Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

Tea and coffee consumption in relation to vitamin D and calcium levels in Saudi adolescents

Background Coffee and tea consumption was hypothesized to interact with variants of vitamin D-receptor polymorphisms, but limited evidence exists. Here we determine for the first time whether increased coffee and tea consumption affects circulating levels of 25-hydroxyvitamin D in a cohort of Saudi adolescents. Methods A total of 330 randomly selected Saudi adolescents were included. Anthropometrics were recorded and fasting blood samples were analyzed for routine analysis of fasting glucose, lipid levels, calcium, albumin and phosphorous. Frequency of coffee and tea intake was noted. 25-hydroxyvitamin D levels were measured using enzyme-linked immunosorbent assays. Results Improved lipid profiles were observed in both boys and girls, as demonstrated by increased levels of HDL-cholesterol, even after controlling for age and BMI, among those consuming 9–12 cups of coffee/week. Vitamin D levels were significantly highest among those consuming 9–12 cups of tea/week in all subjects (p-value 0.009) independent of age, gender, BMI, physical activity and sun exposure. Conclusion This study suggests a link between tea consumption and vitamin D levels in a cohort of Saudi adolescents, independent of age, BMI, gender, physical activity and sun exposure. These findings should be confirmed prospectively

Childhood tuberculosis: progress requires an advocacy strategy now

Childhood tuberculosis (TB) is a preventable and curable infectious disease that remains overlooked by public health authorities, health policy makers and TB control programmes. Childhood TB contributes significantly to the burden of disease and represents the failure to control transmission in the community. Furthermore, the pool of infected children constitutes a reservoir of infection for the future burden of TB. It is time to prioritise childhood TB, advocate for addressing the challenges and grasp the opportunities in its prevention and control. Herein, we propose a scientifically informed advocacy agenda developed at the International Childhood TB meeting held in Stockholm, Sweden, from March 17 to 18, 2011, which calls for a renewed effort to improve the situation for children affected by Mycobacterium tuberculosis exposure, infection or disease. The challenges and needs in childhood TB are universal and apply to all settings and must be addressed more effectively by all stakeholders

Super-resolution far-field ghost imaging via compressive sampling

Much more image details can be resolved by improving the system's imaging resolution and enhancing the resolution beyond the system's Rayleigh diffraction limit is generally called super-resolution. By combining the sparse prior property of images with the ghost imaging method, we demonstrated experimentally that super-resolution imaging can be nonlocally achieved in the far field even without looking at the object. Physical explanation of super-resolution ghost imaging via compressive sampling and its potential applications are also discussed.Comment: 4pages,4figure

QuantiFERON®-TB gold in-tube performance for diagnosing active tuberculosis in children and adults in a high burden setting.

To determine whether QuantiFERON®-TB Gold In-Tube (QFT) can contribute to the diagnosis of active tuberculosis (TB) in children in a high-burden setting and to assess the performance of QFT and tuberculin skin test (TST) in a prospective cohort of TB suspect children compared to adults with confirmed TB in Tanzania. Sensitivity and specificity of QFT and TST for diagnosing active TB as well as indeterminate QFT rates and IFN-γ levels were assessed in 211 TB suspect children in a Tanzanian district hospital and contrasted in 90 adults with confirmed pulmonary TB. Sensitivity of QFT and TST in children with confirmed TB was 19% (5/27) and 6% (2/31) respectively. In adults sensitivity of QFT and TST was 84% (73/87) and 85% (63/74). The QFT indeterminate rate in children and adults was 27% and 3%. Median levels of IFN-γ were lower in children than adults, particularly children <2 years and HIV infected. An indeterminate result was associated with age <2 years but not malnutrition or HIV status. Overall childhood mortality was 19% and associated with an indeterminate QFT result at baseline. QFT and TST showed poor performance and a surprisingly low sensitivity in children. In contrast the performance in Tanzanian adults was good and comparable to performance in high-income countries. Indeterminate results in children were associated with young age and increased mortality. Neither test can be recommended for diagnosing active TB in children with immature or impaired immunity in a high-burden setting

Inferring fish escape behaviour in trawls based on catch comparison data: Model development and evaluation based on data from Skagerrak, Denmark

During the fishing process, fish react to a trawl with a series of behaviours that often are species and size specific. Thus, a thorough understanding of fish behaviour in relation to fishing gear and a scientific understanding of the ability of different gear designs to utilize or stimulate various behavioural patterns during the catching process are essential for developing more efficient, selective, and environmentally friendly trawls. Although many behavioural studies using optical and acoustic observation systems have been conducted, harsh observation conditions on the fishing grounds often hamper the ability to directly observe fish behaviour in relation to fishing gear. As an alternative to optical and acoustic methods, we developed and applied a new mathematical model to catch data to extract detailed and quantitative information about species- and size-dependent escape behaviour in towed fishing gear such as trawls. We used catch comparison data collected with a twin trawl setup; the only difference between the two trawls was that a 12 m long upper section was replaced with 800 mm diamond meshes in one of them. We investigated the length-based escape behaviour of cod (Gadus morhua), haddock (Melanogrammus aeglefinus), saithe (Pollachius virens), witch flounder (Glyptocephalus cynoglossus), and lemon sole (Microstomus kitt) and quantified the extent to which behavioural responses set limits for the large mesh panel's selective efficiency. Around 85% of saithe, 80% of haddock, 44% of witch flounder, 55% of lemon sole, and 55% of cod (below 68 cm) contacted the large mesh panel and escaped. We also demonstrated the need to account for potential selectivity in the trawl body, as it can bias the assessment of length-based escape behaviour. Our indirect assessment of fish behaviour was in agreement with the direct observations made for the same species in a similar section of the trawl body reported in the literature

