Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem

We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless it interacts with the observer, and it can't increase unless it interacts with the environment." The former follows from the quantum Bayes Theorem we derive. We show that because of the long-range entanglement created by cosmological inflation, the cosmic entropy decreases exponentially rather than linearly with the number of bits of information observed, so that a given observer can reduce entropy by much more than the amount of information her brain can store. Indeed, we argue that as long as inflation has occurred in a non-negligible fraction of the volume, almost all sentient observers will find themselves in a post-inflationary low-entropy Hubble volume, and we humans have no reason to be surprised that we do so as well, which solves the so-called inflationary entropy problem. An arguably worse problem for unitary cosmology involves gamma-ray-burst constraints on the "Big Snap", a fourth cosmic doomsday scenario alongside the "Big Crunch", "Big Chill" and "Big Rip", where an increasingly granular nature of expanding space modifies our life-supporting laws of physics. Our tripartite framework also clarifies when it is valid to make the popular quantum gravity approximation that the Einstein tensor equals the quantum expectation value of the stress-energy tensor, and how problems with recent attempts to explain dark energy as gravitational backreaction from super-horizon scale fluctuations can be understood as a failure of this approximation.Comment: Updated to match accepted PRD version, including Quantum Bayes Theorem derivation and rigorous proof that decoherence increases von Neumann entropy. 20 pages, 5 fig

Don’t turn your back on the symptoms of psychosis : a proof-of-principle, quasi-experimental public health trial to reduce the duration of untreated psychosis in Birmingham, UK

Background: Reducing the duration of untreated psychosis (DUP) is an aspiration of international guidelines for first episode psychosis; however, public health initiatives have met with mixed results. Systematic reviews suggest that greater focus on the sources of delay within care pathways, (which will vary between healthcare settings) is needed to achieve sustainable reductions in DUP (BJP 198: 256-263; 2011). Methods/Design: A quasi-experimental trial, comparing a targeted intervention area with a ‘detection as usual’ area in the same city. A proof-of–principle trial, no a priori assumptions are made regarding effect size; key outcome will be an estimate of the potential effect size for a definitive trial. DUP and number of new cases will be collected over an 18-month period in target and control areas and compared; historical data on DUP collected in both areas over the previous three years, will serve as a benchmark. The intervention will focus on reducing two significant DUP component delays within the overall care pathway: delays within the mental health service and help-seeking delay. Discussion: This pragmatic trial will be the first to target known delays within the care pathway for those with a first episode of psychosis. If successful, this will provide a generalizable methodology that can be implemented in a variety of healthcare contexts with differing sources of delay. Trial registration: http://www.controlled-trials.com/ISRCTN45058713 Keywords: Public mental health campaign, First-episode psychosis, Early detection, Duration of untreated psychosis, Youth mental healt

The Spectral Energy Distributions and Infrared Luminosities of z \approx 2 Dust Obscured Galaxies from Herschel and Spitzer

Dust-obscured galaxies (DOGs) are a subset of high-redshift (z \approx 2) optically-faint ultra-luminous infrared galaxies (ULIRGs, e.g. L_{IR} > 10^{12} Lsun). We present new far-infrared photometry, at 250, 350, and 500 um (observed-frame), from the Herschel Space Telescope for a large sample of 113 DOGs with spectroscopically measured redshifts. Approximately 60% of the sample are detected in the far-IR, confirming their high IR luminosities, which range from 10^{11.6} Lsun < L_{IR} (8-1000 um) <10^{13.6} Lsun. 90% of the Herschel detected DOGs in this sample are ULIRGs and 30% have L_{IR} > 10^{13} Lsun. The rest-frame near-IR (1 - 3 um) SEDs of the Herschel detected DOGs are predictors of their SEDs at longer wavelengths. DOGs with "power-law" SEDs in the rest-frame near-IR show observed-frame 250/24 um flux density ratios similar to the QSO-like local ULIRG, Mrk 231. DOGs with a stellar "bump" in their rest-frame near-IR show observed-frame 250/24 um flux density ratios similar to local star-bursting ULIRGs like NGC 6240. For the Herschel detected DOGs, accurate estimates (within \approx 25%) of total IR luminosity can be predicted from their rest-frame mid-IR data alone (e.g. from Spitzer observed-frame 24 um luminosities). Herschel detected DOGs tend to have a high ratio of infrared luminosity to rest-frame 8 um luminosity (the IR8= L_{IR}(8-1000 um)/v L_{v}(8 um) parameter of Elbaz et al. 2011). Instead of lying on the z=1-2 "infrared main-sequence" of star forming galaxies (like typical LIRGs and ULIRGs at those epochs) the DOGs, especially large fractions of the bump sources, tend to lie in the starburst sequence. While, Herschel detected DOGs are similar to scaled up versions of local ULIRGs in terms of 250/24 um flux density ratio, and IR8, they tend to have cooler far-IR dust temperatures (20-40 K for DOGs vs. 40-50 K for local ULIRGs). Abridged.Comment: 24 pages, 14 figures, 3 tables, accepted for publication in the Astronomical Journa

