Global W2,pW^{2,p} estimates for solutions to the linearized Monge--Amp\`ere equations

In this paper, we establish global $W^{2,p}$ estimates for solutions to the linearized Monge-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant analogues of the global $W^{2,p}$ estimates of Winter for fully nonlinear, uniformly elliptic equations, and also linearized counterparts of Savin's global $W^{2,p}$ estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve

The 3-fold vertex via stable pairs

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities. The equivariant vertex governs primary insertions in the theory of stable pairs for toric varieties. We consider also the descendent vertex and conjecture the complete rationality of the descendent theory for stable pairs.Comment: Typos fixed. 40 pages, 8 figure

Restriction theorems for μ\mu-(semi)stable framed sheaves

We provide a generalization of Mehta-Ramanathan theorems to framed sheaves: we prove that the restriction of a $\mu$-semistable framed sheaf on a nonsingular projective irreducible variety, of dimension greater or equal than two, to a general hypersurface of sufficiently high degree is again $\mu$-semistable. The same holds for $\mu$-stability under some additional assumptions.Comment: v2: incorporates changes suggested by the referee. v3: some intermediate results on the (relative) Harder-Narasimhan filtration and the Jordan-Holder filtrations have been extended to the case of framed sheaves on schemes. The main results are unchanged. To appear in Journal of Pure and Applied Algebr

The structure of volcanic cristobalite in relation to its toxicity; relevance for the variable crystalline silica hazard

BACKGROUND: Respirable crystalline silica (RCS) continues to pose a risk to human health worldwide. Its variable toxicity depends on inherent characteristics and external factors which influence surface chemistry. Significant population exposure to RCS occurs during volcanic eruptions, where ashfall may cover hundreds of square km and exposure may last years. Occupational exposure also occurs through mining of volcanic deposits. The primary source of RCS from volcanoes is through collapse and fragmentation of lava domes within which cristobalite is mass produced. After 30 years of research, it is still not clear if volcanic ash is a chronic respiratory health hazard. Toxicological assays have shown that cristobalite-rich ash is less toxic than expected. We investigate the reasons for this by determining the physicochemical/structural characteristics which may modify the pathogenicity of volcanic RCS. Four theories are considered: 1) the reactivity of particle surfaces is reduced due to co-substitutions of Al and Na for Si in the cristobalite structure; 2) particles consist of aggregates of cristobalite and other phases, restricting the surface area of cristobalite available for reactions in the lung; 3) the cristobalite surface is occluded by an annealed rim; 4) dissolution of other volcanic particles affects the surfaces of RCS in the lung. METHODS: The composition of volcanic cristobalite crystals was quantified by electron microprobe and differences in composition assessed by Welch's two sample t-test. Sections of dome-rock and ash particles were imaged by scanning and transmission electron microscopy, and elemental compositions of rims determined by energy dispersive X-ray spectroscopy. RESULTS: Volcanic cristobalite contains up to 4 wt. % combined Al(2)O(3) and Na(2)O. Most cristobalite-bearing ash particles contain adhered materials such as feldspar and glass. No annealed rims were observed. CONCLUSIONS: The composition of volcanic cristobalite particles gives insight into previously-unconsidered inherent characteristics of silica mineralogy which may affect toxicity. The structural features identified may also influence the hazard of other environmentally and occupationally produced silica dusts. Current exposure regulations do not take into account the characteristics that might render the silica surface less harmful. Further research would facilitate refinement of the existing simple, mass-based silica standard by taking into account composition, allowing higher standards to be set in industries where the silica surface is modified.Natural Environment Research Council (NERC)Moyes Foundation - studentshi

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

Curve counting via stable pairs in the derived category

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page

From Triumph to Tragedy: African American Soldiers Fight For Citizenship and Manhood in the Spanish-American-Cuban-Filipino War

The purpose of this study is to provide a re-examination of the black soldier in the Spanish-American-Cuban-Filipino War. Specifically, by adding a gender analysis, this study will demonstrate that black soldiers fought in the war for two principle reasons: first, it was a means of exercising their citizenship; and secondly, it was a means of demonstrating that they were real men. Reflecting on an era when proving one\u27s manhood was a national obsession--this thesis provides a critical window through which we can reconstruct their motivations for fighting in America\u27s first overseas war

Restoration of CFTR function in patients with cystic fibrosis carrying the F508del-CFTR mutation

<div><p>Restoration of BECN1/Beclin 1-dependent autophagy and depletion of SQSTM1/p62 by genetic manipulation or autophagy-stimulatory proteostasis regulators, such as cystamine, have positive effects on mouse models of human cystic fibrosis (CF). These measures rescue the functional expression of the most frequent pathogenic CFTR mutant, F508del, at the respiratory epithelial surface and reduce lung inflammation in <i>Cftr^F508del</i> homozygous mice. Cysteamine, the reduced form of cystamine, is an FDA-approved drug. Here, we report that oral treatment with cysteamine greatly reduces the mortality rate and improves the phenotype of newborn mice bearing the <i>F508del-CFTR</i> mutation. Cysteamine was also able to increase the plasma membrane expression of the F508del-CFTR protein in nasal epithelial cells from <i>F508del</i> homozygous CF patients, and these effects persisted for 24 h after cysteamine withdrawal. Importantly, this cysteamine effect after washout was further sustained by the sequential administration of epigallocatechin gallate (EGCG), a green tea flavonoid, both <i>in vivo</i>, in mice, and <i>in vitro</i>, in primary epithelial cells from CF patients. In a pilot clinical trial involving 10 <i>F508del-CFTR</i> homozygous CF patients, the combination of cysteamine and EGCG restored BECN1, reduced SQSTM1 levels and improved CFTR function from nasal epithelial cells <i>in vivo</i>, correlating with a decrease of chloride concentrations in sweat, as well as with a reduction of the abundance of <i>TNF/TNF-alpha (tumor necrosis factor)</i> and <i>CXCL8</i> (<i>chemokine [C-X-C motif] ligand 8</i>) transcripts in nasal brushing and TNF and CXCL8 protein levels in the sputum. Altogether, these results suggest that optimal schedules of cysteamine plus EGCG might be used for the treatment of CF caused by the <i>F508del-CFTR</i> mutation.</p></div

Yukawa Textures From Heterotic Stability Walls

A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1 can have regions of its Kahler cone where it is slope-stable, that is, where the four-dimensional theory is N=1 supersymmetric, bounded by "walls of stability". On these walls the bundle becomes poly-stable, decomposing into a direct sum, and the low energy gauge group is enhanced by at least one anomalous U(1) gauge factor. In this paper, we show that these additional symmetries can strongly constrain the superpotential in the stable region, leading to non-trivial textures of Yukawa interactions and restrictions on allowed masses for vector-like pairs of matter multiplets. The Yukawa textures exhibit a hierarchy; large couplings arise on the stability wall and some suppressed interactions "grow back" off the wall, where the extended U(1) symmetries are spontaneously broken. A number of explicit examples are presented involving both one and two stability walls, with different decompositions of the bundle structure group. A three family standard-like model with no vector-like pairs is given as an example of a class of SU(4) bundles that has a naturally heavy third quark/lepton family. Finally, we present the complete set of Yukawa textures that can arise for any holomorphic bundle with one stability wall where the structure group breaks into two factors.Comment: 53 pages, 4 figures and 13 table

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.Comment: harvmac, 45 pp. (v2: added references