Rational general solutions of higher order algebraic odes

This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.     

A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s(-1)

Searches for extrasolar planets using the periodic Doppler shift of stellar spectral lines have recently achieved a precision of 60 cm s(-1) (ref. 1), which is sufficient to find a 5-Earth-mass planet in a Mercury-like orbit around a Sun-like star. To find a 1-Earth-mass planet in an Earth-like orbit, a precision of approximately 5 cm s(-1) is necessary. The combination of a laser frequency comb with a Fabry-Pérot filtering cavity has been suggested as a promising approach to achieve such Doppler shift resolution via improved spectrograph wavelength calibration, with recent encouraging results. Here we report the fabrication of such a filtered laser comb with up to 40-GHz (approximately 1-A) line spacing, generated from a 1-GHz repetition-rate source, without compromising long-term stability, reproducibility or spectral resolution. This wide-line-spacing comb, or 'astro-comb', is well matched to the resolving power of high-resolution astrophysical spectrographs. The astro-comb should allow a precision as high as 1 cm s(-1) in astronomical radial velocity measurements.     

Technoscientific approaches to deep time

In this paper, I argue that in order to understand the process behind the knowledge production in the historical sciences, we should change our theoretical focus slightly to consider the historical sciences as technoscientific disciplines. If we investigate the intertwinement of technology and theory, we can provide new insights into historical scientific knowledge production, preconditions, and aims. I will provide evidence for my claim by showing the central features of paleontological and paleobiological data practices of the nineteenth and twentieth centuries. In order to work with something that is imperfect and incomplete (the fossil record), paleontologists used different technological devices. These devices process, extract, correct, simulate, and eventually present paleontological explananda. Therefore, the appearance of anatomical features of non-manipulable fossilized organisms, phenomena such as mass-extinctions, or the life-like display of extinct specimens in a museum's hall, depend both on the correct use of technological devices and on the interplay between these devices and theories. Consequently, in order to capture its underlying epistemology, historical sciences should be analyzed and investigated against other technoscientific disciplines such as chemistry, synthetic biology, and nanotechnology, and not necessarily only against classical experimental sciences. This approach will help us understand how historical scientists can obtain their epistemic access to deep time.     

A structural interpretation of measurement and some related epistemological issues

Measurement is widely applied because its results are assumed to be more reliable than opinions and guesses, but this reliability is sometimes justified in a stereotyped way. After a critical analysis of such stereotypes, a structural characterization of measurement is proposed, as partly empirical and partly theoretical process, by showing that it is in fact the structure of the process that guarantees the reliability of its results. On this basis the role and the structure of background knowledge in measurement and the justification of the conditions of object-relatedness (“objectivity”) and subject-independence (“intersubjectivity”) of measurement are specifically discussed.     

Ultrastructural localization of 5-methylcytosine on DNA and RNA

DNA methylation is the major epigenetic modification and it is involved in the negative regulation of gene expression. Its alteration can lead to neoplastic transformation. Several biomolecular approaches are nowadays used to study this modification on DNA, but also on RNA molecules, which are known to play a role in different biological processes. RNA methylation is one of the most common RNA modifications and 5-methylcytosine presence has recently been suggested in mRNA. However, an analysis of nucleic acid methylation at electron microscope is still lacking. Therefore, we visualized DNA methylation status and RNA methylation sites in the interphase nucleus of HeLa cells and rat hepatocytes by ultrastructural immunocytochemistry and cytochemical staining. This approach represents an efficient alternative to study nucleic acid methylation. In particular, this ultrastructural method makes the visualization of this epigenetic modification on a single RNA molecule possible, thus overcoming the technical limitations for a (pre-)mRNA methylation analysis.     

Cell-permeable dual inhibitors of protein kinases CK2 and PIM-1: structural features and pharmacological potential

It has been proposed that dual inhibitors of protein kinases CK2 and PIM-1 are tools particularly valuable to induce apoptosis of cancer cells, a property, however, implying cell permeability, which is lacking in the case of selective CK2/PIM-1 inhibitors developed so far. To fill this gap, we have derivatized the scaffold of the promiscuous CK2 inhibitor TBI with a deoxyribose moiety, generating TDB, a selective, cell-permeable inhibitor of CK2 and PIM-1. Here, we shed light on the structural features underlying the potency and narrow selectivity of TDB by exploiting a number of TDB analogs and by solving the 3D structure of the TDB/CK2 complex at 1.25?Å resolution, one of the highest reported so far for this kinase. We also show that the cytotoxic efficacy of TDB is almost entirely due to apoptosis, is accompanied by parallel inhibition of cellular CK2 and PIM-1, and is superior to both those observed combining individual inhibitors of CK2 and PIM-1 and by treating cells with the CK2 inhibitor CX4945. These data, in conjunction with the observations that cancer cells are more susceptible than non-cancer cells to TDB and that such a sensitivity is maintained in a multi-drug resistance background, highlight the pharmacological potential of this compound.     

HCN2 channels in local inhibitory interneurons constrain LTP in the hippocampal direct perforant path

Neuronal hyperpolarization-activated cyclic nucleotide-gated (HCN) channels are known to modulate spontaneous activity, resting membrane potential, input resistance, afterpotential, rebound activity, and dendritic integration. To evaluate the role of HCN2 for hippocampal synaptic plasticity, we recorded long-term potentiation (LTP) in the direct perforant path (PP) to CA1 pyramidal cells. LTP was enhanced in mice carrying a global deletion of the channel (HCN2^−/−) but not in a pyramidal neuron-restricted knockout. This precludes an influence of HCN2 located in postsynaptic pyramidal neurons. Additionally, the selective HCN blocker zatebradine reduced the activity of oriens-lacunosum moleculare interneurons in wild-type but not HCN2^−/− mice and decreased the frequency of spontaneous inhibitory currents in postsynaptic CA1 pyramidal cells. Finally, we found amplified LTP in the PP of mice carrying an interneuron-specific deletion of HCN2. We conclude that HCN2 channels in inhibitory interneurons modulate synaptic plasticity in the PP by facilitating the GABAergic output onto pyramidal neurons.     

Genetic organization of Drosophila bithorax complex

The Drosophila bithorax complex is subdivided into three major genes: Ultrabithorax+, abdominal-A+ and Abdominal-B+. Each of these genes plays its principal part in a particular anatomical domain of the body, where it is specifically required to determine the correct segmental pattern.