How many random questions are necessary to identify n distinct objects?

AbstractSuppose that X and A are two finite sets of the same cardinality n ⩾ 2. Assume that there is a bijective mapping φ: X → A which is unknown to us, and we must determine it. We are allowed to ask a sequence of questions each posed as follows. For a given B ⊂ A what is φ−1(B)? In this paper we study a case when the subsets B are chosen uniformly at random. The main result is: if each subset has to split all the atoms of a field generated by the previous subsets, then the total number of questions (needed to determine the mapping completely) is log2 n + (1 + op(1))(2 log2 n)12. Here op(1) stands for a random term approaching 0 in probability as n → ∞

Two-Particle Schroedinger Equation Animations of Wavepacket-Wavepacket Scattering (revised)

A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the coordinates of each particle, arbitrary initial and boundary conditions, and multi-dimensional equations. Plots and animations are given here and on the World Wide Web of the scattering of two wavepackets in one dimension.Comment: 13 pages, 8 figures, animations at http://nacphy.physics.orst.edu/ComPhys/PACKETS

Spatial Degrees of Freedom in Everett Quantum Mechanics

Stapp claims that, when spatial degrees of freedom are taken into account, Everett quantum mechanics is ambiguous due to a "core basis problem." To examine an aspect of this claim I generalize the ideal measurement model to include translational degrees of freedom for both the measured system and the measuring apparatus. Analysis of this generalized model using the Everett interpretation in the Heisenberg picture shows that it makes unambiguous predictions for the possible results of measurements and their respective probabilities. The presence of translational degrees of freedom for the measuring apparatus affects the probabilities of measurement outcomes in the same way that a mixed state for the measured system would. Examination of a measurement scenario involving several observers illustrates the consistency of the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material tangential to main point remove

Evolution of Primordial Black Hole Mass Spectrum in Brans-Dicke Theory

We investigate the evolution of primordial black hole mass spectrum by including both accretion of radiation and Hawking evaporation within Brans-Dicke cosmology in radiation, matter and vacuum-dominated eras. We also consider the effect of evaporation of primordial black holes on the expansion dynamics of the universe. The analytic solutions describing the energy density of the black holes in equilibrium with radiation are presented. We demonstrate that these solutions act as attractors for the system ensuring stability for both linear and nonlinear situations. We show, however, that inclusion of accretion of radiation delays the onset of this equilibrium in all radiation, matter and vacuum-dominated eras.Comment: 18 pages, one figur

An Empirical Study of Public Defender Effectiveness: Self-Selection by the "Marginally Indigent"

Abstract: An econometric study of all felony cases filed in Denver, Colorado, in 2002, shows that public defenders achieved poorer outcomes than their privately retained counterparts, measured by the actual sentences defendants received. But this study suggests that the traditional explanation for this difference—under-funding resulting in overburdened public defenders—may not tell the whole story. The authors discovered a large segment of what they call “marginally indigent” defendants, who appear capable of hiring private counsel if the charges against them are sufficiently serious. When the sentence data was controlled for the seriousness of the charges, however, public defenders still performed more poorly than private counsel. These results suggest that at least one explanation for poor public defender outcomes may be that public defender clients, by self selection, tend to have less defensible cases. If marginally indigent defendants can find the money to hire private counsel when the charges are sufficiently serious, perhaps they can also find the money when they are innocent, or think they have a strong case

Occultation analysis of BATSE data: Operational aspects

The Burst and Transient Source Experiment (BATSE) large area detectors are being used to monitor hard x-ray/gamma ray sources on a daily basis for evidence of transient behavior. Flux measurements are performed using a simple earth occultation technique. Daily searches are also being performed to detect occultation steps of sources which are not being routinely monitored. Topics concerning the operational aspects of the occultation measurements are presented. Preliminary spectral results are also presented for several of the brighter sources

Full Quantum Analysis of Two-Photon Absorption Using Two-Photon Wavefunction: Comparison with One-Photon Absorption

For dissipation-free photon-photon interaction at the single photon level, we analyze one-photon transition and two-photon transition induced by photon pairs in three-level atoms using two-photon wavefunctions. We show that the two-photon absorption can be substantially enhanced by adjusting the time correlation of photon pairs. We study two typical cases: Gaussian wavefunction and rectangular wavefunction. In the latter, we find that under special conditions one-photon transition is completely suppressed while the high probability of two-photon transition is maintained.Comment: 6 pages, 4 figure