Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Is pseudophakia a risk factor for neovascular age-related macular degeneration?

PURPOSE: To examine the possible association between pseudophakia and neovascular age-related macular degeneration (AMD). METHODS: Reports of all patients undergoing fluorescein angiography in the authors' department over a 6-year period were retrospectively reviewed. Four hundred ninety-nine patients with recent onset of neovascular AMD in one eye and early age-related maculopathy (ARM) in the fellow eye were included in the study. Lens status (phakic or pseudophakic) in both eyes at the time of onset of neovascular AMD and the time between cataract surgeries (if performed) and onset of neovascular AMD were determined. RESULTS: There was no significant difference in lens status between eyes with neovascular AMD and fellow eyes with early ARM (115/499 [23.0%] vs. 112/499 [22.4%] pseudophakic; P = 0.88, odds ratio 1.035, 95% CI 0.770-1.391). Subgroup analysis revealed no difference between the groups with large drusen, small drusen, or pigmentary changes only (respectively, 20.3% vs. 19.6% pseudophakic, P = 0.92; 20.5% vs. 23.3% pseudophakic, P = 0.84; 33.3% vs. 31.7% pseudophakic, P = 1.0). Pseudophakic eyes with neovascular AMD had not been pseudophakic for a significantly longer period at the time of onset of neovascular AMD than their pseudophakic fellow eyes at the same time point (225.9 +/- 170.4 vs. 209.9 +/- 158.2 weeks, P = 0.27). CONCLUSIONS: The results do not support the hypothesis that pseudophakia is a major risk factor for the development of neovascular AMD.

Decompressive hemicraniectomy in subarachnoid haemorrhage: the influence of infarction, haemorrhage and brain swelling

OBJECTIVE: To analyse decompressive hemicraniectomy (DHC) in patients with aneurysmal subarachnoid haemorrhage (SAH) with regard to infarction, haemorrhage or brain swelling. METHODS: DHC was performed in 43 of 787 patients with SAH. Patients were stratified according to (1) primary brain swelling without and (2) with additional intracerebral haematoma, (3) secondary brain swelling without rebleeding or infarcts and (4) with infarcts or (5) with rebleeding. Outcome was assessed according to the modified Rankin scale at 6 months RESULTS: Overall, 36 of 43 patients (83.7%) with DHC and 241 of 744 patients (32.4%) without DHC have been of a poor grade on admission (World Federation of Neurological Societies grading 4-5; p<0.0001). Favourable outcome was achieved in 11 of 43 (25.6%) patients with DHC. There was no difference in favourable outcome after primary (25%) versus secondary (26.1%) DHC (p = 1.0). Subgroup analysis (brain swelling vs bleeding vs infarcts) revealed no difference in the rate of favourable outcome. In a multivariate analysis, acute hydrocephalus (p = 0.02) and clinical herniation (p = 0.03) were significantly associated with unfavourable outcome. CONCLUSIONS: We conclude that primary and secondary hemicraniectomy may be warranted, irrespective of the underlying aetiology-infarction, haemorrhage or brain swelling. The time from onset of intractable ICP to DHC seems to be crucial, rather than the time from SAH to DHC.

On restricted families of projections in ℝ3

We study projections onto non-degenerate one-dimensional families of lines and planes in R 3 . Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most 12 -dimensional sets [Math Processing Error] is typically preserved under one-dimensional families of projections onto lines. We improve the result by an ε , proving that if [Math Processing Error], then the packing dimension of the projections is almost surely at least [Math Processing Error]. For projections onto planes, we obtain a similar bound, with the threshold 12 replaced by 1 . In the special case of self-similar sets [Math Processing Error] without rotations, we obtain a full Marstrand-type projection theorem for 1-parameter families of projections onto lines. The [Math Processing Error] case of the result follows from recent work of M. Hochman, but the [Math Processing Error] part is new: with this assumption, we prove that the projections have positive length almost surely.

Search for pair-produced third-generation squarks decaying via charm quarks or in compressed supersymmetric scenarios in pp collisions at √s=8 TeV with the ATLAS detector

Results of a search for supersymmetry via direct production of third-generation squarks are reported, using 20.3  fb −1 of proton-proton collision data at √s =8  TeV recorded by the ATLAS experiment at the LHC in 2012. Two different analysis strategies based on monojetlike and c -tagged event selections are carried out to optimize the sensitivity for direct top squark-pair production in the decay channel to a charm quark and the lightest neutralino (t 1 →c+χ ˜ 0 1 ) across the top squark–neutralino mass parameter space. No excess above the Standard Model background expectation is observed. The results are interpreted in the context of direct pair production of top squarks and presented in terms of exclusion limits in the m ˜t 1, m ˜ X0 1 ) parameter space. A top squark of mass up to about 240 GeV is excluded at 95% confidence level for arbitrary neutralino masses, within the kinematic boundaries. Top squark masses up to 270 GeV are excluded for a neutralino mass of 200 GeV. In a scenario where the top squark and the lightest neutralino are nearly degenerate in mass, top squark masses up to 260 GeV are excluded. The results from the monojetlike analysis are also interpreted in terms of compressed scenarios for top squark-pair production in the decay channel t ˜ 1 →b+ff ′ +χ ˜ 0 1 and sbottom pair production with b ˜ 1 →b+χ ˜ 0 1 , leading to a similar exclusion for nearly mass-degenerate third-generation squarks and the lightest neutralino. The results in this paper significantly extend previous results at colliders.

