An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Risk of tuberculous infection in adolescents and adults in a rural community in Ethiopia

BACKGROUND: The incidence of tuberculosis (TB) in sub-Saharan Africa is one of the highest in the world. OBJECTIVE: To evaluate the prevalence of TB, the annual risk of tuberculous infection (ARTI) and associated risk factors in rural Ethiopia. METHODS: A tuberculin skin test was performed among 2743 individuals in a rural community of Ethiopia around Ginci town, west of Addis Ababa, to estimate the prevalence of tuberculin reactivity and to assess factors associated with tuberculous infection. RE SULTS: Among 2743 volunteer participants, test results were available for 2640, 691 (26.2%) of whom had an identifiable bacille Calmette-Guérin (BCG) scar; 221 (8.3%) reported household contact with a known TB case. The overall prevalence of TST reactions of ≥10 mm was 29.7%. The ARTI was estimated at 1.7%. Tuberculin reactivity varied with age, sex, income and history of household contact with a TB case. Presence of BCG scar was not related to tuberculin reactivity. CONCLUSIONS: Our findings indicate that despite an effective TB control programme, TB transmission rates are still high in rural Ethiopia. Provision of isoniazid prophylaxis in close contacts of active TB cases among the poorest population groups may reduce TB incidence.</p

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Entanglement in the interaction between two quantum oscillator systems

The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a non-linear, angular-momentum oscillator; the second case is, of course, more complex in terms of energy transfer and dynamics. These two scenarios have been the subject of much interest over the years, especially in developing an understanding of modern concepts in quantum optics and quantum electronics. In this work, however, these two scenarios are utilized to consider and discuss the salient features of quantum behaviors resulting from the interactive nature of the two oscillators, i.e., coherence, entanglement, spontaneous emission, etc., and to apply a measure of entanglement in analyzing the nature of the interacting systems. ... For the coupled linear and angular-momentum oscillator system in the fully quantum-mechanical description, we consider special examples of two, three, four-level angular momentum systems, demonstrating the explicit appearances of entanglement. We also show that this entanglement persists even as the coupled angular momentum oscillator is taken to the limit of a large number of levels, a limit which would go over to the classical picture for an uncoupled angular momentum oscillator

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

The impact of correlated projections on weak lensing cluster counts

Large-scale structure projections are an obstacle in converting the shear signal of clusters detected in weak-lensing maps into virial masses. However, this step is not necessary for constraining cosmology with the shear-peak abundance, if we are able to predict its amplitude. We generate a large ensemble of N-body simulations spanning four cosmological models, with total volume V~1 (Gpc/h)^3 per model. Variations to the matter density parameter and amplitude of fluctuations are considered. We measure the abundance of peaks in the mass density projected in ~100 Mpc/h slabs to determine the impact of structures spatially correlated with the simulation clusters, identified by the 3D friends-of-friends algorithm. The halo model shows that the choice of the smoothing filter for the density field is important in reducing the contribution of correlated projections to individual halo masses. Such contributions are less than 2% in the case of the optimal, compensated filter used throughout this analysis. We measure the change in the mass of peaks when projected in slabs of various thicknesses. Peaks in slabs of 26 Mpc/h and 102 Mpc/h suffer an average mass change of less than 2% compared to their mass in slabs of 51 Mpc/h. We then explore the cosmology dependence of the projected-peak mass function, and find that, for a wide range of slab thicknesses (<500 Mpc/h), it scales with cosmology in exactly the same way as the 3D friends-of-friends mass function and the Sheth-Tormen formula. This extends the earlier result of Marian et al. (2009). Finally, we show that for all cosmological models considered, the low and intermediate mass bins of the peak abundance can be described using a modified Sheth-Tormen functional form to within 10%-20% accuracy.Comment: 19 pages, 14 figures, accepted for publication in the Astrophysical Journa

Positivity of relative canonical bundles and applications

Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic equation to show that this metric is strictly positive on $\mathcal X$, unless the family is infinitesimally trivial. For degenerating families we show that the curvature form on the total space can be extended as a (semi-)positive closed current. By fiber integration it follows that the generalized Weil-Petersson form on the base possesses an extension as a positive current. We prove an extension theorem for hermitian line bundles, whose curvature forms have this property. This theorem can be applied to a determinant line bundle associated to the relative canonical bundle on the total space. As an application the quasi-projectivity of the moduli space $\mathcal M_{\text{can}}$ of canonically polarized varieties follows. The direct images $R^{n-p}f_*\Omega^p_{\mathcal X/S}(\mathcal K_{\mathcal X/S}^{\otimes m})$, $m > 0$, carry natural hermitian metrics. We prove an explicit formula for the curvature tensor of these direct images. We apply it to the morphisms $S^p \mathcal T_S \to R^pf_*\Lambda^p\mathcal T_{\mathcal X/S}$ that are induced by the Kodaira-Spencer map and obtain a differential geometric proof for hyperbolicity properties of $\mathcal M_{\text{can}}$.Comment: Supercedes arXiv:0808.3259v4 and arXiv:1002.4858v2. To appear in Invent. mat

An Axiomatic Approach to Liveness for Differential Equations

This paper presents an approach for deductive liveness verification for ordinary differential equations (ODEs) with differential dynamic logic. Numerous subtleties complicate the generalization of well-known discrete liveness verification techniques, such as loop variants, to the continuous setting. For example, ODE solutions may blow up in finite time or their progress towards the goal may converge to zero. Our approach handles these subtleties by successively refining ODE liveness properties using ODE invariance properties which have a well-understood deductive proof theory. This approach is widely applicable: we survey several liveness arguments in the literature and derive them all as special instances of our axiomatic refinement approach. We also correct several soundness errors in the surveyed arguments, which further highlights the subtlety of ODE liveness reasoning and the utility of our deductive approach. The library of common refinement steps identified through our approach enables both the sound development and justification of new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto, Portugal, October 9-11, 201

Blastic plasmacytoid dendritic cell neoplasm: Genomics mark epigenetic dysregulation as a primary therapeutic target

Blastic plasmacytoid dendritic cell neoplasm (BPDCN) is a rare and aggressive hematologic malignancy for which there is still no effective B therapy. In order to identify genetic alterations useful for a new treatment design, we used whole-exome sequencing to analyze 14 BPDCN patients and the patient-derived CAL-1 cell line. The functional enrichment analysis of mutational data reported the epigenetic regulatory program to be the most significantly undermined (P&lt;0.0001). In particular, twenty-five epigenetic modifiers were found mutated (e.g. ASXL1, TET2, SUZ12, ARID1A, PHF2, CHD8); ASXL1 was the most frequently affected (28.6% of cases). To evaluate the impact of the identified epigenetic mutations at the gene-expression and Histone H3 lysine 27 trimethylation/acetylation levels, we performed additional RNA and pathology tissue-chromatin immunoprecipitation sequencing experiments. The patients displayed enrichment in gene signatures regulated by methylation and modifiable by decitabine administration, shared common H3K27-acetylated regions, and had a set of cell-cycle genes aberrantly up-regulated and marked by promoter acetylation. Collectively, the integration of sequencing data showed the potential of a therapy based on epigenetic agents. Through the adoption of a preclinical BPDCN mouse model, established by CAL-1 cell line xenografting, we demonstrated the efficacy of the combination of the epigenetic drugs 5’-azacytidine and decitabine in controlling disease progression in vivo