Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.

Essential role for complex N-glycans in forming an organized layer of bronchial epithelium.

Mice lacking the complex subset of N-glycans due to inactivation of the Mgat1 gene die at mid-gestation, making it difficult to identify specific biological functions for this class of cell surface carbohydrates. To circumvent this embryonic lethality and to uncover tissue-specific functions for complex N-glycans, WW6 embryonic stem cells with inactivated Mgat1 alleles were tracked in chimeric embryos. The Mgat1 gene encodes N-acetylglucosaminyltransferase I (Glc-NAc-TI; EC 2.4.1.101), the transferase that initiates the synthesis of complex N-glycans. WW6 cells carry an inert beta-globin transgene that allows their identification in chimeras by DNA-DNA in situ hybridization. Independent Mgat1-/- and Mgat1+/- mutant WW6 isolates contributed like parent WW6 cells to the tissues of embryonic day (E) 10.5 to E16.5 chimeras. However, a cell type-specific difference was observed in lung. Homozygous null Mgat1-/- WW6 cells did not contribute to the epithelial layer in more than 99% bronchi. This deficiency was corrected by transfection of a Mgat1 transgene. Interestingly, heterozygous Mgat1+/- WW6 cells were also deficient in populating the layer of bronchial epithelium. Furthermore, examination of lung bud in E9.5 Mgat1-/- mutant embryos showed complete absence of an organized epithelial cell layer in the bronchus. Thus, complex N-glycans are required to form a morphologically recognizable bronchial epithelium, revealing an in vivo, cell type-specific function for this class of N-glycans.

Complex dynamics of multilocus systems subjected to cyclical selection.

Earlier we have shown that oscillations with a long period ("supercycles") may arise in two-locus systems experiencing cyclical selection with a short period. However, this mode of complex limiting behavior appeared to be possible for narrow ranges of parameters. Here we demonstrate that a multilocus system subjected to stabilizing selection with cyclically moving optimum can generate ubiquitous complex limiting behavior including supercycles, T-cycles, and chaotic-like phenomena. This mode of multilocus dynamics far exceeds the potential attainable under ordinary selection models resulting in simple behavior. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods.

Genes encoding the same three subunits of respiratory complex II are present in the mitochondrial DNA of two phylogenetically distant eukaryotes.

Although mitochondrial DNA is known to encode a limited number (<20) of the polypeptide components of respiratory complexes I, III, IV, and V, genes for components of complex II [succinate dehydrogenase (ubiquinone); succinate:ubiquinone oxidoreductase, EC 1.3.5.1] are conspicuously lacking in mitochondrial genomes so far characterized. Here we show that the same three subunits of complex II are encoded in the mitochondrial DNA of two phylogenetically distant eukaryotes, Porphyra purpurea (a photosynthetic red alga) and Reclinomonas americana (a heterotrophic zooflagellate). These complex II genes, sdh2, sdh3, and sdh4, are homologs, respectively, of Escherichia coli sdhB, sdhC, and sdhD. In E. coli, sdhB encodes the iron-sulfur subunit of succinate dehydrogenase (SDH), whereas sdhC and sdhD specify, respectively, apocytochrome b558 and a hydrophobic 13-kDa polypeptide, which together anchor SDH to the inner mitochondrial membrane. Amino acid sequence similarities indicate that sdh2, sdh3, and sdh4 were originally encoded in the protomitochondrial genome and have subsequently been transferred to the nuclear genome in most eukaryotes. The data presented here are consistent with the view that mitochondria constitute a monophyletic lineage.

