The Corona Theorem for the Drury-Arveson Hardy space and other holomorphic Besov-Sobolev spaces on the unit ball in Cn\mathbb{C}^{n}

We prove that the multiplier algebra of the Drury-Arveson Hardy space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal space, thus generalizing the famous Corona Theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach space result: the Besov-Sobolev space $B_{p}^{\sigma}$ has the "baby corona property" for all $\sigma \geq 0$ and $1<p<\infty$. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.Comment: v1: 70 pgs; v2: 73 pgs.; introduction expanded, clarified. v3: 73 pgs.; restriction in main result removed (see 9.2), arguments expanded (see 8.1.1). v4: 74 pgs.; systematic arithmetic misprints fixed on pgs. 37-48. v5: 76 pgs.; incorrect embedding corrected via Proposition 4. v6: 80 pgs.; main result extended to vector-valued setting. v7: 82 pgs.; typos removed

Thermally induced magnetic relaxation in square artificial spin ice

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice - we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.Comment: 15 pages, 5 figure

On Breakdown Criteria for Nonvacuum Einstein Equations

The recent "breakdown criterion" result of S. Klainerman and I. Rodnianski stated roughly that an Einstein-vacuum spacetime, given as a CMC foliation, can be further extended in time if the second fundamental form and the derivative of the lapse of the foliation are uniformly bounded. This theorem and its proof were extended to Einstein-scalar and Einstein-Maxwell spacetimes in the author's Ph.D. thesis. In this paper, we state the main results of the thesis, and we summarize and discuss their proofs. In particular, we will discuss the various issues resulting from nontrivial Ricci curvature and the coupling between the Einstein and the field equations.Comment: 62 pages This version: corrected minor typos, expanded Section 6 (geometry of null cones

Acute Hepatic Porphyrias: Review and Recent Progress.

The acute hepatic porphyrias (AHPs) are a group of four inherited diseases of heme biosynthesis that present with episodic, acute neurovisceral symptoms. The four types are 5-aminolevulinic acid (ALA) dehydratase deficiency porphyria, acute intermittent porphyria, hereditary coproporphyria, and variegate porphyria. Their diagnoses are often missed or delayed because the clinical symptoms mimic other more common disorders. Recent results indicate that acute intermittent porphyria, the most severe of the more common types of AHP, is more prevalent than previously thought, occurring in about 1 in 1600 Caucasians, but with low clinical penetrance (approximately 2%-3%). Here we provide an updated review of relevant literature and discuss recent and emerging advances in treatment of these disorders. Symptomatic attacks occur primarily in females between 14 and 45 years of age. AHP is diagnosed by finding significantly elevated levels of porphyrin precursors ALA and porphobilinogen in urine. Acute attacks should be treated promptly with intravenous heme therapy to avoid the development of potentially irreversible neurologic sequelae. All patients should be counseled about avoiding potential triggers for acute attacks and monitored regularly for the development of long-term complications. Their first-degree relatives should undergo targeted gene testing. Patients who suffer recurrent acute attacks can be particularly challenging to manage. Approximately 20% of patients with recurrent symptoms develop chronic and ongoing pain and other symptoms. We discuss newer treatment options in development, including small interfering RNA, to down-regulate ALA synthase-1 and/or wild-type messenger RNA of defective genes delivered selectively to hepatocytes for these patients. We expect that the newer treatments will diminish and perhaps obviate the need for liver transplantation as treatment of these inborn metabolic disorders

The importance of the weak: Interaction modifiers in artificial spin ices

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics, and emergent magnetic properties, in e.g. artificial spin ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here we introduce a new approach: single interaction modifiers, using slave-mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane. We show that by placing these on the vertices of square artificial spin ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule obeying states in square artificial spin ice structures, enabling the exploration of thermal dynamics in a spin liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length-scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.Comment: 17 pages, including methods, 4 figures. Supplementary information contains 16 pages and 15 figure

The predictive value of depression in the years after heart transplantation for mortality during long-term follow-up

