Changes in trabecular bone, hematopoiesis and bone marrow vessels in aplastic anemia, primary osteoporosis, and old age

Retrospective histologic analyses of bone biopsies and of post mortem samples from normal persons of different age groups, and of bone biopsies of age- and sex-matched groups of patients with primary osteoporosis and aplastic anemia show characteristic age dependent as well as pathologic changes including atrophy of osseous trabeculae and of hematopoiesis, and changes in the sinusoidal and arterial capillary compartments. These results indicate the possible role of a microvascular defect in the pathogenesis of osteoporosis and aplastic anemia

Ways to teach modelling—a 50 year study

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed

A Correlation Between Inclination and Color in the Classical Kuiper Belt

We have measured broadband optical BVR photometry of 24 Classical and Scattered Kuiper belt objects (KBOs), approximately doubling the published sample of colors for these classes of objects. We find a statistically significant correlation between object color and inclination in the Classical Kuiper belt using our data. The color and inclination correlation increases in significance after the inclusion of additional data points culled from all published works. Apparently, this color and inclination correlation has not been more widely reported because the Plutinos show no such correlation, and thus have been a major contaminant in previous samples. The color and inclination correlation excludes simple origins of color diversity, such as the presence of a coloring agent without regard to dynamical effects. Unfortunately, our current knowledge of the Kuiper belt precludes us from understanding whether the color and inclination trend is due to environmental factors, such as collisional resurfacing, or primordial population effects. A perihelion and color correlation is also evident, although this appears to be a spurious correlation induced by sampling bias, as perihelion and inclination are correlated in the observed sample of KBOs.Comment: Accepted to Astrophysical Journal Letter

Partial survival and inelastic collapse for a randomly accelerated particle

We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival probability at large times. For the problem of inelastic reflection at the origin, with coefficient of restitution $r$, we give a new derivation of the condition for inelastic collapse, $r<r_c=e^{-\pi/\sqrt{3}}$, and determine the persistence exponent exactly.Comment: 6 page

Studying the scale and q^2 dependence of K^+-->pi^+e^+e^- decay

We extract the K^+-->pi^+e^+e^- amplitude scale at q^2=0 from the recent Brookhaven E865 high-statistics data. We find that the q^2=0 scale is fitted in excellent agreement with the theoretical long-distance amplitude. Lastly, we find that the observed q^2 shape is explained by the combined effect of the pion and kaon form-factor vector-meson-dominance rho, omega and phi poles, and a charged pion loop coupled to a virtual photon-->e^+e^- transition.Comment: 8 pages, 3 figure

Recent BES measurements and the hadronic contribution to the QED vacuum polarization

We have updated our evaluation of the hadronic contribution to the running of the QED fine structure constant using the recent precise measurements of the e+e- annihilation at the center-of-mass (c.m.s.) energy region between 2.6 and 3.65 GeV performed by the BES collaboration. In the low energy region, around the rho resonance, we include the recent measurements from the BABAR, CDM-2, KLOE and SND collaborations. We obtain Delta alpha (5)_had (s) = 0.02750 +/- 0.00033 at s = m_Z^2.Comment: 3 pages, 1 figur

First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Fluctuations of a long, semiflexible polymer in a narrow channel

We consider an inextensible, semiflexible polymer or worm-like chain, with persistence length $P$ and contour length $L$, fluctuating in a cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$, corresponding to a long, tightly confined polymer, the average length of the channel $$ occupied by the polymer and the mean square deviation from the average vary as $=[1-\alpha_\circ(D/P)^{2/3}]L$ and $<\Delta R_\parallel^{\thinspace 2}\thinspace>=\beta_\circ(D^2/P)L$, respectively, where $\alpha_\circ$ and $\beta_\circ$ are dimensionless amplitudes. In earlier work we determined $\alpha_\circ$ and the analogous amplitude $\alpha_\Box$ for a channel with a rectangular cross section from simulations of very long chains. In this paper we estimate $\beta_\circ$ and $\beta_\Box$ from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of $R_\parallel$ or radial distribution function, which is asymptotically exact for large $L$ and has the skewed shape seen experimentally.Comment: 21 pages, including 4 figure

The semimartingale decomposition of one-dimensional quasidiffusions with natural scale

AbstractQuasidiffusions (with natural scale) are semimartingales obtained as time changed Wiener processes. Examples are diffusions and birth- and death-processes. In general, quasidiffusions are not continuous but they are skip-free. In this note we determine the continuous and the purely discontinuous martingale part of all such quasidiffusions