Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo

Theory and experiment of entanglement in a quasi-phase-matched two-crystal source

We report new results regarding a source of polarization entangled photon-pairs created by the process of spontaneous parametric downconversion in two orthogonally oriented, periodically poled, bulk KTiOPO4 crystals (PPKTP). The source emits light colinearly at the non-degenerate wavelengths of 810 nm and 1550 nm, and is optimized for single-mode optical fiber collection and long-distance quantum communication. The configuration favors long crystals, which promote a high photon-pair production rate at a narrow bandwidth, together with a high pair-probability in fibers. The quality of entanglement is limited by chromatic dispersion, which we analyze by determining the output state. We find that such a decoherence effect is strongly material dependent, providing for long crystals an upper bound on the visibility of the coincidence fringes of 41% for KTiOPO4, and zero for LiNbO3. The best obtained raw visibility, when canceling decoherence with an extra piece of crystal, was 91 \pm 0.2%, including background counts. We confirm by a violation of the CHSH-inequality (S = 2.679 \pm 0.004 at 55 s^{-1/2} standard deviations) and by complete quantum state tomography that the fibers carry high-quality entangled pairs at a maximum rate of 55 x 10^3 s^{-1}THz^{-1}mW^{-1}.Comment: 12 pages, 10 figures, REVTeX

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations

Synthesis and evaluation of designed PKC modulators for enhanced cancer immunotherapy.

Bryostatin 1 is a marine natural product under investigation for HIV/AIDS eradication, the treatment of neurological disorders, and enhanced CAR T/NK cell immunotherapy. Despite its promising activity, bryostatin 1 is neither evolved nor optimized for the treatment of human disease. Here we report the design, synthesis, and biological evaluation of several close-in analogs of bryostatin 1. Using a function-oriented synthesis approach, we synthesize a series of bryostatin analogs designed to maintain affinity for bryostatin's target protein kinase C (PKC) while enabling exploration of their divergent biological functions. Our late-stage diversification strategy provides efficient access to a library of bryostatin analogs, which per our design retain affinity for PKC but exhibit variable PKC translocation kinetics. We further demonstrate that select analogs potently increase cell surface expression of CD22, a promising CAR T cell target for the treatment of leukemias, highlighting the clinical potential of bryostatin analogs for enhancing targeted immunotherapies

Characterization of designed, synthetically accessible bryostatin analog HIV latency reversing agents.

HIV latency in resting CD4+ T cell represents a key barrier preventing cure of the infection with antiretroviral drugs alone. Latency reversing agents (LRAs) can activate HIV expression in latently infected cells, potentially leading to their elimination through virus-mediated cytopathic effects, host immune responses, and/or therapeutic strategies targeting cells actively expressing virus. We have recently described several structurally simplified analogs of the PKC modulator LRA bryostatin (termed bryologs) designed to improve synthetic accessibility, tolerability in vivo, and efficacy in inducing HIV latency reversal. Here we report the comparative performance of lead bryologs, including their effects in reducing cell surface expression of HIV entry receptors, inducing proinflammatory cytokines, inhibiting short-term HIV replication, and synergizing with histone deacetylase inhibitors to reverse HIV latency. These data provide unique insights into structure-function relationships between A- and B-ring bryolog modifications and activities in primary cells, and suggest that bryologs represent promising leads for preclinical advancement

Histone chaperone HIRA deposits histone H3.3 onto foreign viral DNA and contributes to anti-viral intrinsic immunity

The HIRA histone chaperone complex deposits histone H3.3 into nucleosomes in a DNA replication- and sequence-independent manner. As herpesvirus genomes enter the nucleus as naked DNA, we asked whether the HIRA chaperone complex affects herpesvirus infection. After infection of primary cells with HSV or CMV, or transient transfection with naked plasmid DNA, HIRA re-localizes to PML bodies, sites of cellular anti-viral activity. HIRA co-localizes with viral genomes, binds to incoming viral and plasmid DNAs and deposits histone H3.3 onto these. Anti-viral interferons (IFN) specifically induce HIRA/PML co-localization at PML nuclear bodies and HIRA recruitment to IFN target genes, although HIRA is not required for IFN-inducible expression of these genes. HIRA is, however, required for suppression of viral gene expression, virus replication and lytic infection and restricts murine CMV replication in vivo. We propose that the HIRA chaperone complex represses incoming naked viral DNAs through chromatinization as part of intrinsic cellular immunity

BLAST Observations of the South Ecliptic Pole field: Number Counts and Source Catalogs

