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

The classification of submerged vegetation using hyperspectral MIVIS data

The aim of this research is to use hyperspectral MIVIS data to map the Posidonia oceanica prairies in a coastal lagoon (Stagnone di Marsala). It is approximately 12 km long and 2 km wide and is linked to the open sea by two shallow openings. This environment is characterised by prairies of phanerogams, the most common of which is Posidonia oceanica, an ideal habitat for numerous species of fish, molluscs and crustaceans. A knowledge of the distribution of submerged vegetation is useful to monitor the health of the lagoon. In order to classify the MIVIS imagery, the attenuation effects of the water column have been removed from the signal using Lyzenga’s technique. A comparison between classifications using indices obtained using band pairs from only the first spectrometer, and using band pairs of the first and second spectrometers, shows that the best classification is obtained from some indices derived from the first spectrometer. Field controls carried out in July 2002 were used to determine the training sites for the supervised classification. Twelve classes of bottom coverage were obtained from the classification, of which four are homogeneous and eight are mixed coverage. The methodology applied demonstrates that hyperspectral sensors can be used to effectively map submerged vegetation in shallow waters

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

Universal properties of correlation transfer in integrate-and-fire neurons

One of the fundamental characteristics of a nonlinear system is how it transfers correlations in its inputs to correlations in its outputs. This is particularly important in the nervous system, where correlations between spiking neurons are prominent. Using linear response and asymptotic methods for pairs of unconnected integrate-and-fire (IF) neurons receiving white noise inputs, we show that this correlation transfer depends on the output spike firing rate in a strong, stereotyped manner, and is, surprisingly, almost independent of the interspike variance. For cells receiving heterogeneous inputs, we further show that correlation increases with the geometric mean spiking rate in the same stereotyped manner, greatly extending the generality of this relationship. We present an immediate consequence of this relationship for population coding via tuning curves

Economic dynamics with financial fragility and mean-field interaction: a model

Following the statistical mechanics methodology, firstly introduced in macroeconomics by Aoki [1996,2002], we provide some insights to the well known works of Greenwald and Stiglitz [1990, 1993]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean field interaction modeling and master equation techniques.Comment: APFA6 proceeding

Seventy years of sex education in Health Education Journal: a critical review

This paper examines key debates and perspectives on sex education in Health Education Journal (HEJ), from the date of the journal’s first publication in March 1943 to the present day. Matters relating to sexuality and sexual health are revealed to be integral to HEJ’s history. First published as Health and Empire (1921 – 1942), a key purpose of the journal since its inception has been to share information on venereal disease and its prevention within the UK and across the former British Empire. From 1943 to the present day, discussions on sex education in the newly-christened HEJ both reflect and respond to evolving socio-cultural attitudes towards sexuality in the UK. Changing definitions of sex education across the decades are examined, from the prevention of venereal disease and moral decline in war-time Britain in the 1940s, to a range of responses to sexual liberation in the 1960s and 1970s; from a focus on preventing sexually-transmitted infections, teenage pregnancy and HIV in the 1980s, to the provision of sexual health services alongside sex education in the 2000s. Over the past 70 years, a shift from prevention of pre-marital sexual activity to the management of its outcomes is apparent; however, while these changes over time are notable, perhaps the most striking findings of this review are the continuities in arguments for and against the discussion of sexual issues. After more than 70 years of debate, it would seem that there is little consensus concerning motivations for and the content of sex education