Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory

Recently two groups have listed all sets of weights (k_1,...,k_5) such that the weighted projective space P_4^{(k_1,...,k_5)} admits a transverse Calabi-Yau hypersurface. It was noticed that the corresponding Calabi-Yau manifolds do not form a mirror symmetric set since some 850 of the 7555 manifolds have Hodge numbers (b_{11},b_{21}) whose mirrors do not occur in the list. By means of Batyrev's construction we have checked that each of the 7555 manifolds does indeed have a mirror. The `missing mirrors' are constructed as hypersurfaces in toric varieties. We show that many of these manifolds may be interpreted as non-transverse hypersurfaces in weighted P_4's, ie, hypersurfaces for which dp vanishes at a point other than the origin. This falls outside the usual range of Landau--Ginzburg theory. Nevertheless Batyrev's procedure provides a way of making sense of these theories.Comment: 29 pages, plain TeX. Two figures submitted separately as a uuencoded file. A plot at the end of the paper requires an extended memory version of TeX. Instructions for suppressing the plot included at head of source fil

Vacuum field energy and spontaneous emission in anomalously dispersive cavities

Anomalously dispersive cavities, particularly white light cavities, may have larger bandwidth to finesse ratios than their normally dispersive counterparts. Partly for this reason, their use has been proposed for use in LIGO-like gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze the quantum noise associated with anomalously dispersive cavity modes. The vacuum field energy associated with a particular cavity mode is proportional to the cavity-averaged group velocity of that mode. For anomalously dispersive cavities with group index values between 1 and 0, this means that the total vacuum field energy associated with a particular cavity mode must exceed $\hbar \omega/2$. For white light cavities in particular, the group index approaches zero and the vacuum field energy of a particular spatial mode may be significantly enhanced. We predict enhanced spontaneous emission rates into anomalously dispersive cavity modes and broadened laser linewidths when the linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure

Do we need to rethink guidance on repeated interviews?

Within the legal system, children are frequently interviewed about their experiences more than once, with different information elicited in different interviews. The presumed positive and negative effects of multiple interviewing have generated debate and controversy within the legal system and among researchers. Some commentators emphasise that repeated interviews foster inaccurate recall and are inherently suggestive, whereas others emphasise the benefits of allowing witnesses more than one opportunity to recall information. In this article we briefly review the literature on repeated interviewing before presenting a series of cases highlighting what happens when children are interviewed more than once for various reasons. We conclude that, when interviewers follow internationally recognised best-practice guidelines emphasising open-questions and free memory recall, alleged victims of abuse should be interviewed more than once to ensure that more complete accounts are obtained. Implications for current legal guidelines concerning repeated interviewing are discussed

High resolution radio study of the Pulsar Wind Nebula within the Supernova Remnant G0.9+0.1

We have conducted a radio study at 3.6, 6 and 20 cm using ATCA and VLA and reprocessed XMM-Newton and Chandra data of the pulsar wind nebula (PWN) in the supernova remnant (SNR) G0.9+0.1. The new observations revealed that the morphology and symmetry suggested by Chandra observations (torus and jet-like features) are basically preserved in the radio range in spite of the rich structure observed in the radio emission of this PWN, including several arcs, bright knots, extensions and filaments. The reprocessed X-ray images show for the first time that the X-ray plasma fills almost the same volume as the radio PWN. Notably the X-ray maximum does not coincide with the radio maximum and the neutron star candidate CXOU J174722.8-280915 lies within a small depression in the radio emission. From the new radio data we have refined the flux density estimates, obtaining S(PWN) ~ 1.57 Jy, almost constant between 3.6 and 20 cm. For the whole SNR (compact core and shell), a flux density S(at 20 cm)= 11.5 Jy was estimated. Based on the new and the existing 90 cm flux density estimates, we derived alpha(PWN)=-0.18+/-0.04 and alpha(shell)=-0.68+/- 0.07. From the combination of the radio data with X-ray data, a spectral break is found near nu ~ 2.4 x 10^(12) Hz. The total radio PWN luminosity is L(radio)=1.2 x 10^(35) erg s^(-1) when a distance of 8.5 kpc is adopted. By assuming equipartition between particle and magnetic energies, we estimate a nebular magnetic field B = 56 muG. The associated particle energy turns out to be U(part)=5 x 10^(47) erg and the magnetic energy U(mag)=2 x 10^(47) erg. Based on an empirical relation between X-ray luminosity and pulsar energy loss rate, and the comparison with the calculated total energy, a lower limit of 1100 yr is derived for the age of this PWN.Comment: 10 pages,8 figures, accepted for publication in A&A, June 13 200

Complementary Metagenomic Approaches Improve Reconstruction of Microbial Diversity in a Forest Soil.

