How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential

Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is decribed by a matrix of dimension three. It turns out not to be diagonalizable for a critical strength of the interaction, also indicated by the transition of two real into a pair of complex energy eigenvalues. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two.Comment: 5 page

On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric

Given a holomorphic line bundle over the complex affine quadric $Q^2$, we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant biholomorphism, these are all contained in a maximal one, say $\Omega_{max}$. By removing the zero section to $\Omega_{max}$ one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.Comment: 15 pages, v2: minor changes, to appear in Transformation Group

DWT-based Method for Partial Discharge Pattern Recognition

The new proposed method of pattern recognition is based on the application of Multiresolution Signal Decomposition (MSD) technique of wavelet transform. This technique has shown interesting properties in capturing the embedded horizontal, vertical and diagonal variations within an image obtained from the PD pattern in a separable form. This feature has been exploited to identify in the PD patterns MSD, relative at various family of PD sources, some detail images typical of a single discharge phenomenon. The classification of a generic PD phenomenon is feasible through a comparison between its detail images and the detail images typical of a single discharge phenomenon. Tests have been performed on specimens having single defects. The obtained results prove that the proposed improved classification methods is quite efficient and accurate. [DOI: 10.1685 / CSC06133] About DO

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

Onboarding Advanced Practice Nurses to Pre-Anesthesia Care

Onboarding advanced practice nurses to the pre-anesthesia clinic (OBPAC) is a complex process that involves the integration and familiarization of new employees with the workplace. It is considered essential for safe and efficient clinical practice and the achievement of organizational goals. Fostering independence and competency are the overall aims of the onboarding process. The preceptor ensures that new advanced practice nurses (APNs) receive the support and guidance needed when learning new skills (Simone et al., 2016). There is evidence to show that dedicating time to a well-organized onboarding plan, laying clear job expectations with precepting, and continuous mentoring increases precepting, job satisfaction, and staff retention (Bowe, 2018). Providing clear objectives, regular and timely feedback, a blueprint for onboarding, and frequent communication such as post-onboarding check-ins are some of the educational resources that were developed with strategies recommended by Benner (1984) as a guide. The pre-anesthesia clinic guidelines learning checklist has offered up-to-date clinical knowledge to ensure that time is assigned to learn and demonstrate skills attained through the OBPAC. As APNs gain competence and become advanced beginners in the clinical aspect, they will routinely be required to call on their abilities of problem-solving and anticipation of challenges. Evaluations post-OBPAC have been favorable, garnered positive feedback from preceptors, new APNs, and the administration, and improved post-testing in new APNs

Sarcopenia: age-related skeletal muscle changes from determinants to physical disability.

Human aging is characterized by skeletal muscle wasting, a debilitating condition which sets the susceptibility for diseases that directly affect the quality of life and often limit life span. Sarcopenia, i.e. the reduction of muscle mass and/or function, is the consequence of a reduction of protein synthesis and an increase in muscle protein degradation. In addition, the capacity for muscle regeneration is severely impaired in aging and this can lead to disability, particularly in patients with other concomitant diseases or organ impairment. Immobility and lack of exercise, increased levels of proinflammatory cytokines, increased production of oxygen free radicals or impaired detoxification, low anabolic hormone output, malnutrition and reduced neurological drive have been advocated as being responsible for sarcopenia. It is intriguing to notice that multiple pathways converge on skeletal muscle dysfunction, but the factors involved sometimes diverge to different pathways, thus intersecting at critical points. It is reasonable to argue that the activity of these nodes results from the net balance of regulating mechanisms, as in the case of the GH/IGF-1 axis, the testosterone and Cortisol functions, the pro- and anti-inflammatory cytokines and receptors. Both genetic and epigenetic mechanisms operate in regulating the final phenotype, the extent of muscle atrophy and reduction in strength and force generation. It is widely accepted that intervention on lifestyle habits represents an affordable and practical way to modify on a large scale some detrimental outcomes of aging, and particularly sarcopenia. The identification of the molecular chain able to reverse sarcopenia is a major goal of studies on human aging

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

Reference-based analysis of lung single-cell sequencing reveals a transitional profibrotic macrophage.

Tissue fibrosis is a major cause of mortality that results from the deposition of matrix proteins by an activated mesenchyme. Macrophages accumulate in fibrosis, but the role of specific subgroups in supporting fibrogenesis has not been investigated in vivo. Here, we used single-cell RNA sequencing (scRNA-seq) to characterize the heterogeneity of macrophages in bleomycin-induced lung fibrosis in mice. A novel computational framework for the annotation of scRNA-seq by reference to bulk transcriptomes (SingleR) enabled the subclustering of macrophages and revealed a disease-associated subgroup with a transitional gene expression profile intermediate between monocyte-derived and alveolar macrophages. These CX3CR1+SiglecF+ transitional macrophages localized to the fibrotic niche and had a profibrotic effect in vivo. Human orthologs of genes expressed by the transitional macrophages were upregulated in samples from patients with idiopathic pulmonary fibrosis. Thus, we have identified a pathological subgroup of transitional macrophages that are required for the fibrotic response to injury

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