An elementary approach to toy models for D. H. Lehmer's conjecture

In 1947, Lehmer conjectured that the Ramanujan's tau function $\tau (m)$ never vanishes for all positive integers $m$, where $\tau (m)$ is the $m$-th Fourier coefficient of the cusp form $\Delta_{24}$ of weight 12. The theory of spherical $t$-design is closely related to Lehmer's conjecture because it is shown, by Venkov, de la Harpe, and Pache, that $\tau (m)=0$ is equivalent to the fact that the shell of norm $2m$ of the $E_{8}$-lattice is a spherical 8-design. So, Lehmer's conjecture is reformulated in terms of spherical $t$-design. Lehmer's conjecture is difficult to prove, and still remains open. However, Bannai-Miezaki showed that none of the nonempty shells of the integer lattice \ZZ^2 in \RR^2 is a spherical 4-design, and that none of the nonempty shells of the hexagonal lattice $A_2$ is a spherical 6-design. Moreover, none of the nonempty shells of the integer lattices associated to the algebraic integers of imaginary quadratic fields whose class number is either 1 or 2, except for \QQ(\sqrt{-1}) and \QQ(\sqrt{-3}) is a spherical 2-design. In the proof, the theory of modular forms played an important role. Recently, Yudin found an elementary proof for the case of \ZZ^{2}-lattice which does not use the theory of modular forms but uses the recent results of Calcut. In this paper, we give the elementary (i.e., modular form free) proof and discuss the relation between Calcut's results and the theory of imaginary quadratic fields.Comment: 18 page

Cryo-Electron Tomography Elucidates the Molecular Architecture of Treponema pallidum, the Syphilis Spirochete

Cryo-electron tomography (CET) was used to examine the native cellular organization of Treponema pallidum, the syphilis spirochete. T. pallidum cells appeared to form flat waves, did not contain an outer coat and, except for bulges over the basal bodies and widening in the vicinity of flagellar filaments, displayed a uniform periplasmic space. Although the outer membrane (OM) generally was smooth in contour, OM extrusions and blebs frequently were observed, highlighting the structure’s fluidity and lack of attachment to underlying periplasmic constituents. Cytoplasmic filaments converged from their attachment points opposite the basal bodies to form arrays that ran roughly parallel to the flagellar filaments along the inner surface of the cytoplasmic membrane (CM). Motile treponemes stably attached to rabbit epithelial cells predominantly via their tips. CET revealed that T. pallidum cell ends have a complex morphology and assume at least four distinct morphotypes. Images of dividing treponemes and organisms shedding cell envelope-derived blebs provided evidence for the spirochete’s complex membrane biology. In the regions without flagellar filaments, peptidoglycan (PG) was visualized as a thin layer that divided the periplasmic space into zones of higher and lower electron densities adjacent to the CM and OM, respectively. Flagellar filaments were observed overlying the PG layer, while image modeling placed the PG-basal body contact site in the vicinity of the stator–P-collar junction. Bioinformatics and homology modeling indicated that the MotB proteins of T. pallidum, Treponema denticola, and Borrelia burgdorferi have membrane topologies and PG binding sites highly similar to those of their well-characterized Escherichia coli and Helicobacter pylori orthologs. Collectively, our results help to clarify fundamental differences in cell envelope ultrastructure between spirochetes and gram-negative bacteria. They also confirm that PG stabilizes the flagellar motor and enable us to propose that in most spirochetes motility results from rotation of the flagellar filaments against the PG

Tumor-associated and immunochemotherapy-dependent long-term alterations of the peripheral blood NK cell compartment in DLBCL patients

Natural Killer (NK) cells are a key component of tumor immunosurveillance and thus play an important role in rituximab-dependent killing of lymphoma cells via an antibody-dependent cellular cytotoxicity (ADCC) mechanism. We evaluated the phenotypic and functional assets of peripheral blood NK cell subsets in 32 newly-diagnosed diffuse large B-cell lymphoma (DLBCL) patients and in 27 healthy controls. We further monitored long-term modifications of patient NK cells for up to 12 months after rituximab-based immunochemotherapy. At diagnosis, patients showed a higher percentage of CD56dim and CD16C NK cells, and a higher frequency of GrzBC cells in CD56dim, CD56bright, and CD16C NK cell subsets than healthy controls. Conversely, DLBCL NK cell killing and interferon g (IFNg) production capability were comparable to those derived from healthy subjects. Notably, NK cells from refractory/relapsed patients exhibited a lower “natural” cytotoxicity. A marked and prolonged therapy-induced reduction of both “natural” and CD16- dependent NK cytotoxic activities was accompanied by the down-modulation of CD16 and NKG2D activating receptors, particularly in the CD56dim subset. However, reduced NK cell killing was not associated with defective lytic granule content or IFNg production capability. This study firstly describes tumor-associated and therapy-induced alterations of the systemic NK cell compartment in DLBCL patients. As these alterations may negatively impact rituximab-based therapy efficacy, our work may provide useful information for improving immunochemotherapeutic strategies

Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

The delivery of heavy menstrual bleeding services in England and Wales after publication of national guidelines: a survey of hospitals.

