A Statistical Treatment of the Gamma-Ray Burst "No Host Galaxy" Problem: II. Energies of Standard Candle Bursts

With the discovery that the afterglows after some bursts are coincident with faint galaxies, the search for host galaxies is no longer a test of whether bursts are cosmological, but rather a test of particular cosmological models. The methodology we developed to investigate the original "no host galaxy" problem is equally valid for testing different cosmological models, and is applicable to the galaxies coincident with optical transients. We apply this methodology to a family of models where we vary the total energy of standard candle bursts. We find that total isotropic energies of E<2e52~erg are ruled out while log(E)~53 erg is favored.Comment: To appear in Ap.J., 514, 15 pages + 7 figures, AASTeX 4.0. Revisions are: additional author, updated data, and minor textual change

Determining a quantum state by means of a single apparatus

The unknown state \hrho of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix \hrho and the probabilities of occurrence of the eigenvalues of a single and factorized observable of S+A, so that \hrho can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their $z$-components after a controlled interaction. The most robust setups are determined in this case, for an initially pure or a completely disordered state of A. They involve an Ising or anisotropic Heisenberg coupling and an external field.Comment: 5 pages revte

Dynamics of nodal points and the nodal count on a family of quantum graphs

We investigate the properties of the zeros of the eigenfunctions on quantum graphs (metric graphs with a Schr\"odinger-type differential operator). Using tools such as scattering approach and eigenvalue interlacing inequalities we derive several formulas relating the number of the zeros of the n-th eigenfunction to the spectrum of the graph and of some of its subgraphs. In a special case of the so-called dihedral graph we prove an explicit formula that only uses the lengths of the edges, entirely bypassing the information about the graph's eigenvalues. The results are explained from the point of view of the dynamics of zeros of the solutions to the scattering problem.Comment: 34 pages, 12 figure

Spectral Hardness Decay with Respect to Fluence in BATSE Gamma-Ray Bursts

We have analyzed the evolution of the spectral hardness parameter Epk as a function of fluence in gamma-ray bursts. We fit 41 pulses within 26 bursts with the trend reported by Liang & Kargatis (1996) which found that Epk decays exponentially with respect to photon fluence. We also fit these pulses with a slight modification of this trend, where Epk decays linearly with energy fluence. In both cases, we found the set of 41 pulses to be consistent with the trend. For the latter trend, which we believe to be more physical, the distribution of the decay constant is roughly log-normal, with a mean of 1.75 +/- 0.07 and a FWHM of 1.0 +/- 0.1. Regarding an earlier reported invariance in the decay constant among different pulses in a single burst, we found probabilities of 0.49 to 0.84 (depending on the test used) that such invariance would occur by coincidence, most likely due to the narrow distribution of decay constant values among pulses.Comment: 17 pages, 7 figure pages, 2 table pages, submitted to The Astrophysical Journa

Theory of four-wave mixing of matter waves from a Bose-Einstein condensate

A recent experiment [Deng et al., Nature 398, 218(1999)] demonstrated four-wave mixing of matter wavepackets created from a Bose-Einstein condensate. The experiment utilized light pulses to create two high-momentum wavepackets via Bragg diffraction from a stationary Bose-Einstein condensate. The high-momentum components and the initial low momentum condensate interact to form a new momentum component due to the nonlinear self-interaction of the bosonic atoms. We develop a three-dimensional quantum mechanical description, based on the slowly-varying-envelope approximation, for four-wave mixing in Bose-Einstein condensates using the time-dependent Gross-Pitaevskii equation. We apply this description to describe the experimental observations and to make predictions. We examine the role of phase-modulation, momentum and energy conservation (i.e., phase-matching), and particle number conservation in four-wave mixing of matter waves, and develop simple models for understanding our numerical results.Comment: 18 pages Revtex preprint form, 13 eps figure

Accuracy of Emergency Medical Services Dispatcher and Crew Diagnosis of Stroke in Clinical Practice.

BACKGROUND: Accurate recognition of stroke symptoms by Emergency Medical Services (EMS) is necessary for timely care of acute stroke patients. We assessed the accuracy of stroke diagnosis by EMS in clinical practice in a major US city. METHODS AND RESULTS: Philadelphia Fire Department data were merged with data from a single comprehensive stroke center to identify patients diagnosed with stroke or TIA from 9/2009 to 10/2012. Sensitivity and positive predictive value (PPV) were calculated. Multivariable logistic regression identified variables associated with correct EMS diagnosis. There were 709 total cases, with 400 having a discharge diagnosis of stroke or TIA. EMS crew sensitivity was 57.5% and PPV was 69.1%. EMS crew identified 80.2% of strokes with National Institutes of Health Stroke Scale (NIHSS) ≥5 and symptom durationmodel, correct EMS crew diagnosis was positively associated with NIHSS (NIHSS 5-9, OR 2.62, 95% CI 1.41-4.89; NIHSS ≥10, OR 4.56, 95% CI 2.29-9.09) and weakness (OR 2.28, 95% CI 1.35-3.85), and negatively associated with symptom duration \u3e270 min (OR 0.41, 95% CI 0.25-0.68). EMS dispatchers identified 90 stroke cases that the EMS crew missed. EMS dispatcher or crew identified stroke with sensitivity of 80% and PPV of 50.9%, and EMS dispatcher or crew identified 90.5% of patients with NIHSS ≥5 and symptom duration \u3c6 \u3eh. CONCLUSION: Prehospital diagnosis of stroke has limited sensitivity, resulting in a high proportion of missed stroke cases. Dispatchers identified many strokes that EMS crews did not. Incorporating EMS dispatcher impression into regional protocols may maximize the effectiveness of hospital destination selection and pre-notification

A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening

Understanding the processes that underlie pollen release is a prime target for controlling fertility to enable selective breeding and the efficient production of hybrid crops. Pollen release requires anther opening, which involves changes in the biomechanical properties of the anther wall. In this research, we develop and use a mathematical model to understand how these biomechanical processes lead to anther opening

On the reliability of the theoretical internal conversion coefficients

Possible sources of uncertainties in the calculations of the internal conversion coefficients are studied. The uncertainties induced by them are estimated.Comment: 16 pages (including 3 figures inserted by 'epsfig' macro

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde