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Background: Terpenoid compounds, despite their established antioxidant ability, are neglected as potential glycation regulators. Methods: In-vitro model systems of lysine (0.1 M) with glucose (0.1 M and 1 M) were incubated at 80 °C and 100 °C for 3 h in the presence of aniseed oil, thymol and linalool (2–8 μΜ). Color development, absorbance at UV-Vis (280 nm, 360 nm, 420 nm), fluorescence intensity (λexc = 370 nm, λemm = 440 nm) and lysine depletion (HPLC-FL) were measured to monitor the progress of the Maillard reaction. Response Surface Methodology was used to analyze the impact of the five experimental conditions on the glycation indices. Results: All terpenoid compounds promoted color development and did not affect lysine depletion. The choice of terpenoid compound impacted glycation at 280 nm, 360 nm and 420 nm (p < 0.02). The effect was stronger at lower temperatures (p < 0.002) and 0.1 M glucose concentrations (p < 0.001). Terpenoid concentration was important only at 360 nm and 420 nm (p < 0.01). No impact was seen for fluorescence intensity from the choice of terpenoid compounds and their dose (p = 0.08 and p = 0.44 respectively). Conclusion: Terpenoid compounds show both anti- and proglycative activity based on the incubation conditions. Thymol showed the largest antiglycative capacity, followed by aniseed oil and linalool. Maximal antiglycative capacity was seen at 0.1 M glucose, 2 μΜ terpenoid concentration, 80 °C and 1 h incubation.

We present, analyze, and numerically evaluate extended algorithms for detecting changes from an acting stochastic process to a number of possible alternatives. The algorithms are sequential, requiring minimal memory capacity and operational complexity, and they incorporate decision thresholds. The performance of the algorithms is controlled by the selection of the thresholds. Asymptotically, the first algorithmic extension detects the acting process correctly in an expected stopping time sense. In addition, the probability of error induced by a reinitialization algorithmic extension converges asymptotically to zero, when the acting process changes infrequently (with order inversely proportional to the value of the decision thresholds). The presented algorithmic systems are quite powerful and their applications are numerous, ranging from industrial quality control to traffic and performance monitoring in highspeed networks.

Two mutually independent traffic streams whose arrivals are modeled as renewal processes are considered. The arrivals are stored in an infinite capacity buffer. One of the processes requires a strict upper bound on the total delay per arrival, and it is assumed that the processing time per arrival for both processes is a constant. Given the above model, the class of nonpreemptive scheduling policies which satisfy the delay constraint while maintaining the system stability is found. The delays induced by the latter policy are analyzed via a methodology based on the regenerative theorem. A numerical example is given in which the policy that minimizes the expected delays for both traffic streams is also considered. >

Utilizing asymptotic results from prediction theory of multivariate stationary random processes and from regression theory for multivariate stationary processes, we develop asymptotic (large sample) expressions for the Chernoff coefficient, Bhattacharyya distance, I -divergence and J -divergence between two s -dimensional, covariance stationary Gaussian processes on the basis of n discrete-time samples. The expressions are given in terms of the two spectral density matrices F_{1}(\lambda), F_{2}(\lambda) derived from the two autocovariance matrix sequences, and of the spectral density matrix M(\lambda) related to the sequence of differences of mean vectors. The resulting spectral expressions are useful in a variety of applications, as discussed in the paper.

We consider stochastic neural networks, the objective of which is robust prediction for spatial control. We develop neural structures and operations, in which the representations of the environment are preprocessed and provided in quantized format to the prediction layer, and in which the response of each neuron is binary. We also identify the pertinent stochastic network parameters, and subsequently develop a supervised learning algorithm for them. The on-line learning algorithm is based an the Kullback-Leibler performance criterion, it induces backpropagation, and guarantees fast convergence to the prediction probabilities induced by the environment, with probability one.

Hypothesis testing is a collective name for problems such as classification, detection, and pattern recognition. In this paper we propose two new classes of supervised learning algorithms for feedforward, binary-output neural network structures whose objective is hypothesis testing. All the algorithms are applications of stochastic approximation and are guaranteed to provide optimization with probability one. The first class of algorithms follows the Neyman-Pearson approach and maximizes the probability of detection, subject to a given false alarm constraint. These algorithms produce layer-by-layer optimal Neyman-Pearson designs. The second class of algorithms minimizes the probability of error and leads to layer-by-layer Bayes optimal designs. Deviating from the layer-by-layer optimization assumption, we propose more powerful learning techniques which unify, in some sense, the already existing algorithms. The proposed algorithms were implemented and tested on a simulated hypothesis testing problem. Backpropagation and perceptron learning were also included in the comparisons. >

In this correspondence, a search for the optimal polynomial mean-square (ms) estimator is undertaken; when the input is a vector with fixed dimensionality and at the calculation of the estimator characteristics the round off errors are considered. It is found that the accumulation of these errors causes divergence of the estimate from the theoretically ideal one. Also, the minimum mean-square error, instead of monotonically decreasing with the degree of the polynomial estimator, increases when This degree exceeds a number that depends on the statistics of the problem. This error is found to be equal to the sum of the ideal error e 0 and a term e e which includes the computational errors and increases monotonically with the degree of the estimator.

