firstly, we prove an analogue to Huisken's distance comparison principle for curve shortening flow for initial curves whose local total cu…

In this paper we study the blow up sequence of mean curvature flow of surfaces in $\mathbb R^3$ 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.

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…

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…

New strategies avoid forced exploration for unimodal bandits.

New gauge fields modify Fokker-Planck dynamics without changing the stationary state.

In this paper, we would like to give an answer to \textbf{Problem 1} below issued firstly in [J. Mao, Eigenvalue estimation and some results on finite topological type, Ph.D. thesis, IST-UTL, 2013]. In fact, by imposing some conditions on the mean curvature of the initial hypersurface and the coefficient function of th…

This paper discusses topological and locally linear actions of finite groups on $S^4$. Local linearity of the orientation preserving actions on $S^4$ forces the group to be a subgroup of $SO(5)$. On the other hand, orientation reversing topological actions of "exotic" groups $G$ (i.e. $G\not\subset O(5)$) on $S^4$ are …

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …

Flow of curves with curvature and forcing vector field exists.

Near isospectrality forces full isospectrality for compact quotients of symmetric spaces.

Study on droplet flow on uneven surfaces, proving existence and properties.

We demonstrate the existence of spherically-symmetric truly naked black holes (TNBH) for which the Kretschmann scalar is finite on the horizon but some curvature components including those responsible for tidal forces as well as the energy density $\barρ$ measured by a free-falling observer are infinite. We choose a ra…

This paper generalizes Michell Truss to higher dimensions using geometric measure theory.

New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.

New algorithm efficiently trains machine learning models to atomic forces data.

The paper integrates dissipative and curl forces using geometric methods.

Improved CG force-field learning from all-atom data.

In classical surface theory there are but few known examples of surfaces admitting nontrivial isometric deformations and fewer still non-simply-connected ones. We consider the isometric deformability question for an immersion x: M \to R^3 of an oriented non-simply-connected surface with constant mean curvature H. We pr…

Let M^7 a manifold with holonomy in G_2, and Y^3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that M_{X,Y}, the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner's technique, we give a vanishing t…

Paper introduces a PDE-free method for decomposing forces in any dimension.

Proposes linking energy and force uncertainty in deep learning potentials.

New algorithm CROP achieves asymptotic optimality with bounded regret.

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…

The paper analyzes optimal retirement timing considering age-dependent mortality risk.

The paper analyzes errors in mechanical systems with external forces.

Unified framework for response-adaptive targeting in multi-treatment experiments

Study curve flows with global forcing terms using a distance comparison principle.

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…

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

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.

In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}. For the first hyperbolic flow, as in \cite{klw}, by using support function, we reduce it to a hyperbolic Monge-Amp$\grave{\rm{e}}$re equation …

Derives variance kernel for reaction boundary in financial models.

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.

Proves uniqueness of blowups for forced mean curvature flow.

Transformers solve parity problems efficiently with step-by-step reasoning.

Derives operational-time variance kernel for reaction boundaries in financial markets.

The paper simplifies complex mechanical systems with external forces.

New insights into Hessian structure of neural networks reveal two forces.

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…

This work tackles force control for contact-rich manipulation tasks with rigid robots using RL.

The paper studies extremal Kaehler metrics induced by complex space forms, proving properties in both finite and infinite dimensions.

Study explains Zipf's law using geometric mechanisms from a finite alphabet.

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…

Study compares employers with and without anticipating strategic labor force responses.

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…