Quantum Algorithms for Some Hidden Shift Problems

Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structures of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation. In this paper, we present three examples of "unknown shift" problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. For one of these problems, the shifted Legendre symbol problem, we give evidence that the problem is hard to solve classically, by showing a reduction from breaking algebraically homomorphic cryptosystems. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure

Factors Associated with Exclusive Breastfeeding in Timor-Leste: Findings from Demographic and Health Survey 2009-2010

Exclusive breastfeeding is known to have nutritional and health benefits. This study investigated factors associated with exclusive breastfeeding among infants aged five months or less in Timor-Leste.The latest data from the national Demographic and Health Survey 2009-2010 were analyzed by binary logistic regression. Of the 975 infants included in the study, overall 49% (95% confidence interval 45.5% to 52.7%) were exclusively breastfed. The exclusive breastfeeding prevalence declined with increasing infant age, mothers with a paid occupation, who perceived their newborn as non-average size, and residence in the capital city Dili, was associated with a lower likelihood of exclusive breastfeeding. On the other hand, women who could decide health-related matters tended to breastfeed exclusively, which was not the case for others whose decisions were made by someone else. The results suggested the need of breastfeeding promotion programs to improve the exclusive breastfeeding rate. Antenatal counseling, peer support network, and home visits by health workers could be feasible options to promote exclusive breastfeeding given that the majority of births occur at home

Model for Cameron band emission in comets: A case for EPOXI mission target comet 103P/Hartley 2

The CO2 production rate has been derived in comets using the Cameron band (a3Pi - X1Sigma) emission of CO molecule assuming that photodissociative excitation of CO2 is the main production mechanism of CO in a3Pi metastable state. We have devoloped a model for the production and loss of CO(a3Pi) which has been applied to comet 103P/Hartley 2: the target of EPOXI mission. Our model calculations show that photoelectron impact excitation of CO and dissociative excitation of CO2 can together contribute about 60-90% to the Cameron band emission. The modeled brightness of (0-0) Cameron band emission on comet Hartley 2 is consistent with Hubble Space Telescope observations for 3-5% CO2 (depending on model input solar flux) and 0.5% CO relative to water, where photoelectron impact contribution is about 50-75%. We suggest that estimation of CO2 abundances on comets using Cameron band emission may be reconsidered. We predict the height integrated column brightness of Cameron band of ~1300 R during EPOXI mission encounter period.Comment: 3 figure

Multicomplementary operators via finite Fourier transform

A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

Decreased nematode clearance & anti-phosphorylcholine specific IgM responses in mannose-binding lectin deficient mice

Brugia malayi is a nematode that causes human lymphatic filariasis. Previously, we showed that mannose binding lectin (MBL) ‐A is necessary for clearance of B. malayi microfilariae in mice and presence of MBL‐A is linked with maximal levels of parasite‐specific IgM. Common human MBL gene polymorphisms result in low MBL expression and lead to recurring bacterial infections. Furthermore, these low‐expressing human MBL polymorphisms result in greatly increased susceptibility to lymphatic filarial infection. Indeed, gain of new filarial infections over a 30‐year period are 10‐fold higher in people with low, compared to high, MBL‐expression phenotypes. Human MBL closely resembles mouse MBL‐C, rather than MBL‐A, therefore we examined the role of mouse MBL‐C in clearance of microfilariae. Absence of MBL‐C alone, or both MBL‐A and ‐C, resulted in delayed clearance of microfilariae and reduced parasite‐specific IgM in mice. There were few profound changes in B cell sub‐populations or in the ability of MBL‐deficient mice to respond to T‐dependent or T‐independent antigens. However, absence of MBL‐A and/or MBL‐C resulted in reduced IgM to phosphorylcholine, a constituent of filarial and bacterial antigens, suggesting that inability to form proficient antibody responses to this moiety leads to lack of microfilarial clearance and overall susceptibility to filariasis

The Extremely High Energy Cosmic Rays

Experimental results from Haverah Park, Yakutsk, AGASA and Fly's Eye are reviewed. All these experiments work in the energy range above 0.1 EeV. The 'dip' structure around 3 EeV in the energy spectrum is well established by all the experiments, though the exact position differs slightly. Fly's Eye and Yakutsk results on the chemical composition indicate that the cosmic rays are getting lighter over the energy range from 0.1 EeV to 10 EeV, but the exact fraction is hadronic interaction model dependent, as indicated by the AGASA analysis. The arrival directions of cosmic rays are largely isotropic, but interesting features may be starting to emerge. Most of the experimental results can best be explained with the scenario that an extragalactic component gradually takes over a galactic population as energy increases and cosmic rays at the highest energies are dominated by particles coming from extragalactic space. However, identification of the extragalactic sources has not yet been successful because of limited statistics and the resolution of the data.Comment: The review paper including 21 figures. 39 pages: To be published in Journal of Physics

Observational and Dynamical Characterization of Main-Belt Comet P/2010 R2 (La Sagra)

We present observations of comet-like main-belt object P/2010 R2 (La Sagra) obtained by Pan-STARRS 1 and the Faulkes Telescope-North on Haleakala in Hawaii, the University of Hawaii 2.2 m, Gemini-North, and Keck I telescopes on Mauna Kea, the Danish 1.54 m telescope at La Silla, and the Isaac Newton Telescope on La Palma. An antisolar dust tail is observed from August 2010 through February 2011, while a dust trail aligned with the object's orbit plane is also observed from December 2010 through August 2011. Assuming typical phase darkening behavior, P/La Sagra is seen to increase in brightness by >1 mag between August 2010 and December 2010, suggesting that dust production is ongoing over this period. These results strongly suggest that the observed activity is cometary in nature (i.e., driven by the sublimation of volatile material), and that P/La Sagra is therefore the most recent main-belt comet to be discovered. We find an approximate absolute magnitude for the nucleus of H_R=17.9+/-0.2 mag, corresponding to a nucleus radius of ~0.7 km, assuming an albedo of p=0.05. Using optical spectroscopy, we find no evidence of sublimation products (i.e., gas emission), finding an upper limit CN production rate of Q_CN<6x10^23 mol/s, from which we infer an H2O production rate of Q_H2O<10^26 mol/s. Numerical simulations indicate that P/La Sagra is dynamically stable for >100 Myr, suggesting that it is likely native to its current location and that its composition is likely representative of other objects in the same region of the main belt, though the relatively close proximity of the 13:6 mean-motion resonance with Jupiter and the (3,-2,-1) three-body mean-motion resonance with Jupiter and Saturn mean that dynamical instability on larger timescales cannot be ruled out.Comment: 23 pages, 13 figures, accepted for publication in A

The photometric observation of the quasi-simultaneous mutual eclipse and occultation between Europa and Ganymede on 22 August 2021

Mutual events (MEs) are eclipses and occultations among planetary natural satellites. Most of the time, eclipses and occultations occur separately. However, the same satellite pair will exhibit an eclipse and an occultation quasi-simultaneously under particular orbital configurations. This kind of rare event is termed as a quasi-simultaneous mutual event (QSME). During the 2021 campaign of mutual events of jovian satellites, we observed a QSME between Europa and Ganymede. The present study aims to describe and study the event in detail. We observed the QSME with a CCD camera attached to a 300-mm telescope at the Hong Kong Space Museum Sai Kung iObservatory. We obtained the combined flux of Europa and Ganymede from aperture photometry. A geometric model was developed to explain the light curve observed. Our results are compared with theoretical predictions (O-C). We found that our simple geometric model can explain the QSME fairly accurately, and the QSME light curve is a superposition of the light curves of an eclipse and an occultation. Notably, the observed flux drops are within 2.6% of the theoretical predictions. The size of the event central time O-Cs ranges from -14.4 to 43.2 s. Both O-Cs of flux drop and timing are comparable to other studies adopting more complicated models. Given the event rarity, model simplicity and accuracy, we encourage more observations and analysis on QSMEs to improve Solar System ephemerides.Comment: 23 pages, 5 appendixes, 16 figures, 7 table

Model for the Production of CO Cameron band emission in Comet 1P/Halley

The abundance of CO2 in comets has been derived using CO Cameron band (a3pi --> X1Sigma+) emission assuming that photodissociative excitation of CO2 is the main production process of CO(a3pi). On comet 1P/Halley the Cameron (1-0) band has been observed by International Ultraviolet Explorer (IUE) on several days in March 1986. A coupled chemistry-emission model is developed for comet 1P/Halley to assess the importance of various production and loss mechanisms of CO(a3pi) and to calculate the intensity of Cameron band emission on different days of IUE observation. Two different solar EUV flux models, EUVAC of Richards et al. (1994) and SOLAR2000 of Tobiska (2004), and different relative abundances of CO and CO2, are used to evaluate the role of photon and photoelectron in producing CO molecule in a3pi state in the cometary coma. It is found that in comet 1P/Halley 60--70% of the total intensity of the Cameron band emission is contributed by electron impact excitation of CO and CO2, while the contribution from photodissociative excitation of CO2 is small (20--30%). Thus, in the comets where CO and CO2 relative abundances are comparable, the Cameron band emission is largely governed by electron impact excitation of CO, and not by the photodissociative excitation of CO2 as assumed earlier. Model calculated Cameron band 1-0 emission intensity (40 R) is consistent with the observed IUE slit-averaged brightness (37 +/- 6 R) using EUVAC model solar flux on 13 March 1986, and also on other days of observations. Since electron impact excitation is the major production mechanism, the Cameron emission can be used to derive photoelectron density in the inner coma rather than the CO2 abundance.Comment: 40 pages 8 figure