Study of interaction between Si(O,C) nanowires and the biological system

Nanomedicine is a new branch of medicine, based on the potentiality and intrinsic properties of nanomaterials. Indeed, the nanomaterials ( i.e. the materials with nano and under micron size) can be suitable to different applications in biomedicine. The nanostructures can be used by taking advantage of their properties (for example superparamagnetic nanoparticles) or functionalized to deliver the drug in a specific target, thanks the ability to cross biological barriers. The size and the shape of 1D-nanostructures (nanotubes and nanowires) have an important role on the cell fate: their morphology plays a key role on the interaction between nanostructure and the biological system. For this reason the 1D nanostructure are interesting for their ability to mime the biological system. An implantable material or device must therefore integrate with the surrounding extracellular matrix (ECM), a complex network of proteins with structural and signaling properties. Innovative techniques allow the generation of complex surface patterns that can resemble the structure of the ECM, such as 1D nanostructures. NWs based on cubic silicon carbide (3C-SiC), either bare (3C-SiC NWs) or surrounded by an amorphous shell (3C-SiC/SiO2 core/shell NWs), and silicon oxycarbide nanowires (SiOxCy NWs) can meet the chemical, mechanical and electrical requirements for tissue engineering and have a strong potential to pave the way for the development of a novel generation of implantable nano-devices. Silicon oxycarbide shows promising physical and chemical properties as elastic modulus, bending strength and hardness, chemical durability superior to conventional silicate glasses in aggressive environments and high temperature stability up to 1300 °C. Moreover, it can easily be engineered through functionalization and decoration with macro-molecules and nanoparticles. Silicon carbide has been extensively studied for applications in harsh conditions, as chemical environment, high electric field and high and low temperature, owing to its high hardness, high thermal conductivity, chemical inertness and high electron mobility. Also, its cubic polytype (3C) is highly biocompatible and hemocompatible, and some prototypes of biomedical applications and biomedical devices have been already realized starting from 3C-SiC thin films. Cubic SiC-based NWs can be used as a biomimetic biomaterial, providing a robust and novel biocompatible biological interface . We cultured in vitro A549 human lung adenocarcinoma epithelial cells and L929 murine fibroblast cells over core/shell SiC/SiO2, SiOxCy and bare 3C-SiC nanowire platforms, and analysed the cytotoxicity, by indirect and direct contact tests, the cell adhesion, and the cell proliferation. These studies showed that all the nanowires are biocompatible according to ISO 10993 standards. We evaluated the blood compatibility through the interaction of the nanowires with platelet rich plasma. The adhesion and activation of platelets on the nanowire bundles, assessed via SEM imaging and soluble P-selectin quantification, indicated that a higher platelet activation is induced by the core/shell structures compared to the bare ones. Further, platelet activation is higher with 3C-SiC/SiO2 NWs and SiOxCyNWs, which therefore appear suitable in view of possible tissue regeneration. On the contrary, bare 3C-SiC NWs show a lower platelet activation and are therefore promising in view of implantable bioelectronics devices, as cardiovascular implantable devices. The NWs properties are suitable to allow the design of a novel subretinal Micro Device (MD). This devices is based on Si NWs and PEDOT:PSS, though the well know principle of the hybrid ordered bulk heterojunction (OBHJ). The aim is to develop a device based on a well-established photovoltaic technology and to adapt this know-how to the prosthetic field. The hybrid OBHJ allows to form a radial p–n junction on a nanowire/organic structure. In addition, the nanowires increase the light absorption by means of light scattering effects: a nanowires based p-n junction increases the light absorption up to the 80%, as previously demonstrated, overcoming the Shockley-Queisser limit of 30 % of a bulk p-n junction. Another interesting employment of these NWs is to design of a SiC based epicardial-interacting patch based on teflon that include SiC nanowires. . Such contact patch can bridge the electric conduction across the cardiac infarct as nanowires can ‘sense’ the direction of the wavefront propagation on the survival cardiac tissue and transmit it to the downstream surivived regions without discontinuity. The SiC NWs are tested in terms of toxicology, biocompatibility and conductance among cardiomyocytes and myofibroblasts.

Synthetic scope and DFT analysis of the chiral binap-gold (I) complex-catalyzed 1,3-dipolar cycloaddition of azlactones with alkenes

The 1,3-dipolar cycloaddition between glycine-derived azlactones with maleimides is efficiently catalyzed by the dimeric chiral complex [(Sa)-Binap·AuTFA]2. The alanine-derived oxazolone only reacts with tert-butyl acrylate giving anomalous regiochemistry, which is explained and supported by Natural Resonance Theory and Nucleus Independent Chemical Shifts calculations. The origin of the high enantiodiscrimination observed with maleimides and tert-butyl acrylate is analyzed using DFT computed at M06/Lanl2dz//ONIOM(b3lyp/Lanl2dz:UFF) level. Several applications of these cycloadducts in the synthesis of new proline derivatives with a 2,5-trans-arrangement and in the preparation of complex fused polycyclic molecules are described.

Neutrosophic and Modal Components of Relations in Complex Systems

Semiotic components in the relations of complex systems depend on the Subject. There are two main semiotic components: Neutrosophic and Modal. Modal components are alethical and deontical. In this paper the authors applied the theory of Neutrosophy and Modal Logic to Deontical Impure Systems.

Complex Congenital Heart Disease: The Influence of Prenatal Diagnosis

INTRODUCTION: Complex congenital heart disease is a group of severe conditions. Prenatal diagnosis has implications on morbidity and mortality for most severe conditions. The purpose of this work was to evaluate the influence of prenatal diagnosis and distance of residence and birth place to a reference center, on immediate morbidity and early mortality of complex congenital heart disease. MATERIAL AND METHODS: Retrospective study of complex congenital heart disease patients of our Hospital, born between 2007 and 2012. RESULTS: There were 126 patients born with complex congenital heart disease. In 95%, pregnancy was followed since the first trimester, with prenatal diagnosis in 42%. There was a statistically significant relation between birth place and prenatal diagnosis. Transposition of great arteries was the most frequent complex congenital heart disease (45.2%), followed by pulmonary atresia with ventricular septal defect (17.5%) and hypoplastic left ventricle (9.5%). Eighty-two patients (65.1%) had prostaglandin infusion and 38 (30.2%)were ventilated before an intervention. Surgery took place in the neonatal period in 73%. Actuarial survival rate at 30 days, 12 and 24 months was 85%, 80% and 75%, respectively. There was no statistically significant relation between prenatal diagnosis and mortality. DISCUSSION: Most patients with complex congenital heart disease did not have prenatal diagnosis. All cases with prenatal diagnosis were born in a tertiary center. Prenatal diagnosis did not influence significantly neonatal mortality, as already described in other studies with heterogeneous complex heart disease. CONCLUSION: prenatal diagnosis of complex congenital heart disease allowed an adequate referral. Most patients with complex congenital heart disease were not diagnosed prenatally. This data should be considered when planning prenatal diagnosis of congenital heart disease.

The theory of functions of a complex variable. [Lectures] New York University, Institute for Mathematics and Mechanics.

"First edition 1948. Second printing 1952."

Functions of real variables. Functions of a complex variable.

Mode of access: Internet.

Elements of the theory of functions of a complex variable with especial reference to the methods of Riemann,

Translation of Elemente der Theorie der Funktionen einer complexen veränderlichen Grösse.

Theory of functions of a complex variable,

Available on demand as hard copy or computer file from Cornell University Library.

Summation of semantic priming and complex sentence comprehension in Parkinson's disease

Research has suggested that the integrity of semantic processing may be compromised in Parkinson's disease (PD), which may account for difficulties in complex sentence comprehension. In order to investigate the time course and integrity of semantic activation in PD, 20 patients with PD and 23 healthy controls performed a lexical decision task based on the multi-priming paradigm. Semantic priming effects were measured across stimulus onset asynchronies of 250 ms, 600 ms, and 1200 ms. Further, PD participants performed an auditory comprehension task. The results revealed significantly different patterns of semantic priming for the PD group at the 250-ms and 1200-ms SOAs. In addition, a delayed time course of semantic activation was evident for PD patients with poor comprehension of complex sentences. These results provide further support to suggest that both automatic and controlled aspects of semantic activation may be compromised in PD. Furthermore, the results also suggest that some sentence comprehension deficits in PD may be related to a reduction in information processing speed.

The importance of modelling heterogeneity in complex disease: application to NIMH Schizophrenia Genetics Initiative data

As for other complex diseases, linkage analyses of schizophrenia (SZ) have produced evidence for numerous chromosomal regions, with inconsistent results reported across studies. The presence of locus heterogeneity appears likely and may reduce the power of linkage analyses if homogeneity is assumed. In addition, when multiple heterogeneous datasets are pooled, intersample variation in the proportion of linked families ( a) may diminish the power of the pooled sample to detect susceptibility loci, in spite of the larger sample size obtained. We compare the significance of linkage. findings obtained using allele- sharing LOD scores ( LODexp) - which assume homogeneity - and heterogeneity LOD scores ( HLOD) in European American and African American NIMH SZ families. We also pool these two samples and evaluate the relative power of the LODexp and two different heterogeneity statistics. One of these ( HLOD- P) estimates the heterogeneity parameter a only in aggregate data, while the second ( HLOD- S) determines a separately for each sample. In separate and combined data, we show consistently improved performance of HLOD scores over LODexp. Notably, genome-wide significant evidence for linkage is obtained at chromosome 10p in the European American sample using a recessive HLOD score. When the two samples are combined, linkage at the 10p locus also achieves genome-wide significance under HLOD- S, but not HLOD- P. Using HLOD- S, improved evidence for linkage was also obtained for a previously reported region on chromosome 15q. In linkage analyses of complex disease, power may be maximised by routinely modelling locus heterogeneity within individual datasets, even when multiple datasets are combined to form larger samples.

Increasing cell biomass in Saccharomyces cerevisiae increases recombinant protein yield:the use of a respiratory strain as a microbial cell factory

BACKGROUND: Recombinant protein production is universally employed as a solution to obtain the milligram to gram quantities of a given protein required for applications as diverse as structural genomics and biopharmaceutical manufacture. Yeast is a well-established recombinant host cell for these purposes. In this study we wanted to investigate whether our respiratory Saccharomyces cerevisiae strain, TM6*, could be used to enhance the productivity of recombinant proteins over that obtained from corresponding wild type, respiro-fermentative strains when cultured under the same laboratory conditions. RESULTS: Here we demonstrate at least a doubling in productivity over wild-type strains for three recombinant membrane proteins and one recombinant soluble protein produced in TM6* cells. In all cases, this was attributed to the improved biomass properties of the strain. The yield profile across the growth curve was also more stable than in a wild-type strain, and was not further improved by lowering culture temperatures. This has the added benefit that improved yields can be attained rapidly at the yeast's optimal growth conditions. Importantly, improved productivity could not be reproduced in wild-type strains by culturing them under glucose fed-batch conditions: despite having achieved very similar biomass yields to those achieved by TM6* cultures, the total volumetric yields were not concomitantly increased. Furthermore, the productivity of TM6* was unaffected by growing cultures in the presence of ethanol. These findings support the unique properties of TM6* as a microbial cell factory. CONCLUSIONS: The accumulation of biomass in yeast cell factories is not necessarily correlated with a proportional increase in the functional yield of the recombinant protein being produced. The respiratory S. cerevisiae strain reported here is therefore a useful addition to the matrix of production hosts currently available as its improved biomass properties do lead to increased volumetric yields without the need to resort to complex control or cultivation schemes. This is anticipated to be of particular value in the production of challenging targets such as membrane proteins.