Probability Distribution Information Research Articles

Robust state estimation for discrete-time genetic regulatory network with random delays

This paper deals with the delay-probability-distribution-dependent state estimation problem for discrete-time genetic regulatory networks (DGRNs) with random time-varying delays. As an important feature the time-varying delays are assumed to be random and their probability distributions are known a priori. The information of probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred DGRNs model. Based on the Lyapunov–Krasovskii functional approach, a delay-probability-distribution-dependent sufficient condition is obtained in terms of linear matrix inequalities (LMIs) such that estimation errors are robustly globally asymptotically stable in the mean-square sense for all admissible uncertainties. The probability distribution dependent delays are introduced to reflect more realistic dynamical behaviors of DGRNs. Finally numerical examples are provided to substantiate the theoretical results.

On Extracting Probability Distribution Information from Time Series

Time-series (TS) are employed in a variety of academic disciplines. In this paper we focus on extracting probability density functions (PDFs) from TS to gain an insight into the underlying dynamic processes. On discussing this “extraction” problem, we consider two popular approaches that we identify as histograms and Bandt–Pompe. We use an information-theoretic method to objectively compare the information content of the concomitant PDFs.

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: II. Probabilistic Guarantees on Constraint Satisfaction

Probabilistic guarantees on constraint satisfaction for robust counterpart optimization are studied in this paper. The robust counterpart optimization formulations studied are derived from box, ellipsoidal, polyhedral, "interval+ellipsoidal" and "interval+polyhedral" uncertainty sets (Li, Z., Ding, R., and Floudas, C.A., A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear and Robust Mixed Integer Linear Optimization, Ind. Eng. Chem. Res, 2011, 50, 10567). For those robust counterpart optimization formulations, their corresponding probability bounds on constraint satisfaction are derived for different types of uncertainty characteristic (i.e., bounded or unbounded uncertainty, with or without detailed probability distribution information). The findings of this work extend the results in the literature and provide greater flexibility for robust optimization practitioners in choosing tighter probability bounds so as to find less conservative robust solutions. Extensive numerical studies are performed to compare the tightness of the different probability bounds and the conservatism of different robust counterpart optimization formulations. Guiding rules for the selection of robust counterpart optimization models and for the determination of the size of the uncertainty set are discussed. Applications in production planning and process scheduling problems are presented.

Reliability Analysis of Zero‐Failure Data with Poor Information

For costly and dangerous experiments, growing attention has been paid to the problem of the reliability analysis of zero‐failure data, with many new findings in world countries, especially in China. The existing reliability theory relies on the known lifetime distribution, such as the Weibull distribution and the gamma distribution. Thus, it is ineffective if the lifetime probability distribution is unknown. For this end, this article proposes the grey bootstrap method in the information poor theory for the reliability analysis of zero‐failure data under the condition of a known or unknown probability distribution of lifetime. The grey bootstrap method is able to generate many simulated zero‐failure data with the help of few zero‐failure data and to estimate the lifetime probability distribution by means of an empirical failure probability function defined in this article. The experimental investigation presents that the grey bootstrap method is effective in the reliability analysis only with the few zero‐failure data and without any prior information of the lifetime probability distribution. Copyright © 2011 John Wiley & Sons, Ltd.

Continuum of Risk Analysis Methods to Assess Tillage System Sustainability at the Experimental Plot Level

