Pattern avoidance in forests of binary shrubs

We investigate pattern avoidance in permutations satisfying some additional restrictions. These are naturally considered in terms of avoiding patterns in linear extensions of certain forest-like partially ordered sets, which we call binary shrub forests. In this context, we enumerate forests avoiding patterns of length three. In four of the five non-equivalent cases, we present explicit enumerations by exhibiting bijections with certain lattice paths bounded above by the line y = lx, for some l in Q+, one of these being the celebrated Duchon’s club paths with l = 2/3. In the remaining case, we use the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate

Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample Breakdown Point, we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points.Comment: 21 pages, 4 figure

Using technology to deliver cancer follow-up : a systematic review

Peer reviewedPublisher PD

Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory

The gluon tree amplitudes of open twistor string theory, defined as contour integrals over the ACCK link variables, are shown to satisfy the BCFW relations, thus confirming that they coincide with the corresponding amplitudes in gauge field theory. In this approach, the integration contours are specified as encircling the zeros of certain constraint functions that force the appropriate relation between the link variables and the twistor string world-sheet variables. To do this, methods for calculating the tree amplitudes using link variables are developed further including diagrammatic methods for organizing and performing the calculations.Comment: 38 page

Options for early breast cancer follow-up in primary and secondary care : a systematic review

Background Both incidence of breast cancer and survival have increased in recent years and there is a need to review follow up strategies. This study aims to assess the evidence for benefits of follow-up in different settings for women who have had treatment for early breast cancer. Method A systematic review to identify key criteria for follow up and then address research questions. Key criteria were: 1) Risk of second breast cancer over time - incidence compared to general population. 2) Incidence and method of detection of local recurrence and second ipsi and contra-lateral breast cancer. 3) Level 1–4 evidence of the benefits of hospital or alternative setting follow-up for survival and well-being. Data sources to identify criteria were MEDLINE, EMBASE, AMED, CINAHL, PSYCHINFO, ZETOC, Health Management Information Consortium, Science Direct. For the systematic review to address research questions searches were performed using MEDLINE (2011). Studies included were population studies using cancer registry data for incidence of new cancers, cohort studies with long term follow up for recurrence and detection of new primaries and RCTs not restricted to special populations for trials of alternative follow up and lifestyle interventions. Results Women who have had breast cancer have an increased risk of a second primary breast cancer for at least 20 years compared to the general population. Mammographically detected local recurrences or those detected by women themselves gave better survival than those detected by clinical examination. Follow up in alternative settings to the specialist clinic is acceptable to women but trials are underpowered for survival. Conclusions Long term support, surveillance mammography and fast access to medical treatment at point of need may be better than hospital based surveillance limited to five years but further large, randomised controlled trials are needed

Unexpected Consequences: Women’s experiences of a self-hypnosis intervention to help with pain relief during labour.

Background Self-hypnosis is becoming increasingly popular as a means of labour pain management. Previous studies have produced mixed results. There are very few data on women’s views and experiences of using hypnosis in this context. As part of a randomized controlled trial of self-hypnosis for intra-partum pain relief (the SHIP Trial) we conducted qualitative interviews with women randomized to the intervention arm to explore their views and experiences of using self-hypnosis during labour and birth. Methods Participants were randomly selected from the intervention arm of the study, which consisted of two antenatal self-hypnosis training sessions and a supporting CD that women were encouraged to listen to daily from 32 weeks gestation until the birth of their baby. Those who consented were interviewed in their own homes 8-12 weeks after birth. Following transcription, the interviews were analysed iteratively and emerging concepts were discussed amongst the authors to generate organizing themes. These were then used to develop a principal organizing metaphor or global theme, in a process known as thematic networks analysis. Results Of the 343 women in the intervention group, 48 were invited to interview, and 16 were interviewed over a 12 month period from February 2012 to January 2013. Coding of the data and subsequent analysis revealed a global theme of ‘unexpected consequences’, supported by 5 organising themes, ‘calmness in a climate of fear’, ‘from sceptic to believer’, ‘finding my space’, ‘delays and disappointments’ and ‘personal preferences’. Most respondents reported positive experiences of self-hypnosis and highlighted feelings of calmness, confidence and empowerment. They found the intervention to be beneficial and used a range of novel strategies to personalize their self-hypnosis practice. Occasionally women reported feeling frustrated or disappointed when their relaxed state was misinterpreted by midwives on admission or when their labour and birth experiences did not match their expectations. Conclusion The women in this study generally appreciated antenatal self-hypnosis training and found it to be beneficial during labour and birth. The state of focused relaxation experienced by women using the technique needs to be recognized by providers if the intervention is to be implemented into the maternity service

General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory

We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al.Comment: 30 pages, minor misprints correcte

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study

Background Regional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood. Methods We simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution. Results Wavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms). Conclusion Regional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve

Mechanical testing of a device for subcutaneous internal anterior pelvic ring fixation versus external pelvic ring fixation

BACKGROUND: Although useful in the emergency treatment of pelvic ring injuries, external fixation is associated with pin tract infections, the patient’s limited mobility and a restricted surgical accessibility to the lower abdomen. In this study, the mechanical stability of a subcutaneous internal anterior fixation (SIAF) system is investigated. METHODS: A standard external fixation and a SIAF system were tested on pairs of Polyoxymethylene testing cylinders using a universal testing machine. Each specimen was subjected to a total of 2000 consecutive cyclic loadings at 1 Hz with sinusoidal lateral compression/distraction (+/−50 N) and torque (+/− 0.5 Nm) loading alternating every 200 cycles. Translational and rotational stiffness were determined at 100, 300, 500, 700 and 900 cycles. RESULTS: There was no significant difference in translational stiffness between the SIAF and the standard external fixation when compared at 500 (p = .089), 700 (p = .081), and 900 (p = .266) cycles. Rotational stiffness observed for the SIAF was about 50 percent higher than the standard external fixation at 300 (p = .005), 500 (p = .020), and 900 (p = .005) cycles. No loosening or failure of the rod-pin/rod-screw interfaces was seen. CONCLUSIONS: In comparison with the standard external fixation system, the tested device for subcutaneous internal anterior fixation (SIAF) in vitro has similar translational and superior rotational stiffness