A computational approach to the Thompson group FF

Let $F$ denote the Thompson group with standard generators $A=x_0$, $B=x_1$. It is a long standing open problem whether $F$ is an amenable group. By a result of Kesten from 1959, amenability of $F$ is equivalent to $$(i)\qquad ||I+A+B||=3$$ and to $$(ii)\qquad ||A+A^{-1}+B+B^{-1}||=4,$$ where in both cases the norm of an element in the group ring $\mathbb{C} F$ is computed in $B(\ell^2(F))$ via the regular representation of $F$. By extensive numerical computations, we obtain precise lower bounds for the norms in $(i)$ and $(ii)$, as well as good estimates of the spectral distributions of $(I+A+B)^*(I+A+B)$ and of $A+A^{-1}+B+B^{-1}$ with respect to the tracial state $\tau$ on the group von Neumann Algebra $L(F)$. Our computational results suggest, that $$||I+A+B||\approx 2.95 \qquad ||A+A^{-1}+B+B^{-1}||\approx 3.87.$$ It is however hard to obtain precise upper bounds for the norms, and our methods cannot be used to prove non-amenability of $F$.Comment: appears in International Journal of Algebra and Computation (2015

An Empirically-Grounded Comparison of the Johnson System versus the Beta as Crop Yield Distribution Models

Previous research established that the expanded Johnson system can accommodate any theoretically possible mean-variance-skewness-kurtosis combination. Therefore, it has been hypothesized that this system can provide for a reasonably accurate modeling approximation of any probability distribution that might be encountered in practice. In order to test that hypothesis, this manuscript develops a more flexible expanded form of the Beta distribution which, in its original form, has been widely used to model and simulate crop yields for risk analysis. Empirically grounded evaluations suggest that the Johnson system can model a variety of typical yield data-generating processes that are based on the Beta distribution much more precisely than the Beta can model representative crop yield data simulated from the Johnson system. The accuracy with which the Johnson system approximates the Beta supports the previously stated hypothesis.Crop Production/Industries,

The Pulse Scale Conjecture and the Case of BATSE Trigger 2193

The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse in GRB 930214c (BATSE trigger 2193), the single most fluent single-pulsed GRB that occurred before May 1998. Furthermore, pulses are hypothesized to start at the same time independent of energy. This "Pulse Start Conjecture" is also confirmed in GRB 930214c. Analysis of GRB 930214c also shows that, in general, higher energy channels show shorter temporal scale factors. Over the energy range 100 KeV - 1 MeV, it is found that the temporal scale factors between a pulse measured at different energies are related to that energy by a power law, possibly indicating a simple relativistic mechanism is at work. To test robustness, the Pulse Start and Pulse Scale Conjectures were also tested on the four next most fluent single-pulse GRBs. Three of the four clearly passed, with a second smaller pulse possibly confounding the discrepant test. Models where the pulse rise and decay are created by different phenomena do not typically predict pulses that satisfy both the Pulse Start Conjecture and the Pulse Scale Conjecture, unless both processes are seen to undergo common time dilation.Comment: 19 pages, 9 figures, analysis revised and extended, accepted to Ap

Semiclassical ordering in the large-N pyrochlore antiferromagnet

We study the semiclassical limit of the $Sp(N)$ generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the $N \to \infty$ saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte-Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N=1) semiclassical ground state.Comment: 4 pages, 4 eps figures; published versio

