The Distribution of the Bit Error Rate for an M Branch Antenna with N Interferers

Given an antenna with M branches, the bit error rate (BER) and mean squared error (MSE) for choosing the antenna weights (to approximately cancel M???1 interferers), are given by $$ \mathit{BER} \approx C \;\exp \left(-\alpha-\alpha Z_N\right) \mbox{ and } \mathit{MSE}=1/\left(1+Z_N\right), $$ where Z _N is the signal-to-interference plus noise ratio and C, α are some fixed parameters. So, obtaining the distribution of Z _N allows one to obtain the distribution of the MSE and to approximate that of the BER. Three cases are presented:

• the case of fixed powers for the interferers, say Q ₁, ..., Q _N , and for the wanted signal, say Q ₀;
• the case of fixed power for the wanted signal and random powers for the interferers;
• the case of random powers for both the wanted signal and the interferers.

We assume that Q ₀,...,Q _N are independent with different distributions. We show that to magnitude 1/N, the distribution of Z is just that of Q ₀ g _M /T, where g _M is a gamma random variable with mean M and T is the average of the total interferer power: $$ T = \mathbb{E} \ \left\{ \sum\limits_{j=1}^N Q_j\right\}. $$ We also show how to obtain an expansion in powers of 1/N for the distribution of $\mathit{TZ}$ about that of Q ₀ g _M . For example, to get the distribution of $\mathit{TZ}$ up to magnitude 1/N ², one requires only the means of Q ₁,...,Q _N and $Q_1^2,\ldots,Q_N^2$ and the distribution of Q ₀.     

Structural, mechanistic, and computational analysis of the effects of anomeric fluorines on anomeric fluoride departure in 5-fluoroxylosyl fluorides

The effects of fluorine substitution at the C-5 center of pyranosyl fluorides on the reactivity at the C-1 anomeric center was probed by studying a series of 5-fluoroxylosyl fluoride derivatives. X-ray structures of their per-O-acetates detailed the effects on the ground-state structures. First-order rate constants for spontaneous hydrolysis, in conjunction with computational studies, revealed that changes in the stereochemistry of the 5-fluorine had minimal effects on the solvolysis rate constants and that the observed rate reductions were broadly similar to those caused by additional fluorine substitution at C-1 but significantly less than those due to substitution at C-2. Differences in the trapping behavior of 5- versus 2-fluoro-substituted glycosyl fluorides with α- and β-glycosidases arise more from differences in steric effects and hydrogen-bonding interactions than from intrinsic reactivity differences.     

Central limit theorems for dependent variables,II

Summary Two families of measures of the dependence between two random variables (rv's) are introduced. They include the strong-mixing ‘distance’. Two Central Limit Theorems (CLT's) are proved for dependent samples or processes where the dependence of the ‘past’ is not too strong. Tightness of the empirical process is shown to hold under conditions involving only the four-dimensional marginals of the sample.     

Gas phase noncovalent protein complexes that retain solution binding properties: Binding of xylobiose inhibitors to the β-1, 4 exoglucanase from <Emphasis Type="Italic">Cellulomonas fimi</Emphasis>

Tandem mass spectrometry has been used to compare gas-phase and solution binding of three small-molecule inhibitors to the wild type and three mutant forms of the catalytic domain of Cex, an enzyme that hydrolyses xylan and xylo-oligosaccharides. The inhibitors, xylobiosyl-deoxynojirimycin, xylobiosyl-isofagomine lactam, and xylobiosyl-isofagomine consist of a common distal xylose linked to different proximal aza-sugars. The three mutant forms of the enzyme contain the substitutions Asn44Ala, Gln87Met, and Gln87Tyr that alter the binding interactions between Cex and the distal sugar of each inhibitor. An electrospray ionization (ESI) triple quadrupole MS/MS system is used to measure the internal energies, DeltaE(int), that must be added to gas-phase ions to cause dissociation of the noncovalent enzyme-inhibitor complexes. Collision cross sections of ions of the apo-enzyme and enzyme-inhibitor complexes, which are required for the calculations of DeltaE(int), have also been measured. The results show that, in the gas phase, enzyme-inhibitor complexes have more compact, folded conformations than the corresponding apo-enzyme ions. With the mutant enzymes, the effects of substituting a single residue can be detected. The energies required to dissociate the gas-phase complexes follow the same trend as the values of DeltaG0 for dissociation of the complexes in solution. This trend is observed both with different inhibitors, which probe binding to the proximal sugar, and with mutants of Cex, which probe binding to the distal sugar. Thus the gas-phase complexes appear to retain much of their solution binding characteristics.     

Suppression of ring artefacts when tomographing anisotropically attenuating samples

There are many objects for which the attenuation varies significantly as they are rotated during computerized X‐ray tomography, for example plate samples. This can lead to significant ring artefacts in the subsequent tomographic reconstructions. In this paper a new method is presented that can successfully suppress such ring artefacts and is applicable to both parallel and cone‐beam geometries. Rapid correction is achieved via an analytical formula which involves only a matrix‐vector multiplication, for which the matrix is known and depends on a regularization parameter. The efficacy of the method is demonstrated for a paleontological sample (calcified shark cartilage) and a carbon–carbon composite/Ti–SiC metal matrix composite test sample.     

An optical fibre sensor for the measurement of pressure

This paper describes the design, construction and testing of a fibre optic pressure sensor based on a reflecting Fabry-Perot etalon. The etalon comprised one fixed mirror and a second mirror designed to flex under the action of the pressure being monitored. A single multimode fibre was used to connect the passive, remote sensor to the transmitter/receiver section, and dual wavelength referencing was used to eliminate the effects of bending-induced attenuation in the fibre.     

Synthesis and structural characterization of bi- and trimetallic octacyanometalate(IV) complexes: [Delta,Lambda-MII(en)3][cis-MII(en)2(OH2)][MIV(CN)8].2H2O and [cis-MII(en)2(OH2)]2[(mu-NC)2MIV(CN)6].4H2O (MII = Mn, Co, Ni; MIV = Mo, W)

Treatment of [M(II)(en)(3)][OTs](2) or methanolic ethylenediamine solutions containing transition metal p-toluenesulfonates (M(II) = Mn, Co) with aqueous K(4)M(IV)(CN)(8).2H(2)O or Cs(3)M(V)(CN)(8) (M(IV) = Mo, W; M(V) = Mo) affords crystalline clusters of [M(II)(en)(3)][cis-M(II)(en)(2)(OH(2))(mu-NC)M(IV)(CN)(7)].2H(2)O (M(IV) = Mo; M(II) = Mn, 1; Ni, 5; M(IV) = W; M(II) = Mn, 2; Ni, 6) and [cis-M(II)(en)(2)(OH(2))](2)[(mu-NC)(2)M(IV)(CN)(6)].4H(2)O (M(IV) = Mo; M(II) = Co, 3; Ni, 7; M(IV) = W; M(II) = Co, 4) stoichiometry. Each cluster contains cis-M(II)(en)(2)(OH(2))(mu-NC)(2+) units that likely result from dissociative loss of en from [M(II)(en)(3)](2+), affording cis-M(II)(en)(2)(OH(2))(2)(2+) intermediates that are trapped by M(IV)(CN)(8)(4-).