Probabilistic Source Research Articles

A probabilistic source assessment framework for leaching from secondary materials in highway applications

Recovered materials from the transportation sector or secondary or by-product materials from the industrial, municipal, or mining sector can be used as substitutes for natural materials in the construction of highway infrastructure. The environmental impact of traditional and newer secondary materials needs to be determined for the conditions of their expected use. The purpose of this paper is to introduce a probabilistic framework for evaluating the environmental acceptability of candidate secondary materials based on the risk of soil and groundwater contamination from leached metals and organics from the pavement. The proposed framework provides a structured guidance for selecting the appropriate model, incorporating uncertainty, variability, and expert opinion, and interpreting results for decision making. This new approach is illustrated by a probabilistic analysis of arsenic leaching from Portland cement concrete and asphalt concrete materials that were constructed using virgin and secondary products.

Size and path length of Patricia tries: Dynamical sources context

AbstractDigital trees, such as tries, and Patricia tries are data structures routinely used in a variety of computer and communication applications including dynamic hashing, partial match retrieval, searching and sorting, conflict resolution algorithms for communication broadcast, data compression, and so forth. Here, we consider tries and Patricia tries built from n words emitted by a probabilistic dynamical source. Such sources encompass classical and many models such as memoryless sources and finite Markov chains. The probabilistic behavior of its main parameters, namely, the size and the path length, appears to be determined by some intrinsic characteristics of the source, such as Shannon entropy and entropy‐like constants, that depend on the spectral properties of specific transfer operators of Ruelle type. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 289–315, 2001

Mean and Modal in the Deaggregation of Probabilistic Ground Motion

An important element of probabilistic seismic-hazard analysis (PSHA) is the incorporation of ground-motion uncertainty from the earthquake sources. The standard normal variate ϵ measures the difference between any specified spectral-acceleration level, or SA, and the estimated median spectral acceleration from each probabilistic source. In this article, mean and modal values of ϵ for a specified SA are defined and computed from all sources considered in the USGS 1996 PSHA maps. Contour maps of ϵ are presented for the conterminous United States for 1-, 0.3-, and 0.2-sec SA and for peak horizontal acceleration, PGA corresponding to a 2% probability of exceedance (PE) in 50 yr, or mean annual rate of exceedance, r , of 0.000404. Mean and modal ϵ exhibit a wide variation geographically for any specified PE. Modal ϵ for the 2% in 50 yr PE exceeds 2 near the most active western California faults, is less than –1 near some less active faults of the western United States (principally in the Basin and Range), and may be less than 0 in areal fault zones of the central and eastern United States (CEUS). This geographic variation is useful for comparing probabilistic ground motions with ground motions from scenario earthquakes on dominating faults, often used in seismic-resistant provisions of building codes. An interactive seismic-hazard deaggregation menu item has been added to the USGS probabilistic seismic-hazard analysis Web site, , allowing visitors to compute mean and modal distance, magnitude, and ϵ corresponding to ground motions having mean return times from 250 to 5000 yr for any site in the United States.

Optimal Prediction for Prefetching in the Worst Case

Response time delays caused by I/O are a major problem in many systems and database applications. Prefetching and cache replacement methods are attracting renewed attention because of their success in avoiding costly I/Os. Prefetching can be looked upon as a type of online sequential prediction, where the predictions must be accurate as well as made in a computationally efficient way. Unlike other online problems, prefetching cannot admit a competitive analysis, since the optimal offline prefetcher incurs no cost when it knows the future page requests. Previous analytical work on prefetching [. Vitter Krishnan 1991.] [J. Assoc. Comput. Mach., 143 (1996), pp. 771--793] consisted of modeling the user as a probabilistic Markov source. In this paper, we look at the much stronger form of worst-case analysis and derive a randomized algorithm for pure prefetching. We compare our algorithm for every page request sequence with the important class of finite state prefetchers, making no assumptions as to how the sequence of page requests is generated. We prove analytically that the fault rate of our online prefetching algorithm converges almost surely for every page request sequence to the fault rate of the optimal finite state prefetcher for the sequence. This analysis model can be looked upon as a generalization of the competitive framework, in that it compares an online algorithm in a worst-case manner over all sequences with a powerful yet nonclairvoyant opponent. We simultaneously achieve the computational goal of implementing our prefetcher in optimal constant expected time per prefetched page using the optimal dynamic discrete random variate generator of [. Matias Matias, Vitter, and Ni [Proc. 4th Annual SIAM/ACM Symposium on Discrete Algorithms, Austin, TX, January 1993].

Probabilistic reconstruction of multiple sources in the bioelectromagnetic inverse problem

A probabilistic multiple source solution for the bioelectromagnetic inverse problem is described. The model-dependent solution assumes a finite number of discrete primary sources at fixed locations within a bounded conductor. Covariance statistics derived from a set of detectors outside the conducting region are used to determine a metric on the space of possible sources. This metric function is used to construct a weighted pseudo-inverse matrix, which, in turn, may be used to estimate the spatio-temporal distribution of source activity. The results are embodied in the form of the PROMS (probabilistic reconstruction of (multiple sources) algorithm. Computer simulations using the algorithm are described. These methods are compared with other algorithms, including minimum norm estimation, and the MUSIC and spatial filtering algorithms.

A note on the Ziv - Lempel model for compressing individual sequences (Corresp.)

The Ziv-Lempel compression algorithm is a string matching and parsing approach to data compression. The symbolwise equivalent for parsing models has been defined by Rissanen and Langdon and gives the same ideal codelength at the same cost in coding parameters. By describing the context and coding parameter for each symbol an insight is provided into how the Ziv-Lempel method achieves compression. This treatment does not employ a probabilistic source for the data string. The Ziv-Lempel method effectively counts symbol instances within parsed phrases. The coding parameter for each symbolwise context is determined by cumulative count ratios. The code string length increase for a symbol <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</tex> following substring <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> , under the symbolwise equivalent, is the log of the ratio of node counts in subtrees <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s\cdot y</tex> of the Ziv-Lempel parsing tree. To demonstrate the symbolwise equivalent of the Ziv-Lempel algorithm, we extend the work of Rissanen and Langdon to incomplete parse trees. The result requires the proper handling of the comma when one phrase is the prefix of another phrase.

Procedure for determining the optimal dose ratio of a deterministic and a probabilistic source

Procedure for determining the optimal dose ratio of a deterministic and a probabilistic source

A statistical model for prediction of quasirealistic strong ground motion.

The total power, the duration, and the starting time of band-pass filtered accelerograms are chosen as model parameters to express amplitude variations of ground acceleration in both the time and frequency domains. In order to estimate model parameters of certain earthquakes and site conditions, a probabilistic source model is used and accelerograms recorded during the Matsushiro earthquake swarm are analyzed statistically. The duration and the starting time of the strong ground motion are found to have close relations to the amplification characteristics of surface layers at the sites. As an example, model parameters are estimated by assuming the source parameters and the site conditions of the Miyagi-Oki earthquake of June 12, 1978. Wave-forms, running spectra, and velocity response spectra of synthetic accelerograms resemble those of observed accelerograms.

Locally optimal block quantizer design

Several properties are developed for a recently proposed algorithm for the design of block quantizers based either on a probabilistic source model or on a long training sequence of data. Conditions on the source and general distortion measures under which the algorithm is well defined and converges to a local minimum are provided. A variation of the ergodic theorem is used to show that if the source is block stationary and ergodic, then in the limit as n → ∝, the algorithm run on a sample distribution of a training sequence of length n will produce the same result as if the algorithm were run on the “true” underlying distribution.

Tree algorithms for packet broadcast channels

The multiaccessing of a broadcast communication channel by independent sources is considered. Previous accessing techniques suffer from long message delays, low throughput, and/or congestion instabilities. A new class of high-speed, high-throughput, stable, multiaccessing algorithms is presented. Contentions resolving tree algorithms are introduced, and they are analyzed for specific probabilistic source models. It is shown that these algorithms are stable (in that all moments of delay exist) and are optimal in a certain sense. Furthermore, they have a maximum throughput of 0.430 packets/slut and have good delay properties. It is also shown that, under heavy traffic, the optimally controlled tree algorithm adaptively changes to the conventional time-division multiple access protocol.

Coding theorems for individual sequences

A quantity called the {\em finite-state} complexity is assigned to every infinite sequence of elements drawn from a finite sot. This quantity characterizes the largest compression ratio that can be achieved in accurate transmission of the sequence by any finite-state encoder (and decoder). Coding theorems and converses are derived for an individual sequence without any probabilistic characterization, and universal data compression algorithms are introduced that are asymptotically optimal for all sequences over a given alphabet. The finite-state complexity of a sequence plays a role similar to that of entropy in classical information theory (which deals with probabilistic ensembles of sequences rather than an individual sequence). For a probabilistic source, the expectation of the finite state complexity of its sequences is equal to the source's entropy. The finite state complexity is of particular interest when the source statistics are unspecified.

Behaviour/structure transformations under uncertainty

This paper analyses the problem of determining a structure for an automaton, optimal in some sense, from observations of its behaviour which are themselves uncertain. It is shown that extension of deterministic modelling techniques based on the Nerode equivalence to probabilistic sources gives meaningless results. The problem of approximate modelling with nondeterministic structures is rigorously formulated leading to the concept of a space of admissible models . The special case where the observed behaviour may be represented as a symbol string is then analysed in terms of measures of string approximation . It is shown that appropriate measures lead to the poorness-of-fit of admissible models of a probabilistic source being an entropy for that source. The formulation is consistent with a computational complexity basis for probability theory and leads to natural expressions for the surprise at each observation and the uncertainty as to the next observation. An implemented algorithm for this modelling process is then described with examples of its application to: probabilistic sources; sampled deterministic sources; grammatical inference; human behaviour; and program derivation from traces.