Optimal control models of biological movements introduce external task factors to specify the pace of movements. Here, we present the dual to the principle of optimality based on a conserved quantity, called "drive," that represents the influence of internal motivation level on movement pace. Optimal control and drive conservation provide equivalent descriptions for the regularities observed wi...

The object studied in this paper is a pair ((; Y), where is a random surface in I R N and Y random vector eld on I R N. The pair is jointly stationary, i.e. its distribution is invariant under translations. The vector eld Y is smooth outside but may have discontinuities on. Gauss' divergence theorem is applied to derive a ow conservation law for Y. For I R 1 this specializes to a well-known rat...

Abstract We propose some algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. With the key observation of the velocity observable and controllable in the motion, the algorithms simulate the Newton Second Law without friction based on symplectic Euler scheme. From the intuitive analysis of analytical sol...

Given a Brownian motion (Bt)t≥0 and a general target law μ (not necessarily centred or even in L) we show how to construct an embedding of μ in B. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of μ. The embedding is then...

In all 2d theories of gravity a conservation law connects the effective (space-time dependent) ADM mass at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric ...

We generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a measure preserving system (X,μ, g) and a family of subsets {An | n ∈ N} of X under which #{1 ≤ n ≤ N | gnx ∈ An} is for μa.e. x ∈ X asymptotically (as N →∞) equal to PN n=1 μ(An). These conditions can be verified for various special cases of systems (X,μ, g, {An}), including actions of nonquasiunip...

We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of ...

In this paper we give an analytic interpretation of free convolution of type B, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is essentially a re-casting of conditionally free convolution. We put in evidence several aspects of this operation, the most significant being its apparition as an “intertwiner” between derivation ...

A new approach to DSMC collision modelling, called viscosity-DSMC or μ-DSMC, is described in which the time-averaged temperature is used to set the characteristic collision cross-section in each cell such that the Chapman-Enskog viscosity is that given by any desired viscosity law μ = μ (T ), including a curve fit to experimental data. For example, a hard sphere collision model, with hard spher...