This study applied a broad continuum of risk analysis methods including mean-variance and coefficient of variation (CV) statistical criteria, second-degree stochastic dominance (SSD), stochastic dominance with respect to a function (SDRF), and stochastic efficiency with respect to a function (SERF) for comparing income-risk efficiency sustainability of conventional and reduced tillage systems. Fourteen years (1990–2003) of economic budget data derived from 35 treatments on 36 experimental plots under corn (Zea mays L.) and soybean (Glycine max L.) at the Iowa State University Northeast Research Station near Nashua, IA, USA were used. In addition to the other analyses, a visually-based Stoplight or “probability of target value” procedure was employed for displaying gross margin and net return probability distribution information. Mean-variance and CV analysis of the economic measures alone provided somewhat contradictive and inconclusive sustainability rankings, i.e., corn/soybean gross margin and net return showed that different tillage system alternatives were the highest ranked depending on the criterion and type of crop. Stochastic dominance analysis results were similar for SSD and SDRF in that both the conventional and reduced tillage system alternatives were highly ranked depending on the type of crop and tillage system. For the SERF analysis, results were dependent on the type of crop and level of risk aversion. The conventional tillage system was preferred for both corn and soybean for the Stoplight analysis. The results of this study are unique in that they highlight the potential of both traditional stochastic dominance and SERF methods for distinguishing economically sustainable choices between different tillage systems across a range of risk aversion. This study also indicates that the SERF risk analysis method appears to be a useful and easily understood tool to assist farm managers, experimental researchers, and potentially policy makers and advisers on problems involving agricultural risk and sustainability.

Reliable control for networked control systems with probabilistic actuator fault and random delays

In this paper, the reliable control design is considered for networked control systems (NCSs) against probabilistic actuator fault with different failure rates, measurements distortion, random network-induced delay and packet dropout . A new distribution-based fault model is proposed, which also contains the probability distribution information of the random delay and packet dropout. By using Lyapunov functional and new technique in dealing with time delay, stability and stabilization criteria are derived in terms of linear matrix inequalities . The provided numerical example and vertical takeoff and landing (VTOL) aircraft system illustrate that: firstly, using the distribution information of the delay, the maximum effective delay bound (MEDB) can be greatly improved, secondly, the proposed reliable controller can stabilize the NCSs with probabilistic actuator fault and measurements distortion, which may be unstable under the controller designed without considering the unreliable cases.

Double coefficients support vector machine with probability and equivalence class

The effectiveness of a Support Vector Machine (SVM) depends on the accuracy of the acquired data information. Considering the low prediction accuracy and poor generalization capacity of SVM caused by simply mining data,a new model was proposed. Combining probability distribution and equivalence class information among data,this model optimized the traditional SVM by adopting double coefficients to promote the capability of acquiring information. Each instance will be assigned two coefficients of probability value and equivalence class. The comparison with SVM,Rough Support Vector Machine (RSVM) and Fuzzy Support Vector Machine (FSVM) illustrates the new model can not only utilize information effectively but also assure a remarkable prediction accuracy and classification ability,and be more robust.

A Bayesian approach for estimating extreme flood probabilities with upper-bounded distribution functions

Some recent research on fluvial processes suggests the idea that some hydrological variables, such as flood flows, are upper-bounded. However, most probability distributions that are currently employed in flood frequency analysis are unbounded to the right. This paper describes an exploratory study on the joint use of an upper-bounded probability distribution and non-systematic flood information, within a Bayesian framework. Accordingly, the current PMF maximum discharge appears as a reference value and a reasonable estimate of the upper-bound for maximum flows, despite the fact that PMF determination is not unequivocal and depends strongly on the available data. In the Bayesian context, the uncertainty on the PMF can be included into the analysis by considering an appropriate prior distribution for the maximum flows. In the sequence, systematic flood records, historical floods, and paleofloods can be included into a compound likelihood function which is then used to update the prior information on the upper-bound. By combining a prior distribution describing the uncertainties of PMF estimates along with various sources of flood data into a unified Bayesian approach, the expectation is to obtain improved estimates of the upper-bound. The application example was conducted with flood data from the American river basin, near the Folsom reservoir, in California, USA. The results show that it is possible to put together concepts that appear to be incompatible: the deterministic estimate of PMF, taken as a theoretical limit for floods, and the frequency analysis of maximum flows, with the inclusion of non-systematic data. As compared to conventional analysis, the combination of these two concepts within the logical context of Bayesian theory, contributes an advance towards more reliable estimates of extreme floods.

