A comparative analysis of the value of information in a continuous time market model with partial information: the cases of log-utility and CRRA

We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis

Ledoux-Convection in Protoneutron Stars --- a Clue to Supernova Nucleosynthesis?

Two-dimensional hydrodynamical simulations of the deleptonization of a newly formed neutron star were performed. Driven by negative lepton fraction and entropy gradients, convection starts near the neutrinosphere about 20-30 ms after core bounce, but moves deeper into the protoneutron star, and after about one second the whole protoneutron star is convective. The deleptonization of the star proceeds much faster than in the corresponding spherically symmetrical model because the lepton flux and the neutrino luminosities increase by up to a factor of two. The convection below the neutrinosphere raises the neutrinospheric temperatures and mean energies of the emitted neutrinos by 10-20%. This can have important implications for the supernova explosion mechanism and changes the detectable neutrino signal from the Kelvin-Helmholtz cooling of the protoneutron star. In particular, the enhanced electron neutrino flux relative to the electron antineutrino flux during the early post-bounce evolution might solve the overproduction problem of certain elements in the neutrino-heated ejecta in models of type-II supernova explosions.Comment: 17 pages, LaTeX, 8 postscript figures, uses epsf.sty. To appear in ApJ 473 (Letters), 1996 December 1

Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals

We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $\omega /\Delta \omega$ ($\omega$: frequency of an x ray, $\Delta\omega$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.Comment: 4 pages, 2 figures. Title change

Parent-only interventions in the treatment of childhood obesity: a systematic review of randomized controlled trials

Background An effective and cost-effective treatment is required for the treatment of childhood obesity. Comparing parent-only interventions with interventions including the child may help determine this. Methods A systematic review of published and ongoing studies until 2013, using electronic database and manual searches. Inclusion criteria: randomized controlled trials, overweight/obese children aged 5-12 years, parent-only intervention compared with an intervention that included the child, 6 months or more follow-up. Outcomes included measures of overweight. Results Ten papers from 6 completed studies, and 2 protocols for ongoing studies, were identified. Parent-only groups are either more effective than or similarly effective as child-only or parent-child interventions, in the change in degree of overweight. Most studies were at unclear risk of bias for randomization, allocation concealment and blinding of outcome assessors. Two trials were at high risk of bias for incomplete outcome data. Four studies showed higher dropout from parent-only interventions. One study examined programme costs and found parent-only interventions to be cheaper. Conclusions Parent-only interventions appear to be as effective as parent-child interventions in the treatment of childhood overweight/obesity, and may be less expensive. Reasons for higher attrition rates in parent-only interventions need further investigatio

Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Field-induced structure transformation in electrorheological solids

We have computed the local electric field in a body-centered tetragonal (BCT) lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to examine the effects of a structure transformation on the local field strength. For the ground state of an electrorheological solid of hard spheres, we identified a novel structure transformation from the BCT to the face-centered cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard sphere constraint. In contrast to the previous results, the local field exhibits a non-monotonic transition from BCT to FCC. As c increases from the BCT ground state, the local field initially decreases rapidly towards the isotropic value at the body-centered cubic lattice, decreases further, reaching a minimum value and increases, passing through the isotropic value again at an intermediate lattice, reaches a maximum value and finally decreases to the FCC value. An experimental realization of the structure transformation is suggested. Moreover, the change in the local field can lead to a generalized Clausius-Mossotti equation for the BCT lattices.Comment: Submitted to Phys. Rev.

Effects of geometric anisotropy on local field distribution: Ewald-Kornfeld formulation

We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric anisotropy has a significant impact on the local field distribution. The change in the local field can lead to a generalized Clausius-Mossotti equation for the anisotropic case.Comment: Accepted for publications, Journal of Physics: Condensed Matte

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health

Boundary conditions for interfaces of electromagnetic (photonic) crystals and generalized Ewald-Oseen extinction principle

The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of incident wave, eigenmodes excited in the crystal and scattered spatial harmonics. Generalized Ewald-Oseen extinction principle is formulated on the base of deduced boundary conditions. The knowledge of properties of infinite crystal's eigenmodes provides option to solve the diffraction problem for the corresponding semi-infinite crystal numerically. In the case when the crystal is formed by small inclusions which can be treated as point dipolar scatterers with fixed direction the problem admits complete rigorous analytical solution. The amplitudes of excited modes and scattered spatial harmonics are expressed in terms of the wave vectors of the infinite crystal by closed-form analytical formulae. The result is applied for study of reflection properties of metamaterial formed by cubic lattice of split-ring resonators.Comment: 15 pages, 8 figures, submitted to PR