Herbal medicines:physician's recommendation and clinical evaluation of St.John's Wort for depression

Why some physicians recommend herbal medicines while others do not is not well understood. We undertook a survey designed to identify factors, which predict recommendation of herbal medicines by physicians in Malaysia. About a third (206 out of 626) of the physicians working at the University of Malaya Medical Centre ' were interviewed face-to-face, using a structured questionnaire. Physicians were asked about their personal use of, recommendation of, perceived interest in and, usefulness and safety of herbal medicines. Using logistic regression modelling we identified personal use, general interest, interest in receiving training, race and higher level of medical training as significant predictors of recommendation. St. John's wort is one of the most widely used herbal remedies. It is also probably the most widely evaluated herbal remedy with no fewer than 57 randomised controlled trials. Evidence from the depression trials suggests that St. John's wort is more effective than placebo while its comparative efficacy to conventional antidepressants is not well established. We updated previous meta-analyses of St. John's wort, described the characteristics of the included trials, applied methods of data imputation and transformation for incomplete trial data and examined sources of heterogeneity in the design and results of those trials. Thirty randomised controlled trials, which were heterogeneous in design, were identified. Our meta-analysis showed that St. John's wort was significantly more effective than placebo [pooled RR 1.90 (1.54-2.35)] and [Pooled WMD 4.09 (2.33 to 5.84)]. However, the remedy was similar to conventional antidepressant in its efficacy [Pooled RR I. 0 I (0.93 -1.10)] and [Pooled WMD 0.18 (- 0.66 to 1.02). Subgroup analyses of the placebo-controlled trials suggested that use of different diagnostic classifications at the inclusion stage led to different estimates of effect. Similarly a significant difference in the estimates of efficacy was observed when trials were categorised according to length of follow-up. Confounding between the variables, diagnostic classification and length of trial was shown by loglinear analysis. Despite extensive study, there is still no consensus on how effective St. lohn's wort is in depression. However, most experts would agree that it has some effect. Our meta-analysis highlights the problems associated with the clinical evaluation of herbal medicines when the active ingredients are poorly defined or unknown. The problem is compounded when the target disease (e.g. depression) is also difficult to define and different instruments are available to diagnose and evaluate it.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Subgroup-specific structural variation across 1,000 medulloblastoma genomes.

Medulloblastoma, the most common malignant paediatric brain tumour, is currently treated with nonspecific cytotoxic therapies including surgery, whole-brain radiation, and aggressive chemotherapy. As medulloblastoma exhibits marked intertumoural heterogeneity, with at least four distinct molecular variants, previous attempts to identify targets for therapy have been underpowered because of small samples sizes. Here we report somatic copy number aberrations (SCNAs) in 1,087 unique medulloblastomas. SCNAs are common in medulloblastoma, and are predominantly subgroup-enriched. The most common region of focal copy number gain is a tandem duplication of SNCAIP, a gene associated with Parkinson's disease, which is exquisitely restricted to Group 4α. Recurrent translocations of PVT1, including PVT1-MYC and PVT1-NDRG1, that arise through chromothripsis are restricted to Group 3. Numerous targetable SCNAs, including recurrent events targeting TGF-β signalling in Group 3, and NF-κB signalling in Group 4, suggest future avenues for rational, targeted therapy.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

Subgroup-specific structural variation across 1,000 medulloblastoma genomes

Medulloblastoma, the most common malignant paediatric brain tumour, is currently treated with nonspecific cytotoxic therapies including surgery, whole-brain radiation, and aggressive chemotherapy. As medulloblastoma exhibits marked intertumoural heterogeneity, with at least four distinct molecular variants, previous attempts to identify targets for therapy have been underpowered because of small samples sizes. Here we report somatic copy number aberrations (SCNAs) in 1,087 unique medulloblastomas. SCNAs are common in medulloblastoma, and are predominantly subgroup-enriched. The most common region of focal copy number gain is a tandem duplication of SNCAIP, a gene associated with Parkinson's disease, which is exquisitely restricted to Group 4 alpha. Recurrent translocations of PVT1, including PVT1-MYC and PVT1-NDRG1, that arise through chromothripsis are restricted to Group 3. Numerous targetable SCNAs, including recurrent events targeting TGF-beta signalling in Group 3, and NF-kappa B signalling in Group 4, suggest future avenues for rational, targeted therapy.