Recently, interest in shuffle algebra has been renewed due to their connections with multiple zeta values. In this paper, we prove a new shuffle convolution that implies a reduction formula for the multiple zeta value ζ ({5, 1}n).

Weextend the basic shuffle onwords and languages, awell-known operation in theoretical computer science, by introducing three synchronized shuffles. These synchronized shuffles have some relevance to molecular biology since they may be viewed as the formal representations of various forms of gene linkage during genome shuffling. More precisely, each synchronized shuffle preserves the genetic ba...

To determine the role of protein kinase Cdelta in mouse skin carcinogenesis, we have developed transgenic FVB/N mouse lines expressing in the epidermis an epitope-tagged protein kinase Cdelta (T7-PKCdelta) regulated by the human keratin 14 promoter. The untreated T7-PKCdelta mice displayed excessive dryness in the skin of the tail with a variable penetrance over time. Histologically, the tail s...

In their seminal paper, Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values. One of their key ideas is to study the formal double space and apply the double shuffle relations. They also proved the double shuffle relations for the double Eisenstein series. More recently, Kaneko and Tasaka extended the double Eisenstein series ...

There is an increasing interest in the shuffle product on formal languages, mainly because it is a standard tool for modeling process algebras. It still remains a mysterious operation on regular languages. Antonio Restivo proposed as a challenge to characterize the smallest class of languages containing the singletons and closed under Boolean operations, product and shuffle. This problem is sti...

PAC learning of unrestricted regular languages is long known to be a difficult problem. The class of shuffle ideals is a very restricted subclass of regular languages, where the shuffle ideal generated by a string u is the collection of all strings containing u as a subsequence. This fundamental language family is of theoretical interest in its own right and provides the building blocks for oth...

A shuffle is a permutation and rerandomization of a set of ciphertexts. Among other things, it can be used to construct mix-nets that are used in anonymization protocols and voting schemes. While shuffling is easy, it is hard for an outsider to verify that a shuffle has been performed correctly. We suggest two efficient honest verifier zero-knowledge (HVZK) arguments for correctness of a shuffl...

Effective gene therapy requires efficient delivery of DNA to transfected cells followed by high levels of gene expression. Our laboratory has developed two new delivery formulations LPDI containing the DNA condensing agent protamine sulfate and reconstitued chylomicrons containing a hydrophobic lipidDNA complex. LPDI can produce higher levels of gene expression than the corresponding liposome/D...

The inability of T7 to develop in cells of Escherichia coli containing F(+) or substituted F' episomes is a result of the failure to synthesize late proteins; no in vivo translation of mRNA species synthesized by the T7 RNA polymerase occurs. Further experiments have been performed to measure the amount of late mRNA in T7-infected F'(PIF(+)) cells. (We have designated the property of phage inhi...

The rat brain IIA Na+ channel a-subunit was expressed and studied in mammalian cells. Cells were infected with a recombinant vaccinia virus (VV) carrying the bacteriophage T7 RNA polymerase gene and were transfected with cDNA encoding the IIA Na+ channel a-subunit under control of a T7 promoter. Whole-cell patch-clamp recording showed that functional IIA channels were expressed efficiently (10 ...