We consider the decidability of existence of solutions to language equations involving the operations of shuffle and deletion along trajectories. These operations generalize the operations of concatenation, insertion, shuffle, quotient, sequential and scattered deletion, as well as many others. Our results are constructive in the sense that if a solution exists, it can be effectively represente...

The goal of our work is to study the spaces of primitive elements of the Hopf algebras associated to the permutaedra and the associaedra. We introduce the notion of shuffle and preshuffle bialgebras, and compute the subpaces of primitive elements associated to these algebras. These spaces of primitive elements are free objects for some types of algebras which we describe in terms of generators ...

Molecular information theory was used to create sequence logos and promoter models for eight phages of the T7 group: T7, phiA1122, T3, phiYeO3-12, SP6, K1-5, gh-1 and K11. When these models were used to scan the corresponding genomes, a significant gap in the individual information distribution was observed between functional promoter sites and other sequences, suggesting that the models can be...

Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck is shuffled to create a random permutation. Shuffling is used to assure that an aggregate of data elements for a sequence S is randomly arranged, but avoids a...

Methods for index reduction of general nonlinear differential-algebraic equations are generally difficult to implement due to the recurring use of functions defined only via the implicit function theorem. By adding structure to the equations, these implicit funcitons may become possible to implement. In particular, this is so for the quasilinear and linear time-invariant (LTI) structures, and i...

Load balancing in publish/subscribe (pub/sub) broker networks is challenging as the workload is multi-dimensional and content-dependent. In this paper we present the framework design of a middleware , called Shuffle, to achieve optimal load balancing in a pub/sub broker network. Shuffle features a suite of active workload management schemes within a single overlay topology on message parsing, m...

Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication ∗ on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be viewed as a generalization of the shuffle product III . We extend this commutative algebra structure to a Hopf algebra (A, ∗,1); in the case where A is the s...

The lysozyme of bacteriophage T7 is a bifunctional protein that cuts amide bonds in the bacterial cell wall and binds to and inhibits transcription by T7 RNA polymerase. The structure of a mutant T7 lysozyme has been determined by x-ray crystallography and refined at 2.2-A resolution. The protein folds into an alpha/beta-sheet structure that has a prominent cleft. A zinc atom is located in the ...

I use bacteriophage T7, a lytic virus that infects bacterium E. coli, as a model system to explore how the genetic information encoded in a genome determines the phenotype of an organism in a given environment. By incorporating the existing experimental data and mechanisms, our group previously developed a genetically structured model of T7 intracellular growth. I extended and improved the mode...