Achieving efficient end-effector planning for manipulators in real world workspaces is challenging due to the fact that planning is performed in manipulator joint space, while the planning goal is given in end-effector or tool space. For manipulator planning, the problem becomes a joint path planning and inverse kinematics problem to be resolved efficiently, in spite of the potentially infinite number of inverse solutions to the end-effector goal state and the nonlinear relationship between joint configurations and world obstacles. The Forage-RRT algorithm described in this paper attempts to efficiently and quickly resolve the end-effector or tool planning problem. Using ideas from foraging theory, Forage-RRT implements a diffusion-based search strategy with two rates of diffusion, one high and one low, which simulate both long jumps (coarse search) and focused small area exploration (fine search) in the joint space, respectively. During coarse search, it is important to keep track of past fine searches, therefore the traditional RRT algorithm is augmented with a goal heap that keeps track of potential focused search regions and discards them when they result in failure. By mixing between two search distributions with different spreads, the search space is rapidly covered and potentially fruitful avenues are finely explored. The search coverage advantages of foraging identified in the biological research literature are demonstrated here for end-effector based, manipulator path planning.

We present a fixed point algorithm for bit rate optimal time domain equalization in multicarrier systems. The algorithm outperforms standard MMSE equalizers in capacity measure. Moreover, it adaptively estimates the optimal signal delay which was an exhaustive search problem in MMSE equalizers. We discuss the convergence properties and demonstrate the performance of the algorithm on a twisted pair copper wire loop with additive non-white noise.

Some properties of the eigenproblem for a three-dimensional rotation matrix are shown, and related to the geometrical rotation parameters. The problem of assigning a unique canonical coordinate frame to a set of three mutually orthogonal axes is considered. The assignment is such that it corresponds to a minimal overall rotation with respect to the reference system. It is noted that this problem is of interest for the unique and consistent labeling of the principal axes of various tensors related to physical properties of materials, and symmetric matrices that appear in various disciplines of engineering.>

For a discreteN-valued random variable (Npossibly denumerably infinite) Leung-Yan-Cheong and Cover have given bounds for the minimal expected length of a one-to-one (not necessarily uniquely decodable) codeL_{1:1}=\sum_{i=1}^{N} p_{i} \log \left( \frac{1}{2} + 1 \right).It is shown that the best possible case occurs for certain denumerably infinite sets of nonzero probabilities. This absolute bound is related to the Shannon entropyHof the distribution by(h (\cdot)is the binary entropy function).

A stochastic error model for floating point arithmetic is developed and used to study the effects of finite wordlength on linear recursive formulas. Optimal realizations exist, but they are highly sensitive.

A novel solution on approximation to the least squares filter problem under floating point arithmetic is presented for a linear stochastic model.

The wiretap channel introduced by Wyner is studied for the special case when the main channel is a noiseless binary channel and the wiretap channel is a binary symmetric channel. With a rate-one convolutional encoder, the steady-state uncertainty of the wiretapper is shown to depend only on the constraint lengthvof the code, not on the specific taps, and is complete on k successive bits providedk\leq v. During the initial transient period, the rate of growth of uncertainty does depend on the tap connections of the shift register.