Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

Acceptability and feasibility of an isometric resistance exercise program for abdominal cancer surgery: An embedded qualitative study

Although it is recognized in the early stages of cancer recovery that changes in lifestyle including increases in physical activity improves physical function, there are no clear findings whether low versus moderate intensity activity or home or gym exercise offer optimal benefit. Isometric-resistance exercises can be carried out with very little equipment and space and can be performed while patients are bed-bound in hospital or at home. This embedded qualitative study, based in an English hospital trust providing specialist cancer care, was undertaken as a component of a feasibility trial to evaluate the acceptability and feasibility of an isometric-resistance exercise program and explore the suitability of functional assessments by drawing from the experiences of abdominal cancer patients following surgery. Telephone interviews were undertaken with 7 participants in the intervention group, and 8 interviews with the usual care group (n¼ 15). The gender composition consisted of 11 females and 4 males. Participants’ ages ranged from 27 to 84 (M¼ 60.07, SD ¼ 15.40). Interviews were conducted between August 2017 and May 2018, with audio files digitally recorded and data coded using thematic framework analysis. Our results show that blinding to intervention or usual care was a challenge, participants felt the intervention was safe and suitable aided by the assistance of a research nurse, yet, found the self-completion questionnaire tools hard to complete. Our study provides an insight of trial processes, participants’ adherence and completion of exercise interventions, and informs the design and conduct of larger RCTs based on the experiences of abdominal cancer surgery patients

The molecular epidemiology of human immunodeficiency virus type 1 in six cities in Britain and Ireland

The authors sequenced the p17 coding regions of the gag gene from 211 patients infected either through injecting drug use (IDU) or by sexual intercourse between men from six cities in Scotland, N. England, N. Ireland, and the Republic of Ireland. All sequences were of subtype 5. Phylogenetic analysis revealed substantial heterogeneity in the sequences from homosexual men. In contrast, sequence from over 80% of IDUs formed a relatively tight cluster, distinct both from those of published isolates and of the gay men. There was no large-scale clustering of sequences by city in either risk group, although a number of close associations between pairs of individuals were observed. From the known date of the HIV-1 epidemic among IDUs in Edinburgh, the rate of sequence divergence at synonymous sites is estimated to be about 0.8%. On this basis it has been estimated that the date of divergence of the sequences among homosexual men to be about 1975, which may correspond to the origin of the B subtype epidemic

Moral courage in the workplace: moving to and from the desire and decision to act

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72135/1/j.1467-8608.2007.00484.x.pd

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Aveiro discretization method in mathematics: a new discretization principle

We found a very general discretization method for solving wide classes of mathematical problems by applying the theory of reproducing kernels. An illustration of the generality of the method is here performed by considering several distinct classes of problems to which the method is applied. In fact, one of the advantages of the present method -- in comparison to other well-known and well established methods -- is its global nature and no need of special or very particular data conditions. Numerical experiments have been made, and consequent results are here exhibited. Due to the powerful results which arise from the application of the present method, we consider that this method has everything to become one of the next generation methods of solving general analytical problems by using computers. In particular, we would like to point out that we will be able to solve very global linear partial differential equations satisfying very general boundary conditions or initial values (and in a somehow independent way of the boundary and domain). Furthermore, we will be able to give an ultimate sampling theory and an ultimate realization of the consequent general reproducing kernel Hilbert spaces. The general theory is here presented in a constructive way, and containing some related historical and concrete examples

Quantum Rotation of HCN and DCN in Helium-4

We present calculations of rotational absorption spectra of the molecules HCN and DCN in superfluid helium-4, using a combination of the Diffusion Monte Carlo method for ground state properties and an analytic many-body method (Correlated Basis Function theory) for the excited states. Our results agree with the experimentally determined effective moment of inertia which has been obtained from the $J=0\to 1$ spectral transition. The correlated basis function analysis shows that, unlike heavy rotors such as OCS, the J=2 and higher rotational excitations of HCN and DCN have high enough energy to strongly couple to rotons, leading to large shifts of the lines and accordingly to anomalous large spectroscopic distortion constants, to the emergence of roton-maxon bands, and to secondary peaks in the absorption spectra for J=2 and J=3.Comment: accepted by Phys. Rev. B; changes: included referee suggestions, removed typos, added 10 ref

Rapid and highly variable warming of lake surface waters around the globe

In this first worldwide synthesis of in situ and satellite-derived lake data, we find that lake summer surface water temperatures rose rapidly (global mean = 0.34°C decade−1) between 1985 and 2009. Our analyses show that surface water warming rates are dependent on combinations of climate and local characteristics, rather than just lake location, leading to the counterintuitive result that regional consistency in lake warming is the exception, rather than the rule. The most rapidly warming lakes are widely geographically distributed, and their warming is associated with interactions among different climatic factors—from seasonally ice-covered lakes in areas where temperature and solar radiation are increasing while cloud cover is diminishing (0.72°C decade−1) to ice-free lakes experiencing increases in air temperature and solar radiation (0.53°C decade−1). The pervasive and rapid warming observed here signals the urgent need to incorporate climate impacts into vulnerability assessments and adaptation efforts for lakes.Peer reviewe