Open-Loop Spatial Multiplexing and Diversity Communications in Ad Hoc Networks

This paper investigates the performance of open-loop multi-antenna point-to-point links in ad hoc networks with slotted ALOHA medium access control (MAC). We consider spatial multiplexing transmission with linear maximum ratio combining and zero forcing receivers, as well as orthogonal space time block coded transmission. New closed-form expressions are derived for the outage probability, throughput and transmission capacity. Our results demonstrate that both the best performing scheme and the optimum number of transmit antennas depend on different network parameters, such as the node intensity and the signal-to-interference-and-noise ratio operating value. We then compare the performance to a network consisting of single-antenna devices and an idealized fully centrally coordinated MAC. These results show that multi-antenna schemes with a simple decentralized slotted ALOHA MAC can outperform even idealized single-antenna networks in various practical scenarios.Comment: 51 pages, 19 figures, submitted to IEEE Transactions on Information Theor

Eta Products, BPS States and K3 Surfaces

Inspired by the multiplicative nature of the Ramanujan modular discriminant, Δ, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present identities arising from q-expansions as well as relations to the sporadic Mathieu group M 24

Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl

Modular Solutions to Equations of Generalized Halphen Type

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have $q$--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

Moonshine and the Meaning of Life

With a jocund air, we present an observation on the first 24 coefficients of the modular invariant and of the modular discriminant. The observation is purely for the sake of entertainment and could be of some diversion to a mathematical audience.Comment: 1 pag

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

Preliminary study of the characteristics of a high Mg containing Al-Mg-Si alloy

An Al-20Mg-4Si high Mg containing alloy has been produced and its characteristics investigated. The as-cast alloy revealed primary Mg 2Si particles evenly distributed throughout an α-Al matrix with a β-Al 3Mg 2 fully divorced eutectic phase observed in interdendritic regions. The Mg 2Si particles displayed octahedral, truncated octahedral, and hopper morphologies. Additions of Sb, Ti and Zr had a refining influence reducing the size of the Mg 2Si from 52 ± 4 μm to 25 ± 0.1 μm, 35 ± 1 μm and 34 ± 1 μm respectively. HPDC tensile test samples could be produced with a 0.6 wt.% Mn addition which prevented die soldering. Solution heating for 1 hr was found to dissolve the majority of the Al 3Mg 2 eutectic phase with no evidence of any effect on the primary Mg 2Si. Preliminary results indicate that the heat treatment has a beneficial effect on the elongation and the UTS

Review of the initial validation and characterization of a chicken 3K SNP array.

In 2004 the chicken genome sequence and more than 2.8 million single nucleotide polymorphisms (SNPs) were reported. This information greatly enhanced the ability of poultry scientists to understand chicken biology, especially with respect to identification of quantitative trait loci (QTL) and genes that control simple and complex traits. To validate and address the quality of the reported SNPs, assays for 3072 SNPS were developed and used to genotype 2576 DNAs isolated from commercial and experimental birds. Over 90% of the SNPs were valid based on the criterion used for segregating, and over 88% had a minor allele frequency of 2% or greater. As the East Lansing (EL) and Wageningen University (WAU) reference panels were genotyped, 1933 SNPs were added to the chicken genetic map, which was used in the second chicken genome sequence assembly. It was also discovered that linkage disequilibrium varied considerably between commercial layers and broilers; with the latter having haplotype blocks averaging 10 to 50 kb in size. Finally, it was estimated that commercial lines have lost 70% or more of their genetic diversity, with the majority of allele loss attributable to the limited number of chicken breeds used

Random access quantum information processors

Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access -- the ability of arbitrary qubit pairs to interact directly. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-bit quantum memory, with a single transmon serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. The memory bits are superpositions of vacuum and single-photon states, controlled by a single superconducting transmon coupled to the edge of the array. We selectively stimulate single-photon vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency, producing sidebands resonant with the modes. Utilizing these oscillations for state transfer, we perform a universal set of single- and two-qubit gates between arbitrary pairs of modes, using only the charge and flux bias of the transmon. Further, we prepare multimode entangled Bell and GHZ states of arbitrary modes. The fast and flexible control, achieved with efficient use of cryogenic resources and control electronics, in a scalable architecture compatible with state-of-the-art quantum memories is promising for quantum computation and simulation.Comment: 7 pages, 5 figures, supplementary information ancillary file, 21 page