of the weaker problem. It is shown that, like the original Byzantine Generals Problem, the weak version can be solved only ff fewer than one-third of the processes may fad. Unlike the onginal problem, an approximate solution exists that can tolerate arbaranly many failures.

It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard

small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render—or synthesize—images of the face under novel poses and illumination

. For example, the popular approach in which access is via one designer's favorite single word will result in 80-90 percent failure rates in many common situations. An optimal strategy, unlimited aliasing, is derived and shown to be capable of several-fold improvements.

this dilemma is the regret, that is the loss due to the fact that the globally optimal policy is not followed all the times. One of the simplest examples of the exploration/exploitation dilemma is the multi-armed bandit problem. Lai and Robbins were the first ones to show that the regret for this problem has

The ability to simultaneously localize a robot and accurately map its surroundings is considered by many to be a key prerequisite of truly autonomous robots. However, few approaches to this problem scale up to handle the very large number of landmarks present in real environments. Kalman filter

For any given research area, one cannot tell how many studies have been con-ducted but never reported. The extreme view of the "file drawer problem " is that journals are filled with the 5 % of the studies that show Type I errors, while the file drawers are filled with the 95

Broadcasting is a common operation in a network to resolve many issues. In a mobile ad hoc network (MANET) in par-ticular, due to host mobility, such operations are expected to be executed more frequently (such as finding a route to a particular host, paging a particular host, and sending an alarm

Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a

How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis