Positive definite rational functions of two variables which are not the sum of three squares

AbstractCassels, Ellison, and Pfister have shown that there is a positive semidefinite function of R(x, y) that is not the sum of three squares. In this paper positive definite functions of R(x, y) are found having the same property. The proof involves showing the nonexistence of points on some elliptic curves defined over C(x), and extends the methods of [1]

Optogenetic manipulation of stomatal kinetics improves carbon assimilation, water use, and growth

Stomata serve dual and often conflicting roles, facilitating carbon dioxide influx into the plant leaf for photosynthesis and restricting water efflux via transpiration. Strategies for reducing transpiration without incurring a cost for photosynthesis must circumvent this inherent coupling of carbon dioxide and water vapor diffusion. We expressed the synthetic, light-gated K+ channel BLINK1 in guard cells surrounding stomatal pores in Arabidopsis to enhance the solute fluxes that drive stomatal aperture. BLINK1 introduced a K+ conductance and accelerated both stomatal opening under light exposure and closing after irradiation. Integrated over the growth period, BLINK1 drove a 2.2-fold increase in biomass in fluctuating light without cost in water use by the plant. Thus, we demonstrate the potential of enhancing stomatal kinetics to improve water use efficiency without penalty in carbon fixation

Pade/renormalization-group improvement of inclusive semileptonic B decay rates

Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works favorably in the b \to u case whereas the pole mass scheme shows better convergence in the b \to c case. Upon the inclusion of the estimated three-loop contribution, we find the full perturbative decay rate to be 192\pi^3\Gamma(b\to u\bar\nu_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2065 \pm 290{\rm GeV^5} and 192\pi^3\Gamma(b\to c\ell^-\bar\nu_\ell)/(G_F^2|V_{cb}|^2)= 992 \pm 198 {\rm GeV^5}, respectively. The errors are inclusive of theoretical uncertainties and non-perturbative effects. Ultimately, these perturbative contributions reduce the theoretical uncertainty in the extraction of the CKM matrix elements |V_{ub}| and |V_{cb}| from their respective measured inclusive semileptonic branching ratio(s).Comment: 3 pages, latex using espcrc2.sty. Write-up of talk given at BEACH 2002, UBC, Vancouve

COVID-19 unmasked global collaboration protocol:Longitudinal cohort study examining mental health of young children and caregivers during the pandemic

Background: Early empirical data shows that school-aged children, adolescents and adults are experiencing elevated levels of anxiety and depression during the COVID-19 pandemic. Currently, there is very little research on mental health outcomes for young children. Objectives: To describe the formation of a global collaboration entitled, 'COVID-19 Unmasked'. The collaborating researchers aim to (1) describe and compare the COVID-19 related experiences within and across countries; (2) examine mental health outcomes for young children (1 to 5 years) and caregivers over a 12-month period during the COVID-19 pandemic; (3) explore the trajectories/time course of psychological outcomes of the children and parents over this period and (4) identify the risk and protective factors for different mental health trajectories. Data will be combined from all participating countries into one large open access cross-cultural dataset to facilitate further international collaborations and joint publications. Methods: COVID-19 Unmasked is an online prospective longitudinal cohort study. An international steering committee was formed with the aim of starting a global collaboration. Currently, partnerships have been formed with 9 countries (Australia, Cyprus, Greece, the Netherlands, Poland, Spain, Turkey, the UK, and the United States of America). Research partners have started to start data collection with caregivers of young children aged 1-5 years old at baseline, 3-months, 6-months, and 12-months. Caregivers are invited to complete an online survey about COVID-19 related exposure and experiences, child's wellbeing, their own mental health, and parenting. Data analysis: Primary study outcomes will be child mental health as assessed by scales from the Patient-Reported Outcomes Measurement Information System - Early Childhood (PROMIS-EC) and caregiver mental health as assessed by the Depression Anxiety Stress Scale (DASS-21). The trajectories/time course of mental health difficulties and the impact of risk and protective factors will be analysed using hierarchical linear models, accounting for nested effects (e.g. country) and repeated measures

Partonic flow and ϕ\phi-meson production in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We present first measurements of the $\phi$-meson elliptic flow ($v_{2}(p_{T})$) and high statistics $p_{T}$ distributions for different centralities from $\sqrt{s_{NN}}$ = 200 GeV Au+Au collisions at RHIC. In minimum bias collisions the $v_{2}$ of the $\phi$ meson is consistent with the trend observed for mesons. The ratio of the yields of the $\Omega$ to those of the $\phi$ as a function of transverse momentum is consistent with a model based on the recombination of thermal $s$ quarks up to $p_{T}\sim 4$ GeV/$c$, but disagrees at higher momenta. The nuclear modification factor ($R_{CP}$) of $\phi$ follows the trend observed in the $K^{0}_{S}$ mesons rather than in $\Lambda$ baryons, supporting baryon-meson scaling. Since $\phi$-mesons are made via coalescence of seemingly thermalized $s$ quarks in central Au+Au collisions, the observations imply hot and dense matter with partonic collectivity has been formed at RHIC.Comment: 6 pages, 4 figures, submit to PR

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

The energy dependence of ptp_t angular correlations inferred from mean-ptp_{t} fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure suggests that the principal source of $p_t$ correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related fluctuations near 10 GeV.Comment: 10 pages, 4 figure

Measurement of Transverse Single-Spin Asymmetries for Di-Jet Production in Proton-Proton Collisions at s=200\sqrt{s} = 200 GeV

We report the first measurement of the opening angle distribution between pairs of jets produced in high-energy collisions of transversely polarized protons. The measurement probes (Sivers) correlations between the transverse spin orientation of a proton and the transverse momentum directions of its partons. With both beams polarized, the wide pseudorapidity ($-1 \leq \eta \leq +2$) coverage for jets permits separation of Sivers functions for the valence and sea regions. The resulting asymmetries are all consistent with zero and considerably smaller than Sivers effects observed in semi-inclusive deep inelastic scattering (SIDIS). We discuss theoretical attempts to reconcile the new results with the sizable transverse spin effects seen in SIDIS and forward hadron production in pp collisions.Comment: 6 pages total, 1 Latex file, 3 PS files with figure

Energy and system size dependence of \phi meson production in Cu+Cu and Au+Au collisions

We study the beam-energy and system-size dependence of \phi meson production (using the hadronic decay mode \phi -- K+K-) by comparing the new results from Cu+Cu collisions and previously reported Au+Au collisions at \sqrt{s_NN} = 62.4 and 200 GeV measured in the STAR experiment at RHIC. Data presented are from mid-rapidity (|y|<0.5) for 0.4 < pT < 5 GeV/c. At a given beam energy, the transverse momentum distributions for \phi mesons are observed to be similar in yield and shape for Cu+Cu and Au+Au colliding systems with similar average numbers of participating nucleons. The \phi meson yields in nucleus-nucleus collisions, normalised by the average number of participating nucleons, are found to be enhanced relative to those from p+p collisions with a different trend compared to strange baryons. The enhancement for \phi mesons is observed to be higher at \sqrt{s_NN} = 200 GeV compared to 62.4 GeV. These observations for the produced \phi(s\bar{s}) mesons clearly suggest that, at these collision energies, the source of enhancement of strange hadrons is related to the formation of a dense partonic medium in high energy nucleus-nucleus collisions and cannot be alone due to canonical suppression of their production in smaller systems.Comment: 20 pages and 5 figure

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure