A note on estimating false alarm rates via importance sampling

When the statistics of the noise are non-Gaussian, analytic expressions for the probability of false alarms in detection systems are rarely available. Monte Carlo estimation techniques are therefore typically necessary. The author presents an importance sampling biasing distribution which renders exponential savings over standard Monte Carlo simulations. Two important features of this biasing strategy are that no importance sampling parameters need to be determined and no additional computations are required for implementation     

Application of glycodiversification: expedient synthesis and antibacterial evaluation of a library of kanamycin B analogues

[reaction: see text] The expedient synthesis of a library of kanamycin B analogues is reported. The revealed SAR will guide future designs in developing kanamycin-type aminoglycoside antibiotics against drug-resistant bacteria.     

On the relationship between measures of discrimination and theperformance of suboptimal detectors

The problem of designing and analyzing suboptimal detectors via statistical distance measures is considered. As a preliminary result, we show that only the minimum and maximum probability of error are valid measures of discrimination between the input statistics. This result would seem then to imply that the use of distance measures in this context can be inappropriate. However, to overcome this apparent obstacle, we demonstrate explicit relationships between various f-divergences and the loss in performance of an arbitrary detector relative to the optimal detector. In particular, we establish both upper and lower bounds on the performance loss of a suboptimal detector in terms of the “distance” between the pertinent statistics of both the optimal and suboptimal detectors. While designing detectors by minimizing these upper bounds can be an elusive task, in many practical cases, the lower bound presented herein holds with equality. In this case, minimizing the separation of the output statistics of the detector with respect to a particular f-divergence equivalently minimizes the resulting probability of error of the detector. To facilitate design, other researchers have established conditions under which one may design arbitrary detection strategies with respect to a specific f-divergence (Kullback-Leibler distance being a principal example). We extend this approach by deriving necessary and sufficient conditions under which one may design detection strategies with respect to an arbitrarily chosen f-divergence. Thus when these conditions are met, one may optimize a detector with respect to the most analytically tractable distance measure to obtain the minimum probability of error detector over a selected class of detection strategies. Examples demonstrating the utility of this theory for the problem of designing optimal linear detectors and optimal signal sets are presented     

Origins of cell selectivity of cationic steroid antibiotics

A key factor in the potential clinical utility of membrane-active antibiotics is their cell selectivity (i.e., prokaryote over eukaryote). Cationic steroid antibiotics were developed to mimic the lipid A binding character of polymyxin B and are shown to bind lipid A derivatives with affinity greater than that of polymyxin B. The outer membranes of Gram-negative bacteria are comprised primarily of lipid A, and a fluorophore-appended cationic steroid antibiotic displays very high selectivity for Gram-negative bacterial membranes over Gram-positive bacteria and eukaryotic cell membranes. This cell selectivity of cationic steroid antibiotics may be due, in part, to the affinity of these compounds for lipid A.     

Synthesis and characterization of peptide-cationic steroid antibiotic conjugates

[reaction: see text] New cationic steroid antibiotics have been prepared by conjugating tripeptides to a triamino analogue of cholic acid. These compounds were synthesized on a solid phase in an indexed library that was screened for antibacterial activity against Gram-negative and Gram-positive bacteria. Selected compounds were synthesized on a larger scale, and minimum inhibition concentrations were measured. These results correlated very well with the screening of the indexed library of antibiotics. The most active antibiotics demonstrate a marked improvement over a related and well characterized cationic steroid antibiotic.     

Constrained solutions in importance via robust statistics

The problem of estimating estimating expectations of functions of random vectors via simulation is investigated. Monte Carlo simulations, also known as simple averaging, have been used as a direct means of estimation. A technique known as importance sampling can be used to modify the simulation via weighted averaging in the hope that the estimate will converge more rapidly to the expected value than standard Monte Carlo simulations. A constrained optimal solution to the problem of minimizing the variance of the importance sampling estimator is derived. This is accomplished by finding the distribution which is closest to the unconstrained optimal solution in the Ali-Silvey sense (S. Ali et al., 1966). The solution from the constraint class is shown to be the least favorable density function in terms of Bayes risk against the optimal density function. Examples of constraint classes, which include ϵ-mixture, show that the constrained optimal solution can be made arbitrarily close to the optimal solution. Applications to estimating probability of error in communication systems are presented     

Designing Pre-College Engineering Curricula and Technology: Lessons Learned From the Infinity Project

The importance of mathematics and science education in today's modern, technology-driven society cannot be understated. This paper describes the history of and ongoing efforts in curricular and educational technology development for the infinity project, a joint effort between educators, administrators, and industry leaders to establish an engineering curriculum at the high school level. Several issues are considered, including the choice and design of the technology platform used in the curriculum, the curricular and technology development timeline, and the design examples chosen to illuminate important engineering concepts within the curriculum. We also provide a list of key best practices and challenges in developing novel pre-college engineering curricula for future engineers.     

Efficient importance sampling techniques for simulation ofmultiuser communication systems

The problem of simulating error rates in direct sequence spread-spectrum code division multiple-access (CDMA) systems is examined. Due to the computational complexity required to simulate these systems, an importance sampling technique is developed based upon previous work by the authors. A conditional weighting function is derived such that the linear shift class of biasing densities can be employed. Results are given for a variety of detector structures and background noise distributions. It is shown that this biasing scheme can dramatically reduce the run time of realistic multiple-access simulations     

Relation of signal set choice to the performance of optimalnon-Gaussian detectors

The optimal procedure for detecting the presence of discrete-time signals in additive noise can be derived from the likelihood ratio test. When the noise has statistically independent, identically distributed components, the dependence of the detector's performance on signal characteristics can be related to the Kullback-Leibler (KL) distance between the distributions governing the hypotheses. Performance predictions based on the central limit theorem are shown to be poor approximations to the true performance. Performance of the optimal detector has long been known to increase exponentially with increasing KL distance. Symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals' amplitudes at each time index. Small-signal (locally optimal) detection performance is shown to depend on signal energy, whereas large-signal performance depends on the signal waveform. When a distance measure can be defined, performance depends on a different measure than that used in the detector with one exception (the Gaussian)