Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Dataset for the proteomic inventory and quantitative analysis of the breast cancer hypoxic secretome associated with osteotropism

The cancer secretome includes all of the macromolecules secreted by cells into their microenvironment. Cancer cell secretomes are significantly different to that of normal cells reflecting the changes that normal cells have undergone during their transition to malignancy. More importantly, cancer secretomes are known to be active mediators of both local and distant host cells and play an important role in the progression and dissemination of cancer. Here we have quantitatively profiled both the composition of breast cancer secretomes associated with osteotropism, and their modulation under normoxic and hypoxic conditions. We detect and quantify 162 secretome proteins across all conditions which show differential hypoxic induction and association with osteotropism. Mass Spectrometry proteomics data have been deposited to the ProteomeXchange Consortium with the dataset identifier PXD000397 and the complete proteomic, bioinformatic and biological analyses are reported in Cox et al. (2015) [1]

Cubic Curves, Finite Geometry and Cryptography

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.Comment: This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in the third paragraph. The final publication is available at springerlink.com at http://www.springerlink.com/content/xh85647871215644

Computing L-series of hyperelliptic curves

We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic methods.Comment: 15 pages, corrected minor typo

Numerical analysis and simulation of the dynamics of mountain glaciers

In this chapter, we analyze and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solutions are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice, which describes the time evolution of a glacier. The accumulation due to snow precipitation and melting are accounted for in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a two-grids method. As an illustration, we simulate the evolution of Aletsch glacier, Switzerland, over the 21st century by using realistic climatic conditions

Introduction to Configuration Path Integral Monte Carlo

In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte Carlo methods are among the most successful approaches to first-principle simulations of many-body quantum systems. In this chapter we present a recently developed method---the configuration path integral Monte Carlo (CPIMC) method for moderately coupled, highly degenerate fermions at finite temperatures. It is based on the second quantization representation of the $N$-particle density operator in a basis of (anti-)symmetrized $N$-particle states (configurations of occupation numbers) and allows to tread arbitrary pair interactions in a continuous space. We give a detailed description of the method and discuss the application to electrons or, more generally, Coulomb-interacting fermions. As a test case we consider a few quantum particles in a one-dimensional harmonic trap. Depending on the coupling parameter (ratio of the interaction energy to kinetic energy), the method strongly reduces the sign problem as compared to direct path integral Monte Carlo (DPIMC) simulations in the regime of strong degeneracy which is of particular importance for dense matter in laser plasmas or compact stars. In order to provide a self-contained introduction, the chapter includes a short introduction to Metropolis Monte Carlo methods and the second quantization of quantum mechanics.Comment: chapter in book "Introduction to Complex Plasmas: Scientific Challenges and Technological Opportunities", Michael Bonitz, K. Becker, J. Lopez and H. Thomsen (Eds.) Springer Series "Atomic, Optical and Plasma Physics", vol. 82, Springer 2014, pp. 153-194 ISBN: 978-3-319-05436-0 (Print) 978-3-319-05437-7 (Online

Chromatin accessibility dynamics across C. elegans development and ageing

An essential step for understanding the transcriptional circuits that control development and physiology is the global identification and characterization of regulatory elements. Here we present the first map of regulatory elements across the development and ageing of an animal, identifying 42,245 elements accessible in at least one C. elegans stage. Based on nuclear transcription profiles, we define 15,714 protein-coding promoters and 19,231 putative enhancers, and find that both types of element can drive orientation-independent transcription. Additionally, more than 1000 promoters produce transcripts antisense to protein coding genes, suggesting involvement in a widespread regulatory mechanism. We find that the accessibility of most elements changes during development and/or ageing and that patterns of accessibility change are linked to specific developmental or physiological processes. The map and characterization of regulatory elements across C. elegans life provides a platform for understanding how transcription controls development and ageing