Using the Δ3\Delta_3 statistic to test for missed levels in mixed sequence neutron resonance data

The $\Delta_3(L)$ statistic is studied as a tool to detect missing levels in the neutron resonance data where 2 sequences are present. These systems are problematic because there is no level repulsion, and the resonances can be too close to resolve. $\Delta_3(L)$ is a measure of the fluctuations in the number of levels in an interval of length $L$ on the energy axis. The method used is tested on ensembles of mixed Gaussian Orthogonal Ensemble (GOE) spectra, with a known fraction of levels ($x$) randomly depleted, and can accurately return $x$. The accuracy of the method as a function of spectrum size is established. The method is used on neutron resonance data for 11 isotopes with either s-wave neutrons on odd-A, or p-wave neutrons on even-A. The method compares favorably with a maximum likelihood method applied to the level spacing distribution. Nuclear Data Ensembles were made from 20 isotopes in total, and their $\Delta_3(L)$ statistic are discussed in the context of Random Matrix Theory.Comment: 22 pages, 12 figures, 4 table

Review of finite fields: Applications to discrete Fourier, transforms and Reed-Solomon coding

An attempt is made to provide a step-by-step approach to the subject of finite fields. Rigorous proofs and highly theoretical materials are avoided. The simple concepts of groups, rings, and fields are discussed and developed more or less heuristically. Examples are used liberally to illustrate the meaning of definitions and theories. Applications include discrete Fourier transforms and Reed-Solomon coding

Ergodicity of the Δ3\Delta_3 statistic and purity of neutron resonance data

The $\Delta_3(L)$ statistic characterizes the fluctuations of the number of levels as a function of the length of the spectral interval. It is studied as a possible tool to indicate the regular or chaotic nature of underlying dynamics, detect missing levels and the mixing of sequences of levels of different symmetry, particularly in neutron resonance data. The relation between the ensemble average and the average over different fragments of a given realization of spectra is considered. A useful expression for the variance of $\Delta_3(L)$ which accounts for finite sample size is discussed. An analysis of neutron resonance data presents the results consistent with a maximum likelihood method applied to the level spacing distribution.Comment: 24 pages, 19 figures, 1 tabl

Number of states with fixed angular momentum for identical fermions and bosons

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same ${\cal M}$ and n but different J is identical if $I \ge (n-2)J - {1/2} (n-1)(n-2)$ for fermions and $I \ge (n-2)J$ for bosons, and that the number of states is also identical for the same ${\cal M}$ but different n and J if ${\cal M} \le$min(n, 2J+1 - n) for fermions and for ${\cal M} \le$min(n, 2J) for bosons. Here ${\cal M} =I_{max}-I$, n is the particle number, and J refers to the angular momentum of a single-particle orbit for fermions, or the spin L carried by bosons.Comment: 9 pages, no figure

Osteoporotic Hip Fractures: The Burden of Fixation Failure

Osteoporotic hip fractures are a major cause of morbidity and mortality in the elderly. Furthermore, reduced implant anchorage in osteoporotic bone predisposes towards fixation failure and with an ageing population, even low failure rates represent a significant challenge to healthcare systems. Fixation failure in fragility fractures of the hip ranges from 5% in peritrochanteric fractures through to 15% and 41% in undisplaced and displaced fractures of the femoral neck, respectively. Our findings, in general, support the view that failed internal fixation of these fragility fractures carries a poor prognosis: it leads to a twofold increase in the length of hospital stay and a doubling of healthcare costs. Patients are more likely to suffer a downgrade in their residential status upon discharge with a consequent increase in social dependency. Furthermore, the marked disability and reduction in quality of life evident before salvage procedures may persist at long-term followup. The risk, of course, for the elderly patient with a prolonged period of decreased functioning is that the disability becomes permanent. Despite this, however, no clear link between revision surgery and an increase in mortality has been demonstrated in the literature

Transcriptional responses in the adaptation to ischaemia-reperfusion injury: a study of the effect of ischaemic preconditioning in total knee arthroplasty patients

<p>Abstract</p> <p>Background</p> <p>Ischaemic preconditioning (IPC) has emerged as a method of reducing ischaemia-reperfusion injury. However, the complex mechanism through which IPC elicits this protection is not fully understood. The aim of this study was to investigate the genomic response induced by IPC in muscle biopsies taken from the operative leg of total knee arthroplasty patients in order to gain insight into the IPC mechanism.</p> <p>Methods</p> <p>Twenty patients, undergoing primary total knee arthroplasty, were randomly assigned to IPC (n = 10) and control (n = 10) groups. Patients in the IPC group received ischaemic preconditioning immediately prior to surgery. IPC was induced by three five-minute cycles of tourniquet insufflation interrupted by five-minute cycles of reperfusion. A muscle biopsy was taken from the operative knee of control and IPC-treated patients at the onset of surgery and, again, at one hour into surgery. The gene expression profile of muscle biopsies was determined using the Affymetrix Human U113 2.0 microarray system and validated using real-time polymerase chain reaction (RT-PCR). Measurements of C-reactive protein (CRP), erythrocyte sedimentation (ESR), white cell count (WCC), cytokines and haemoglobin were also made pre- and post-operatively.</p> <p>Results</p> <p>Microarray analysis revealed a significant increase in the expression of important oxidative stress defence genes, immediate early response genes and mitochondrial genes. Upregulation of pro-survival genes was also observed and correlated with a downregulation of pro-apoptotic gene expression. CRP, ESR, WCC, cytokine and haemoglobin levels were not significantly different between control and IPC patients.</p> <p>Conclusions</p> <p>The findings of this study suggest that IPC of the lower limb in total knee arthroplasty patients induces a protective genomic response, which results in increased expression of immediate early response genes, oxidative stress defence genes and pro-survival genes. These findings indicate that ischaemic preconditioning may be of potential benefit in knee arthroplasty and other musculoskeletal conditions.</p