Towards Mixed Gr{\"o}bner Basis Algorithms: the Multihomogeneous and Sparse Case

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of unmixed polynomial systems, that is systems with polynomials having the same support, using the approach of Faug{\`e}re, Spaenlehauer, and Svartz [ISSAC'14]. We present two algorithms for sparse Gr{\"o}bner bases computations for mixed systems. The first one computes with mixed sparse systems and exploits the supports of the polynomials. Under regularity assumptions, it performs no reductions to zero. For mixed, square, and 0-dimensional multihomogeneous polynomial systems, we present a dedicated, and potentially more efficient, algorithm that exploits different algebraic properties that performs no reduction to zero. We give an explicit bound for the maximal degree appearing in the computations

High resolution simulations of the reionization of an isolated Milky Way - M31 galaxy pair

We present the results of a set of numerical simulations aimed at studying reionization at galactic scale. We use a high resolution simulation of the formation of the Milky Way-M31 system to simulate the reionization of the local group. The reionization calculation was performed with the post-processing radiative transfer code ATON and the underlying cosmological simulation was performed as part of the CLUES project. We vary the source models to bracket the range of source properties used in the literature. We investigate the structure and propagation of the galatic ionization fronts by a visual examination of our reionization maps. Within the progenitors we find that reionization is patchy, and proceeds locally inside out. The process becomes patchier with decreasing source photon output. It is generally dominated by one major HII region and 1-4 additional isolated smaller bubbles, which eventually overlap. Higher emissivity results in faster and earlier local reionization. In all models, the reionization of the Milky Way and M31 are similar in duration, i.e. between 203 Myr and 22 Myr depending on the source model, placing their zreion between 8.4 and 13.7. In all models except the most extreme, the MW and M31 progenitors reionize internally, ignoring each other, despite being relatively close to each other even during the epoch of reionization. Only in the case of strong supernova feedback suppressing star formation in haloes less massive than 10^9 M_sun, and using our highest emissivity, we find that the MW is reionized by M31.Comment: Accepted for publication in ApJ. 14 pages, 4 figures, 1 tabl

A tale of seven narrow spikes and a long trough: Constraining the timing of the percolation of HII bubbles at the tail end of reionization with ULAS J1120+0641

High-signal to noise observations of the Ly$\alpha$ forest transmissivity in the z = 7.085 QSO ULAS J1120+0641 show seven narrow transmission spikes followed by a long 240 cMpc/h trough. Here we use radiative transfer simulations of cosmic reionization previously calibrated to match a wider range of Ly$\alpha$ forest data to show that the occurrence of seven transmission spikes in the narrow redshift range z = 5.85 - 6.1 is very sensitive to the exact timing of reionization. Occurrence of the spikes requires the most under dense regions of the IGM to be already fully ionised. The rapid onset of a long trough at z = 6.12 requires a strong decrease of the photo-ionisation rate at z$\sim$6.1 in this line-of-sight, consistent with the end of percolation at this redshift. The narrow range of reionisation histories that we previously found to be consistent with a wider range of Ly$\alpha$ forest data have a reasonable probability of showing seven spikes and the mock absorption spectra provide an excellent match to the spikes and the trough in the observed spectrum of ULAS J1120+0641. Despite the large overall opacity of Ly$\alpha$ at z > 5.8, larger samples of high signal-to-noise observations of rare transmission spikes should therefore provide important further insights into the exact timing of the percolation of HII bubbles at the tail-end of reionizatio

320g Ionization-Heat Cryogenic Detector for Dark Matter Search in the EDELWEISS Experiment

The EDELWEISS experiment used in 2001 a 320g heat-and-ionization cryogenic Ge detector operated in a low-background environment in the Laboratoire Souterrain de Modane for direct WIMP detection. This detector presents an increase of more than 4 times the mass of previous detectors. Calibrations of this detector are used to determine its energy resolution and fiducial volume, and to optimize the detector design for the 1kg phase of the EDELWEISS-I experiment. Analysis of the calibrations and characteristics of a first series of 320g-detectors are presented.Comment: 4 pages, 3 figure

Constraining the second half of reionization with the Ly β forest

We present an analysis of the evolution of the Lyman-series forest into the epoch of reionization using cosmological radiative transfer simulations in a scenario where reionization ends late. We explore models with different midpoints of reionization and gas temperatures. We find that once the simulations have been calibrated to match the mean flux of the observed Lyman-$\alpha$ forest at $4 < z < 6$, they also naturally reproduce the distribution of effective optical depths of the Lyman-$\beta$ forest in this redshift range. We note that the tail of the largest optical depths that is most challenging to match corresponds to the long absorption trough of ULAS J0148+0600, which we have previously shown to be rare in our simulations. We consider the evolution of the Lyman-series forest out to higher redshifts, and show that future observations of the Lyman-$\beta$ forest at $z>6$ will discriminate between different reionization histories. The evolution of the Lyman-$\alpha$ and Lyman-$\gamma$ forests are less promising as a tool for pushing studies of reionization to higher redshifts due to the stronger saturation and foreground contamination, respectively

Regularity of prime ideals

We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud\u2013Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not rely on the Mayr\u2013Meyer construction. Furthermore, examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given. Using a result of Ananyan-Hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

CPT symmetry and antimatter gravity in general relativity

The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is self-attractive, the interaction between matter and antimatter might be either attractive or repulsive. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion, i.e. antigravity appears as a prediction of general relativity when CPT is applied. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter repulsive interaction.Comment: 6 pages, to be published in EPL (http://epljournal.edpsciences.org/

Large Ly α opacity fluctuations and low CMB τ in models of late reionization with large islands of neutral hydrogen extending to z &lt; 5.5

High-redshift QSO spectra show large spatial fluctuations in the Ly-alpha opacity of the intergalactic medium on surprisingly large scales at z>~5.5. We present a radiative transfer simulation of cosmic reionization driven by galaxies that reproduces this large scatter and the rapid evolution of the Ly-alpha opacity distribution at 5<z<6. The simulation also reproduces the low Thomson scattering optical depth reported by the latest CMB measurement and is consistent with the observed short near-zones and strong red damping wings in the highest-redshift QSOs. It also matches the rapid disappearance of observed Ly-alpha emission by galaxies at z>~6. Reionization is complete at z=5.3 in our model, and 50% of the volume of the Universe is ionized at z=7. Agreement with the Ly-alpha forest data in such a late reionization model requires a rapid evolution of the ionizing emissivity of galaxies that peaks at z~6.8. The late end of reionization results in a large scatter in the photoionisation rate and the neutral hydrogen fraction at redshifts as low as z<~5.5 with large residual neutral 'islands' that can produce very long Gunn-Peterson troughs resembling those seen in the data

Large-scale opacity fluctuations in the Lyα\alpha forest: evidence for QSOs dominating the ionizing UV background at zz ~ 5.5–6?

Ly$\alpha$ forest data probing the post-reionization Universe show surprisingly large opacity fluctuations over rather large (≥50 $h^{−1}$ comoving Mpc) spatial scales. We model these fluctuations using a hybrid approach utilizing the large-volume Millennium simulation to predict the spatial distribution of QSOs combined with smaller scale full hydrodynamical simulation performed with $\small \text{RAMSES}$ and post-processed with the radiative transfer code $\small \text{ATON}$. We produce realistic mock absorption spectra that account for the contribution of galaxies and QSOs to the ionizing UV background. These improved models confirm our earlier findings that a significant ($\gtrsim$50 per cent) contribution of ionizing photons from QSOs can explain the large reported opacity fluctuations on large scales. The inferred QSO luminosity function is thereby consistent with recent estimates of the space density of QSOs at this redshift. Our simulations still somewhat struggle, however, to reproduce the very long (110 $h^{−1}$ comoving Mpc) high-opacity absorption through observed in ULAS J0148+0600, perhaps suggesting an even later end of reionization than assumed in our previously favoured model. Medium-deep/medium area QSO surveys as well as targeted searches for the predicted strong transverse QSO proximity effect would illuminate the origin of the observed large-scale opacity fluctuations. They would allow us to substantiate whether UV fluctuations due to QSO are indeed primarily responsible, or whether significant contributions from other recently proposed mechanisms such as large-scale fluctuations in temperature and mean free path (even in the absence of rare bright sources) are required.This work was supported by the ERC Advanced Grant 320596 ‘The Emergence of Structure during the epoch of Reionization’. This work was performed using the COSMOS and Darwin Supercomputers of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council. This work furthermore used the Wilkes GPU cluster at the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc., NVIDIA and Mellanox, and part funded by STFC with industrial sponsorship from Rolls Royce and Mitsubishi Heavy Industries. Some of the hydrodynamical simulations used in this work were performed with supercomputer time awarded by the Partnership for Advanced Computing in Europe (PRACE) 8th Call. We acknowledge PRACE for enabling access to the Curie supercomputer, based in France at the Tres Grand Centre de Calcul (TGCC). EP acknowledges support by ` the Kavli foundation. The research of JC and MH was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence ‘Origin and Structure of the Universe’