Approaches to Estimating the Health State Dependence of the Utility Function

If the marginal utility of consumption depends on health status, this will affect the economic analysis of a number of central problems in public finance, including the optimal structure of health insurance and optimal life cycle savings. In this paper, we describe the promises and challenges of various approaches to estimating the effect of health on the marginal utility of consumption. Our basic conclusion is that while none of these approaches is a panacea, many offer the potential to shed important insights on the nature of health state dependence.

Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in Europhys. Let

One-dimensional collision carts computer model and its design ideas for productive experiential learning

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In the field of designing computer simulations, we discuss briefly three pedagogical considerations such as 1) consistent simulation world view with pen paper representation, 2) data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and 3) game for simple concept testing that can further support learning. We also suggest using physical world setup to be augmented complimentary with simulation while highlighting three advantages of real collision carts equipment like tacit 3D experience, random errors in measurement and conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes. 2015 Resources added: http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/02-dynamics/46-one-dimension-collision-js-model http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/02-dynamics/195-elastic-collisionComment: 6 pages, 8 figures, 1 table, 1 L. K. Wee, Physics Education 47 (3), 301 (2012); ISSN 0031-912

Variation of the density of states in amorphous GdSi at the metal-insulator transition

We performed detailed conductivity and tunneling mesurements on the amorphous, magnetically doped material $\alpha$-Gd$_x$Si$_{1-x}$ (GdSi), which can be driven through the metal-insulator transition by the application of an external magnetic field. Conductivity increases linearly with field near the transition and slightly slower on the metallic side. The tunneling conductance, proportional to the density of states $N(E)$, undergoes a gradual change with increasing field, from insulating, showing a soft gap at low bias, with a slightly weaker than parabolic energy dependence, i.e. $N(E) \sim E^c$, $c \lesssim 2$, towards metallic behavior, with $E^d$, $0.5 \lt d \lt 1$ energy dependence. The density of states at the Fermi level appears to be zero at low fields, as in an insulator, while the sample shows already small, but metal-like conductivity. We suggest a possible explanation to the observed effect.Comment: 6 pages, 6 figure

Faint AGNs at z>4 in the CANDELS GOODS-S field: looking for contributors to the reionization of the Universe

In order to derive the AGN contribution to the cosmological ionizing emissivity we have selected faint AGN candidates at $z>4$ in the CANDELS GOODS-South field which is one of the deepest fields with extensive multiwavelength coverage from Chandra, HST, Spitzer and various groundbased telescopes. We have adopted a relatively novel criterion. As a first step high redshift galaxies are selected in the NIR $H$ band down to very faint levels ($H\leq27$) using reliable photometric redshifts. This corresponds at $z>4$ to a selection criterion based on the galaxy rest-frame UV flux. AGN candidates are then picked up from this parent sample if they show X-ray fluxes above a threshold of $F_X\sim 1.5\times 10^{-17}$ cgs (0.5-2 keV). We have found 22 AGN candidates at $z>4$ and we have derived the first estimate of the UV luminosity function in the redshift interval $4<z<6.5$ and absolute magnitude interval $-22.5\lesssim M_{1450} \lesssim -18.5$ typical of local Seyfert galaxies. The faint end of the derived luminosity function is about two/four magnitudes fainter at $z\sim 4-6$ than that derived from previous UV surveys. We have then estimated ionizing emissivities and hydrogen photoionization rates in the same redshift interval under reasonable assumptions and after discussion of possible caveats, the most important being the large uncertainties involved in the estimate of photometric redshift for sources with featureless, almost power-law SEDs and/or low average escape fraction of ionizing photons from the AGN host galaxies. We argue that, under reasonable evaluations of possible biases, the probed AGN population can produce at $z=4-6.5$ photoionization rates consistent with that required to keep highly ionized the intergalactic medium observed in the Lyman-$\alpha$ forest of high redshift QSO spectra, providing an important contribution to the cosmic reionization.Comment: 15 pages, 8 figures, A&A accepted, updated figure 6, corrected typo in table 3, updated reference

Simplicial quantum dynamics

Present-day quantum field theory can be regularized by a decomposition into quantum simplices. This replaces the infinite-dimensional Hilbert space by a high-dimensional spinor space and singular canonical Lie groups by regular spin groups. It radically changes the uncertainty principle for small distances. Gaugeons, including the gravitational, are represented as bound fermion-pairs, and space-time curvature as a singular organized limit of quantum non-commutativity. Keywords: Quantum logic, quantum set theory, quantum gravity, quantum topology, simplicial quantization.Comment: 25 pages. 1 table. Conference of the International Association for Relativistic Dynamics, Taiwan, 201

The Role of Bulge Formation in the Homogenization of Stellar Populations at z∼2z\sim2 as revealed by Internal Color Dispersion in CANDELS

We use data from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey to study how the spatial variation in the stellar populations of galaxies relate to the formation of galaxies at $1.5 < z < 3.5$. We use the Internal Color Dispersion (ICD), measured between the rest-frame UV and optical bands, which is sensitive to age (and dust attenuation) variations in stellar populations. The ICD shows a relation with the stellar masses and morphologies of the galaxies. Galaxies with the largest variation in their stellar populations as evidenced by high ICD have disk-dominated morphologies (with S\'{e}rsic indexes $< 2$) and stellar masses between $10 < \mathrm{Log~M/ M_\odot}< 11$. There is a marked decrease in the ICD as the stellar mass and/or the S\'ersic index increases. By studying the relations between the ICD and other galaxy properties including sizes, total colors, star-formation rate, and dust attenuation, we conclude that the largest variations in stellar populations occur in galaxies where the light from newly, high star-forming clumps contrasts older stellar disk populations. This phase reaches a peak for galaxies only with a specific stellar mass range, $10 < \mathrm{Log~M/ M_\odot} < 11$, and prior to the formation of a substantial bulge/spheroid. In contrast, galaxies at higher or lower stellar masses, and/or higher S\'{e}rsic index ($n > 2$) show reduced ICD values, implying a greater homogeneity of their stellar populations. This indicates that if a galaxy is to have both a quiescent bulge along with a star forming disk, typical of Hubble Sequence galaxies, this is most common for stellar masses $10 < \mathrm{Log~M/M_\odot} < 11$ and when the bulge component remains relatively small ($n<2$).Comment: 15 pages, 14 figure

Stellar Populations of Lyman Break Galaxies at z=1-3 in the HST/WFC3 Early Release Science Observations

We analyze the spectral energy distributions (SEDs) of Lyman break galaxies (LBGs) at z=1-3 selected using the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) UVIS channel filters. These HST/WFC3 observations cover about 50 sq. arcmin in the GOODS-South field as a part of the WFC3 Early Release Science program. These LBGs at z=1-3 are selected using dropout selection criteria similar to high redshift LBGs. The deep multi-band photometry in this field is used to identify best-fit SED models, from which we infer the following results: (1) the photometric redshift estimate of these dropout selected LBGs is accurate to within few percent; (2) the UV spectral slope (beta) is redder than at high redshift (z>3), where LBGs are less dusty; (3) on average, LBGs at z=1-3 are massive, dustier and more highly star-forming, compared to LBGs at higher redshifts with similar luminosities (0.1L*<~L<~2.5L*), though their median values are similar within 1-sigma uncertainties. This could imply that identical dropout selection technique, at all redshifts, find physically similar galaxies; and (4) stellar masses of these LBGs are directly proportional to their UV luminosities with a logarithmic slope of ~0.46, and star-formation rates are proportional to their stellar masses with a logarithmic slope of ~0.90. These relations hold true --- within luminosities probed in this study --- for LBGs from z~1.5 to 5. The star-forming galaxies selected using other color-based techniques show similar correlations at z~2, but to avoid any selection biases, and for direct comparison with LBGs at z>3, a true Lyman break selection at z~2 is essential. The future HST UV surveys, both wider and deeper, covering a large luminosity range are important to better understand LBG properties, and their evolution.Comment: Accepted for publication in ApJ (29 pages, 9 figures

Right eigenvalue equation in quaternionic quantum mechanics

We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations. Our discussion is also extended to complex linear operators, whose spectrum is characterized by 2n complex eigenvalues. We show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products. Finally, we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution.Comment: 24 pages, AMS-Te