Partial magmatic bialgebras

A partial magmatic bialgebra, (T;S)-magmatic bialgebra where T \subset S are subsets of the set of positive integers, is a vector space endowed with an n-ary operation for each n in S and an m-ary co-operation for each m in T satisfying some compatibility and unitary relations. We prove an analogue of the Poincar\'e-Birkhoff-Witt theorem for these partial magmatic bialgebras.Comment: Revised version, after suggestions of the anonymous referee, 20 page

Tridendriform structure on combinatorial Hopf algebras

We extend the definition of tridendriform bialgebra by introducing a weight q. The subspace of primitive elements of a q-tridendriform bialgebra is equipped with an associative product and a natural structure of brace algebra, related by a distributive law. This data is called q-Gerstenhaber-Voronov algebras. We prove the equivalence between the categories of connected q-tridendriform bialgebras and of q-Gerstenhaber-Voronov algebras. The space spanned by surjective maps, as well as the space spanned by parking functions, have natural structures of q-tridendriform bialgebras, denoted ST(q) and PQSym(q)*, in such a way that ST(q) is a sub-tridendriform bialgebra of PQSym(q)*. Finally we show that the bialgebra of M-permutations defined by T. Lam and P. Pylyavskyy may be endowed with a natural structure of q-tridendriform algebra which is a quotient of ST(q)

Recollections of Ben Burgunder

"In 1921-22, when I was collecting historical information from pioneers of Whitman County, I was informed by Ray Walter, a newspaper man of Colfax, Washington, that Ben Burgunder, at that time one of the oldest pioneers of the Inland Empire, had in his possession a manuscript of his own preparation that contained a description of his early experiences in the Pacific Northwest...

Chorea: An Update on Genetics.

BACKGROUND Chorea may be present in a number of diseases including hereditary disorders. Major advances have occurred in our understanding of the genetic background of those disorders, and the present short review aims at highlighting the most salient ones. SUMMARY Chorea is one of the major manifestations of Huntington's disease. However, there are a number of other diseases, in which chorea is present as well and their list is in constant increase thanks to the availability of advanced molecular genetic diagnostic techniques. Finding of new genes followed by the investigation of further cases with part of the phenotype first described often leads to the recognition of additional aspects of the disorders, thus widening the scope of investigation and management. Likewise, assessment of genetic variations associated with specific aspects of the phenotype, in a way similar to approaches established in nongenetic disorders, has improved our understanding of phenotype variation. Knowledge on genetic background of chorea has ameliorated our diagnostic approaches. Furthermore, it opens new therapeutic strategies aimed at modifying expression both of the genes primarily implicated as the ones involved in further phenotype modification. KEY MESSAGES Recent research on the genetic background of disorders with chorea has provided data, which can now better guide differential diagnostic investigations in practical ways. Furthermore, they provide avenues for research on the disease mechanisms opening the door for clinical therapeutic trials

The Supreme Court Performs the Right Notes for Dish in Aereo

In American Broadcasting Companies, Inc. v. Aereo, Inc., the Supreme Court addressed whether a company publicly performs copyrighted works when it allocates separate antennas on its property to customers who individually decide what shows they each want to watch. This case was hotly debated because it provided a new opportunity for the Court to identify the responsible actors when copyrighted materials are transmitted over the Internet. Unfortunately, the Court ruled against Aereo without clearly articulating governing standards that might inform future decisions, relying instead on what the dissent called a looks-like-cable-TV approach. The deficiency has already provided additional ammunition for Fox Broadcasting Company to sue Dish Network over certain features that the satellite television provider proudly promotes to customers. This Article articulates some concrete benchmarks the Court could have used to substantiate its decision that would have highlighted the weaknesses in Fox\u27s latest copyright claims against Dish

The Scoop on Betty Boop: A Proposal to Limit Overreaching Trademarks

The Ninth Circuit temporarily stunned marketers in 2011 when it ruled that Betty Boop did not serve as a trademark on merchandise due to aesthetic functionality and because protection would conflict with the copyright system. The opinion endangered merchandising rights in all trademarks and jeopardized the duration of trademark rights in images and media characters. The court soon withdrew the decision and substituted it with one that denied protection on technical grounds, leaving the controversies for another day. This article demonstrates that the court’s apprehension about copyrights made sense, and proposes a new approach to distinguish when copyrighted images might also serve as trademarks

Can the PTO Find Its Way with Jesus?

Non