Objective Current understanding of the prognostic impact of depression on mortality after heart transplantation (HTx) is limited. We examined whether depression after HTx is a predictor of mortality during extended follow-up. Subsequently, we explored whether different symptom dimensions of depression could be identified and whether they were differentially associated with mortality. Methods Survival analyses were performed in a sample of 141 HTx recipients assessed for depression, measured by self-report of depressive symptoms (Beck Depression Inventory – version 1A [BDI-1A]), at median 5.0 years after HTx, and followed thereafter for survival status for up to 18.6 years. We used uni- and multivariate Cox proportional hazard models to examine the association of clinically significant depression (BDI-1A total score ≥10), as well as the cognitive-affective and the somatic subscales of the BDI-1A (resulting from principal component analysis) with mortality. In the multivariate analyses, we adjusted for relevant sociodemographic and clinical variables. Results Clinically significant depression was a significant predictor of mortality (hazard ratio = 2.088; 95% confidence interval = 1.366–3.192; p = .001). Clinically significant depression also was an independent predictor of mortality in the multivariate analysis (hazard ratio = 1.982; 95% confidence interval = 1.220–3.217; p = .006). The somatic subscale, but not the cognitive-affective subscale, was significantly associated with increased mortality in univariate analyses, whereas neither of the two subscales was an independent predictor of mortality in the multivariate analysis. Conclusions Depression measured by self-report after HTx is associated with increased mortality during extended follow-up. Clinical utility and predictive validity of specific depression components require further study.acceptedVersio

Can sexual selection drive female life histories? A comparative study on Galliform birds

Sexual selection is an important driver of many of the most spectacular morphological traits that we find in the animal kingdom (for example see Andersson, 1994). As such, sexual selection is most often emphasized as

Change in quality of life and their predictors in the long-term follow-up after group cognitive behavioral therapy for social anxiety disorder: a prospective cohort study

<p>Abstract</p> <p>Background</p> <p>Social anxiety disorder (SAD) is one of the most common anxiety disorders. The efficacy of cognitive behaviour therapy (CBT) has been examined but to date its effects on Quality of Life (QoL) have not been appropriately evaluated especially in the long term.</p> <p>The study aimed to examine, in the long term, what aspects of Quality of Life (QoL) changed among social anxiety disorder (SAD) patients treated with group cognitive behaviour therapy (CBT) and what predictors at baseline were associated with QoL.</p> <p>Methods</p> <p>Outpatients diagnosed with SAD were enrolled into group CBT, and assessed at follow-ups for up to 12 months in a typical clinical setting. QoL was evaluated using the Short Form 36. Various aspects of SAD symptomatology were also assessed. Each of the QoL domains and scores on symptomatology were quantified and compared with those at baseline. Baseline predictors of QoL outcomes at follow-up were investigated.</p> <p>Results</p> <p>Fifty-seven outpatients were enrolled into group CBT for SAD, 48 completed the whole program, and 44 and 40 completed assessments at the 3-month and 12-month follow-ups, respectively. All aspects of SAD symptomatology and psychological subscales of the QoL showed statistically significant improvement throughout follow-ups for up to 12 months. In terms of social functioning, no statistically significant improvement was observed at either follow-up point except for post-treatment. No consistently significant pre-treatment predictors were observed.</p> <p>Conclusions</p> <p>After group CBT, SAD symptomatology and some aspects of QoL improved and this improvement was maintained for up to 12 months, but the social functioning domain did not prove any significant change statistically. Considering the limited effects of CBT on QoL, especially for social functioning, more powerful treatments are needed.</p

Multi-site genetic analysis of diffusion images and voxelwise heritability analysis : a pilot project of the ENIGMA–DTI working group

The ENIGMA (Enhancing NeuroImaging Genetics through Meta-Analysis) Consortium was set up to analyze brain measures and genotypes from multiple sites across the world to improve the power to detect genetic variants that influence the brain. Diffusion tensor imaging (DTI) yields quantitative measures sensitive to brain development and degeneration, and some common genetic variants may be associated with white matter integrity or connectivity. DTI measures, such as the fractional anisotropy (FA) of water diffusion, may be useful for identifying genetic variants that influence brain microstructure. However, genome-wide association studies (GWAS) require large populations to obtain sufficient power to detect and replicate significant effects, motivating a multi-site consortium effort. As part of an ENIGMA–DTI working group, we analyzed high-resolution FA images from multiple imaging sites across North America, Australia, and Europe, to address the challenge of harmonizing imaging data collected at multiple sites. Four hundred images of healthy adults aged 18–85 from four sites were used to create a template and corresponding skeletonized FA image as a common reference space. Using twin and pedigree samples of different ethnicities, we used our common template to evaluate the heritability of tract-derived FA measures. We show that our template is reliable for integrating multiple datasets by combining results through meta-analysis and unifying the data through exploratory mega-analyses. Our results may help prioritize regions of the FA map that are consistently influenced by additive genetic factors for future genetic discovery studies. Protocols and templates are publicly available at (http://enigma.loni.ucla.edu/ongoing/dti-working-group/)