Completely Bounded Homomorphisms of the Fourier Algebras

For locally compact groups G and H let A(G) denote the Fourier algebra of G and B(H) the Fourier-Stieltjes algebra of H. Any continuous piecewise affine map alpha:Y -> G (where Y is an element of the open coset ring of H) induces a completely bounded homomorphism Phi_alpha:A(G) -> B(H) by setting Phi_alpha u(.)=u(alpha(.)) on Y and Phi_alpha u=0 off of Y. We show that if G is amenable then any completely bounded homomorphism Phi:A(G) -> B(H) is of this form; and this theorem fails if G contains a discrete nonabelian free group. Our result generalises results of P.J. Cohen, B. Host and of the first author. We also obtain a description of all the idempotents in the Fourier-Stieltjes algebras which are contractive or positive definite.Comment: 19 page

Are we seeing the beginnings of Inflation?

Phantom Cosmology provides an unique opportunity to "connect" the phantom driven (low en- ergy meV scale) dark energy phase to the (high energy GUT scale) inflationary era. This is possible because the energy density increases in phantom cosmology. We present a concrete model where the energy density, but not the scale factor, cycles through phases of standard radiation/matter domi- nation followed by dark energy/inflationary phases, and the pattern repeating itself. An interesting feature of the model is that once we include interactions between the "phantom fluid" and ordinary matter, the Big rip singularity is avoided with the phantom phase naturally giving way to a near exponential inflationary expansion.Comment: 17 pages, 1 figur

Antibody binding increases the flexibility of the prion protein

Prion diseases are associated with the conversion of the cellular prion protein (PrP) into a pathogenic conformer (PrPSc). A proposed therapeutic approach to avoid the pathogenic transformation is to develop antibodies that bind to PrP and stabilize its structure. POM1 and POM6 are two monoclonal antibodies that bind the globular domain of PrP and have different biological responses, i.e., trigger neurotoxicity mimicking prion infections (POM1) or prevent neurotoxicity (POM6). The crystal structures of PrP in complex with the two antibodies show similar epitopes which seems inconsistent with the opposite phenotypes. Here, we investigate the influence of the POM1 and POM6 antibodies on the flexibility of the mouse PrP by molecular dynamics simulations. The simulations reveal that the POM6/PrP interface is less stable than the POM1/PrP interface, ascribable to localized polar mismatches at the interface, despite the former complex having a larger epitope than the latter. In the presence of any of the two antibodies, the flexibility of the globular domain increases everywhere except for the β1-α1 loop in the POM1/PrP complex which suggests the involvement of this loop in the pathological conversion. The secondary structure of PrP is preserved whereas the polar interactions involving residues Glu146, Arg156 and Arg208 are modified upon antibody binding

A simple algorithm for computing the Lempel-Ziv factorization

We give a space-efficient simple algorithm for computing the Lempel?Ziv factorization ofa string. For a string of length n over an integer alphabet, it runs in O(n) time independentlyof alphabet size and uses o(n) additional space

On the maximal number of cubic subwords in a string

We investigate the problem of the maximum number of cubic subwords (of the form $www$) in a given word. We also consider square subwords (of the form $ww$). The problem of the maximum number of squares in a word is not well understood. Several new results related to this problem are produced in the paper. We consider two simple problems related to the maximum number of subwords which are squares or which are highly repetitive; then we provide a nontrivial estimation for the number of cubes. We show that the maximum number of squares $xx$ such that $x$ is not a primitive word (nonprimitive squares) in a word of length $n$ is exactly $\lfloor \frac{n}{2}\rfloor - 1$, and the maximum number of subwords of the form $x^k$, for $k\ge 3$, is exactly $n-2$. In particular, the maximum number of cubes in a word is not greater than $n-2$ either. Using very technical properties of occurrences of cubes, we improve this bound significantly. We show that the maximum number of cubes in a word of length $n$ is between $(1/2)n$ and $(4/5)n$. (In particular, we improve the lower bound from the conference version of the paper.)Comment: 14 page

Statistical analysis of storm-time near-Earth current systems

Currents from the Hot Electron and Ion Drift Integrator (HEIDI) inner magnetospheric model results for all of the 90 intense storms (disturbance storm-time (Dst) minimum \u3c −100 nT) from solar cycle 23 (1996–2005) are calculated, presented, and analyzed. We have categorized these currents into the various systems that exist in near-Earth space, specifically the eastward and westward symmetric ring current, the partial ring current, the banana current, and the tail current. The current results from each run set are combined by a normalized superposed epoch analysis technique that scales the timeline of each phase of each storm before summing the results. It is found that there is a systematic ordering to the current systems, with the asymmetric current systems peaking during storm main phase (tail current rising first, then the banana current, followed by the partial ring current) and the symmetric current systems peaking during the early recovery phase (westward and eastward symmetric ring current having simultaneous maxima). The median and mean peak amplitudes for the current systems ranged from 1 to 3 MA, depending on the setup configuration used in HEIDI, except for the eastward symmetric ring current, for which the mean never exceeded 0.3 MA for any HEIDI setup. The self-consistent electric field description in HEIDI yielded larger tail and banana currents than the Volland–Stern electric field, while the partial and symmetric ring currents had similar peak values between the two applied electric field models