3D printing dimensional calibration shape: Clebsch Cubic

3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the complete building envelope. The validation process involves the growing and measuring of a shape with known parameters. The measured result is compared with the intended digital model. Processes with the risk of deformation after time or post processing may find this technique beneficial. We propose to use objects from algebraic geometry as test shapes. A cubic surface is given as the zero set of a 3rd degree polynomial with 3 variables. A class of cubics in real 3D space contains exactly 27 real lines. We provide a library for the computer algebra system Singular which, from 6 given points in the plane, constructs a cubic and the lines on it. A surface shape derived from a cubic offers simplicity to the dimensional comparison process, in that the straight lines and many other features can be analytically determined and easily measured using non-digital equipment. For example, the surface contains so-called Eckardt points, in each of which three of the lines intersect, and also other intersection points of pairs of lines. Distances between these intersection points can easily be measured, since the points are connected by straight lines. At all intersection points of lines, angles can be verified. Hence, many features distributed over the build volume are known analytically, and can be used for the validation process. Due to the thin shape geometry the material required to produce an algebraic surface is minimal. This paper is the first in a series that proposes the process chain to first define a cubic with a configuration of lines in a given print volume and then to develop the point cloud for the final manufacturing. Simple measuring techniques are recommended.Comment: 8 pages, 1 figure, 1 tabl

Computing automorphic forms on Shimura curves over fields with arbitrary class number

We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke eigenvalues associated to Hilbert modular forms of arbitrary level over a totally real field of odd degree. We conclude with two examples which illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I

K-Rational D-Brane Crystals

In this paper the problem of constructing spacetime from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of certain Calabi-Yau varieties. The collections of D-branes involved have algebraic base points, leading to the notion of K-arithmetic D-crystals for algebraic number fields K. This idea can be tested for D0-branes in the framework of toroidal compactifications via the conjectures of Birch and Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these conjectures can be interpreted as formulae that relate the canonical Neron-Tate height of the base points of the D-crystals to special values of the motivic L-function at the central point. In simple cases the knowledge of the D-crystals of Heegner type suffices to uniquely determine the geometry.Comment: 36 page

Peak shape clustering reveals biological insights

Background: ChIP-seq experiments are widely used to detect and study DNA-protein interactions, such as transcription factor binding and chromatin modifications. However, downstream analysis of ChIP-seq data is currently restricted to the evaluation of signal intensity and the detection of enriched regions (peaks) in the genome. Other features of peak shape are almost always neglected, despite the remarkable differences shown by ChIP-seq for different proteins, as well as by distinct regions in a single experiment. Results: We hypothesize that statistically significant differences in peak shape might have a functional role and a biological meaning. Thus, we design five indices able to summarize peak shapes and we employ multivariate clustering techniques to divide peaks into groups according to both their complexity and the intensity of their coverage function. In addition, our novel analysis pipeline employs a range of statistical and bioinformatics techniques to relate the obtained peak shapes to several independent genomic datasets, including other genome-wide protein-DNA maps and gene expression experiments. To clarify the meaning of peak shape, we apply our methodology to the study of the erythroid transcription factor GATA-1 in K562 cell line and in megakaryocytes. Conclusions: Our study demonstrates that ChIP-seq profiles include information regarding the binding of other proteins beside the one used for precipitation. In particular, peak shape provides new insights into cooperative transcriptional regulation and is correlated to gene expression

Exhaled nitric oxide in patients with PiZZ Phenotype-related α 1-anti-trypsin deficiency

AbstractThere is no report of exhaled NO (eNO) in subjects with different phenotypes ofα1 -anti-trypsin (AAT) deficiency.Exhaled nitric oxide was evaluated by means of single-breath chemiluminescence analysis (fractional exhaled concentration at the plateau level [plFENO]) in 40 patients with AAT deficiency. Patients were divided according to the protease inhibitor (Pi) phenotype: PiMZ/MS, n=25; PiSZ n=6; PiZZ, n=9. Nineteen healthy subjects served as controls. Levels of eNO in PiZZ patients were also compared with those of subjects, without AAT deficiency (PiMM), matched for diagnosis, sex, age, smoking habit and forced expiratory volume in 1 sec (FEV1). In AAT deficiency subjects airway hyper-responsiveness to methacholine (PD20FEV1) was also assessed.plFENOwas significantly lower in the PiZZ group (4·5±1·4 ppb) than in matched PiMM subjects (8·2±3·8 ppb), in healthy controls (9·3±2·8 ppb) and in patients of other phenotypes. Dynamic lung volumes and DLCOwere significantly lower in PiZZ than in other AAT-deficient patients. Bronchial hyper-responsiveness was not different among AAT phenotypes.These results suggest that eNO may be significantly reduced in PiZZ as compared to healthy control subjects and to AAT subjects with other phenotypes, independent of the level of airway obstruction. Whether, at least potentially, eNO may be considered as an early marker of lung involvement in AAT deficiency must be confirmed with studies on larger number of subjects

Equivariant Birch-Swinnerton-Dyer conjecture for the base change of elliptic curves: An example

Let E be an elliptic curved defined over \Q and let K/\Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h^1(E\times_{\Q} K)(1) viewed as a motive over \Q with coefficients in \Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper we prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S_3-extension of \Q.Comment: 21 page

Probabilistic and predictive performance-based approach for assessing reinforced concrete structures lifetime: The applet project

International audienceConcrete deterioration results in different damage extents, from cracking to concrete spalling, from losses of reinforcement cross-sections to bond losses. A relevant prediction of this performance is the basis for a successful management of the concrete structures. Conversely, the large amount of uncertainties related to parameters and models require a specific analysis in order to provide relevant results. The APPLET project intends to develop a probabilistic and predictive performance-based approach by quantifying the various sources of variability (material and structure), studying the interaction between environmental aggressive agents and the concrete material, ensuring a transfer of the physical-chemical models at the material scale towards models at the structure level, including and understanding in a better manner the corrosion process, integrating interface models between reinforcement and concrete, proposing relevant numerical models, integrating know-how from monitoring or inspection. To provide answers, a consortium of 19 partners has been established and has promoted a research project funded by the French Research Science Agency (ANR). Started in May 2007, the project has ended in November 2010. This paper will resume the most significant advances targeted by this research project

Modular symbols and Hecke operators

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and Robert MacPherson.Comment: 11 pp, 2 figures, uses psfrag.st

Exceptional elliptic curves over quartic fields

We study the number of elliptic curves, up to isomorphism, over a fixed quartic field $K$ having a prescribed torsion group $T$ as a subgroup. Let $T=\Z/m\Z \oplus \Z/n\Z$, where $m|n$, be a torsion group such that the modular curve $X_1(m,n)$ is an elliptic curve. Let $K$ be a number field such that there is a positive and finite number of elliptic curves $E_T$ over $K$ having $T$ as a subgroup. We call such pairs $(E_T, K)$ \emph{exceptional}. It is known that there are only finitely many exceptional pairs when $K$ varies through all quadratic or cubic fields. We prove that when $K$ varies through all quartic fields, there exist infinitely many exceptional pairs when $T=\Z/14\Z$ or $\Z/15\Z$ and finitely many otherwise

Highly Luminescent Europium(III) Complexes in Solution and PMMA-Doped Films for Bright Red Electroluminescent Devices

This paper reports the synthesis, structure, photophysical, and optoelectronic properties of five eight-coordinate Europium(III) ternary complexes, namely, [Eu(hth)3(L)2], bearing 4,4,5,5,6,6,6-heptafluoro-1-(2-thienyl)-1,3-hexanedione (hth) as a sensitizer and L = H2O (1), dpso (diphenyl sulphoxide, 2), dpsoCH3 (4,4′-dimethyl diphenyl sulfoxide, 3), dpsoCl (bis(4-chlorophenyl)sulphoxide, 4), and tppo (triphenylphosphine oxide, 5) as co-ligands. The NMR and the crystal structure analysis confirmed the eight-coordinate structures of the complexes in solution and in a solid state. Upon UV-excitation on the absorption band of the β-diketonate ligand hth, all complexes showed the characteristic bright red luminescence of the Europium ion. The tppo derivative (5) displayed the highest quantum yield (up to 66%). As a result, an organic light-emitting device, OLED, was fabricated with a multi-layered structure—ITO/MoO3/mCP/SF3PO:[complex 5] (10%)/TPBi:[complex 5] (10%)/TmPyPB/LiF/Al—using complex 5 as the emitting component