We consider Poisson packet traffic accessing a single-slotted channel. We assume the existence of a ternary feedback per channel slot. We also adopt the limited feedback sensing model where each user senses the feedback only while he has a packet to transmit. For this model we develop a collision resolution algorithm with last come-first served characteristics. The algorithm attains the same throughput as Gallager's algorithm without the latter's full feedback sensing requirement. In addition, it is easy to implement, requires reasonable memory storage, induces uniformly good transmission delays, and is insensitive to feedback errors. In the presence of binary (collision versus noncollision) feedback the algorithm may attain a throughput of 0.4493 .

In this correspondence the problem of sequential estimation is considered when the observation delays are, in general, costly. General theorems determining the "optimal" stopping time in this case are stated, and specific cases are worked out.

In the models used by Hampel as well as by Gray and the author for the qualitative analysis of robust parameter estimators, the Prohorov stability criterion was used. The Vasershtein distance is proposed here as an alternative stability measure. This measure, in contrast to the Prohorov criterion, implies performance stability of the estimators and leads to a constructive analysis for exponentially fast convergence.

A slotted packet broadcast channel with an infinite user population is considered. A limited feedback sensing algorithm is proposed and analyzed for collision versus noncollision binary feedback. The algorithm bas maximum throughput equal to 0.42 (packets/slot), has uniformly good delay characteristics within its stability region, and is robust in the presence of feedback errors. A variation of the algorithm, for ternary feedback, attains maximum throughput 0.425 and bas uniformly good delay characteristics within its stability region. In contrast, the highest throughput limited feedback sensing algorithm existing for ternary feedback attains maximum throughput 0.456 , but induces relatively high delays for Poisson intensities below 0.3 .

The problem of detecting a change from one given stationary and ergodic stochastic process to another such process is considered. It is assumed that both stochastic processes are processes with memory and that they are mutually independent. A sequential test is proposed and analyzed. It is proved that the proposed test is asymptotically optimal in a mathematically precise sense.

A simple full-feedback-sensing window random-access algorithm is proposed and analyzed in the presence of the Poisson user model. The throughput of the algorithm is 0.43. The proposed algorithm is better than J.I. Capetanaki's dynamic algorithm (1979) with respect to its delay and resistance to channel errors. The simple operations of the algorithm, along with its regenerative properties, facilitate the computation of the output traffic interdeparture distribution. The obtained distribution is useful in the evaluation of interacting systems which adopt the algorithm for their internal transmissions. >

The problem of sequential detection between Poisson processes is analyzed and resolved. Wald's results on sequential analysis are used, but a substantial modification is shown to be necessary due to the discontinuous nature of the likelihood ratio. It is shown that, in general, one can take into account the "excess over the boundary" so as to design sequential tests with a given error performance.

We consider a stationary Gaussian information process transmitted through an additive noise channel. We assume that the noise and information processes are mutually independent, and we model the noise process as nominally Gaussian with additive outliers. For the above system model, we first develop a theory for outlier resistant filtering and smoothing operations. We then design specific such nonlinear operations, and we study their performance. The performance criteria are the asymptotic mean squared error at the Gaussian nominal model, the breakdown point, and the influence function. We find that the proposed operations combine excellent performance at the nominal model with strong resistance to outliers.

We consider the problem of asymptotic noncausal linear filtering for multivariable second-order stationary time series, under spectral uncertainty in both the signal and the noise processes. The spectral uncertainty is modeled by e-contaminated and p -point classes. For the case where both the signal and noise spectra are e-contaminated, we assume that the eigenvectors of the corresponding nominal spectral density matrices are identical. The problem is formulated as a game, whose saddle point solutions are found and analyzed.

The mathematical complexity of the minimum mean square estimators made inevitable the consideration of suboptimal solutions, such as the linear minimum mean square (m.m.s.) estimators. The compromise between performance and complexity can be, in general, less serious if the estimator that will substitute the optimum one is polynomial. If the minimum mean square estimator happens to be equal to a polynomial one, the polynomial substitution does not involve any compromise with respect to performance. Balakrishnan found a necessary and sufficient condition satisfied by the joint characteristic functions of observations and variable to be estimated, so that the m.m.s. estimate is a polynomial. The equivalent moment relationships in this case were found in the present paper. A matrix expression of the error difference from two different m.m.s. polynomial estimators was also found. This form involves much fewer calculations than required for finding separately the two errors.

The RC filter-hard limiter-RC filter nonlinear system is the subject of this paper. Because of computational difficulties implicated in the analysis of the above system, only its response to the zero mean Gaussian system input has been analytically investigated. An approximate output density has also been found for nonzero mean Gaussian, while verified to be “close” to the real one for finite means. In the present paper, a close form of the system output density is obtained when the input mean tends to infinity. For that, e-upcrossing methods were used.

The choice of the proper evaluation measure is critical for the design of a good parameter estimator. The mean-square

Outlier-resistant algorithms that detect a change from a given nominal stationary process to another such process are given. The nominal processes are assumed to be mutually independent and to satisfy some general regularity conditions. The outlier sequences are assumed to be independently and identically distributed and independent of the nominal processes. The proposed algorithms are sequential and consist of uniformly bounded steps. The asymptotic performance of the algorithms is analyzed, both in the absence and the presence of outliers. Breakdown points and influence functions are defined and analyzed. The algorithms are studied in more detail for Gaussian autoregressive nominal processes. >

Sliding block encoders operating within a statistically contaminated source environment are considered. Stationary analog sources are studied using the rho-bar distance as the measure of contamination. Sufficient constructive conditions are developed for the design of sliding block encoders that guarantee rho-bar stability of their output when operating within a statistically contaminated source environment. The relationship of this stability to the robustness of the encoding scheme is discussed, where robustness is a local stability property applied on the output entropy and the average distortion.

Nonparametric tests have been extensively investigated asymptotically for small signals and large numbers of samples. More realistic, though, in many engineering applications is the small-sample large-signal case, which has had little study because of its complexity. The problem of testing the hypothesis of probability density symmetry about a positive versus a negative value is investigated. The efficiency of the optimum rank and the efficiency of the Wilcoxon rank-sum test are found with respect to the optimum parametric test for normally distributed independent samples with large signal-to-noise ratios. Specifically, it is found that for the same signal-to-noise ratio and probability of error the optimum rank test requires at most 4/3 of the number of samples (or equivalently, 4/3 higher signal-to-noise ratio for the same number of samples) of the optimum parametric test; the Wilcoxon nonparametric test requires at most a factor of 2/\sqrt{2} more. Thus, the efficiency of the Wilcoxon nonparametric test is very close to that of the optimum rank test for normal alternatives, although neither are as close to the efficiency of the optimum parametric test as in the large-sample small-signal problem (where, as is well known, the asymptotic relative efficiencies are \pi/3 and 1).

A three-element detector, consisting of an RC filter with time constant 1/a , a hard limiter, and finally an RC filter with time constant 1/b , is considered. The detector is stimulated by a nonzero-mean white Gaussian noise input, and the system output is observed. A Markov assumption on the hard limiter output leads to a closed-form expression for the output density, which is verified to be close to the actual output density of the detector by computer simulations.

Suppose white noise is put into an RC filter with time constant 1/a whose output is hard limited and fed into a second RC filter with time constant 1/b . The density of the output y(t) of the system has been the subject of several investigations. Most recently, Pawula and Tsai made the conjecture that for Gaussian white noise the y(t) density is given by a certain expression, a special case of which was derived earlier by Doyle, McFadden, and Marx for b/a = 2 . In this paper an expression for the n th moment of y(t) is found. From the expression for the fourth moment, it is proven that the Pawula-Tsai conjecture is not true in general. It is further found that if the output of the hard limiter were wide-sense Markov, the Pawula-Tsai conjecture would be true.

We consider robust operations in time series. We present a definition and subsequent qualitative analysis of robustness. We also present meaningful definitions of performance criteria, such as the breakdown point and the sensitivity of robust operations. We present some specific classes of robust operations, and we discuss and analyze their properties. Finally, we fully analyze a particular class of robust predictors and interpolators, for a linearly contaminated class of stationary stochastic processes.

It is known that under certain restrictions on the posterior density and assigned cost function, the Bayes estimate of a random parameter is the conditional mean. The restrictions on the cost function are that it must be a symmetric convex upward function of the difference between the parameter and the estimate. In this correspondence, asymmetrical cost functions of the following form are examined: \begin{equation} C(a, \hat{a})= \begin{cases} f_1(a- \hat{a}),& a \geq \hat{a} \\ f_2(\hat{a}- a),& a f_1(\cdot), f_2(\cdot) are both twice-differentiable convex upward positive functions on [0, \infty] that intersect the origin. It is shown that for posterior densities satisfying a certain symmetry condition, the biased Bayes estimate is a generalized median. Furthermore, for linear polynomial functions f_1(\cdot), f_2(\cdot) , the unbiased Bayes estimate is shown to be the conditional mean.