Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo H. To any unitary representation, r of pi_1(S)/H we associate a higher-order rho_r-invariant and a signature 2-cocycle sigma_r. These signature cocycles are shown to be generalizations of the Meyer cocycle. In particular each rho_r is a quasimorphism and each sigma_r is a bounded 2-cocycle on J(H). In one of the simplest non-trivial cases, by varying r, we exhibit infinite families of linearly independent quasimorphisms and signature cocycles. We show that the rho_r restrict to homomorphisms on certain interesting subgroups. Many of these invariants extend naturally to the full mapping class group and some extend to the monoid of homology cylinders based on S.Comment: 38 pages. This is final version for publication in IMRN, deleted some material and many references (sorry-at referee's insistence

Cromakalim (BRL 34915) restores in vitro the membrane potential of depolarized human skeletal muscle fibres

The purpose of the present study was to analyze the effects of cromakalim (BRL 34915), a potent drug from a new class of drugs characterized as K+ channel openers, on the electrical activity of human skeletal muscle. Therefore, intracellular recordings were used to measure the effects of cromakalim on the membrane potential and input conductance of fibres from human skeletal muscle biopsies. Cromakalim in a concentration above 1 mol/l induced an increase in membrane K+ conductance. This effect resulted in a membrane hyperpolarization. The magnitude of this polarization depended on the difference between resting and K+ equilibrium potential. The effect had a rapid onset and was quickly reversible after washing. Fibres from two patients with hyperkalaemic periodic paralysis showed an excessive membrane depolarization during and also after exposure to an slightly elevated extracellular K+ concentration. In the latter situation, cromakalim repolarized the fibres to the normal resting potential. Tolbutamide (1 mmol/l) and Ba2+ (3 mmol/l) strongly antagonized the effect of cromakalim. The data show that cromakalim hyperpolarizes depolarized human skeletal muscle fibres maintained in vitro. The underlying mechanism is probably an activation of otherwise silent, ATP-regulated K+ channels. Such an effect may be of therapeutic benefit in a situation in which a membrane depolarization causes muscle paralysis

Taxation of Electronic Commerce

No other innovation, or way of doing business, has revolutionized the international economy faster than the Internet. It took generations for the Industrial Revolution to play out around the world while the Internet Revolution has unfolded in less than a decade. The speed of this change has been astounding. In the Industrial Age, as change took place, governments were able to react accordingly. In the Internet Age, today\u27s innovation is tomorrow\u27s standard. Government are finding that they must act on Internet time, which is a daunting challenge. This paper examines the current state of affairs with regards to the taxation of Internet commerce. It analysis the historical perspective of the United States of America, the OECD, the WTO, and the European Union; and attempts to answer the question “What happens next?” Is there an opportunity here for developing countries to increase their tax base