A Security Monitoring Framework For Virtualization Based HEP Infrastructures

High Energy Physics (HEP) distributed computing infrastructures require automatic tools to monitor, analyze and react to potential security incidents. These tools should collect and inspect data such as resource consumption, logs and sequence of system calls for detecting anomalies that indicate the presence of a malicious agent. They should also be able to perform automated reactions to attacks without administrator intervention. We describe a novel framework that accomplishes these requirements, with a proof of concept implementation for the ALICE experiment at CERN. We show how we achieve a fully virtualized environment that improves the security by isolating services and Jobs without a significant performance impact. We also describe a collected dataset for Machine Learning based Intrusion Prevention and Detection Systems on Grid computing. This dataset is composed of resource consumption measurements (such as CPU, RAM and network traffic), logfiles from operating system services, and system call data collected from production Jobs running in an ALICE Grid test site and a big set of malware. This malware was collected from security research sites. Based on this dataset, we will proceed to develop Machine Learning algorithms able to detect malicious Jobs.Comment: Proceedings of the 22nd International Conference on Computing in High Energy and Nuclear Physics, CHEP 2016, 10-14 October 2016, San Francisco. Submitted to Journal of Physics: Conference Series (JPCS

Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model

Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.Comment: 4 pages, 1 figure, typeset with ReVTe

Bioreactors for high cell density and continuous multi-stage cultivations: options for process intensification in cell culture-based viral vaccine production

With an increasing demand for efficacious, safe, and affordable vaccines for human and animal use, process intensification in cell culture-based viral vaccine production demands advanced process strategies to overcome the limitations of conventional batch cultivations. However, the use of fed-batch, perfusion, or continuous modes to drive processes at high cell density (HCD) and overextended operating times has so far been little explored in large-scale viral vaccine manufacturing. Also, possible reductions in cell-specific virus yields for HCD cultivations have been reported frequently. Taking into account that vaccine production is one of the most heavily regulated industries in the pharmaceutical sector with tough margins to meet, it is understandable that process intensification is being considered by both academia and industry as a next step toward more efficient viral vaccine production processes only recently. Compared to conventional batch processes, fed-batch and perfusion strategies could result in ten to a hundred times higher product yields. Both cultivation strategies can be implemented to achieve cell concentrations exceeding 10(7) cells/mL or even 10(8) cells/mL, while keeping low levels of metabolites that potentially inhibit cell growth and virus replication. The trend towards HCD processes is supported by development of GMP-compliant cultivation platforms, i.e., acoustic settlers, hollow fiber bioreactors, and hollow fiber-based perfusion systems including tangential flow filtration (TFF) or alternating tangential flow (ATF) technologies. In this review, these process modes are discussed in detail and compared with conventional batch processes based on productivity indicators such as space-time yield, cell concentration, and product titers. In addition, options for the production of viral vaccines in continuous multi-stage bioreactors such as two- and three-stage systems are addressed. While such systems have shown similar virus titers compared to batch cultivations, keeping high yields for extended production times is still a challenge. Overall, we demonstrate that process intensification of cell culture-based viral vaccine production can be realized by the consequent application of fed-batch, perfusion, and continuous systems with a significant increase in productivity. The potential for even further improvements is high, considering recent developments in establishment of new (designer) cell lines, better characterization of host cell metabolism, advances in media design, and the use of mathematical models as a tool for process optimization and control

The detailed chemical composition of the terrestrial planet host Kepler-10

Chemical abundance studies of the Sun and solar twins have demonstrated that the solar composition of refractory elements is depleted when compared to volatile elements, which could be due to the formation of terrestrial planets. In order to further examine this scenario, we conducted a line-by-line differential chemical abundance analysis of the terrestrial planet host Kepler-10 and fourteen of its stellar twins. Stellar parameters and elemental abundances of Kepler-10 and its stellar twins were obtained with very high precision using a strictly differential analysis of high quality CFHT, HET and Magellan spectra. When compared to the majority of thick disc twins, Kepler-10 shows a depletion in the refractory elements relative to the volatile elements, which could be due to the formation of terrestrial planets in the Kepler-10 system. The average abundance pattern corresponds to ~ 13 Earth masses, while the two known planets in Kepler-10 system have a combined ~ 20 Earth masses. For two of the eight thick disc twins, however, no depletion patterns are found. Although our results demonstrate that several factors (e.g., planet signature, stellar age, stellar birth location and Galactic chemical evolution) could lead to or affect abundance trends with condensation temperature, we find that the trends give further support for the planetary signature hypothesis.Comment: 12 pages, 11 figures, accepted for publication in MNRA