Soil ecosystems harbor diverse microorganisms and yet remain only partially characterized as neither single-cell sequencing nor whole-community sequencing offers a complete picture of these complex communities. Thus, the genetic and metabolic potential of this "uncultivated majority" remains underexplored. To address these challenges, we applied a pooled-cell-sorting-based mini-metagenomics approach and compared the results to bulk metagenomics. Informatic binning of these data produced 200 mini-metagenome assembled genomes (sorted-MAGs) and 29 bulk metagenome assembled genomes (MAGs). The sorted and bulk MAGs increased the known phylogenetic diversity of soil taxa by 7.2% with respect to the Joint Genome Institute IMG/M database and showed clade-specific sequence recruitment patterns across diverse terrestrial soil metagenomes. Additionally, sorted-MAGs expanded the rare biosphere not captured through MAGs from bulk sequences, exemplified through phylogenetic and functional analyses of members of the phylum Bacteroidetes Analysis of 67 Bacteroidetes sorted-MAGs showed conserved patterns of carbon metabolism across four clades. These results indicate that mini-metagenomics enables genome-resolved investigation of predicted metabolism and demonstrates the utility of combining metagenomics methods to tap into the diversity of heterogeneous microbial assemblages.IMPORTANCE Microbial ecologists have historically used cultivation-based approaches as well as amplicon sequencing and shotgun metagenomics to characterize microbial diversity in soil. However, challenges persist in the study of microbial diversity, including the recalcitrance of the majority of microorganisms to laboratory cultivation and limited sequence assembly from highly complex samples. The uncultivated majority thus remains a reservoir of untapped genetic diversity. To address some of the challenges associated with bulk metagenomics as well as low throughput of single-cell genomics, we applied flow cytometry-enabled mini-metagenomics to capture expanded microbial diversity from forest soil and compare it to soil bulk metagenomics. Our resulting data from this pooled-cell sorting approach combined with bulk metagenomics revealed increased phylogenetic diversity through novel soil taxa and rare biosphere members. In-depth analysis of genomes within the highly represented Bacteroidetes phylum provided insights into conserved and clade-specific patterns of carbon metabolism

ANIS: High Energy Neutrino Generator for Neutrino Telescopes

We present the high-energy neutrino Monte Carlo event generator ANIS (All Neutrino Interaction Simulation). The program provides a detailed and flexible neutrino event simulation for high-energy neutrino detectors, such as AMANDA, ANTARES or ICECUBE. It generates neutrinos of any flavor according to a specified flux and propagates them through the Earth. In a final step neutrino interactions are simulated within a specified volume. All relevant standard model processes are implemented. We discuss strengths and limitations of the program.Comment: 15 pages, 4 figure

Matrices commuting with a given normal tropical matrix

Consider the space $M_n^{nor}$ of square normal matrices $X=(x_{ij})$ over $\mathbb{R}\cup\{-\infty\}$, i.e., $-\infty\le x_{ij}\le0$ and $x_{ii}=0$. Endow $M_n^{nor}$ with the tropical sum $\oplus$ and multiplication $\odot$. Fix a real matrix $A\in M_n^{nor}$ and consider the set $\Omega(A)$ of matrices in $M_n^{nor}$ which commute with $A$. We prove that $\Omega(A)$ is a finite union of alcoved polytopes; in particular, $\Omega(A)$ is a finite union of convex sets. The set $\Omega^A(A)$ of $X$ such that $A\odot X=X\odot A=A$ is also a finite union of alcoved polytopes. The same is true for the set $\Omega'(A)$ of $X$ such that $A\odot X=X\odot A=X$. A topology is given to $M_n^{nor}$. Then, the set $\Omega^{A}(A)$ is a neighborhood of the identity matrix $I$. If $A$ is strictly normal, then $\Omega'(A)$ is a neighborhood of the zero matrix. In one case, $\Omega(A)$ is a neighborhood of $A$. We give an upper bound for the dimension of $\Omega'(A)$. We explore the relationship between the polyhedral complexes $span A$, $span X$ and $span (AX)$, when $A$ and $X$ commute. Two matrices, denoted $\underline{A}$ and $\bar{A}$, arise from $A$, in connection with $\Omega(A)$. The geometric meaning of them is given in detail, for one example. We produce examples of matrices which commute, in any dimension.Comment: Journal versio

Engineering—an introduction to a creative profession, G. C. Beakley and H. W. Leach, MaCmillan Company, New York (1968). 548 pages

No Abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37351/1/690150304_ftp.pd

The Shifting Origins of International Law

Both state-centrism and Euro-centrism are under challenge in international law today and this double challenge, this work argues, is being fruitfully mirrored back into the study of the history of international law. It examines, in the first section, the effects of the rise of positivism as a method of norm-identification and the role of methodological nationalism over the study of the history of international law in the modern foundational period of international law. This is extended by an examination of how this bequeathed a double exclusionary bias regarding time and space to the study of the history of international law as well as a reiterative focus on a series of canonical events and authors to the exclusion of others such as those related to the Islamic history of international law. In the second section, the analysis turns to address why this state of historiographical affairs is changing, specifically highlighting intra-disciplinary developments within the field of the history of international law and the effects that the “international turn in the writing of history” is having on the writing of a new history of international law for a global age. The conclusion reflects on some of the tasks ahead by providing a series of historiographical signposts for the history of international law as a field of new research

Introduction to engineering design, Thomas T. Woodson, Mcgraw-Hill, New York (1966). 434 pages, $9.95

No Abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/37349/1/690130502_ftp.pd