56,546 research outputs found
p-adic Welch Bounds and p-adic Zauner Conjecture
No full textLet be a prime. For , let be the standard -dimensional p-adic Hilbert space. Let and be the p-adic Hilbert space of symmetric m-tensors. We prove the following result. Let be a collection in satisfying (i) for all and (ii) there exists satisfying for all Then
\begin{align}\label{WELCHNONABSTRACT}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{WELCHNONABSTRACT}) as the p-adic version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. Inequality (\ref{WELCHNONABSTRACT}) differs from the non-Archimedean Welch bound obtained recently by M. Krishna as one can not derive one from another. We formulate p-adic Zauner conjecture
p-adic Welch Bounds and p-adic Zauner Conjecture
No full textLet be a prime. For , let be the standard -dimensional p-adic Hilbert space. Let and be the p-adic Hilbert space of symmetric m-tensors. We prove the following result. Let be a collection in satisfying (i) for all and (ii) there exists satisfying for all Then
\begin{align}
(1) \quad \quad \quad \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle τ_j, τ_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (1) as the p-adic version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. Inequality (1) differs from the non-Archimedean Welch bound obtained recently by M. Krishna as one can not derive one from another. We formulate p-adic Zauner conjecture.10 Pages, 0 Figure
Time to full publication of studies of anti-cancer medicines for breast cancer, and the potential for publication bias: a short systematic review
No full textObjectives: To identify the expected delay between publication of conference abstracts and full publication of results from trials of new anti-cancer agents for breast cancer and to identify whether there are any apparent biases in publication and reporting.Data sources: Major electronic databases were searched to identify randomised controlled trials (RCTs) of the selected interventions for the treatment of breast cancer.Review methods: A systematic review was conducted according to standard methods. Data were extracted from the included studies using a predesigned and piloted data extraction template.Results: Six anti-cancer treatments for breast cancer were included in the review: docetaxel, paclitaxel, trastuzumab, gemcitabine, lapatinib and bevacizumab. The literature searches generated 1556 references, from which 71 publications were retrieved and screened for inclusion. Screening identified 41 publications of 18 RCTs with at least one arm of treatment meeting the inclusion criteria for the review. Of the 18 included RCTs, only four publications (from three RCTs) reported the same outcomes in both an abstract and a full publication. Time between the abstract and full publication was 5 months in two cases, 7 months in one case and 19 months in one case (overall mean delay = 9 months). Eleven trials were identified that have not currently published in a full publication the data presented in an abstract or conference proceeding. The duration between publication of the abstracts and the end of August 2007 varied from 3 months to 38 months (mean delay 16.5 months). The longest delays in publication were for trials investigating gemcitabine (38 months) or bevacizumab (33 months). Observational analysis of the published and unpublished trials did not indicate any particular biases in terms of whether positive results were more likely to be fully published than non-significant ones.Conclusions: It was surprising that only three of the 18 relevant RCTs had one or more full papers that reported the same outcome measures (and stage of analysis) as an earlier conference abstract. However, a limitation of this review is the small number of studies included. With a larger sample size than that in the present report, investigation into the effect of publication delay on decision-making might be feasible. Future research should include extension of this work to other anticancer drugs and investigation into the reasons for lengthy delays to full publication noted for some trials
A 2 h periodic variation in the low-mass X-ray binary Ser X-1
No full textSpectroscopy of the low-mass X-ray binary Ser X-1 using the Gran Telescopio Canarias have revealed a ?2 h periodic variability that is present in the three strongest emission lines. We tentatively interpret this variability as due to orbital motion, making it the first indication of the orbital period of Ser X-1. Together with the fact that the emission lines are remarkably narrow, but still resolved, we show that a main-sequence K dwarf together with a canonical 1.4 M? neutron star gives a good description of the system. In this scenario, the most likely place for the emission lines to arise is the accretion disc, instead of a localized region in the binary (such as the irradiated surface or the stream-impact point), and their narrowness is due instead to the low inclination (?10°) of Ser X-1
Extracting Boer-Mulders functions from p+D Drell-Yan processes
No full textWe extract the Boer- Mulders functions of valence and sea quarks in the proton from unpolarized p + D Drell- Yan data measured by the FNAL E866 Collaboration. Using these Boer- Mulders functions, we calculate the cos2 phi asymmetries in unpolarized pp Drell- Yan processes, both for the FNAL E866/ NuSea and the BNL Relativistic Heavy Ion Collider experiments. We also estimate the cos2 phi asymmetries in the unpolarized p (P) over bar Drell- Yan processes at GSI.Astronomy & AstrophysicsPhysics, Particles & FieldsSCI(E)37ARTICLE5null7
Non-Archimedean and p-adic Functional Welch Bounds
No full textWe prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results.
\begin{enumerate}[\upshape(i)]
\item Let be a non-Archimedean (complete) valued field satisfying for all , for all Let be a -dimensional non-Archimedean Banach space over . If is any collection in and is any collection in (dual of )
satisfying for all and the operator , is diagonalizable, then
\begin{align}\label{NONFUNCTIONALWELCH}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds.
\item For a prime , let be the p-adic number field. Let be a -dimensional p-adic Banach space over . If is any collection in and is any collection in (dual of ) satisfying for all and there exists such that for all then
\begin{align}\label{PADICFUNCTIONALWELCH}
\max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }.
\end{align}
We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds.
\end{enumerate}
We formulate non-Archimedean functional and p-adic functional Zauner conjectures
Immunotherapy
No full textA chapter covering metastasis immunotherapy in multi-author volume devoted to all aspects of cancer metastasis
Life of occam-Pi
No full textThis paper considers some questions prompted by a brief review of the history of computing. Why is programming so hard? Why is concurrency considered an “advanced” subject? What’s the matter with Objects? Where did all the Maths go? In searching for answers, the paper looks at some concerns over fundamental ideas within object orientation (as represented by modern programming languages), before focussing on the concurrency model of communicating processes and its particular expression in the occam family of languages. In that focus, it looks at the history of occam, its underlying philosophy (Ockham’s Razor), its semantic foundation on Hoare’s CSP, its principles of process oriented design and its development over almost three decades into occam-? (which blends in the concurrency dynamics of Milner’s ?-calculus). Also presented will be an urgent need for rationalisation – occam-? is an experiment that has demonstrated significant results, but now needs time to be spent on careful review and implementing the conclusions of that review. Finally, the future is considered. In particular, is there a future
50 Years of the Golomb–Welch Conjecture
No full textSince 1968, when the Golomb–Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb–Welch conjecture. Further, new results on Golomb–Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given
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