On the interactions of lipids and proteins in the red blood cell membrane

The effects of temperature and of the action of a purified phospholipase C enzyme preparation on human red blood cell membranes has been investigated by chemical analyses, circular dichroism, and proton magnetic resonance measurements. The results indicate that a substantial fraction of the phospholipids and the proteins of the membranes can change structure independently of one another, suggesting a mosaic pattern for the organization of the lipids and proteins in membranes

Backbone Fragility and the Local Search Cost Peak

The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably effective at solving hard Random 3-SAT instances near the so-called `satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over different instances. We make a number of significant contributions to the analysis of WSat on high-cost random instances, using the recently-introduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for small-backbone instances but is much less relevant for the large-backbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSat's search. This pattern leads us to introduce a measure of the backbone fragility of an instance, which indicates how persistent the backbone is as clauses are removed. We propose that high-cost random instances for local search are those with very large backbones which are also backbone-fragile. We suggest that the decay in cost beyond the satisfiability threshold is due to increasing backbone robustness (the opposite of backbone fragility). Our hypothesis makes three correct predictions. First, that the backbone robustness of an instance is negatively correlated with the local search cost when other factors are controlled for. Second, that backbone-minimal instances (which are 3-SAT instances altered so as to be more backbone-fragile) are unusually hard for WSat. Third, that the clauses most often unsatisfied during search are those whose deletion has the most effect on the backbone. In understanding the pathologies of local search methods, we hope to contribute to the development of new and better techniques

Trick or treat: the effect of placebo on the power of pharmacogenetic association studies

The genetic mapping of drug-response traits is often characterised by a poor signal-to-noise ratio that is placebo related and which distinguishes pharmacogenetic association studies from classical case-control studies for disease susceptibility. The goal of this study was to evaluate the statistical power of candidate gene association studies under different pharmacogenetic scenarios, with special emphasis on the placebo effect. Genotype/phenotype data were simulated, mimicking samples from clinical trials, and response to the drug was modelled as a binary trait. Association was evaluated by a logistic regression model. Statistical power was estimated as a function of the number of single nucleotide polymorphisms (SNPs) genotyped, the frequency of the placebo 'response', the genotype relative risk (GRR) of the response polymorphism, the strategy for selecting SNPs for genotyping, the number of individuals in the trial and the ratio of placebo-treated to drug-treated patients. We show that: (i) the placebo 'response' strongly affects the statistical power of association studies--even a highly penetrant drug-response allele requires at least a 500-patient trial in order to reach 80 per cent power, several-fold more than the value estimated by standard tools that are not calibrated to pharmacogenetics; (ii) the power of a pharmacogenetic association study depends primarily on the penetrance of the response genotype and, when this penetrance is fixed, power decreases for larger placebo effects; (iii) power is dramatically increased when adding markers; (iv) an optimal study design includes a similar number of placebo- and drug-treated patients; and (v) in this setting, straightforward haplotype analysis does not seem to have an advantage over single marker analysis

Modular Forms and the Cosmological Constant

The vacuum amplitude of the heterotic string in a flat background vanishes for the first twenty orders of string perturbation theory. The proof relies on the algebraic geometry of modular forms

The Algebras of Large N Matrix Mechanics

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark

Inverse moment problem for elementary co-adjoint orbits

We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.Comment: 13 page

Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Solving Pure Yang Mills in 2+1 Dimensions

We analytically compute the spectrum of the spin zero glueballs in the planar limit of pure Yang-Mills theory in 2+1 dimensions. The new ingredient is provided by our computation of a new non-trivial form of the ground state wave-functional. The mass spectrum of the theory is determined by the zeroes of Bessel functions, and the agreement with large N lattice data is excellent.Comment: 4 page letter; version to appear in Physical Review Letter