In this paper we describe an on-line method of training neural networks which is based on solving the linearized least-squares problem using the pseudo-inverse for the underdetermined case. This Underdetermined Linearized Least Squares (ULLS) method requires significantly less computation and memory for implementation than standard higher-order methods such as the Gauss-Newton method or extende...

Elliptic partial differential equations (PDEs) are frequently used to model a variety of engineering phenomena, such as steady-state heat conduction in a solid, or reaction-diffusion type problems. However, computing a solution can sometimes be difficult or inefficient using standard solvers. Techniques have been developed, including the method of lines (Schiesser, 1991), which can solve parabo...

This the original TEX file for my article Jacobian Varieties, published as Chapter VII of Arithmetic geometry (Storrs, Conn., 1984), 167–212, Springer, New York, 1986. The table of contents has been restored, some corrections and minor improvements to the exposition have been made, and an index has been added. The numbering is unchanged.

We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a vector of random numbers u, in such a way that the outcome, knowing u, is deterministic. For each instantiation of u we run an optimization procedure to minimize...

We present an algorithm based on the birthday paradox, which is a low-memory parallel counterpart to the algorithm of Matsuo, Chao and Tsujii. This algorithm computes the group order of the Jacobian of a genus 2 curve over a finite field for which the characteristic polynomial of the Frobenius endomorphism is known modulo some integer. The main tool is a 2-dimensional pseudo-random walk that al...

Abstraet--Jacobians are used in robotics for motion planning and control. They are also used in algorithms that determine linkage parameter errors of robots and in algorithms that determine pair variable corrections for accurate motion. Most applications require that the inverse of the Jacobian be obtained. The causes of singularities in Jacobians and a procedure to detect their presence are gi...

This paper discusses how to utilise the known advantages of redundancy in the design of haptic interfaces. The use of additional joints allows a significantly larger workspace, while reducing the overall device size. Moreover, an increase in a variety of dexterity measures and a singularity robust redundancy resolution can be achieved. Besides a review of standard redundant kinematical designs ...

the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these have different merits and limitations. Algorithms that guarantee local convergence typically require approximation high‐dimensional Jacobians. Alternatively, Nested Pseudo‐Likelihood (NPL) algorithm is a fixed‐point iterative procedure, which avoids comp...