Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the $R$-radius hyperboloid model of $d$-dimensional hyperbolic geometry with $R>0$ and $d\ge 2$, we compute azimuthal Fourier expansions for a fundamental solution of Laplace's equation. For $d\ge 2$, we compute a Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace's equation on this negative-constant sectional curvature Riemannian manifold. In three-dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace's equation is obtained through comparison with its corresponding Gegenbauer expansion.Comment: arXiv admin note: substantial text overlap with arXiv:1201.440

Vacuum effects in an asymptotically uniformly accelerated frame with a constant magnetic field

In the present article we solve the Dirac-Pauli and Klein Gordon equations in an asymptotically uniformly accelerated frame when a constant magnetic field is present. We compute, via the Bogoliubov coefficients, the density of scalar and spin 1/2 particles created. We discuss the role played by the magnetic field and the thermal character of the spectrum.Comment: 17 pages. RevTe

The rationale and design of the perindopril genetic association study (PERGENE): A pharmacogenetic analysis of angiotensin-converting enzyme inhibitor therapy in patients with stable coronary artery disease

Background: Angiotensin-converting enzyme (ACE) inhibitors reduce clinical symptoms and improve outcome in patients with hypertension, heart failure, and stable coronary artery disease (CAD) and are among the most frequently used drugs in these patient groups. For hypertension, treatment is guided by the level of blood pressure. In the secondary prevention setting, there are no means of guiding therapy. Prior attempts to target ACE-inhibitors to those patients that are most likely to benefit have not been successful, mainly due to the consistency in the treatment effect in clinical subgroups. Still, for prolonged prophylactic treatment with ACE-inhibitors it would be best to target treatment to only those patients most likely to benefit, which would considerably lower the number needed to treat and increase cost-effectiveness. A new approach for such "tailored-therapy" may be to integrate information on the genetic variation between patients. Until now, pharmacogenetic research of the efficacy of ACE-inhibitor therapy in CAD patients is still in a preliminary stage. Methods: The PERindopril GENEtic association study (PERGENE) is a substudy of the EUROPA trial, a randomized double-blind placebo-controlled multicentre clinical trial which demonstrated a beneficial effect of the ACE-inhibitor perindopril in reducing cardiovascular morbidity and mortality in 12.218 patients with stable coronary artery disease (mean follow-up 4.2 years). Blood tubes were received from patients at the beginning of the EUROPA trial and buffy coats were stored at -40°C at the central core laboratory. Candidate genes were selected in the renin-angiotensin-system and bradykinin pathways. Polymorphisms were selected based on haplotype tagging principles using the HapMap genome project, Seattle and other up-to-date genetic database platforms to comprehensively cover all common genetic variation within the genes. Selection also took into consideration the functionality of SNP's, location within the gene (promoter) and existing relevant literature. The main outcome measure of PERGENE is the effect of genetic factors on the treatment benefit with ACE-inhibitors. The size of this pharmacogenetic substudy allows detection with a statistical power of 98% to detect a difference in hazard ratios (treatment effect) of 20% between genotypes with minor allele frequency of 0.20 (two-sided alpha 0.05). Conclusion: The PERGENE study is a large cardiovascular pharmacogenetic study aimed to assess the feasibility of pharmacogenetic profiling of the treatment effect of ACE-inhibitor use with the perspective to individualize treatment in patients with stable coronary artery disease

Massless geodesics in AdS5×Y(p,q)AdS_5\times Y(p,q) as a superintegrable system

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusion

Disruption of Ant-Aphid Mutualism in Canopy Enhances the Abundance of Beetles on the Forest Floor

Ant-aphid mutualism is known to play a key role in the structure of the arthropod community in the tree canopy, but its possible ecological effects for the forest floor are unknown. We hypothesized that aphids in the canopy can increase the abundance of ants on the forest floor, thus intensifying the impacts of ants on other arthropods on the forest floor. We tested this hypothesis in a deciduous temperate forest in Beijing, China. We excluded the aphid-tending ants Lasius fuliginosus from the canopy using plots of varying sizes, and monitored the change in the abundance of ants and other arthropods on the forest floor in the treated and control plots. We also surveyed the abundance of ants and other arthropods on the forest floor to explore the relationships between ants and other arthropods in the field. Through a three-year experimental study, we found that the exclusion of ants from the canopy significantly decreased the abundance of ants on the forest floor, but increased the abundance of beetles, although the effect was only significant in the large ant-exclusion plot (80*60 m). The field survey showed that the abundance of both beetles and spiders was negatively related to the abundance of ants. These results suggest that aphids located in the tree canopy have indirect negative effects on beetles by enhancing the ant abundance on the forest floor. Considering that most of the beetles in our study are important predators, the ant-aphid mutualism can have further trophic cascading effects on the forest floor food web

Entanglement Dynamics between Inertial and Non-uniformly Accelerated Detectors

We study the time-dependence of quantum entanglement between two Unruh-DeWitt detectors, one at rest in a Minkowski frame, the other non-uniformly accelerated in some specified way. The two detectors each couple to a scalar quantum field but do not interact directly. The primary challenge in problems involving non-uniformly accelerated detectors arises from the fact that an event horizon is absent and the Unruh temperature is ill-defined. By numerical calculation we demonstrate that the correlators of the accelerated detector in the weak coupling limit behaves like those of an oscillator in a bath of time-varying "temperature" proportional to the instantaneous proper acceleration of the detector, with oscillatory modifications due to non-adiabatic effects. We find that in this setup the acceleration of the detector in effect slows down the disentanglement process in Minkowski time due to the time dilation in that moving detectorComment: 20 pages, 15 figures; References added; More analysis given in Appendix C; Typos correcte

Ki-67 expression predicts locoregional recurrence in stage I oral tongue carcinoma

Oral tongue squamous cell carcinoma (OTSCC) is an aggressive cancer associated with poor prognosis. Methods for determining the aggressiveness of OTSCC from analysis of the primary tumour specimen are thus highly desirable. We investigated whether genomic instability and proliferative activity (by means of Ki-67 activity) could be of clinical use for prediction of locoregional recurrence in 76 pretreatment OTSCC paraffin samples (stage I, n=22; stage II, n=33; stage III, n=8; stage IV, n=13). Eleven surgical tumour specimens were also analysed for remnants of proliferative activity after preoperative radiotherapy. Ninety-seven percent of cases (n=72) were characterised as being aneuploid as measured by means of image cytometry. Preoperative radiotherapy (50–68 Gy) resulted in significant reduction of proliferative activity in all patients for which post-treatment biopsies were available (P-value=0.001). Proliferative activity was not associated with response to radiation in stage II patients. However, we report a significant correlation between high proliferation rates and locoregional recurrences in stage I OTSCC patients (P-value=0.028). High-proliferative activity is thus related to an elevated risk of recurrence after surgery alone. We therefore conclude that Ki-67 expression level is a potentially useful clinical marker for predicting recurrence in surgically treated stage I OTSCC

Parents' psychological adjustment in families of children with Spina Bifida: a meta-analysis

BACKGROUND: Spina Bifida (SB) is the second most common birth defect worldwide. Since the chances of survival in children with severe SB-forms have increased, medical care has shifted its emphasis from life-saving interventions to fostering the quality of life for these children and their families. Little is known, however, about the impact of SB on family adjustment. Reviewers have struggled to synthesize the few contradictory studies available. In this systematic review a new attempt was made to summarize the findings by using meta-analysis and by delimiting the scope of review to one concept of family adjustment: Parents' psychological adjustment. The questions addressed were: (a) do parents of children with SB have more psychological distress than controls? (b) do mothers and fathers differ? and (c) which factors correlate with variations in psychological adjustment? METHODS: PsycInfo, Medline, and reference lists were scanned. Thirty-three relevant studies were identified of which 15 were eligible for meta-analysis. RESULTS: SB had a negative medium-large effect on parents' psychological adjustment. The effect was more heterogeneous for mothers than for fathers. In the reviewed studies child factors (age, conduct problems, emotional problems, and mental retardation), parent factors (SES, hope, appraised stress, coping, and parenting competence), family factors (family income, partner relationship, and family climate), and environmental factors (social support) were found to be associated with variations in parents' psychological adjustment. CONCLUSION: Meta-analysis proved to be helpful in organizing studies. Clinical implications indicate a need to be especially alert to psychological suffering in mothers of children with SB. Future research should increase sample sizes through multi-center collaborations