We present results from a survey carried out by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST) on a 9 deg^2 field near the South Ecliptic Pole at 250, 350 and 500 {\mu}m. The median 1{\sigma} depths of the maps are 36.0, 26.4 and 18.4 mJy, respectively. We apply a statistical method to estimate submillimeter galaxy number counts and find that they are in agreement with other measurements made with the same instrument and with the more recent results from Herschel/SPIRE. Thanks to the large field observed, the new measurements give additional constraints on the bright end of the counts. We identify 132, 89 and 61 sources with S/N>4 at 250, 350, 500 {\mu}m, respectively and provide a multi-wavelength combined catalog of 232 sources with a significance >4{\sigma} in at least one BLAST band. The new BLAST maps and catalogs are available publicly at http://blastexperiment.info.Comment: 25 pages, 6 figures, 4 tables, Accepted by ApJS. Maps and catalogs available at http://blastexperiment.info

The impact of opiate substitution treatment on mortality risk in drug addicts: a natural experiment study

Background Opiate substitution treatment (OST) is the main treatment for people addicted to heroin and other opioid drugs. However, there is limited information on how the delivery of this treatment affects mortality risk.Objectives To investigate the associations of mortality risk with periods during treatment and following cessation of treatment, medication type, co-prescription of other medication and dosing regimens during titration and detoxification. The trends with time of prescribed medication, dose and treatment duration were also explored.Design Prospective longitudinal observational study.Setting UK primary care between 1998 and 2014.Participants A total of 12,780 patients receiving methadone, buprenorphine or dihydrocodeine.Main outcome measures All-cause mortality relating to 657 deaths and drug-related poisoning relating to 113 deaths.Data sources Clinical Practice Research Datalink with linked information on cause of death from the Office for National Statistics.Results For both outcomes, the lowest mortality risk was observed after 4 weeks of treatment and the highest risk was observed in the first 4 weeks following cessation of treatment [e.g. for drug-related poisoning, incidence rate ratio (IRR) 8.15, 95% confidence interval (CI) 5.45 to 12.19]. There was evidence that the treatment period risks varied with OST medication. The largest difference in risk was for the first 4 weeks of treatment for both outcomes, with patients on buprenorphine being at lower risk than those on methadone (e.g. for drug-related poisoning, IRR 0.08, 95% CI 0.01 to 0.48). The co-prescription of benzodiazepines was associated with linearly increasing the risk of drug-related deaths by dose (IRR 2.02, 95% CI 1.66 to 2.47), whereas z-drugs (zolpidem, zopiclone and zaleplon) were associated with increased risk of both all-cause (IRR 1.83, 95% CI 1.59 to 2.12) and drug-related (IRR 3.31, 95% CI 2.45 to 4.47) mortality. There was weak evidence that higher initial and final doses were associated with increased all-cause mortality risk. In the first 4 weeks of treatment, the risk increased by 4% for each 5-mg increment in methadone dose (1-mg increase in buprenorphine) (hazard ratio 1.04, 95% CI 1.00 to 1.09). In the first 4 weeks after treatment ceased, a similar increment in final dose increased the risk by 3% (hazard ratio 1.03, 95% CI 0.99 to 1.07). There were too few deaths to evaluate the effects on drug-related poisoning. The proportion of OST patients receiving buprenorphine increased between 1998 and 2006. Median treatment duration was consistently shorter for buprenorphine than for methadone for each year studied (overall median duration of 48 and 106 days, respectively).Limitations As this was an observational study, the possibility remains of bias from unmeasured factors, which covariate adjustment and inverse probability weighting can eliminate only partially.Conclusions Using buprenorphine as an alternative to methadone may not reduce mortality overall despite resulting in lower IRRs from shorter treatment duration. Clinical guidance needs to consider strengthening warnings about the co-prescription of a range of drugs for OST patients.Future work Our analyses need to be replicated using other clinical data sets in the UK and in other countries. New interventions and trials are required to investigate improving the retention of OST patients in primary care.Funding The National Institute for Health Research Health Services and Delivery Research programme

Implementation of the LANS-alpha turbulence model in a primitive equation ocean model

This paper presents the first numerical implementation and tests of the Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a primitive equation ocean model. The ocean model in which we work is the Los Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full POP-alpha algorithm is derived from the LANS-alpha primitive equations, but requires a nested iteration that makes it too slow for practical simulations; a reduced POP-alpha algorithm is proposed, which lacks the nested iteration and is two to three times faster than the full algorithm. The reduced algorithm does not follow from a formal derivation of the LANS-alpha model equations. Despite this, simulations of the reduced algorithm are nearly identical to the full algorithm, as judged by globally averaged temperature and kinetic energy, and snapshots of temperature and velocity fields. Both POP-alpha algorithms can run stably with longer timesteps than standard POP. Comparison of implementations of full and reduced POP-alpha algorithms are made within an idealized test problem that captures some aspects of the Antarctic Circumpolar Current, a problem in which baroclinic instability is prominent. Both POP-alpha algorithms produce statistics that resemble higher-resolution simulations of standard POP. A linear stability analysis shows that both the full and reduced POP-alpha algorithms benefit from the way the LANS-alpha equations take into account the effects of the small scales on the large. Both algorithms (1) are stable; (2) make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity waves.Comment: Submitted to J. Computational Physics March 21, 200