Complementation of Subquandles

Saki and Kiani proved that the subrack lattice of a rack $R$ is necessarily complemented if $R$ is finite but not necessarily complemented if $R$ is infinite. In this paper, we investigate further avenues related to the complementation of subquandles. Saki and Kiani's example of an infinite rack without complements is a quandle, which is neither ind-finite nor profinite. We provide an example of an ind-finite quandle whose subobject lattice is not complemented, and conjecture that profinite quandles have complemented subobject lattices. Additionally, we provide a complete classification of subquandles whose set-theoretic complement is also a subquandle, which we call \textit{strongly complemented}, and provide a partial transitivity criterion for the complementation in chains of strongly complemented subquandles. One technical lemma used in establishing this is of independent interest: the inner automorphism group of a subquandle is always a subquotient of the inner automorphism group of the ambient quandle

Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay

Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm i\epsilon$ of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the $S$-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time $t=0$, a beginning of time. Its interpretation and observations are discussed in the last section.Comment: 27 pages, 3 figure

Absolute Frequency Measurements of the Hg^+ and Ca Optical Clock Transitions with a Femtosecond Laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg^+ and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be f_Hg=1 064 721 609 899 143(10) Hz and f_Ca=455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg^+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of |(df_Ca/dt)/f_Ca| < 8 x 10^{-14} yr^{-1}, and |(df_Hg/dt)/f_Hg|< 30 x 10^{-14} yr^{-1}.Comment: 6 pages, including 4 figures. RevTex 4. Submitted to Phys. Rev. Let

Protocol for the development of a core outcome set for clinical trials in primary sclerosing cholangitis

Background: Primary sclerosing cholangitis (PSC) is a progressive immune-mediated liver disease, for which no medical therapy has been shown to slow disease progression. However, the horizon for new therapies is encouraging, with several innovative clinical trials in progress. Despite these advancements, there is considerable heterogeneity in the outcomes studied, with lack of consensus as to what outcomes to measure, when to measure and how to measure. Furthermore, there has been a paradigm shift in PSC treatment targets over recent years, moving from biochemistry-based endpoints to histological assessment of liver fibrosis, imaging-based biomarkers and patient-reported outcome measures. The abundance of new interventional trials and evolving endpoints pose opportunities for all stakeholders involved in evaluating novel therapies. To this effect, there is a need to harmonise measures used in clinical trials through the development of a core outcome set (COS). Methods and analysis: Synthesis of a PSC-specific COS will be conducted in four stages. Initially, a systematic literature review will be performed to identify outcomes previously used in PSC trials, followed by semistructured qualitative interviews conducted with key stakeholders. The latter may include patients, clinicians, researchers, pharmaceutical industry representatives and healthcare payers and regulatory agencies, to identify additional outcomes of importance. Using the outcomes generated from the literature review and stakeholder interviews, an international two-round Delphi survey will be conducted to prioritise outcomes for inclusion in the COS. Finally, a consensus meeting will be convened to ratify the COS and disseminate findings for application in future PSC trials. Ethics and dissemination: Ethical approval has been granted by the East Midlands—Leicester Central Research Ethics Committee (Ref: 24/EM/0126) for this study. The COS from this study will be widely disseminated including publication in peer-reviewed journals, international conferences, promotion through patient-support groups and made available on the Core Outcomes Measurement in Effectiveness Trials (COMET) database. Trial registration number: 1239

Protocol for the development of a core outcome set for clinical trials in primary sclerosing cholangitis

Background: Primary sclerosing cholangitis (PSC) is a progressive immune-mediated liver disease, for which no medical therapy has been shown to slow disease progression. However, the horizon for new therapies is encouraging, with several innovative clinical trials in progress. Despite these advancements, there is considerable heterogeneity in the outcomes studied, with lack of consensus as to what outcomes to measure, when to measure and how to measure. Furthermore, there has been a paradigm shift in PSC treatment targets over recent years, moving from biochemistry-based endpoints to histological assessment of liver fibrosis, imaging-based biomarkers and patient-reported outcome measures. The abundance of new interventional trials and evolving endpoints pose opportunities for all stakeholders involved in evaluating novel therapies. To this effect, there is a need to harmonise measures used in clinical trials through the development of a core outcome set (COS). Methods and analysis: Synthesis of a PSC-specific COS will be conducted in four stages. Initially, a systematic literature review will be performed to identify outcomes previously used in PSC trials, followed by semistructured qualitative interviews conducted with key stakeholders. The latter may include patients, clinicians, researchers, pharmaceutical industry representatives and healthcare payers and regulatory agencies, to identify additional outcomes of importance. Using the outcomes generated from the literature review and stakeholder interviews, an international two-round Delphi survey will be conducted to prioritise outcomes for inclusion in the COS. Finally, a consensus meeting will be convened to ratify the COS and disseminate findings for application in future PSC trials. Ethics and dissemination: Ethical approval has been granted by the East Midlands—Leicester Central Research Ethics Committee (Ref: 24/EM/0126) for this study. The COS from this study will be widely disseminated including publication in peer-reviewed journals, international conferences, promotion through patient-support groups and made available on the Core Outcomes Measurement in Effectiveness Trials (COMET) database. Trial registration number: 1239

