A Universal Magnification Theorem III. Caustics Beyond Codimension Five

In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.Comment: 8 page

Lensing by Kerr Black Holes. II: Analytical Study of Quasi-Equatorial Lensing Observables

In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter epsilon, which is the ratio of the angular gravitational radius to the angular Einstein radius. We obtain new formulas and results for the bending angle, image positions, image magnifications, total unsigned magnification, and centroid, all to third order in epsilon and including the displacement. New results on the time delay between images are also given to second order in epsilon, again including displacement. For all lensing observables we show that the displacement begins to appear only at second order in epsilon. When there is no spin, we obtain new results on the lensing observables for Schwarzschild lensing with displacement.Comment: 23 pages; final published versio

Exploring a string-like landscape

We explore inflationary trajectories within randomly-generated two-dimensional potentials, considered as a toy model of the string landscape. Both the background and perturbation equations are solved numerically, the latter using the two-field formalism of Peterson and Tegmark which fully incorporates the effect of isocurvature perturbations. Sufficient inflation is a rare event, occurring for only roughly one in $10^5$ potentials. For models generating sufficient inflation, we find that the majority of runs satisfy current constraints from WMAP. The scalar spectral index is less than 1 in all runs. The tensor-to-scalar ratio is below the current limit, while typically large enough to be detected by next-generation CMB experiments and perhaps also by Planck. In many cases the inflationary consistency equation is broken by the effect of isocurvature modes.Comment: 24 pages with 8 figures incorporated, matches version accepted by JCA

Supersymmetric Vacua in Random Supergravity

We determine the spectrum of scalar masses in a supersymmetric vacuum of a general N=1 supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P = exp(-2N^2|W|^2/m_{susy}^2), with W denoting the superpotential and m_{susy} the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N >> 1. We conclude that for |W| \gtrsim m_{susy}/N, tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.Comment: 26 pages, 6 figure

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page

Local eosinophils are associated with increased IgA subclass levels in the sinonasal mucosa of chronic rhinosinusitis with polyp patients

Background: Chronic rhinosinusitis (CRS) describes an inflammatory condition affecting the sinonasal mucosa. As the immune system players such as immunoglobulins play prominent roles in the development of CRS, we aimed to investigate the expression of IgA subclasses and factors involved in IgA class switching in the sinonasal mucosa of CRS patients. Methods: Specimens were collected from the sinonasal mucosa of the healthy controls and CRS patients. Histological assessments were performed by H&E and immunohistochemistry. Real-time PCR and ELISA methods were applied to measure gene expression and protein levels extracted from tissue samples, respectively. Results: We observed that total IgA and subclass-positive cells were higher in the patient groups than controls. There was a significant correlation between the number of eosinophils and total IgA and subclasses-positive cells (Pv < 0.0001). The expression of CXCL13, BAFF, AID, and germline transcripts were increased in CRSwNP patients. In contrast to IgA2 levels, IgA1 levels were significantly increased in the sinonasal tissue of CRSwNP patients (Pv < 0.01). TGF-β was significantly elevated in the sinonasal tissue of patients with CRSsNP. Conclusions: Increased protein levels of IgA subclasses and related antibody-producing cells were associated with elevated eosinophils in CRSwNP patients which may result in eosinophil pathological functions. Several therapeutic approaches might be developed to modulate the IgA production to ameliorate the inflammatory mechanisms in CRSwNP patients.Figure not available: see fulltext. © 2020 The Author(s)

Frequency of CD4+ and CD8+ T cells in Iranian chronic rhinosinusitis patients

Background: Chronic Rhinosinusitis (CRS) is a persistent inflammatory disease affecting paranasal sinuses. CRS is categorized into two distinct subgroups defined as CRS with nasal polyps (CRSwNP) and CRS without nasal polyps (CRSsNP). Although several immune cells are involved in the CRS pathogenesis, the role of T cells is not fully understood. The objective of the present study was to evaluate the frequency of CD4+ and CD8+ T cells and macrophages in the sinonasal mucosa of CRS patients, as well as to investigate the specific transcription factors for Th1, Th2, Th17, and Treg cells. Methods: In this study, 15 healthy controls, 12 CRSsNP, and 23 CRSwNP patients participated. CD4+, CD8+, and CD68+ cells were investigated in the sinonasal tissues using immunohistochemistry. The expression of transcription factors related to Th subsets (T-bet, GATA3, Ror-γt, and FoxP3) was evaluated using real-time PCR. Furthermore, CRSwNP patients were defined as eosinophilic when eosinophils consisted of more than 10 of total inflammatory cells. The Kruskal-Wallis, Mann-Whitney, and Spearman tests were used in statistical analyses. Results: The median (range) age of the studied groups was: 32 (14-67) for CRSwNP, 28 (10-43) for CRSsNP, and 27 (17-44) for controls. The number of eosinophils in CRSwNP patients was higher than two other groups, whereas neutrophils were elevated in both CRSwNP and CRSsNP groups in comparison to controls. The frequency of CD4+ and CD8+ T cells, macrophages, and total inflammatory cells were significantly increased in CRSwNP and CRSsNP patients compared with controls. The mRNA expression of GATA3 was increased in CRSwNP patients while mRNA expression of Ror-γt was elevated in CRSsNP patients. No significant difference was observed in T-bet mRNA expression among three groups. Both CRSwNP and CRSsNP patients showed decreased FoxP3 mRNA expression in comparison to controls. Conclusion: The frequency of CD4+ and CD8+ T cells was elevated in CRS patients. In addition, we demonstrated Th2 dominance in CRSwNP patients and Th17 dominance in CRSsNP patients, implicating different mechanisms may underlie the disease. Better CRS classification and targeted therapeutic strategies may be achievable by determining the pattern of infiltrating inflammatory cells. Therefore, further experimental investigations on T cells are needed. © 2018 The Author(s)

Accidental Inflation in the Landscape

We study some aspects of fine tuning in inflationary scenarios within string theory flux compactifications and, in particular, in models of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy parameters of the theory needed to have inflation can be generically obtained by scanning the values of the fluxes over the landscape. Furthermore, we find that the existence of a landscape of eternal inflation in this model provides us with a natural theory of initial conditions for the inflationary period in our vacuum. We demonstrate how these two effects work in a small corner of the landscape associated with the complex structure of the Calabi-Yau manifold P^4_[1,1,1,6,9] by numerically investigating the flux vacua of a reduced moduli space. This allows us to obtain the distribution of observable parameters for inflation in this mini-landscape directly from the fluxes.Comment: 40 pages, 11 figure