Angular reduction in multiparticle matrix elements

A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of the spherical harmonics. For non-scalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products, with tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, nor do they have complex tensor terms for couplings to a scalar. Consequently, they are easily interpretable from the properties of the physical vectors they contain.Comment: This version contains added comments and typographical corrections to the original article. Now 27 pages, 0 figure

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Luteinizing Hormone-Releasing Hormone in the Vomeronasal System and Terminal Nerve of the Hamster a

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74742/1/j.1749-6632.1987.tb36300.x.pd

Population coding by globally coupled phase oscillators

A system of globally coupled phase oscillators subject to an external input is considered as a simple model of neural circuits coding external stimulus. The information coding efficiency of the system in its asynchronous state is quantified using Fisher information. The effect of coupling and noise on the information coding efficiency in the stationary state is analyzed. The relaxation process of the system after the presentation of an external input is also studied. It is found that the information coding efficiency exhibits a large transient increase before the system relaxes to the final stationary state.Comment: 7 pages, 9 figures, revised version, new figures added, to appear in JPSJ Vol 75, No.

Model Calculations for the Two-Fragment Electro-Disintegration of 4^4He

Differential cross sections for the electro-disintegration process $e + {^4He} \longrightarrow {^3H}+ p + e'$ are calculated, using a model in which the final state interaction is included by means of a nucleon-nucleus (3+1) potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach (IDEA). In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p{^3H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our Plane-Wave Impulse Approximation results exhibit, similarly to other calculations, a dip in the five-fold differential cross-section around a missing momentum of $\sim 450 MeV/c$, it is argued that this is an artifact of the omission of re-scattering four-nucleon processes.Comment: 16 pages, 6 figures, accepted for publication by Phys.Rev.

Risk of cardiovascular disease and total mortality in adults with type 1 diabetes: Scottish registry linkage study

<p>Background: Randomized controlled trials have shown the importance of tight glucose control in type 1 diabetes (T1DM), but few recent studies have evaluated the risk of cardiovascular disease (CVD) and all-cause mortality among adults with T1DM. We evaluated these risks in adults with T1DM compared with the non-diabetic population in a nationwide study from Scotland and examined control of CVD risk factors in those with T1DM.</p> <p>Methods and Findings: The Scottish Care Information-Diabetes Collaboration database was used to identify all people registered with T1DM and aged ≥20 years in 2005–2007 and to provide risk factor data. Major CVD events and deaths were obtained from the national hospital admissions database and death register. The age-adjusted incidence rate ratio (IRR) for CVD and mortality in T1DM (n = 21,789) versus the non-diabetic population (3.96 million) was estimated using Poisson regression. The age-adjusted IRR for first CVD event associated with T1DM versus the non-diabetic population was higher in women (3.0: 95% CI 2.4–3.8, p<0.001) than men (2.3: 2.0–2.7, p<0.001) while the IRR for all-cause mortality associated with T1DM was comparable at 2.6 (2.2–3.0, p<0.001) in men and 2.7 (2.2–3.4, p<0.001) in women. Between 2005–2007, among individuals with T1DM, 34 of 123 deaths among 10,173 who were <40 years and 37 of 907 deaths among 12,739 who were ≥40 years had an underlying cause of death of coma or diabetic ketoacidosis. Among individuals 60–69 years, approximately three extra deaths per 100 per year occurred among men with T1DM (28.51/1,000 person years at risk), and two per 100 per year for women (17.99/1,000 person years at risk). 28% of those with T1DM were current smokers, 13% achieved target HbA1c of <7% and 37% had very poor (≥9%) glycaemic control. Among those aged ≥40, 37% had blood pressures above even conservative targets (≥140/90 mmHg) and 39% of those ≥40 years were not on a statin. Although many of these risk factors were comparable to those previously reported in other developed countries, CVD and mortality rates may not be generalizable to other countries. Limitations included lack of information on the specific insulin therapy used.</p> <p>Conclusions: Although the relative risks for CVD and total mortality associated with T1DM in this population have declined relative to earlier studies, T1DM continues to be associated with higher CVD and death rates than the non-diabetic population. Risk factor management should be improved to further reduce risk but better treatment approaches for achieving good glycaemic control are badly needed.</p&gt