We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in R N. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimension n meeting any n-plane passing through t...

Iterative algorithms, such as the well known Belief Propagation algorithm, have had much success in solving problems in statistical inference and coding and information theory. Survey Propagation attempts to apply iterative message passing algorithms to solve difficult combinatorial problems, in particular constraint satisfaction problems such as k-sat and coloring problems. Intuition from stat...

Clustering large data sets can be time consuming and processor intensive. This project is an implementation of the parallel version of a popular clustering algorithm, the k-means algorithm, to provide faster clustering solutions. This algorithm was tested such that 3,4,5,7 clusters were created on a cluster of Sun workstations. Optimal levels of speedup were not achieved; but the benefits of pa...

The transaction commit problem in a distributed database system is an instance of the Weak Byzantine Generals problem. It is shown that even under the assumption that a process can fail only by “crashing”—failing to send any more messages—a solution to this problem that can tolerate k failures must, in the worst case, require at least k + 1 message-passing delays. Under this same assumption, a ...

In this paper, we study the complexity of computing with mobile agents having small local knowledge. In particular, we show that the number of mobile agents and the amount of local information given initially to agents can significantly influence the time complexity of resolving a distributed problem. Our results are based on a generic scheme allowing to transform a message passing algorithm, r...

Lifted message passing approaches can be extremely fast at computing approximate marginal probability distributions over single variables and neighboring ones in the underlying graphical model. They do, however, not prescribe a way to solve more complex inference tasks such as computing joint marginals for k-tuples of distant random variables or satisfying assignments of CNFs. A popular solutio...

This paper presents a new approach to implement global reduction operations in wormhole k-ary n-cubes. The novelty lies in using multidestination message passing mechanism instead of single destination (unicast) messages. Using pairwise exchange worms along each dimension, it is shown that complete global reduction and barrier synchronization operations , as deened by the Message Passing Interf...

objectives the aim of this study was to examine temporal changes in technical and physical performances during a small-sided game (ssg) in elite soccer players. methods sixty elite youth players (age 14.8 ± 0.2 yr; stature 177 ± 5 cm; body mass 66.2 ± 4.7 kg) completed a 5 v 5 ssg using two repetitions of 8 minutes interspersed by 3 minutes of passive recovery. to evaluate temporal changes in p...

I prove two theorems: Let X ⊂ P be a hypersurface and let x ∈ X be a general point. If the set of lines having contact to order k with X at x is of dimension greater than expected, then the lines having contact to order k are actually contained in X. A variety X is said to be covered by lines if there exist a finite number of lines in X passing through a general point. Let X ⊂ P be a variety co...

Let ~ Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. For clauses/variables ratio m/n ≤ rk-SAT ∼ 2 ln 2 the formula ~ Φ is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond m/n ∼ 2k ln(k)/k with a non-vanishing probability. Non-rigorous statistical mechanics work on k-CNF led to the devel...