defined by the shuffle of tensors. If the product of A is commutative, then the bar differential is a derivation with respect to the shuffle product so that B(A) is still an associative and commutative differential graded algebra. Unfortunately, in algebraic topology, algebras are usually commutative only up to homotopy: a motivating example is provided by the cochain algebra of a topological s...

AbstructA free-space optical interconnection module for the sliding Banyan (SB) multistage interconnection network is experimentally evaluated. This three-dimensional (3-D) optical shuffle topology employs a mucro-lens array in a reflective architecture. Interconnections for multiple stages are interleaved across a single two-dimensional (2-D) multichip array of “smart pixels.” The experimental...

A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the problem of recognizing square permutations from both the point of view of algebra and algorithms. On the one hand, we present some algebraic and combinatorial p...

In this paper, we study the shuffle operator on concurrent processes (represented as trees) using analytic combinatorics tools. As a first result, we show that the mean width of shuffle trees is exponentially smaller than the worst case upperbound. We also study the expected size (in total number of nodes) of shuffle trees. We notice, rather unexpectedly, that only a small ratio of all nodes do...

The Jacobian conjecture [Keller, Monatsh. Math. Phys., 1939] gives rise to a problem in combinatorial linear algebra: Is the vector space generated by rooted trees spanned by forest shuffle vectors? In order to make headway on this problem we must study the algebraic and combinatorial properties of rooted trees. We prove three theorems about the vector space generated by binary rooted trees: Sh...

Considering the emergence of highly pathogenic influenza viruses and threat of worldwide pandemics, there is an urgent need to develop broadly-protective influenza vaccines. In this study, we demonstrate the potential of T7 bacteriophage-based nanoparticles with genetically fused ectodomain of influenza A virus M2 protein (T7-M2e) as a candidate universal flu vaccine. Immunization of mice with ...

We describe a security-preserving construction of a random permutation of domain size N from a random function, the construction tolerating adversaries asking all N plaintexts, yet employing just Θ(lgN) calls, on average, to the one-bit-output random function. The approach is based on card shuffling. The basic idea is to use the sometimes-recurse transformation: lightly shuffle the deck (with s...

A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic programming algorithm to determine if a given string z is the shuffle of two given strings x, y; however, it has been an open question whether there is a pol...