Volumes of polytopes in spaces of constant curvature

We overview the volume calculations for polyhedra in Euclidean, spherical and hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary tetrahedron in $H^3$ and $S^3$. We also present some results, which provide a solution for Seidel problem on the volume of non-Euclidean tetrahedron. Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle, horocycle or one branch of equidistant curve. This is a natural hyperbolic analog of the cyclic quadrilateral in the Euclidean plane. We find a few versions of the Brahmagupta formula for the area of such quadrilateral. We also present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference

Irrigating with polyacrylamide (PAM) - Nine years and a million acres of experience

Polyacrylamide (PAM) has been available commercially since 1995 for reducing irrigation-induced erosion and enhancing infiltration. The first series of practical field tests was conducted in 1991. PAM used for erosion control is a large water soluble (non-crosslinked) anionic molecule (12-15 megagrams per mole) containing < 0.05% acrylamide monomer. In controlled field studies PAM eliminated, on average, 94% (80-99% range) of sediment loss in field runoff from furrow irrigation, with a typical 15-50% relative infiltration increase on medium to fine textured soils compared to untreated controls. Similar but less dramatic results have been seen with sprinkler irrigation. Under some conditions infiltration is unchanged or can even be slightly reduced, e.g. in sandy soils or where PAM application rates are very high. Results are achieved with per irrigation field application rates of about 1 kg per hectare, for furrow irrigation, and 2 to 4 kg per hectare for sprinkler irrigation. Cost of PAM is $7 to$13 per kg. Seasonal application totals vary from 3 to 7 kg per hectare. Farmer field sediment control has been around 80% of test plot results. Substantial runoff reductions have been documented for nutrients, pesticides, microorganisms, BOD, and weed seed. No adverse effects have been seen for soil microbial populations. Crop yields have not been widely documented, though evidence exists for yield increases related to infiltration improvement. High effectiveness, low cost, and ease of application, compared to traditional conservation measures, has resulted in rapid technology acceptance in the US and internationally. PAM-use for runoff water quality protection is one of the most potent new irrigation environmental technologies in the market place. New uses in construction and dryland erosion control are being developed rapidly. This paper discusses new insights and understanding of PAM-use and potential for future development

The British Army, information management and the First World War revolution in military affairs

Information Management (IM) – the systematic ordering, processing and channelling of information within organisations – forms a critical component of modern military command and control systems. As a subject of scholarly enquiry, however, the history of military IM has been relatively poorly served. Employing new and under-utilised archival sources, this article takes the British Expeditionary Force (BEF) of the First World War as its case study and assesses the extent to which its IM system contributed to the emergence of the modern battlefield in 1918. It argues that the demands of fighting a modern war resulted in a general, but not universal, improvement in the BEF’s IM techniques, which in turn laid the groundwork, albeit in embryonic form, for the IM systems of modern armies. KEY WORDS: British Army, Information Management, First World War, Revolution in Military Affairs, Adaptatio

Effectiveness of a cognitive behavioural intervention for patients with undifferentiated somatoform disorder: results from the CIPRUS cluster randomized controlled trial in primary care

Objective: To examine the effectiveness of a cognitive behavioural intervention delivered by mental health nurse practitioners (MHNPs) to patients with undifferentiated somatoform disorder (USD), compared to usual care. Methods: We conducted a cluster randomized trial among primary care patients with USD comparing the intervention to usual care. The intervention consisted of six sessions with the MHNP. Primary outcome was physical functioning (RAND-36 physical component summary score). Secondary outcomes were the RAND-36 mental component summary score and the eight subscales; anxiety and depression (Hospital Anxiety and Depression Scale) and somatic symptom severity (Patient Health Questionnaire-15). Outcomes were assessed at baseline, 2, 4 and 12 months. We analysed data using linear mixed models by intention-to-treat, and investigated effect modifiers. Results: Compared to usual care (n=87), the intervention group (n=111) showed an improvement in physical functioning (mean difference 2.24 [95% CI 0.51; 3.97]; p=.011), a decrease in limitations due to physical problems (mean difference 10.82 [95% CI 2.14; 19.49]; p.=0.015) and in pain (mean difference 5.08 [95% CI 0.58; 9.57]; p=.027), over 12 months. However effect sizes were small and less clinically relevant than expected. We found no differences for anxiety, depression and somatic symptom severity. Effects were larger and clinically relevant for patients with more recent symptoms and fewer physical diseases. Conclusion: The cognitive behavioural intervention was effective in improving pain and physical functioning components of patients' health. It was particularly suitable for patients with symptoms that had been present for a limited number of years and with few comorbid physical diseases. Trial registration: The trial is registered in the Dutch Trial Registry, www.trialregister.nl, under NTR4686

Effects of sleep deprivation on neural functioning: an integrative review

Sleep deprivation has a broad variety of effects on human performance and neural functioning that manifest themselves at different levels of description. On a macroscopic level, sleep deprivation mainly affects executive functions, especially in novel tasks. Macroscopic and mesoscopic effects of sleep deprivation on brain activity include reduced cortical responsiveness to incoming stimuli, reflecting reduced attention. On a microscopic level, sleep deprivation is associated with increased levels of adenosine, a neuromodulator that has a general inhibitory effect on neural activity. The inhibition of cholinergic nuclei appears particularly relevant, as the associated decrease in cortical acetylcholine seems to cause effects of sleep deprivation on macroscopic brain activity. In general, however, the relationships between the neural effects of sleep deprivation across observation scales are poorly understood and uncovering these relationships should be a primary target in future research

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Characterization of the probabilistic traveling salesman problem

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E((L) over bar (pruned))=rootnp(0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np-->infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L-a priori)=rootn/pbeta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05less than or equal topless than or equal to0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required