Delay-probability-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delay

The delay-probability-distribution-dependent robust stability problem for a class of uncertain stochastic neural networks (SNNs) with time-varying delay is investigated. The information of probability distribution of the time delay is considered and transformed into parameter matrices of the transferred SNNs model. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) format such that delayed SNNs are robustly globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability conditions are dependent on the probability distribution of the delay and upper bound of the delay derivative, and the upper bound is allowed to be greater than or equal to 1. Finally, numerical examples are given to illustrate the effectiveness and less conservativeness of the proposed method.

Atomic jumps during surface diffusion

The characteristics of atomic displacements during surface diffusion of Cu on Cu(111) are studied by means of molecular dynamics simulations. It is found that even at very low substrate temperatures, the majority of the jumps are correlated, i.e., the displacement directions are not randomly chosen but rather keep some sort of memory from the previous moves and are influenced by them. Long jumps, spanning several surface unit cells, are observed at all temperatures. From an analysis of their length probability distribution information can be obtained about the mechanisms of friction and energy transfer between the diffusing adatom and the substrate. Both long jumps and recrossings (displacements in which the adatom moves back and forth between two adjacent adsorption sites) appear with a higher activation energy than normal diffusion. Finally, the influence of the instantaneous atomic configuration of the substrate on the adatom's trajectory is also highlighted.

TU‐C‐303A‐02: Intrafraction Prostate Motion Monitoring with Cine‐MV and Minimal As‐Needed Onboard KV Imaging

Purpose: To examine the feasibility and performance of using treatment MV beam imaging with prior knowledge to estimate 3D prostate intrafraction motion and to instantaneously reposition based on information from minimal usage of on‐board kV imaging during IMRT. Methods and Materials: In contrast with current motion monitoring techniques which seek to accurately and continuously localize a moving target, we attempted for the first step only to detect potential motion beyond a pre‐defined threshold using MV images and in the second step through combined MV‐kV imaging (by turning on the kV imager) to confirm the over‐threshold event as well as obtaining accurate position information which could be used for instantaneously repositioning. EPID images were used to measure 2D prostate displacement in the imaging plane. By taking into account the strong correlation between prostate SI and AP motion, small displacement in the LR direction, and data from a previous IMRT session (different gantry angle), we estimated in‐line prostate motion as well which in turn allowed us to detect potential 3D over‐threshold motion. To minimize the influence from training data, no statistical motion probability distribution information was used. Simulation has been done using 536 patient‐measured trajectories from 17 patients. Experiments were performed on a Varian Trilogy linac using a motion phantom programmed for selected typical trajectories, and the results were compared with simulations. Results: Prostate displacement beyond a set threshold (3mm) was detected for over 99% of the time at the cost of negligible kV dose (< 3 images/fraction on average). The position information required for repositioning was found to have sub‐millimeter accuracy using combined MV‐kV data. Conclusion: Significant reduction of adverse effects of intrafraction prostate motion is achievable. The technique can be readily implemented in clinics and incurs minimal imaging dose to the patient as compared with other stereoscopic imaging techniques.

The t-information and its use in multivariate problems and time-series analysis

The second moment of recently introduced scalar inference function can be viewed as generalized Fisher information of the continuous probability distributions. In this paper we call it the t-information and give some possible applications of the new concept.

Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi-Sugeno (T-S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the new type of T-S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov-Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods.

Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSP) method was developed for water resources management under uncertainty. As a new extension of mathematical programming methods, the developed ITSSP approach has advantages in uncertainty reflection and policy analysis. In order to better account for uncertainties, the ITSSP approach is expressed with discrete intervals, functional intervals and probability density functions. The ITSSP method integrates the two-stage stochastic programming (TSP), interval programming (IP) and semi-infinite programming (SIP) within a general optimization framework. The ITSSP has an infinite number of constraints because it uses functional intervals with time (t) being an independent variable. The different t values within the range [0, 90] lead to different constraints. At same time, ITSSP also includes probability distribution information. The ITSSP method can incorporate pre-defined water resource management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a water resource management system with three users and four periods (corresponding to winter, spring, summer and fall, respectively). Solutions of the ITSSP model provide desired water allocation patterns, which maximize both the system’s benefits and feasibility. The results indicate that reasonable interval solutions were generated for objective function values and decision variables, thus a number of decision alternatives can be generated under different levels of stream flow. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system reliability criteria.

ITSSIP: Interval-parameter two-stage stochastic semi-infinite programming for environmental management under uncertainty

In this study, an interval-parameter two-stage stochastic semi-infinite programming (ITSSIP) method is developed for municipal solid waste (MSW) management under uncertainty. In order to better account for uncertainties, the uncertainties are expressed with discrete intervals, functional intervals and probability distributions. The ITSSIP method integrates the two-stage stochastic programming (TSP), interval programming (IP), chance-constrained programming (CCP) and semi-infinite programming (SIP) within a general optimization framework. ITSSIP has infinite constraint because it uses functional intervals with time ( s) being an independent variable. At the same time, ITSSIP also presents probability distribution information. The ITSSIP method can incorporate pre-regulated MSW management policies directly into its optimization process to analyze various policy scenarios having different economic penalties when the promised amounts are not delivered. The model is applied to a MSW management system with three waste treatment facilities, three cities and three periods. As an extension of mathematical programming methods, the developed ITSSIP approach has advantages in uncertainty reflection and policy analysis. Firstly, ITSSIP can help generate optimal solutions for decision variables under different levels of waste-generation rate and different levels of constraint-violation probability, which are informative for decision makers; secondly, it has the capability in addressing the parameter's dynamic feature, i.e., variations of the parameters with time; this could hardly be reflected in the previous methods. The obtained solutions are useful for decision makers to obtain insight regarding the tradeoffs between environmental, economic and system-reliability criteria.

Robustness of Quantum Markov Chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.

A key predistribution scheme for deployable sensor networks using the node deployment probability density function

AbstractIn order to establish encrypted communications in deployable sensor networks, it is essential that encryption keys be shared between nodes. However, the sharing of keys is not simple given the restricted resources of such devices. In recent years, several random key predistribution schemes have been proposed; in the scheme proposed by Du and colleagues, improved performance is achieved by using information regarding the deployment location when predistributing keys. However, this scheme suffers from the problem that it is possible to apply only for the so‐called group deployment model whereby nodes are partitioned into groups and deployed from locations that are arranged systematically. In this paper we propose a random key predistribution scheme that can be applied to arbitrary deployment models by making use of probability distribution information regarding the deployment when the key predistribution is performed. In addition, we confirm from computational experiments that this method is able to construct networks that are more consolidated than those created by Du and colleagues' scheme. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(10): 73–83, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20390

Universal space-time codes from demultiplexed trellis codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents two-dimensional trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes, found by exhaustive search, guarantee consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or, in some cases, superior, frame-error rate and bit-error rate performance under quasi-static Rayleigh fading, as compared with trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh-fading scenario

Universal Space–Time Codes From Demultiplexed Trellis Codes

In broadcast scenarios or in the absence of accurate channel probability distribution information, code design for consistent channel-by-channel performance, rather than average performance over a channel distribution, may be desirable. Root and Varaiya's compound channel theorem for linear Gaussian channels promises the existence of universal codes that operate reliably whenever the channel mutual information (MI) is above the transmitted rate. This paper presents 2-D trellis codes that provide such universal performance over the compound linear vector Gaussian channel when demultiplexed over two, three, and four transmit antennas. The presented trellis codes are found by an exhaustive search that guarantees consistent performance on every matrix channel that supports the information transmission rate with an MI gap that is similar to the capacity gap of a well-designed additive white Gaussian noise (AWGN)-specific code on the AWGN channel. As a result of their channel-by-channel consistency, the universal trellis codes presented here also deliver comparable, or in some cases, superior frame-error rate and bit-error rate performance under quasi-static Rayleigh fading to trellis codes of similar complexity that are designed specifically for the quasi-static Rayleigh fading scenario.

Quantum Correlations and Secret Bits

It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret correlations, then this state has to be entangled. These results prove the existence of a two-way connection between secret and quantum correlations in the process of preparation. They also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists.