Stationary Random Fields on the Unitary Dual of a Compact Group

We generalise the notion of wide-sense stationarity from sequences of complex-valued random variables indexed by the integers, to fields of random variables that are labelled by elements of the unitary dual of a compact group. The covariance is positive definite, and so it is the Fourier transform of a finite central measure (the spectral measure of the field) on the group. Analogues of the Cramer and Kolmogorov theorems are extended to this framework. White noise makes sense in this context and so, for some classes of group, we can construct time series and investigate their stationarity. Finally we indicate how these ideas fit into the general theory of stationary random fields on hypergroups

Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method

The newly developed nonadiabatic method based on the coupled-channel Schroedinger equation with Gamow states is used to study the phenomenon of proton radioactivity. The new method, adopting the weak coupling regime of the particle-plus-rotor model, allows for the inclusion of excitations in the daughter nucleus. This can lead to rather different predictions for lifetimes and branching ratios as compared to the standard adiabatic approximation corresponding to the strong coupling scheme. Calculations are performed for several experimentally seen, non-spherical nuclei beyond the proton dripline. By comparing theory and experiment, we are able to characterize the angular momentum content of the observed narrow resonance.Comment: 12 pages including 10 figure

Role of dynamical particle-vibration coupling in reconciliation of the d3/2d_{3/2} puzzle for spherical proton emitters

It has been observed that decay rate for proton emission from $d_{3/2}$ single particle state is systematically quenched compared with the prediction of a one dimensional potential model although the same model successfully accounts for measured decay rates from $s_{1/2}$ and $h_{11/2}$ states. We reconcile this discrepancy by solving coupled-channels equations, taking into account couplings between the proton motion and vibrational excitations of a daughter nucleus. We apply the formalism to proton emitting nuclei $^{160,161}$Re to show that there is a certain range of parameter set of the excitation energy and the dynamical deformation parameter for the quadrupole phonon excitation which reproduces simultaneously the experimental decay rates from the 2$d_{3/2}$, 3$s_{1/2}$ and 1$h_{11/2}$ states in these nuclei.Comment: RevTex, 12 pages, 4 eps figure

Superprocesses as models for information dissemination in the Future Internet

Future Internet will be composed by a tremendous number of potentially interconnected people and devices, offering a variety of services, applications and communication opportunities. In particular, short-range wireless communications, which are available on almost all portable devices, will enable the formation of the largest cloud of interconnected, smart computing devices mankind has ever dreamed about: the Proximate Internet. In this paper, we consider superprocesses, more specifically super Brownian motion, as a suitable mathematical model to analyse a basic problem of information dissemination arising in the context of Proximate Internet. The proposed model provides a promising analytical framework to both study theoretical properties related to the information dissemination process and to devise efficient and reliable simulation schemes for very large systems

AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

Decay properties of the new isotopes 172Hg and 173Hg

The α decays of the two neutron-deficient nuclei 172Hg and 173Hg were observed for the first time using the 78Kr(96Ru,2n) and 80Kr(96Ru,3n) reactions, respectively. The reaction products were dispersed according to their mass-to-charge state ratios in the Argonne Fragment Mass Analyzer and implanted in a double-sided silicon strip detector, where their subsequent decays were studied using spatial and time correlations between implants and decays. A half-life of 250(+350-90) μs and an energy of 7350(12) keV were deduced for the α decay of 172Hg. In 173Hg the half-life was measured to be 0.93(+0.57-0.26) ms and the corresponding energy is 7211(11) keV. In addition, the half-life and energy of the α decay of 174Hg were measured more precisely. The reduced widths deduced for these Hg isotopes indicate that the observed decays correspond to unhindered Δl = 0 transitions. The α-decay Q values are compared with the values calculated using mass tables by Möller and Nix, and by Liran and Zeldes. The latter mass tables show better agreement with the data

Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009

Democracy, emancipation and widening participation in the UK: changing the ‘distribution of the sensible’

The broad concern of this paper is how the relationship between education, democracy and emancipation might be conceived. This theme is explored through examining the contribution of a Rancierian conception of emancipation and democracy to rethinking widening participation in higher education. Following Ranciere, it is argued that taking equality as a starting point in higher education, rather than as a goal to be achieved through education, disrupts a prevailing logic of education as necessarily providing a pathway to emancipation. From this view the pedagogic practices of explication and mastery, which Ranciere argues work to separate academic reason and practical reason, need no longer be understood as the only way to be academic. It is proposed that this ‘redistribution of the sensible’ enables higher education to be conceived in ways other than available in ongoing educational debates and enables a move beyond an assimilation/recognition binary. Instead, widening participation can be understood as a space for opening up to experience, transformation and change for both academics and students. From this view, democracy is enacted in the here and now, rather than a goal for the future, and practice can be understood as a site for change

Post-acute COVID-19 neuropsychiatric symptoms are not associated with ongoing nervous system injury

A proportion of patients infected with severe acute respiratory syndrome coronavirus 2 experience a range of neuropsychiatric symptoms months after infection, including cognitive deficits, depression and anxiety. The mechanisms underpinning such symptoms remain elusive. Recent research has demonstrated that nervous system injury can occur during COVID-19. Whether ongoing neural injury in the months after COVID-19 accounts for the ongoing or emergent neuropsychiatric symptoms is unclear. Within a large prospective cohort study of adult survivors who were hospitalized for severe acute respiratory syndrome coronavirus 2 infection, we analysed plasma markers of nervous system injury and astrocytic activation, measured 6 months post-infection: neurofilament light, glial fibrillary acidic protein and total tau protein. We assessed whether these markers were associated with the severity of the acute COVID-19 illness and with post-acute neuropsychiatric symptoms (as measured by the Patient Health Questionnaire for depression, the General Anxiety Disorder assessment for anxiety, the Montreal Cognitive Assessment for objective cognitive deficit and the cognitive items of the Patient Symptom Questionnaire for subjective cognitive deficit) at 6 months and 1 year post-hospital discharge from COVID-19. No robust associations were found between markers of nervous system injury and severity of acute COVID-19 (except for an association of small effect size between duration of admission and neurofilament light) nor with post-acute neuropsychiatric symptoms. These results suggest that ongoing neuropsychiatric symptoms are not due to ongoing neural injury