Certain fractional quantum Hall states, including the experimentally observed ν = 5/2 state, and, possibly, the ν = 12/5 state, may have a sufficiently rich form of topological order (i.e. they may be nonabelian) to be used for topological quantum computation, an intrinsically fault tolerant form of quantum computation which is carried out by braiding the world lines of quasiparticle excitation...

One problematic feature of Hall algebras is the fact that the standard multiplication and comultiplication maps do not satisfy the bialgebra compatibility condition in the underlying symmetric monoidal category Vect. In the past this problem has been resolved by working with a weaker structure called a ‘twisted’ bialgebra. In this paper we solve the problem differently by first switching to a d...

This Article studies the relationship between formal and informal contract enforcement. The theoretical literature treats the two strategies as separate phenomena. By contrast, a rich experimental literature considers whether the introduction of formal contracting and state enforcement “crowds out” the operation of informal contracting. Both literatures focus too narrowly on how formal contract...

The braiding of the solar coronal magnetic field via photospheric motions – with subsequent relaxation and magnetic reconnection – is one of the most widely debated ideas of solar physics. We readdress the theory in the light of developments in three-dimensional magnetic reconnection theory. It is known that the integrated parallel electric field along field lines is the key quantity determinin...

In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...

Here, we report on the design of braided peripheral nerve conduits with barrier coatings. Braiding of extruded polymer fibers generates nerve conduits with excellent mechanical properties, high flexibility, and significant kink-resistance. However, braiding also results in variable levels of porosity in the conduit wall, which can lead to the infiltration of fibrous tissue into the interior of ...

A laycle is the categorical analogue of a lazy cocycle. Twines (as introduced by Bruguières) and strong twines (as introduced by the authors) are laycles satisfying some extra conditions. If c is a braiding, the double braiding c is always a twine; we prove that it is a strong twine if and only if c satisfies a sort of modified braid relation (we call such c pseudosymmetric, as any symmetric br...

A common braiding machine cannot perform continuous using closed annular axis mandrels. To solve this problem, a modified vertical was made to braid composite preforms with irregular cross-section The finite element method used simulate the process, and an efficient also derived predict angles. results show that predicted angles are basically consistent actual angles, at distinctive locations o...