Mercury isotope evidence for Arctic summertime re-emission of mercury from the cryosphere

During Arctic springtime, halogen radicals oxidize atmospheric elemental mercury (Hg-0), which deposits to the cryosphere. This is followed by a summertime atmospheric Hg-0 peak that is thought to result mostly from terrestrial Hg inputs to the Arctic Ocean, followed by photoreduction and emission to air. The large terrestrial Hg contribution to the Arctic Ocean and global atmosphere has raised concern over the potential release of permafrost Hg, via rivers and coastal erosion, with Arctic warming. Here we investigate Hg isotope variability of Arctic atmospheric, marine, and terrestrial Hg. We observe highly characteristic Hg isotope signatures during the summertime peak that reflect re-emission of Hg deposited to the cryosphere during spring. Air mass back trajectories support a cryospheric Hg emission source but no major terrestrial source. This implies that terrestrial Hg inputs to the Arctic Ocean remain in the marine ecosystem, without substantial loss to the global atmosphere, but with possible effects on food webs.Arctic warming thaws permafrost, leading to enhanced soil mercury transport to the Arctic Ocean. Mercury isotope signatures in arctic rivers, ocean and atmosphere suggest that permafrost mercury is buried in marine sediment and not emitted to the global atmospherePeer reviewe

Early deletion of neuromeres in Wnt-1 -/- mutant mice: Evaluation by morphological and molecular markers

The Wnt-1 gene is required for the development of midbrain and cerebellum; previous work showed that knockout of Wnt-1 causes the loss of most molecular markers of these structures in early embryos and deletion of these structures by birth. However, neither the extent of early neuronal defects nor any possible alterations in structures adjacent to presumptive midbrain and cerebellum were examined. By using a neuron-specific antibody and fluorescent axon tracers, we show that central and peripheral neuronal development are altered in mutants during initial axonogenesis on embryonic day 9.5. The absence of neuronal landmarks, including oculomotor and trochlear nerves and cerebellar plate, suggests that both mesencephalon and rhombomere 1 (r1) are deleted, with the remaining neural tube fused to form a new border between the caudalmost portion of the prosencephalon (prosomere 1, or p1) and r2. Central axons accurately traverse this novel border by forming normal longitudinal tracts into the rhombencephalon, implying that the cues that direct these axons are aligned across neuromeres and are not affected by the deletion. The presence of intact p1 and r2 is further supported by the retention of markers for these two neuromeres, including a marker of p1, the Sim-2 gene, and an r2-specific lacZ transgene in mutant embryos. In addition, alterations in the Sim-2 expression domain in ventral prosencephalon, rostral to p1, provide novel evidence for Wnt-1 function in this region. © 1996 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50070/1/7_ftp.pd

Gas/particle Interaction in Ultrasound Agitated Gas Flow

AbstractAcoustic waves imply specific force and stress distributions onto particles in a gaseous environment. In this paper time-dependent and time-averaged acoustic forces of resonant standing ultrasound waves on rigid particles and agglomerates in gaseous environment are investigated by numerical simulation. The calculated resonant standing wave field is validated using experimental data. Acoustic forces are calculated for cylindrical and spherical particle geometries and the resulting values are compared with analytic correlations from literature. The position of the bodies in respect to the sound source was varied to study the local dependence of the acoustic force. Characteristics of gas/particle interaction in ultrasound agitated gas flow are discussed

Educational development between faculty and administration

This essay employs Identity Theory to explore the professional identities of educational developers, arguing that it is important to pay attention to the different saliences, or weights, that developers attach to the faculty and administrative sides of their identities

Reduced Photoinhibition under Low Irradiance Enhanced Kacip Fatimah (Labisia pumila Benth) Secondary Metabolites, Phenyl Alanine Lyase and Antioxidant Activity

A randomized complete block design experiment was designed to characterize the relationship between production of total flavonoids and phenolics, anthocyanin, photosynthesis, maximum efficiency of photosystem II (Fv/Fm), electron transfer rate (Fm/Fo), phenyl alanine lyase activity (PAL) and antioxidant (DPPH) in Labisia pumila var. alata, under four levels of irradiance (225, 500, 625 and 900 μmol/m2/s) for 16 weeks. As irradiance levels increased from 225 to 900 μmol/m2/s, the production of plant secondary metabolites (total flavonoids, phenolics and antocyanin) was found to decrease steadily. Production of total flavonoids and phenolics reached their peaks under 225 followed by 500, 625 and 900 μmol/m2/s irradiances. Significant positive correlation of production of total phenolics, flavonoids and antocyanin content with Fv/Fm, Fm/Fo and photosynthesis indicated up-regulation of carbon-based secondary metabolites (CBSM) under reduced photoinhibition on the under low light levels condition. At the lowest irradiance levels, Labisia pumila extracts also exhibited a significantly higher antioxidant activity (DPPH) than under high irradiance. The improved antioxidative activity under low light levels might be due to high availability of total flavonoids, phenolics and anthocyanin content in the plant extract. It was also found that an increase in the production of CBSM was due to high PAL activity under low light, probably signifying more availability of phenylalanine (Phe) under this condition