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At least 307 records · Page 17

Good Practices in Free-energy Calculations

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.

Pohorille, Andrew↗

The random coding bound is tight for the average code.

The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.

Gallager, R. G.↗

Efficient algorithms for robust feature matching

One of the basic building blocks in any point-based registration scheme involves matching feature points that are extracted from the sensed image to their counterparts in the reference image. This leads to the fundamental problem of point matching: given two sets of points, find the affine transformation that transforms one point set so that its distance from the other point set is minimized. Because of measurement errors and the presence of outlying data points, it is important that the distance measure between two point sets be robust to these effects. We measure distances using the generalized Hausdorff distance. Point matching can be a computationally intensive task, and there have been a number of algorithms and approaches proposed for solving this problem both theoretical and applied. We present two approaches to the point matching problem, in an attempt to reduce the computational complexity of the problem, while still providing guarantees on the quality of the final match. Our first method is an approximation algorithm, which is loosely based on a branch-and-bound approach due to Huttenlocher and Rucklidge. We show that by varying the approximation error bounds, it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm. Our second method involves a Monte Carlo method for accelerating the search process used in the first algorithm. With high probability this method succeeds in finding an approximately optimal match. We establish the efficiency of our approaches empirically.

Mount, David M.↗

The undetected error probability for Reed-Solomon codes

McEliece and Swanson (1986) offered an upper bound on P(E)u, the decoder error probability given u symbol errors occur. In the present study, by using a combinatoric technique such as the principle of inclusion and exclusion, an exact formula for P(E)u is derived. The P(E)u of a maximum distance separable code is observed to approach Q rapidly as u gets large, where Q is the probability that a completely random error pattern will cause decoder error. An upper bound for the expansion P(E)u/Q - 1 is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P(E)u indeed approaches Q as u becomes large, and that some laws of large number come into play.

Cheung, Kar-Ming↗

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

In connection with difficulties concerning an accurate mathematical representation of a linear quadratic state feedback (LQSF) system, it is often necessary to investigate the robustness (stability) of an LQSF design in the presence of system uncertainty and obtain some quantitative measure of the perturbations which such a design can tolerate. A study is conducted concerning the problem of expressing the robustness property of an LQSF design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices. Bounds are obtained for the general case of nonlinear, time-varying perturbations. It is pointed out that most of the presented results are readily applicable to practical situations for which a designer has estimates of the bounds on the system parameter perturbations. Relations are provided which help the designer to select appropriate weighting matrices in the quadratic performance index to attain a robust design. The developed results are employed in the design of an autopilot logic for the flare maneuver of the Augmentor Wing Jet STOL Research Aircraft.

Patel, R. V.↗

An hp-adaptivity and error estimation for hyperbolic conservation laws

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

Bey, Kim S.↗

Sloppy-slotted ALOHA

Random access signaling, which allows slotted packets to spill over into adjacent slots, is investigated. It is shown that sloppy-slotted ALOHA can always provide higher throughput than conventional slotted ALOHA. The degree of improvement depends on the timing error distribution. Throughput performance is presented for Gaussian timing error distributions, modified to include timing error corrections. A general channel capacity lower bound, independent of the specific timing error distribution, is also presented.

Crozier, Stewart N.↗

136 MHz interferometer error due to galactic nucleus.

Extraneous interfering signals are discussed which limit the basic accuracy of the 136 MHz Minitrack radio-interferometer system providing electrical phase data from which direction cosines for determining spacecraft orbits are generated. In particular, the fundamental error due to interference caused by the passage of the galactic nucleus is investigated. An expression is developed for the lower bound of the phase error when the noise source is not uniformly distributed across the Minitrack's zenith-pointed fan beam. In addition, the threshold of the Minitrack input power levels is determined below which the electrical phase is no longer determined unambiguously. The effect of the passage of the galactic nucleus coincident with the presence of a spacecraft is analyzed, and the corresponding phase error established.

