The realization of input-output maps using bialgebras

The theory of bialgebras is used to prove a state space realization theorem for input/output maps of dynamical systems. This approach allows for the consideration of the classical results of Fliess and more recent results on realizations involving families of trees. Two examples of applications of the theorum are given

Recovery priorities in degenerative cervical myelopathy: a cross-sectional survey of an international, online community of patients.

OBJECTIVES: To establish the recovery priorities of individuals suffering with degenerative cervical myelopathy (DCM). DESIGN: A cross-sectional, observational study. SETTING: Patients from across the world with a diagnosis of DCM accessed the survey over an 18-month period on Myelopathy.org, an international myelopathy charity. PARTICIPANTS: 481 individuals suffering from DCM completed the online survey fully. MAIN OUTCOME MEASURES: Functional recovery domains were established through qualitative interviews and a consensus process. Individuals were asked about their disease characteristics, including limb pain (Visual Analogue Scale) and functional disability (patient-derived version of the modified Japanese Orthopaedic Association score). Individuals ranked recovery domains (arm and hand function, walking, upper body/trunk function, sexual function, elimination of pain, sensation and bladder/bowel function) in order of priority. Priorities were analysed as the modal first priority and mean ranking. The influence of demographics on selection was analysed, with significance p<0.05. RESULTS: Of 659 survey responses obtained, 481 were complete. Overall, pain was the most popular recovery priority (39.9%) of respondents, followed by walking (20.2%), sensation (11.9%) and arm and hand function (11.5%). Sexual function (5.7%), bladder and bowel (3.7%) and trunk function (3.5%) were chosen less frequently. When considering the average ranking of symptoms, while pain remained the priority (2.6±2.0), this was closely followed by walking (2.9±1.7) and arm/hand function (3.0±1.4). Sensation ranked lower (4.3±2.1). With respect to disease characteristics, overall pain remained the recovery priority, with the exception of patients with greater walking impairment (p<0.005) who prioritised walking, even among patients with lower pain scores. CONCLUSIONS: This is the first study investigating patient priorities in DCM. The patient priorities reported provide an important framework for future research and will help to ensure that it is aligned with patient needs.NIHR Welcome Trus

Exploring CP Violation through Correlations in B --> pi K, B_d --> pi^+pi^-, B_s --> K^+K^- Observable Space

We investigate allowed regions in observable space of B --> pi K, B_d --> pi^+pi^- and B_s --> K^+K^- decays, characterizing these modes in the Standard Model. After a discussion of a new kind of contour plots for the $B\to\pi K$ system, we focus on the mixing- induced and direct CP asymmetries of the decays B_d --> pi^+pi^- and B_s--> K^+K^-. Using experimental information on the CP-averaged B_d --> pi^{+/-}K^{+/-} and B_d --> pi^+pi^- branching ratios, the relevant hadronic penguin parameters can be constrained,implying certain allowed regions in observable space. In the case of B_d --> pi^+pi^-, an interesting situation arises now in view of the recent B-factory measurements of CP violation in this channel, allowing us to obtain new constraints on the CKM angle gamma as a function of the B^0_d--\bar{B^0_d} mixing phase phi_d=2beta, which is fixed through A_{CP}^{mix}(B_d --> J/psi K_S) up to a twofold ambiguity. If we assume that A_{CP}^{mix}(B_d --> pi^+pi^-) is positive, as indicated by recent Belle data, and that phi_d is in agreement with the ``indirect'' fits of the unitarity triangle, also the corresponding values for gamma around 60 degrees can be accommodated. On the other hand, for the second solution of phi_d, we obtain a gap around gamma ~ 60 degrees. The allowed region in the space of A_{CP}^{mix}(B_s --> K^+K^-) and A_{CP}^{dir}(B_s --> K^+K^-) is very constrained in the Standard Model, thereby providing a narrow target range for run II of the Tevatron and the experiments of the LHC era.Comment: 34 pages, LaTeX, 12 figures. More detailed introduction and a few Comments added, conclusions unchanged. To appear in Phys. Rev.

CP violating polarizations in semileptonic heavy meson decays

We study the $T$-violating lepton transverse polarization ($P^\perp_l$) in three body semileptonic heavy meson decays to pseudoscalar mesons and to vector mesons. We calculate these polarizations in the heavy quark effective limit, which simplifies the expressions considerably. After examining constraints from $CP$ conserving (including $b \rightarrow s \gamma$) and $CP$ violating processes, we find that in $B$ decays, $P^\perp$ of the muon in multi-Higgs doublet models can be of order $10\%$, while $P^\perp$ of the $\tau$ can even approach unity. In contrast, $P^\perp_\mu$ in $D$ decays is at most 1.5\%. We discuss possibilities for detection of $P^\perp_l$ at current and future $B$ factories. We also show that $P^\perp_l$ in decays to vector mesons, unlike in decays to pseudoscalars, can get contributions from left-right models. Unfortunately, $P^\perp_l$ in that case is proportional to $W_L$-$W_R$ mixing, and is thus small.Comment: 32pp plain LATEX, 3 figs (by EMAIL request), TRI-PP-94-1