A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study curve flows with global forcing terms using a distance comparison principle.
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 bi-harmonic flow with forcing term on smooth curves.
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…
Proves uniqueness of blowups for forced mean curvature flow.
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.
In recent years, there has been a growing interest in geometric evolution in heterogeneous media. Here we consider curvature driven fows of planar curves, with an additional space-dependent forcing term. Motivated by a homogenization problem, we look for estimates which depend only on the uniform norm of the forcing te…
We study the mean curvature flow with given non-smooth transport term and forcing term, in suitable Sobolev spaces. We prove the global existence of the weak solutions for the mean curvature flow with the terms, by using the modified Allen-Cahn equation that holds useful properties such as the monotonicity formula.
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when …
The paper analyzes errors in mechanical systems with external forces.
With a view to constructing a Morse/Floer homology theory for CMC hypersurfaces, we prove a compactness result modulo broken trajectories for eternal mean curvature flows with forcing term in compact, hyperbolic manifolds.
Paper introduces a PDE-free method for decomposing forces in any dimension.
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
Bayesian modelling of dynamic systems must achieve a compromise between providing a complete mechanistic specification of the process while retaining the flexibility to handle those situations in which data is sparse relative to model complexity, or a full specification is hard to motivate. Latent force models achieve …
The evolution of the rate of price inflation and unemployment in Japan has been modeled within the Phillips curve framework. As an extension to the Phillips curve, we represent both variables as linear functions of the change rate of labor force. All models were first estimated in 2005 for the period between 1980 and 2…
Study preserves symplectic structure in forced discrete mechanical systems.
A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covari…
We complete the theoretical framework required for the construction of a Morse homology theory for certain types of forced mean curvature flows. The main result of this paper describes the asymptotic behaviour of these flows as the forcing term tends to infinity in a certain manner. This result allows the Morse homolog…
RFC enhances humanoid control to imitate complex human motions.
In this paper we provide generalized Helmholtz conditions, in terms of a semi-basic 1-form, which characterize when a given system of second order ordinary differential equations is equivalent to the Lagrange equations, for some given arbitrary non-conservative forces. For the particular cases of dissipative or gyrosco…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the state and GP terms allows strong a priori control of the model geometry at the ex…
In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in The classification gives some interesting phenomena and consequences including: the family of curves conv…
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCM…
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of , allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the Conley index theory of discrete braid classes as introduced in [Ghrist et al., C. …
Volatility of S&P 500 daily returns increases over 60 years.
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…
MACE uses higher-order messages to create fast, accurate force fields.
Deep learning predicts adhesive forces in soft viscoelastic contacts quickly and accurately.
We model the rate of inflation and unemployment in Austria since the early 1960s within the Phillips/Fisher framework. The change in labour force is the driving force representing economic activity in the Phillips curve. For Austria, this macroeconomic variable was first tested as a predictor of inflation and unemploym…
We consider the problem of how an individual can use term life insurance to maximize the probability of reaching a given bequest goal, an important problem in financial planning. We assume that the individual buys instantaneous term life insurance with a premium payable continuously. By contrast with Bayraktar et al. (…
Unified field theory from higher-order Riemannian geometry.
In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but sometimes can be observed. This paper proposes a methodology to produce a hybrid mode…
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…
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…
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
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-Ampre equation …
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.
DJIA is tested whether it can be described as a mechanical system conserving total energy with K (=v*v/2) + U, where U is calculated as the negative of work done by force obtained in terms of the second derivative of price, assuming unit mass.
The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force mo…
Proposes linking energy and force uncertainty in deep learning potentials.
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…
New framework embeds physics in coarse-grained models without big data.
In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.
Following the approach of Bryant we study the intrinsic torsion of a SU(3)-manifold deriving a number of formulae for the Ricci and the scalar curvature in terms of torsion forms. As a consequence we prove that in some special cases the Einstein condition forces the vanishing of the intrinsic torsion.
This paper generalizes Michell Truss to higher dimensions using geometric measure theory.
This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifyi…