Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

Artificial-Noise-Aided Secure Multi-Antenna Transmission with Limited Feedback

We present an optimized secure multi-antenna transmission approach based on artificial-noise-aided beamforming, with limited feedback from a desired single-antenna receiver. To deal with beamformer quantization errors as well as unknown eavesdropper channel characteristics, our approach is aimed at maximizing throughput under dual performance constraints - a connection outage constraint on the desired communication channel and a secrecy outage constraint to guard against eavesdropping. We propose an adaptive transmission strategy that judiciously selects the wiretap coding parameters, as well as the power allocation between the artificial noise and the information signal. This optimized solution reveals several important differences with respect to solutions designed previously under the assumption of perfect feedback. We also investigate the problem of how to most efficiently utilize the feedback bits. The simulation results indicate that a good design strategy is to use approximately 20% of these bits to quantize the channel gain information, with the remainder to quantize the channel direction, and this allocation is largely insensitive to the secrecy outage constraint imposed. In addition, we find that 8 feedback bits per transmit antenna is sufficient to achieve approximately 90% of the throughput attainable with perfect feedback.Comment: to appear in IEEE Transactions on Wireless Communication

Sample preparation for point of care molecular diagnostics of STIs

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Brunel DoCLab is part of the esti2 consortium developing electronic self-testing instruments for sexually transmitted infections using nucleic acid amplification testing (NAAT). A proprietary sample collection device has been designed to integrate directly with a microfluidic cartridge. Cell lysis was conducted using a chemical method and nucleic acid purification was done on an activated cellulose membrane. The microfluidic device incorporates passive mixing of the lysis-binding buffers and sample. Preliminary results have shown extraction efficiencies for this new membrane of 69% and 57% compared to the commercial Qiagen extraction method of 85% and 59.4% for 0.1ng/μL and 100ng/μL salmon sperm DNA spiked in phosphate buffered solution. Preliminary extraction experiments in the passive mixer cartridges with lysis and nucleic acid purification showed extraction efficiency around 80% of the commercial Qiagen kit. Isothermal amplification was conducted using thermophillic helicase dependant amplification. A low cost benchtop real-time isothermal amplification platform has been developed capable of running six amplifications simultaneously. Work to integrate sample collection, nucleic acid extraction and isothermal amplification is currently underway

Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

Asymptotic behavior of the number of Eulerian orientations of graphs

We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominanceComment: arXiv admin note: text overlap with arXiv:1104.304

The Complicated and Confusing Ecology of Microcystis Blooms

Blooms of the toxin-producing cyanobacterium are increasing globally, leading to the loss of ecosystem services, threats to human health, as well as the deaths of pets and husbandry animals. While nutrient availability is a well-known driver of algal biomass, the factors controlling who is present in fresh waters are more complicated. possesses multiple strategies to adapt to temperature, light, changes in nutrient chemistry, herbivory, and parasitism that provide a selective advantage over its competitors. Moreover, its ability to alter ecosystem pH provides it a further advantage that helps exclude many of its planktonic competitors. While decades of nutrient monitoring have provided us with the tools to predict the accumulation of phytoplankton biomass, here, we point to factors on the horizon that may inform us why is presently the dominant bloom former in freshwaters around the world

Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems

We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or static statistically inhomogeneous. The results allow for the estimation of field statistics and confidence intervals when a single spatial or temporal stochastic process produces randomization of the field. Results for both coherent and incoherent detection techniques are derived, for Cartesian, planar and full-vectorial fields. We show that the functional form of the sampling pdf depends on whether the random variable is dimensioned (e.g., the sampled electric field proper) or is expressed in dimensionless standardized or normalized form (e.g., the sampled electric field divided by its sampled standard deviation). For dimensioned quantities, the electric field, its amplitude and intensity exhibit different types of Bessel $K$ sampling pdfs, which differ significantly from the asymptotic Gauss normal and $\chi^{(2)}_{2p}$ ensemble pdfs when $\nu$ is relatively small. By contrast, for the corresponding standardized quantities, Student $t$, Fisher-Snedecor $F$ and root-$F$ sampling pdfs are obtained that exhibit heavier tails than comparable Bessel $K$ pdfs. Statistical uncertainties obtained from classical small-sample theory for dimensionless quantities are shown to be overestimated compared to dimensioned quantities. Differences in the sampling pdfs arising from de-normalization versus de-standardization are obtained.Comment: 12 pages, 15 figures, accepted for publication in Phys. Rev. E, minor typos correcte

Atmospheric, Evolutionary, and Spectral Models of the Brown Dwarf Gliese 229 B

Theoretical spectra and evolutionary models that span the giant planet--brown dwarf continuum have been computed based on the recent discovery of the brown dwarf, Gliese 229 B. A flux enhancement in the 4--5 micron window is a universal feature from Jovian planets to brown dwarfs. We confirm the existence of methane and water in Gl 229 B's spectrum and find its mass to be 30 to 55 Jovian masses. Although these calculations focus on Gliese 229 B, they are also meant to guide future searches for extra-solar giant planets and brown dwarfs.Comment: 8 pages, plain TeX, plus four postscript figures, gzipped and uuencoded, accepted for Scienc

Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page

MERLIN observations of relativistic ejections from GRS 1915+105

We present high resolution MERLIN radio images of multiple relativistic ejections from GRS 1915+105 in 1997 October / November. The observations were made at a time of complex radio behaviour, corresponding to multiple optically-thin outbursts and several days of rapid radio flux oscillations. The radio imaging resolved four major ejection events from the system. As previously reported from earlier VLA observations of the source, we observe apparent superluminal motions resulting from intrinsically relativistic motions of the ejecta. However, our measured proper motions are significantly greater than those observed on larger angular scales with the VLA. Under the assumption of an intrinsically symmetric ejection, we can place an upper limit on the distance to GRS 1915+105 of 11.2 +/- 0.8 kpc. Solutions for the velocities unambiguously require a higher intrinsic speed by about 0.1c than that derived from the earlier VLA observations, whilst the angle to the line-of-sight is not found to be significantly different. At a distance of 11 kpc, we obtain solutions of v = 0.98 (-0.05,+0.02)c and theta = 66 +/- 2 degrees. The jet also appears to be curved on a scale which corresponds to a period of around 7 days. We observe significant evolution of the linear polarisation of the approaching component, with large rotations in position angle and a general decrease in fractional polarisation. The power input into the formation of the jet is very large, >10^38 erg/s at 11 kpc for a pair plasma. If the plasma contains a cold proton for each electron, then the mass outflow rate, >10^18 g/sec is comparable to inflow rates previously derived from X-ray spectral fits.Comment: 14 pages, 7 figures. Accepted for publication in MNRA