Group Irregularity Strength of Connected Graphs

We investigate the group irregularity strength ($s_g(G)$) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group \gr of order $s$, there exists a function f:E(G)\rightarrow \gr such that the sums of edge labels at every vertex are distinct. We prove that for any connected graph $G$ of order at least 3, $s_g(G)=n$ if $n\neq 4k+2$ and $s_g(G)\leq n+1$ otherwise, except the case of some infinite family of stars

Fatigue Intervention by Nurses Evaluation - The FINE Trial. A randomised controlled trial of nurse led self-help treatment for patients in primary care with chronic fatigue syndrome: study protocol. [ISRCTN74156610]

Background: Chronic fatigue syndrome, also known as ME (CFS/ME), is a condition characterised primarily by severe, disabling fatigue, of unknown origin, which has a poor prognosis and serious personal and economic consequences. Evidence for the effectiveness of any treatment for CFS/ME in primary care, where most patients are seen, is sparse. Recently, a brief, pragmatic treatment for CFS/ME, based on a physiological dysregulation model of the condition, was shown to be successful in improving fatigue and physical functioning in patients in secondary care. The treatment involves providing patients with a readily understandable explanation of their symptoms, from which flows the rationale for a graded rehabilitative plan, developed collaboratively with the therapist. The present trial will test the effectiveness and cost-effectiveness of pragmatic rehabilitation when delivered by specially trained general nurses in primary care. We selected a client-centred counselling intervention, called supportive listening, as a comparison treatment. Counselling has been shown to be as effective as cognitive behaviour therapy for treating fatigue in primary care, is more readily available, and controls for supportive therapist contact time. Our control condition is treatment as usual by the general practitioner (GP). Methods and design: This study protocol describes the design of an ongoing, single-blind, pragmatic randomized controlled trial of a brief (18 week) self-help treatment, pragmatic rehabilitation, delivered by specially trained nurse-therapists in patients' homes, compared with nurse-therapist delivered supportive listening and treatment as usual by the GP. An economic evaluation, taking a societal viewpoint, is being carried out alongside the clinical trial. Three adult general nurses were trained over a six month period to deliver the two interventions. Patients aged over 18 and fulfilling the Oxford criteria for CFS are assessed at baseline, after the intervention, and again one year later. Primary outcomes are self-reported physical functioning and fatigue at one year, and will be analysed on an intention-to-treat basis. A qualitative study will examine the interventions' mechanisms of change, and also GPs' drivers and barriers towards referral

A putative relay circuit providing low-threshold mechanoreceptive input to lamina I projection neurons via vertical cells in lamina II of the rat dorsal horn

Background: Lamina I projection neurons respond to painful stimuli, and some are also activated by touch or hair movement. Neuropathic pain resulting from peripheral nerve damage is often associated with tactile allodynia (touch-evoked pain), and this may result from increased responsiveness of lamina I projection neurons to non-noxious mechanical stimuli. It is thought that polysynaptic pathways involving excitatory interneurons can transmit tactile inputs to lamina I projection neurons, but that these are normally suppressed by inhibitory interneurons. Vertical cells in lamina II provide a potential route through which tactile stimuli can activate lamina I projection neurons, since their dendrites extend into the region where tactile afferents terminate, while their axons can innervate the projection cells. The aim of this study was to determine whether vertical cell dendrites were contacted by the central terminals of low-threshold mechanoreceptive primary afferents. Results: We initially demonstrated contacts between dendritic spines of vertical cells that had been recorded in spinal cord slices and axonal boutons containing the vesicular glutamate transporter 1 (VGLUT1), which is expressed by myelinated low-threshold mechanoreceptive afferents. To confirm that the VGLUT1 boutons included primary afferents, we then examined vertical cells recorded in rats that had received injections of cholera toxin B subunit (CTb) into the sciatic nerve. We found that over half of the VGLUT1 boutons contacting the vertical cells were CTb-immunoreactive, indicating that they were of primary afferent origin. Conclusions: These results show that vertical cell dendritic spines are frequently contacted by the central terminals of myelinated low-threshold mechanoreceptive afferents. Since dendritic spines are associated with excitatory synapses, it is likely that most of these contacts were synaptic. Vertical cells in lamina II are therefore a potential route through which tactile afferents can activate lamina I projection neurons, and this pathway could play a role in tactile allodynia