Ascending sequences in permutations

AbstractThe problem of the number p(n , r), (1 ⩽r⩽n), of permutations on the set {1,…,n} with longest ascending subsequence of given length r is considered. By placing further restrictions on the ascending subsequence, combinatorial identities are obtained which allow the explicit calculation of p(n , r) in some cases

The joint law of the extrema, final value and signature of a stopped random walk

A complete characterization of the possible joint distributions of the maximum and terminal value of uniformly integrable martingale has been known for some time, and the aim of this paper is to establish a similar characterization for continuous martingales of the joint law of the minimum, final value, and maximum, along with the direction of the final excursion. We solve this problem completely for the discrete analogue, that of a simple symmetric random walk stopped at some almost-surely finite stopping time. This characterization leads to robust hedging strategies for derivatives whose value depends on the maximum, minimum and final values of the underlying asset

Coloring translates and homothets of a convex body

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in \RR^n.Comment: 11 pages, 2 figure

Translation to practice: a randomised controlled study of an evidenced based booklet targeted at breast care nurses in the United Kingdom

BACKGROUND: In the United Kingdom (UK), it was documented that a problem of knowledge transfer existed within the speciality of breast-cancer care, thus depriving patients of receiving optimal care. Despite increasingly robust research evidence indicating recommendation of whole body exercise for people affected by breast cancer, commensurate changes to practice were not noted amongst breast-care nurses (BCNs). AIM: To evaluate the effect of a targeted booklet, Exercise and Breast Cancer: A Booklet for Breast-Care Nurses, on changes in knowledge, reported practice, and attitudes of BCNs in the UK. METHOD: A prospective, experimental approach was used for designing a pre- and post-test randomised controlled study. Comparisons of knowledge, reported practice, and attitudes based on responses to a questionnaire were made at two time-points in two groups of BCNs (control and experimental). The unit of randomisation and analysis was hospital clusters of BCNs. The sample comprised 92 nurses from 62 hospitals. Analysis consisted of descriptive statistics and clustered regression techniques: clustered logistic regression for knowledge items, clustered linear regression for knowledge scores, ologit for attitude and reported practice items, and clustered multiple regression for paired and multiple variable analysis. RESULTS: A statistically significant increase in knowledge and changes in reported practice and attitudes were found. Robust variables affecting knowledge acquisition were: promotion of health, promotion of exercise, and understanding how exercise can reduce cancer-related fatigue. DISCUSSION: The study has shown that evidence-based printed material, such as an information booklet, can be used as an effective research dissemination method when developed for needs, values, and context of a target audience. CONCLUSIONS: This practical approach to research dissemination could be replicated and applied to other groups of nurses.</p

Stellar evolution and modelling stars

In this chapter I give an overall description of the structure and evolution of stars of different masses, and review the main ingredients included in state-of-the-art calculations aiming at reproducing observational features. I give particular emphasis to processes where large uncertainties still exist as they have strong impact on stellar properties derived from large compilations of tracks and isochrones, and are therefore of fundamental importance in many fields of astrophysics.Comment: Lecture presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201

Standards for plant synthetic biology: A common syntax for exchange of DNA parts

© 2015 New Phytologist Trust. Inventors in the field of mechanical and electronic engineering can access multitudes of components and, thanks to standardization, parts from different manufacturers can be used in combination with each other. The introduction of BioBrick standards for the assembly of characterized DNA sequences was a landmark in microbial engineering, shaping the field of synthetic biology. Here, we describe a standard for Type IIS restriction endonuclease-mediated assembly, defining a common syntax of 12 fusion sites to enable the facile assembly of eukaryotic transcriptional units. This standard has been developed and agreed by representatives and leaders of the international plant science and synthetic biology communities, including inventors, developers and adopters of Type IIS cloning methods. Our vision is of an extensive catalogue of standardized, characterized DNA parts that will accelerate plant bioengineering

First observation of the decay Bˉs0→D0K∗0\bar{B}^0_s \to D^0 K^{*0} and a measurement of the ratio of branching fractions B(Bˉs0→D0K∗0)B(Bˉ0→D0ρ0)\frac{{\cal B}(\bar{B}^0_s \to D^0 K^{*0})}{{\cal B}(\bar{B}^0 \to D^0 \rho^0)}

The first observation of the decay $\bar{B}^0_s \to D^0 K^{*0}$ using $pp$ data collected by the LHCb detector at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 36 pb$^{-1}$, is reported. A signal of $34.4 \pm 6.8$ events is obtained and the absence of signal is rejected with a statistical significance of more than nine standard deviations. The $\bar{B}^0_s \to D^0 K^{*0}$ branching fraction is measured relative to that of $\bar{B}^0 \to D^0 \rho^0$: $\frac{{\cal B}(\bar{B}^0_s \to D^0 K^{*0})}{{\cal B}(\bar{B}^0 \to D^0 \rho^0)} = 1.48 \pm 0.34 \pm 0.15 \pm 0.12$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $B^0$ and $B^0_s$ hadronisation fractions.Comment: 10 pages, 3 figures, submitted to Phys. Lett. B; ISSN 0370-269

Maximum Likelihood Analysis of Low Energy CDMS II Germanium Data

We report on the results of a search for a Weakly Interacting Massive Particle (WIMP) signal in low-energy data of the Cryogenic Dark Matter Search experiment using a maximum likelihood analysis. A background model is constructed using geant4 to simulate the surface-event background from Pb210 decay-chain events, while using independent calibration data to model the gamma background. Fitting this background model to the data results in no statistically significant WIMP component. In addition, we perform fits using an analytic ad hoc background model proposed by Collar and Fields, who claimed to find a large excess of signal-like events in our data. We confirm the strong preference for a signal hypothesis in their analysis under these assumptions, but excesses are observed in both single- and multiple-scatter events, which implies the signal is not caused by WIMPs, but rather reflects the inadequacy of their background model