Kyriakopoulos, N.↗

Multi-stage decoding for multi-level block modulation codes

Various types of multistage decoding for multilevel block modulation codes, in which the decoding of a component code at each stage can be either soft decision or hard decision, maximum likelihood or bounded distance are discussed. Error performance for codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. It was found that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. It was found that the difference in performance between the suboptimum multi-stage soft decision maximum likelihood decoding of a modulation code and the single stage optimum decoding of the overall code is very small, only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

Lin, Shu↗

Accuracy of Pressure Sensitive Paint

Uncertainty in pressure sensitive paint (PSP) measurement is investigated from a standpoint of system modeling. A functional relation between the imaging system output and luminescent emission from PSP is obtained based on studies of radiative energy transports in PSP and photodetector response to luminescence. This relation provides insights into physical origins of various elemental error sources and allows estimate of the total PSP measurement uncertainty contributed by the elemental errors. The elemental errors and their sensitivity coefficients in the error propagation equation are evaluated. Useful formulas are given for the minimum pressure uncertainty that PSP can possibly achieve and the upper bounds of the elemental errors to meet required pressure accuracy. An instructive example of a Joukowsky airfoil in subsonic flows is given to illustrate uncertainty estimates in PSP measurements.

Liu, Tianshu↗

Determination and error analysis of emittance and spectral emittance measurements by remote sensing

Theoretical and experimental determinations of the emittance of soils and leaves are reviewed, and an error analysis of emittance and spectral emittance measurements is developed as an aid to remote sensing applications. In particular, an equation for the upper bound of the absolute error in an emittance determination is derived. The absolute error is found to decrease with an increase in contact temperature and to increase with an increase in environmental integrated radiant flux density. The difference between temperature and band radiance temperature is plotted as a function of emittance for the wavelength intervals 4.5 to 5.5 microns, 8 to 13.5 microns and 10.2 to 12.5 microns.

Kumar, R.↗

Upper bounds on sequential decoding performance parameters

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Jelinek, F.↗

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.

Johannesson, R.↗

More On The Decoder-Error Probability Of Reed-Solomon Codes

Paper extends theory of decoder-error probability for linear maximum-distance separable (MDS) codes. General class of error-correcting codes includes Reed-Solomon codes, important in communications with distant spacecraft, military communications, and compact-disk recording industry. Advancing beyond previous theoretical developments that placed upper bounds on decoder-error probabilities, author derives an exact formula for probability PE(u) that decoder will make error when u code symbols in error.

Cheung, Kar-Ming↗

Transfer function bounds on the performance of turbo codes

In this article we apply transfer function bounding techniques to obtain upper bounds on the bit-error rate for maximum likelihood decoding of turbo codes constructed with random permutations. These techniques are applied to two turbo codes with constraint length 3 and later extended to other codes. The performance predicted by these bounds is compared with simulation results. The bounds are useful in estimating the 'error floor' that is difficult to measure by simulation, and they provide insight on how to lower this floor. More refined bounds are needed for accurate performance measures at lower signal-to-noise ratios.

Divsalar, D.↗

Feature combinations and the Bhattacharyya criterion

A procedure for calculating a kxn rank k matrix B for data compression using the Bhattacharyya bound on the probability of error and an iterative construction using Householder transformation was developed. Two sets of remotely sensed agricultural data are used to demonstrate the application of the procedure. The results of the applications gave some indication of the extent to which the Bhattacharyya bound on the probability of error is affected by such transformations for multivariate normal populations.

Decell, H. P., Jr.↗

Analysis of synchronous digital-modulation schemes for satellite communication

The multipath communication channel for space communications is modeled as a multiplicative channel. This paper discusses the effects of multiplicative channel processes on the symbol error rate for quadrature modulation (QM) digital modulation schemes. An expression for the upper bound on the probability of error is derived and numerically evaluated. The results are compared with those obtained for additive channels.

Takhar, G. S.↗