Deterministic Measures Research Articles

Seasonal Prediction of Sea Surface Temperature Anomalies Using a Suite of 13 Coupled Atmosphere–Ocean Models

Abstract Improved seasonal prediction of sea surface temperature (SST) anomalies over the global oceans is the theme of this paper. Using 13 state-of-the-art coupled global atmosphere–ocean models and 13 yr of seasonal forecasts, the performance of individual models, the ensemble mean, the bias-removed ensemble mean, and the Florida State University (FSU) superensemble are compared. A total of 23 400 seasonal forecasts based on 1-month lead times were available for this study. Evaluation metrics include both deterministic and probabilistic skill measures, such as verification of anomalies based on model and observed climatology, time series of specific climate indices, standard deterministic ensemble mean scores including anomaly correlations, root-mean-square (RMS) errors, and probabilistic skill measures such as equitable threat scores for seasonal SST forecasts. This study also illustrates the Niño-3.4 SST forecast skill for the equatorial Pacific Ocean and for the dipole index for the Indian Ocean. The relative skills of total SST fields and of the SST anomalies from the 13 coupled atmosphere–ocean models are presented. Comparisons of superensemble-based seasonal forecasts with recent studies on SST anomaly forecasts are also shown. Overall it is found that the multimodel superensemble forecasts are characterized by considerable RMS error reductions and increased accuracy in the spatial distribution of SST. Superensemble SST skill also persists for El Niño and La Niña forecasts since the large comparative skill of the superensemble is retained across such years. Real-time forecasts of seasonal sea surface temperature anomalies appear to be possible.

Uncertainty and precaution in European environmental risk assessment of chemicals

It is recognised that there is a need for a proper treatment and transparency of uncertainty in risk assessment and management, especially in view of the upcoming proposed new chemical policy REACH, which delegates the responsibility for conducting risk assessments to industry. The current EU risk assessment for new and existing substances is largely deterministic and prudential measures are implicitly embedded in calculation schemes and rules. In this paper, a more probabilistic approach to risk assessment is advocated. The advantage is twofold: 1) inherent variability and other uncertainty pertaining to exposure and effects are transparently taken into account, while at the same time 2) issues of caution are explicitly transferred to the risk management phase. The result of a probabilistic risk assessment as suggested is improved transparency with quantitative and qualitative uncertainty estimates. Such uncertainty information can be used to discuss precautionary measures in the context of risk management.

A Consolidated CLIPER Model for Improved August–September ENSO Prediction Skill

Abstract A prime challenge for ENSO seasonal forecast models is to predict boreal summer ENSO conditions at lead. August–September ENSO has a strong influence on Atlantic hurricane activity, Northwest Pacific typhoon activity, and tropical precipitation. However, summer ENSO skill is low due to the spring predictability barrier between March and May. A “consolidated” ENSO–climatology and persistence (CLIPER) seasonal prediction model is presented to address this issue with promising initial results. Consolidated CLIPER comprises the ensemble of 18 model variants of the statistical ENSO–CLIPER prediction model. Assessing August–September ENSO skill using deterministic and probabilistic skill measures applied to cross-validated hindcasts from 1952 to 2002, and using deterministic skill measures applied to replicated real-time forecasts from 1900 to 1950, shows that the consolidated CLIPER model consistently outperforms the standard CLIPER model at leads from 2 to 6 months for all the main ENSO indices (3, 3.4, and 4). The consolidated CLIPER August–September 1952–2002 hindcast skill is also positive to 97.5% confidence at leads out to 4 months (early April) for all ENSO indices. Optimization of the consolidated CLIPER model may lead to further skill improvements.

Reconfigurable layout problem

This paper addresses the reconfigurable layout problem, which differs from traditional, robust and dynamic layout problems mainly in two aspects: first, it assumes that production data are available only for the current and upcoming production period. Second, it considers queuing performance measures such as work in progress inventory and product lead time in the objective function of the layout problem. A process to solve the reconfigurable layout problem is proposed. A previously developed, open queuing network-based analytical model, called Manufacturing system Performance Analyser, is used to estimate the stochastic performance measures of a layout. These are combined with deterministic performance measures such as material handling cost to determine the layout for the next period. A case study is used to illustrate the process of solving the reconfigurable layout problem.

Cautious Control of Industrial Process Variability With Uncertain Input and Disturbance Model Parameters

This article discusses a method for controlling variation in industrial processes when the model parameters are estimated from data and subject to uncertainty. A static input/output relationship with multiple input variables and an integrated moving average disturbance model are assumed. Most robust control methods use deterministic measures of uncertainty and a control objective that focuses on worst-case performance. This work uses a probabilistic measure of uncertainty and a control objective that relates more closely to minimizing variation, where parameter estimation errors are treated simply as an additional source of variability. We show that this approach results in a higher probability of closed-loop stability than the standard minimum variance control and can substantially lessen the adverse impact of parameter uncertainty on closed-loop variance. Guidelines for designing and evaluating the experiment used to estimate the model parameters are also discussed.