Point Source Polarimetry with the Gemini Planet Imager: Sensitivity Characterization with T5.5 Dwarf Companion HD 19467 B

Detecting polarized light from self-luminous exoplanets has the potential to provide key information about rotation, surface gravity, cloud grain size, and cloud coverage. While field brown dwarfs with detected polarized emission are common, no exoplanet or substellar companion has yet been detected in polarized light. With the advent of high contrast imaging spectro-polarimeters such as GPI and SPHERE, such a detection may now be possible with careful treatment of instrumental polarization. In this paper, we present 28 minutes of H-band GPI polarimetric observations of the benchmark T5.5 companion HD 19467 B. We detect no polarization signal from the target, and place an upper limit on the degree of linear polarization of p_(CL99.73%) ⩽ 2.4%. We discuss our results in the context of T dwarf cloud models and photometric variability

The Spectral Energy Distribution of Fermi bright blazars

(Abridged) We have conducted a detailed investigation of the broad-band spectral properties of the \gamma-ray selected blazars of the Fermi LAT Bright AGN Sample (LBAS). By combining our accurately estimated Fermi gamma-ray spectra with Swift, radio, infra-red, optical and other hard X-ray/gamma-ray data, collected within three months of the LBAS data taking period, we were able to assemble high-quality and quasi-simultaneous Spectral Energy Distributions (SED) for 48 LBAS blazars.The SED of these gamma-ray sources is similar to that of blazars discovered at other wavelengths, clearly showing, in the usual Log $\nu$ - Log $\nu$ F$_\nu$ representation, the typical broad-band spectral signatures normally attributed to a combination of low-energy synchrotron radiation followed by inverse Compton emission of one or more components. We have used these SEDs to characterize the peak intensity of both the low and the high-energy components. The results have been used to derive empirical relationships that estimate the position of the two peaks from the broad-band colors (i.e. the radio to optical and optical to X-ray spectral slopes) and from the gamma-ray spectral index. Our data show that the synchrotron peak frequency $\nu_p^S$ is positioned between 10$^{12.5}$ and 10$^{14.5}$ Hz in broad-lined FSRQs and between $10^{13}$ and $10^{17}$ Hz in featureless BL Lacertae objects.We find that the gamma-ray spectral slope is strongly correlated with the synchrotron peak energy and with the X-ray spectral index, as expected at first order in synchrotron - inverse Compton scenarios. However, simple homogeneous, one-zone, Synchrotron Self Compton (SSC) models cannot explain most of our SEDs, especially in the case of FSRQs and low energy peaked (LBL) BL Lacs. (...)Comment: 85 pages, 38 figures, submitted to Ap

IgA in the horse: cloning of equine polymeric Ig receptor and J chain and characterization of recombinant forms of equine IgA

As in other mammals, immunoglobulin A (IgA) in the horse has a key role in immune defense. To better dissect equine IgA function, we isolated complementary DNA (cDNA) clones for equine J chain and polymeric Ig receptor (pIgR). When coexpressed with equine IgA, equine J chain promoted efficient IgA polymerization. A truncated version of equine pIgR, equivalent to secretory component, bound with nanomolar affinity to recombinant equine and human dimeric IgA but not with monomeric IgA from either species. Searches of the equine genome localized equine J chain and pIgR to chromosomes 3 and 5, respectively, with J chain and pIgR coding sequence distributed across 4 and 11 exons, respectively. Comparisons of transcriptional regulatory sequences suggest that horse and human pIgR expression is controlled through common regulatory mechanisms that are less conserved in rodents. These studies pave the way for full dissection of equine IgA function and open up possibilities for immune-based treatment of equine diseases

A personalized platform identifies trametinib plus zoledronate for a patient with KRAS-mutant metastatic colorectal cancer

Colorectal cancer remains a leading source of cancer mortality worldwide. Initial response is often followed by emergent resistance that is poorly responsive to targeted therapies, reflecting currently undruggable cancer drivers such as KRAS and overall genomic complexity. Here, we report a novel approach to developing a personalized therapy for a patient with treatment-resistant metastatic KRAS-mutant colorectal cancer. An extensive genomic analysis of the tumor's genomic landscape identified nine key drivers. A transgenic model that altered orthologs of these nine genes in the Drosophila hindgut was developed; a robotics-based screen using this platform identified trametinib plus zoledronate as a candidate treatment combination. Treating the patient led to a significant response: Target and nontarget lesions displayed a strong partial response and remained stable for 11 months. By addressing a disease's genomic complexity, this personalized approach may provide an alternative treatment option for recalcitrant disease such as KRAS-mutant colorectal cancer

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie