6 research outputs found
Clones with finitely many relative R-classes
For each clone C on a set A there is an associated equivalence relation
analogous to Green's R-relation, which relates two operations on A iff each one
is a substitution instance of the other using operations from C. We study the
clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde
All Inequalities for the Relative Entropy
The relative entropy of two n-party quantum states is an important quantity
exhibiting, for example, the extent to which the two states are different. The
relative entropy of the states formed by reducing two n-party to a smaller
number of parties is always less than or equal to the relative entropy of
the two original n-party states. This is the monotonicity of relative entropy.
Using techniques from convex geometry, we prove that monotonicity under
restrictions is the only general inequality satisfied by relative entropies. In
doing so we make a connection to secret sharing schemes with general access
structures.
A suprising outcome is that the structure of allowed relative entropy values
of subsets of multiparty states is much simpler than the structure of allowed
entropy values. And the structure of allowed relative entropy values (unlike
that of entropies) is the same for classical probability distributions and
quantum states.Comment: 15 pages, 3 embedded eps figure
Bubbles detection for inter-war European hyperinflation: A threshold cointegration approach
Natalizumab plus interferon beta-1a for relapsing multiple sclerosis.
Item does not contain fulltextBACKGROUND: Interferon beta is used to modify the course of relapsing multiple sclerosis. Despite interferon beta therapy, many patients have relapses. Natalizumab, an alpha4 integrin antagonist, appeared to be safe and effective alone and when added to interferon beta-1a in preliminary studies. METHODS: We randomly assigned 1171 patients who, despite interferon beta-1a therapy, had had at least one relapse during the 12-month period before randomization to receive continued interferon beta-1a in combination with 300 mg of natalizumab (589 patients) or placebo (582 patients) intravenously every 4 weeks for up to 116 weeks. The primary end points were the rate of clinical relapse at 1 year and the cumulative probability of disability progression sustained for 12 weeks, as measured by the Expanded Disability Status Scale, at 2 years. RESULTS: Combination therapy resulted in a 24 percent reduction in the relative risk of sustained disability progression (hazard ratio, 0.76; 95 percent confidence interval, 0.61 to 0.96; P=0.02). Kaplan-Meier estimates of the cumulative probability of progression at two years were 23 percent with combination therapy and 29 percent with interferon beta-1a alone. Combination therapy was associated with a lower annualized rate of relapse over a two-year period than was interferon beta-1a alone (0.34 vs. 0.75, P<0.001) and with fewer new or enlarging lesions on T(2)-weighted magnetic resonance imaging (0.9 vs. 5.4, P<0.001). Adverse events associated with combination therapy were anxiety, pharyngitis, sinus congestion, and peripheral edema. Two cases of progressive multifocal leukoencephalopathy, one of which was fatal, were diagnosed in natalizumab-treated patients. CONCLUSIONS: Natalizumab added to interferon beta-1a was significantly more effective than interferon beta-1a alone in patients with relapsing multiple sclerosis. Additional research is needed to elucidate the benefits and risks of this combination treatment. (ClinicalTrials.gov number, NCT00030966.)