BACKGROUND: In 2007-2008, two UK-based organisations, the National Institute for Health and Clinical Excellence and the Royal College of Obstetricians and Gynaecologists, published guidelines for the management of care and organisation of outpatient services for women with heavy menstrual bleeding (HMB). In 2010, this study was conducted to provide an update on guideline-related services provided in England and Wales, and whether they are consistent with national clinical guidelines two to three years after publication. METHODS: An organisational survey of outpatient gynaecology clinics was conducted of 221 hospitals in 154 acute National Health Service (NHS) trusts in England and Wales. A questionnaire was distributed to all hospitals to examine provision of diagnostic and therapeutic services in outpatient settings. Descriptive statistics were used to summarize results. RESULTS: The response rate was 100%. For diagnosis, 80% of hospitals had ultrasound, 87% had hysteroscopy, and 98% had endometrial biopsy available. Overall, 76% of hospitals provided an information leaflet, 8% referred patients to a website for information, and 20% did not provide any written information. A dedicated menstrual bleeding clinic was present in 38% of hospitals. Only 30% of hospitals reported that they have a local written protocol regarding the care and management of women with HMB. CONCLUSION: The majority of hospitals offer appropriate diagnostic and surgical services for women with HMB. However, local protocol development may not reflect the local services. It may be that hospitals are finding it difficult to summon resources to provide clinics for women with menstrual disorders

Survey of the needs of patients with spinal cord injury: impact and priority for improvement in hand function in tetraplegics\ud

Objective: To investigate the impact of upper extremity deficit in subjects with tetraplegia.\ud \ud Setting: The United Kingdom and The Netherlands.\ud \ud Study design: Survey among the members of the Dutch and UK Spinal Cord Injury (SCI) Associations.\ud \ud Main outcome parameter: Indication of expected improvement in quality of life (QOL) on a 5-point scale in relation to improvement in hand function and seven other SCI-related impairments.\ud \ud Results: In all, 565 subjects with tetraplegia returned the questionnaire (overall response of 42%). Results in the Dutch and the UK group were comparable. A total of 77% of the tetraplegics expected an important or very important improvement in QOL if their hand function improved. This is comparable to their expectations with regard to improvement in bladder and bowel function. All other items were scored lower.\ud \ud Conclusion: This is the first study in which the impact of upper extremity impairment has been assessed in a large sample of tetraplegic subjects and compared to other SCI-related impairments that have a major impact on the life of subjects with SCI. The present study indicates a high impact as well as a high priority for improvement in hand function in tetraplegics.\ud \u

Ground State of Relaxor Ferroelectric Pb(Zn1/3Nb2/3)O3Pb(Zn_{1/3}Nb_{2/3})O_3

High energy x-ray diffraction measurements on Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN) single crystals show that the system does not have a rhombohedral symmetry at room temperature as previously believed. The new phase (X) in the bulk of the crystal gives Bragg peaks similar to that of a nearly cubic lattice with a slight tetragonal distortion. The Bragg profile remains sharp with no evidence of size broadening due to the polar micro crystals (MC). However, in our preliminary studies of the skin, we have found the expected rhombohedral (R) phase as a surface state. On the other hand, studies on an electric-field poled PZN single crystal clearly indicate a rhombohedral phase at room temperature.Comment: 11 pages with 3 figure

Predictions of Quasar Clustering: Redshift, Luminosity and Selection Dependence

We show that current clustering observations of quasars and luminous AGN can be explained by a merger model augmented by feedback from outflows. Using numerical simulations large enough to study clustering out to 25 comoving h^{-1} Mpc, we calculate correlation functions, biases, and correlation lengths as a function of AGN redshift and optical and X-ray luminosity. At optical wavelengths, our results match a wide range of current observations and generate predictions for future data sets. We reproduce the weak luminosity dependence of clustering over the currently well-measured range, and predict a much stronger dependence at higher luminosities. The increase in the amplitude of binary quasar clustering observed in the Sloan Digital Sky Survey (SDSS) is also reproduced and is predicted to occur at higher redshift, an effect that is due to the one halo term in the correlation function. On the other hand, our results do not match the rapid evolution of the correlation length observed in the SDSS at z\simeq 3, a discrepancy that is at least partially due to differences in the scales probed by our simulation versus this survey. In fact, we show that changing the distances sampled from our simulations can produce changes as large as 40% in the fitted correlation lengths. Finally, in the X-ray, our simulations produce correlation lengths similar to that observed in the Chandra Deep Field (CDF) North, but not the significantly larger correlation length observed in the CDF South.Comment: 13 page, 7 figures. Accepted for publication in Ap