We investigate the stability of a dynamic brain model using conventional techniques of linearization of the state space equations of motion for two nearby solutions followed by solution via expansion in the eigenvectors of the Jacobian matrix with eigenvalues λ1, λ2, ..., λn. The fundamental stability condition for brains is then |λk| ≅ 1. By equating terms in two versions of the characteristic...

In this paper, we present a linear transformation (LT) to obtain warped features from unwarped features during vocal-tract length normalisation (VTLN). This LT between the warped and unwarped features is obtained within the conventional MFCC framework without any modification in the signal processing steps involved during the feature extraction stage. Further using the proposed LT, we study the...

For a legged robot such as a humanoid, balancing its body during a given motion is natural but the most important problem. Recently, a motion given to a humanoid is more and more complicated, and thus the balancing problem becomes much more critical. This paper suggests a real-time motion generation algorithm that guarantees a humanoid to be balanced during the motion. A desired motion of each ...

Let x 0 be a locally optimal solution of a smooth parametric nonlinear optimization problem minff(x; y) : g(x; y) 0; h(x; y) = 0g for a xed value y = y 0. If the strong suucient optimality condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint qualiications are satissed, then x 0 is strongly stable in the sense of Kojima and the corresponding function...

Let n be an integer such that the modular curve X0(n) is hyperelliptic of genus ≥ 2 and such that the Jacobian of X0(n) has rank 0 over Q. We determine all points of X0(n) defined over quadratic fields, and we give a moduli interpretation of these points. As a consequence, we show that up to Q-isomorphism, all but finitely many elliptic curves with n-isogenies over quadratic fields are in fact ...

A survey of swept volume concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into five major categories: method with envelope theory, method with sweep differential equation (SDE)/sweep envelope differential equation (SEDE), method with Jacobian rank deficiency, Voxel-based method, and free-form solids’ sweeping met...

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all Q-rank one lattices in semisimple groups of R-rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion

We propose a new termination criteria suitable for potentially singular, zero or non-zero residual, least-squares problems, with which cubic regularization variants take at most O(ǫ) residualand Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below ǫ; this is the best-known bound for potentially rank-deficient nonlinear least-squares problems. We then app...

This paper provides a method for computing force-feasible paths on the Stewart platform. Given two configurations of the platform, the method attempts to connect them through a path that, at any point, allows the platform to counteract any external wrench lying inside a predefined six-dimensional region. In particular, the Jacobian matrix of the manipulator will be full rank along such path, so...

where H: I R " x N ~ R " is a C 2 function. We would like to numerically trace this curve F from the point (Xo, to) to the point (x*, t*). For the simplicity of discussion we shall assume that 0EIt" is a regular value for H, i.e., the n x (n+ 1) Jacobian matrix DH(x, t) has full rank at every point on F. in recent years a number of approaches have been proposed for the numerical computation of ...