On the lowest eigenvalue of Laplace operators with mixed boundary conditions

In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions

Simulations of Oligomeric Intermediates in Prion Diseases

We extend our previous stochastic cellular automata based model for areal aggregation of prion proteins on neuronal surfaces. The new anisotropic model allow us to simulate both strong beta-sheet and weaker attachment bonds between proteins. Constraining binding directions allows us to generate aggregate structures with the hexagonal lattice symmetry found in recently observed in vitro experiments. We argue that these constraints on rules may correspond to underlying steric constraints on the aggregation process. We find that monomer dominated growth of the areal aggregate is too slow to account for some observed doubling time-to-incubation time ratios inferred from data, and so consider aggregation dominated by relatively stable but non-infectious oligomeric intermediates. We compare a kinetic theory analysis of oligomeric aggregation to spatially explicit simulations of the process. We find that with suitable rules for misfolding of oligomers, possibly due to water exclusion by the surrounding aggregate, the resulting oligomeric aggregation model maps onto our previous monomer aggregation model. Therefore it can produce some of the same attractive features for the description of prion incubation time data. We propose experiments to test the oligomeric aggregation model.Comment: 8 pages, 10 figures For larger versions of several figures, see http://asaph.ucdavis.edu/~dmobley and click on the prion paper lin

Modeling Amyloid Beta Peptide Insertion into Lipid Bilayers

Inspired by recent suggestions that the Alzheimer's amyloid beta peptide (A beta) can insert into cell membranes and form harmful ion channels, we model insertion of the 40 and 42 residue forms of the peptide into cell membranes using a Monte Carlo code which is specific at the amino acid level. We examine insertion of the regular A-beta peptide as well as mutants causing familial Alzheimer's disease, and find that all but one of the mutants change the insertion behavior by causing the peptide to spend more simulation steps in only one leaflet of the bilayer. We also find that A-beta 42, because of the extra hydrophobic residues relative to A-beta 40, is more likely to adopt this conformation than A-beta 40 in both wild-type and mutant forms. We argue qualitatively why these effects happen. Here, we present our results and develop the hypothesis that this partial insertion increases the probability of harmful channel formation. This hypothesis can partly explain why these mutations are neurotoxic simply due to peptide insertion behavior. We further apply this model to various artificial A-beta mutants which have been examined experimentally, and offer testable experimental predictions contrasting the roles of aggregation and insertion with regard to toxicity of A-beta mutants. These can be used through further experiments to test our hypothesis.Comment: 14 pages; 8 figures; 2nd revisio

A Point's Point of View of Stringy Geometry

The notion of a "point" is essential to describe the topology of spacetime. Despite this, a point probably does not play a particularly distinguished role in any intrinsic formulation of string theory. We discuss one way to try to determine the notion of a point from a worldsheet point of view. The derived category description of D-branes is the key tool. The case of a flop is analyzed and Pi-stability in this context is tied in to some ideas of Bridgeland. Monodromy associated to the flop is also computed via Pi-stability and shown to be consistent with previous conjectures.Comment: 15 pages, 3 figures, ref adde

Complex Kerr Geometry and Nonstationary Kerr Solutions

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in PRD), added the relation to twistors and algorithm of numerical computations, English is correcte

C^2/Z_n Fractional branes and Monodromy

We construct geometric representatives for the C^2/Z_n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of Harvey-Moore BPS algebras update

Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact Calabi-Yau spaces. These symplectic invariants are used to remove redundancies in examples. The construction of the B-model propagators leads to compatibility conditions, which constrain multi-parameter mirror maps. For K3 fibered Calabi-Yau spaces without reducible fibers we find closed formulas for all genus contributions in the fiber direction from the geometry of the fibration. If the heterotic dual to this geometry is known, the higher genus invariants can be identified with the degeneracies of BPS states contributing to gravitational threshold corrections and all genus checks on string duality in the perturbative regime are accomplished. We find, however, that the BPS degeneracies do not uniquely fix the non-perturbative completion of the heterotic string. For these geometries we can write the topological partition function in terms of the Donaldson-Thomas invariants and we perform a non-trivial check of S-duality in topological strings. We further investigate transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2 quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur

Mirror Symmetry and Other Miracles in Superstring Theory

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many string theorists in fact espouse. String theory leads to many surprising, useful, and well-confirmed mathematical 'predictions' - here I focus on mirror symmetry. These predictions are made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for framework that generated them. I attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a high (philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty Years Of String Theory: Reflecting On the Foundations" (edited by G. `t Hooft, E. Verlinde, D. Dieks and S. de Haro)

Spin dependent scattering of a domain-wall of controlled size

Magnetoresistance measurements in the CPP geometry have been performed on single electrodeposited Co nanowires exchange biased on one side by a sputtered amorphous GdCo layer. This geometry allows the stabilization of a single domain wall in the Co wire, the thickness of which can be controlled by an external magnetic field. Comparing magnetization, resistivity, and magnetoresistance studies of single Co nanowires, of GdCo layers, and of the coupled system, gives evidence for an additional contribution to the magnetoresistance when the domain wall is compressed by a magnetic field. This contribution is interpreted as the spin dependent scattering within the domain wall when the wall thickness becomes smaller than the spin diffusion length.Comment: 9 pages, 13 figure

Should the ultrasound probe replace your stethoscope? A SICS-I sub-study comparing lung ultrasound and pulmonary auscultation in the critically ill

BACKGROUND: In critically ill patients, auscultation might be challenging as dorsal lung fields are difficult to reach in supine-positioned patients, and the environment is often noisy. In recent years, clinicians have started to consider lung ultrasound as a useful diagnostic tool for a variety of pulmonary pathologies, including pulmonary edema. The aim of this study was to compare lung ultrasound and pulmonary auscultation for detecting pulmonary edema in critically ill patients. METHODS: This study was a planned sub-study of the Simple Intensive Care Studies-I, a single-center, prospective observational study. All acutely admitted patients who were 18 years and older with an expected ICU stay of at least 24 h were eligible for inclusion. All patients underwent clinical examination combined with lung ultrasound, conducted by researchers not involved in patient care. Clinical examination included auscultation of the bilateral regions for crepitations and rhonchi. Lung ultrasound was conducted according to the Bedside Lung Ultrasound in Emergency protocol. Pulmonary edema was defined as three or more B lines in at least two (bilateral) scan sites. An agreement was described by using the Cohen κ coefficient, sensitivity, specificity, negative predictive value, positive predictive value, and overall accuracy. Subgroup analysis were performed in patients who were not mechanically ventilated. RESULTS: The Simple Intensive Care Studies-I cohort included 1075 patients, of whom 926 (86%) were eligible for inclusion in this analysis. Three hundred seven of the 926 patients (33%) fulfilled the criteria for pulmonary edema on lung ultrasound. In 156 (51%) of these patients, auscultation was normal. A total of 302 patients (32%) had audible crepitations or rhonchi upon auscultation. From 130 patients with crepitations, 86 patients (66%) had pulmonary edema on lung ultrasound, and from 209 patients with rhonchi, 96 patients (46%) had pulmonary edema on lung ultrasound. The agreement between auscultation findings and lung ultrasound diagnosis was poor (κ statistic 0.25). Subgroup analysis showed that the diagnostic accuracy of auscultation was better in non-ventilated than in ventilated patients. CONCLUSION: The agreement between lung ultrasound and auscultation is poor