The COLA Anomaly Coupled Model: Ensemble ENSO Prediction

Abstract Results are described from a large sample of coupled ocean–atmosphere retrospective forecasts during 1980–99. The prediction system includes a global anomaly coupled general circulation model and a state-of-the-art ocean data assimilation system. The retrospective forecasts are initialized each January, April, July, and October of each year, and ensembles of six forecasts are run for each initial month, yielding a total of 480 1-yr predictions. In generating the ensemble members, perturbations are added to the atmospheric initial state only. The skill of the prediction system is analyzed from both a deterministic and a probabilistic perspective. The probabilistic approach is used to quantify the uncertainty in any given forecast. The deterministic measures of skill for eastern tropical Pacific SST anomalies (SSTAs) suggest that the ensemble mean forecasts are useful up to lead times of 7–9 months. At somewhat shorter leads, the forecasts capture some aspects of the variability in the tropical Ind...

On the rate-distortion region for multiple descriptions

We study the problem of source coding with multiple descriptions, which is described as follows. Let X be a discrete memoryless source. There are two encoders, Encoders 1 and 2, and three decoders, Decoders 0, 1, and 2. Encoders 1 and 2 describe the source X at respective rates R/sub 1/ and R/sub 2/. Decoder 1 receives the output of Encoder 1 only, and it can recover X with distortion D/sub 1/. Decoder 2 receives the output of Encoder 2 only, and it can recover X with distortion D/sub 2/. Decoder 0 receives the outputs of both Encoders 1 and 2, and it can recover X with distortion D/sub 0/. We show that if Decoder 2 (or Decoder 1) is required to recover a function of the source X perfectly in the usual Shannon sense, the El Gamal-Cover (1982) inner bound on the rate distortion region is tight. This finding subsumes the Rimoldi (1994) rate-distortion region for successive refinement of information, the Kaspi (1994) rate-distortion function when side information may be present at the decoder, and the El Gamal-Cover achievable rate region for multiple descriptions with deterministic distortion measures. We have also obtained a new outer bound on the rate-distortion region which enhances the outer bound due to Witsenhausen (1981) and Wyner. This new outer bound implies some interesting facts regarding the achievable rate-distortion vectors. Finally, we pose a multilevel diversity source coding problem for further study.

CHAOS AND STOCHASTICITY IN DETERMINISTICALLY GENERATED MULTIFRACTAL MEASURES

Successful usage of a large family of deterministically generated measures to model complex nonlinear phenomena (e.g. rainfall, turbulence and groundwater contaminant transport) has been reported recently.1–7 As these measures, generated as derived distributions of multifractal measures via fractal interpolating functions (FIF), i.e. the fractal-multifractal (FM) approach, have been found to share the inherent character of natural sets, the present study further investigates their dynamical (chaotic or stochastic) properties. It is shown, through a variety of examples and via the use of power spectrum, mass exponents and false nearest neighbors in the state-space, that the FM approach indeed generates deterministic measures whose behavior (depending on their parameters) may be classified as low-dimensional and chaotic or as high-dimensional and stochastic. These results suggest the general suitability of the FM approach for understanding and modeling nonlinear natural phenomena.

Comparison of partition evaluation measures in an adaptive partitioning algorithm for global optimization

An adaptive partitioning algorithm with random search is proposed to locate the global optimum of multimodal functions. Partitioning algorithms divide the feasible region into nonoverlapping partitions in order to restrict and direct the search to the most promising region expected to contain the global optimum. In such a scheme a partition evaluation measure is required to assess sub-regions in order to re-partition the most promising sub-region and intensify the search within that area. This study provides computational results on several classes of partition evaluation measures used in the assessment of samples taken from all partitions. Among the partition evaluation classes used in our comparison are fuzzy, statistical, and deterministic interval estimation measures. Performance in terms of solution quality is reported on an extensive set of 77 test functions collected from the literature.

Controller performance assessment based on minimum and open-loop output variance

The need to achieve reliable and effective automatic control systems has directed numerous research efforts towards the development of monitoring and assessment methods of the closed-loop performance. A new controller assessment index, called relative variance index (RVI) is introduced in this work, according to which the closed-loop performance is compared with the best theoretical control action (minimum variance control) and no control action. For the estimation of RVI, an identification method is employed to extract the system models and an estimate of the process unit delays. The proposed index, RVI, is in agreement with the classical deterministic closed-loop assessment measures and thus can be utilized for the controller performance evaluation more effectively.

A GEOMETRIC PLATONIC APPROACH TO MULTIFRACTALITY AND TURBULENCE

A large family of deterministic measures built as projections off fractal functions has been introduced recently.1,2 These constructed measures, which transform either simple multifractals as defined by deterministic cascades3 or uniform measures via fractal interpolating functions,4,5 range from nontrivial multifractals to absolutely continuous measures, and include as a limiting case the Gaussian distribution.6 In this work, examples of deterministic measures which possess multiscaling properties when analyzed following the multifractal formalism are given. It is shown that suitable measures which not only preserve the singularity spectrum of turbulence but also capture the inherent details present in turbulent data sets may be obtained. These results suggest a plausible deterministic framework for the study of intermittent phenomena via a new geometric approach — one which closely evokes Plato's ideas that all we observe may be "shadows" of simple objects.7

A Control Performance Index Based on Minimum and Open-Loop Output Variance

The need to achieve reliable and effective automatic control systems has directed numerous research efforts towards the development of monitoring and assessment methods of the closed-loop performance. A new controller assessment index, called Relative Variance Index or RVI, is introduced in this work, according to which the closed loop performance is compared with the theoretically best control action (minimum variance control) and no control action. For the estimation of RVI, an identification method is employed to extract the system models and an estimate of the process unit delays. The proposed index, RVI, is in agreement with the classical deterministic closed-loop assessment measures and thus can be utilized for the controller performance evaluation more effectively.

National product related welfare measures in the presence of technological change: Externalities and uncertainty

The purpose of this paper is to discuss under what conditions welfare can be measured by observables related to the national product (or Hamiltonian along the optimal trajectory). Under nonattributable technological or environmental change, welfare will depend on time itself, meaning that the Hamiltonian along the optimal trajectory will be a biased measure of welfare. This result will also hold if we make the time dependence of welfare endogenous, by replacing technological change will externalities that are not internalized during optimization. On the other hand, if we take the externalities fully into account, then the Hamiltonian will represent the appropriate measure of welfare. Similar results also hold in the case of uncertainty, where we show that a ‘generalized’ Hamiltonian provides a welfare measure, and that the deterministic measures are special cases of their stochastic counterparts.

A spreadsheet model approach for integrating static capacity planning and stochastic queueing models

This paper proposes a manufacturing system modelling approach using computer spreadsheet software, in which a static capacity planning model and stochastic queueing model are integrated. Most stochastic performance measures such as throughput time or work in process as well as deterministic measures can be captured directly from the proposed model. Several special manufacturing features such as machine breakdown and batch production can be included in the model. The performance of the proposed model is evaluated by comparing its results with those obtained from other existing approaches.

Farm‐Level Economic Analysis Incorporating Stochastic Environmental Risk Assessment

AbstractA farm‐level risk programming framework is presented which evaluates income/ environmental risk tradeoffs. This framework uses a time‐series of environmental risk indices to incorporate the stochastic, multiattribute characteristics of environmental outcomes associated with agricultural production practices. The model is applied to a representative farm in the Oklahoma Panhandle region of the Central High Plains. Results indicate that expected income is sensitive to nitrate loading restrictions, and relatively less sensitive to pesticide loading restrictions. Results also indicate that prescriptions derived using deterministic environmental risk measures may ignore significant probabilities of exceeding an environmental standard.

Use of the Kohonen self-organizing map to study the mechanisms of action of chemotherapeutic agents.

Many natural and synthetic compounds might prove to be effective in cancer chemotherapy. To identify potentially useful agents, the National Cancer Institute screens over 10,000 compounds annually against a panel of 60 distinct human tumor cell lines in vitro. This screening program generates large amounts of data that are organized into relational databases. Important questions concern the information content of the data and ways to extract that information. Previously, statistical techniques have revealed that compounds with similar patterns of activity against the 60 cell lines are often similar in structure and mechanism of action. Feed-forward, back-propagation neural networks have been trained on this type of data to predict broadly defined mechanisms of action of chemotherapeutic agents. In this report, we examine the information that can be extracted from the screening data by means of another type of neural network paradigm, the Kohonen self-organizing map. This is a topology-preserving function, obtained by unsupervised learning, that nonlinearly projects the high-dimensional activity patterns into two dimensions. Our dataset is almost identical to that used in the earlier neural network study. The self-organizing maps we constructed have several important characteristics. 1) They partition the two-dimensional array into distinct regions, each of which is principally occupied by agents having the same broadly defined mechanism of action. 2) These regions can be resolved into distinct subregions that conform to plausible submechanisms and chemically defined subgroups of submechanism. 3) These results (and exceptions to them) are consistent with those obtained with the use of such deterministic measures of similarity among activity patterns as the Euclidean distance or Pearson correlation coefficient. Our results indicate that the activity patterns obtained from the screen contain detailed information about mechanism of action and its basis in chemical structure. The self-organizing map can be used to suggest the mechanism of action of compounds identified by the screen as potentially useful chemotherapeutic agents and to probe the biology of the cell lines in the cancer screen. Kohonen self-organizing maps, unlike the previously applied neural networks, preserve and reveal the relationships among compounds acting by similar mechanisms and therefore have the potential to identify compounds that act by novel cytotoxic mechanisms.

PREDICTABILITY OF MULTIPLICATIVE PROCESSES: A PRELIMINARY STUDY

We define a multifractal analysis for correlations. We present explicit results in the case of deterministic multinomial measures, and show that the multifractal formalism does not hold for correlations on binomial measures.

Assuring SS7 dependability: a robustness characterization of signaling network elements

Current and evolving telecommunication services will rely on signaling network performance and reliability properties to build competitive call and connection control mechanisms under increasing demands on flexibility without compromising on quality. The dimensions of signaling dependability most often evaluated are the rate of call loss and end-to-end route unavailability. A third dimension of dependability that captures the concern about large or catastrophic failures can be termed network robustness. The paper is concerned with the dependability aspects of the evolving Signaling System No. 7 (SS7) networks and attempts to strike a balance between the probabilistic and deterministic measures that must be evaluated to accomplish a risk-trend assessment to drive architecture decisions. Starting with high-level network dependability objectives and field experience with SS7 in the U.S., potential areas of growing stringency in network element (NE) dependability are identified to improve against current measures of SS7 network quality, as per-call signaling interactions increase. A sensitivity analysis is presented to highlight the impact due to imperfect coverage of duplex network component or element failures (i.e., correlated failures), to assist in the setting of requirements on NE robustness. A benefit analysis, covering several dimensions of dependability, is used to generate the domain of solutions available to the network architect in terms of network and network element fault tolerance that may be specified to meet the desired signaling quality goals. >

An analysis of edge fault tolerance in recursively decomposable regular networks

Fault tolerance of interconnection networks is one of the major considerations in evaluating the reliability of large scale multiprocessor systems. In the paper, the reliability of a family of regular networks with respect to edge failures is investigated using four different fault tolerance measures. Two probabilistic measures, resilience and restricted resilience, are developed, used to evaluate disconnection likelihoods using two different failure models, and compared with corresponding deterministic measures. The network topologies chosen for the present study all have the recursive decomposition property, where larger networks can be decomposed into copies of smaller networks of the same topology. This family of graphs includes the k-ary n-cube, star and cube connected cycle graphs, which have optimal deterministic connectivities. The probabilistic fault tolerance measures, however, are found to depend on topological properties such as network size and degree. >

Neurocardiology: Brain Mechanisms Underlying Fatal Cardiac Arrhythmias

Chaos theory may have a widespread application in medicine, from the analysis of protein structure at one end of the spectrum to fetal monitoring and the measurement of aging on the other. This application is especially on firm ground in cardiology, where it is simple and precise for the experimenter, and a primer exists for the clinician. As just presented, the point-correlation-dimension analysis of heartbeat variability is able to characterize the patterns of low-dimensional chaos produced by the heartbeat generator, a mechanism that is a composite of the voltage-dependent, neurotransmitter-dependent, and circulation-dependent ionic conductances that are all located in the myocardium where the heartbeat is formed. Most importantly, this deterministic measure of heartbeat variability is able to predict imminent lethal arrhythmogenesis with an accuracy that the more familiar stochastic measures do not have. This may arise because the PD2 is sensitive to the net degrees of freedom of the heartbeat generator, which, under the influence of the nerves and the coronary circulation, can be shifted so the resulting dynamics cause the initiation of lethal arrhythmogenesis. Application of chaos theory in neurology may be equally fruitful because the deterministic measures can discriminate among neuronal firing patterns, reveal subtle changes in brain waves, and be related to higher cognitive processes. Psychiatry also seems quite likely to benefit more and more from the application because the algorithms can discriminate schizophrenic brain functions from normal ones. Thus it can be expected that future applications will enable observation of biologic processes all along the brain-heart axis by which lethal ventricular fibrillation is regulated and perhaps even caused by its determination of the heartbeat dynamics. The subfield of neurocardiology has come a long way since it was first positively identified as an important research area. It took a lot of experiments to show how lethal cardiac arrhythmogenesis is involved with cerebral activities delivered over autonomic pathways. Although we do not yet fully understand the causal mechanism of lethal arrhythmogenesis, we may be getting close. It will become increasingly imperative for the clinical neurologist, along with the cardiologist, to understand the importance of neurocardiology in medical therapy and for the neurologist, along with the cardiologist and psychiatrist, to understand its importance in preventive treatments.