Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Влияние магнитомеханического резонанса на амплитудно- и фазочастотные зависимости переменных составляющих эффекта Фарадея

В рамках модели продольных колебаний тонкого стержня из магнитооптического кристалла в условиях магнитомеханического резонанса показано, что вынужденные колебания могут создавать не только амплитудные, но и фазочастотные зависимости переменных составляющих эффекта Фарадея.У рамках моделі поздовжніх коливань тонкого стрижня із магнітооптичного кристала в умовах магнітомеханічного резонансу показано, що вимушені коливання можуть створювати не тільки амплітудні, але й фазочастотні залежності змінних складових ефекту Фарадея.In the framework of a model of longitudinal vibrations of a thin rod fabricated of the magneto-optical crystal under a magnetomechanical resonance, it is shown that the forced oscillations can create not only the amplitude but also phase-frequency dependences of the variable components of the Faraday effect

Lpg0393 of Legionella pneumophila is a guanine-nucleotide exchange factor for Rab5, Rab21 and Rab22

Legionella pneumophila, a human intracellular pathogen, encodes about 290 effector proteins that are translocated into host cells through a secretion machinery. Some of these proteins have been shown to manipulate or subvert cellular processes during infection, but functional roles of a majority of them remain unknown. Lpg0393 is a newly identified Legionella effector classified as a hypothetical protein. Through X-ray crystallographic analysis, we show that Lpg0393 contains a Vps9-like domain, which is structurally most similar to the catalytic core of human Rabex-5 that activates the endosomal Rab proteins Rab5, Rab21 and Rab22. Consistently, Lpg0393 exhibited a guanine-nucleotide exchange factor activity toward the endosomal Rabs. This work identifies the first example of a bacterial guanine-nucleotide exchange factor that is active towards the Rab5 sub-cluster members, implying that the activation of these Rab proteins might be advantageous for the intracellular survival of Legionella

The Impact of the C-Terminal Domain on the Interaction of Human DNA Topoisomerase II α and β with DNA

<b>Background</b> Type II DNA topoisomerases are essential, ubiquitous enzymes that act to relieve topological problems arising in DNA from normal cellular activity. Their mechanism of action involves the ATP-dependent transport of one DNA duplex through a transient break in a second DNA duplex; metal ions are essential for strand passage. Humans have two isoforms, topoisomerase IIα and topoisomerase IIβ, that have distinct roles in the cell. The C-terminal domain has been linked to isoform specific differences in activity and DNA interaction. <b>Methodology/Principal Findings</b> We have investigated the role of the C-terminal domain in the binding of human topoisomerase IIα and topoisomerase IIβ to DNA in fluorescence anisotropy assays using full length and C-terminally truncated enzymes. We find that the C-terminal domain of topoisomerase IIβ but not topoisomerase IIα affects the binding of the enzyme to the DNA. The presence of metal ions has no effect on DNA binding. Additionally, we have examined strand passage of the full length and truncated enzymes in the presence of a number of supporting metal ions and find that there is no difference in relative decatenation between isoforms. We find that calcium and manganese, in addition to magnesium, can support strand passage by the human topoisomerase II enzymes. <b>Conclusions/Significance</b> The C-terminal domain of topoisomerase IIβ, but not that of topoisomerase IIα, alters the enzyme's KD for DNA binding. This is consistent with previous data and may be related to the differential modes of action of the two isoforms in vivo. We also show strand passage with different supporting metal ions for human topoisomerase IIα or topoisomerase IIβ, either full length or C-terminally truncated. They all show the same preferences, whereby Mg > Ca > Mn

A verification protocol for the probe sequences of Affymetrix genome arrays reveals high probe accuracy for studies in mouse, human and rat

BACKGROUND: The Affymetrix GeneChip technology uses multiple probes per gene to measure its expression level. Individual probe signals can vary widely, which hampers proper interpretation. This variation can be caused by probes that do not properly match their target gene or that match multiple genes. To determine the accuracy of Affymetrix arrays, we developed an extensive verification protocol, for mouse arrays incorporating the NCBI RefSeq, NCBI UniGene Unique, NIA Mouse Gene Index, and UCSC mouse genome databases. RESULTS: Applying this protocol to Affymetrix Mouse Genome arrays (the earlier U74Av2 and the newer 430 2.0 array), the number of sequence-verified probes with perfect matches was no less than 85% and 95%, respectively; and for 74% and 85% of the probe sets all probes were sequence verified. The latter percentages increased to 80% and 94% after discarding one or two unverifiable probes per probe set, and even further to 84% and 97% when, in addition, allowing for one or two mismatches between probe and target gene. Similar results were obtained for other mouse arrays, as well as for human and rat arrays. Based on these data, refined chip definition files for all arrays are provided online. Researchers can choose the version appropriate for their study to (re)analyze expression data. CONCLUSION: The accuracy of Affymetrix probe sequences is higher than previously reported, particularly on newer arrays. Yet, refined probe set definitions have clear effects on the detection of differentially expressed genes. We demonstrate that the interpretation of the results of Affymetrix arrays is improved when the new chip definition files are used

FORG3D: Force-directed 3D graph editor for visualization of integrated genome scale data

<p>Abstract</p> <p>Background</p> <p>Genomics research produces vast amounts of experimental data that needs to be integrated in order to understand, model, and interpret the underlying biological phenomena. Interpreting these large and complex data sets is challenging and different visualization methods are needed to help produce knowledge from the data.</p> <p>Results</p> <p>To help researchers to visualize and interpret integrated genomics data, we present a novel visualization method and bioinformatics software tool called FORG3D that is based on real-time three-dimensional force-directed graphs. FORG3D can be used to visualize integrated networks of genome scale data such as interactions between genes or gene products, signaling transduction, metabolic pathways, functional interactions and evolutionary relationships. Furthermore, we demonstrate its utility by exploring gene network relationships using integrated data sets from a <it>Caenorhabditis elegans </it>Parkinson's disease model.</p> <p>Conclusion</p> <p>We have created an open source software tool called FORG3D that can be used for visualizing and exploring integrated genome scale data.</p

High-Throughput Top-Down Fabrication of Uniform Magnetic Particles

Ion Beam Aperture Array Lithography was applied to top-down fabrication of large dense (108–109 particles/cm2) arrays of uniform micron-scale particles at rates hundreds of times faster than electron beam lithography. In this process, a large array of helium ion beamlets is formed when a stencil mask containing an array of circular openings is illuminated by a broad beam of energetic (5–8 keV) ions, and is used to write arrays of specific repetitive patterns. A commercial 5-micrometer metal mesh was used as a stencil mask; the mesh size was adjusted by shrinking the stencil openings using conformal sputter-deposition of copper. Thermal evaporation from multiple sources was utilized to form magnetic particles of varied size and thickness, including alternating layers of gold and permalloy. Evaporation of permalloy layers in the presence of a magnetic field allowed creation of particles with uniform magnetic properties and pre-determined magnetization direction. The magnetic properties of the resulting particles were characterized by Vibrating Sample Magnetometry. Since the orientation of the particles on the substrate before release into suspension is known, the orientation-dependent magnetic properties of the particles could be determined

Application of Approximate Pattern Matching in Two Dimensional Spaces to Grid Layout for Biochemical Network Maps

Background For visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process. Results We propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor) algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts. Conclusions Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html

Essential versus accessory aspects of cell death: recommendations of the NCCD 2015

Cells exposed to extreme physicochemical or mechanical stimuli die in an uncontrollable manner, as a result of their immediate structural breakdown. Such an unavoidable variant of cellular demise is generally referred to as ‘accidental cell death’ (ACD). In most settings, however, cell death is initiated by a genetically encoded apparatus, correlating with the fact that its course can be altered by pharmacologic or genetic interventions. ‘Regulated cell death’ (RCD) can occur as part of physiologic programs or can be activated once adaptive responses to perturbations of the extracellular or intracellular microenvironment fail. The biochemical phenomena that accompany RCD may be harnessed to classify it into a few subtypes, which often (but not always) exhibit stereotyped morphologic features. Nonetheless, efficiently inhibiting the processes that are commonly thought to cause RCD, such as the activation of executioner caspases in the course of apoptosis, does not exert true cytoprotective effects in the mammalian system, but simply alters the kinetics of cellular demise as it shifts its morphologic and biochemical correlates. Conversely, bona fide cytoprotection can be achieved by inhibiting the transduction of lethal signals in the early phases of the process, when adaptive responses are still operational. Thus, the mechanisms that truly execute RCD may be less understood, less inhibitable and perhaps more homogeneous than previously thought. Here, the Nomenclature Committee on Cell Death formulates a set of recommendations to help scientists and researchers to discriminate between essential and accessory aspects of cell death