Probabilistic Perspective Research Articles

A Low-Sensitivity Recurrent Neural Network

The problem of high sensitivity in modeling is well known. Small perturbations in the model parameters may result in large, undesired changes in the model behavior. A number of authors have considered the issue of sensitivity in feedforward neural networks from a probabilistic perspective. Less attention has been given to such issues in recurrent neural networks. In this article, we present a new recurrent neural network architecture, that is capable of significantly improved parameter sensitivity properties compared to existing recurrent neural networks. The new recurrent neural network generalizes previous architectures by employing alternative discrete-time operators in place of the shift operator normally used. An analysis of the model demonstrates the existence of parameter sensitivity in recurrent neural networks and supports the proposed architecture. The new architecture performs significantly better than previous recurrent neural networks, as shown by a series of simple numerical experiments.

Noisy Nonlinear Motions of Moored System. Part I: Analysis and Simulations

Nonlinear responses of a submerged moored structure are investigated taking into account the presence of environment random noise. Sources of nonlinearity of the system include a quadratic Morison hydrodynamic damping and a geometrically nonlinear restoring force. The random perturbations are modeled by a white-noise process to examine their effects on nonlinear responses analytically and numerically. The analysis procedure includes a generalized Melnikov process to study response stabilities in a global sense and the Fokker-Planck equation to demonstrate response characteristics from a probabilistic perspective. Rich non­ linear phenomena including bifurcations. coexistence of attractors. and chaos are identified and demonstrated. Probability density functions solved from the Fokker-Planck equation are used to depict (co)existing response attractors on the Poincare section and demonstrate their probabilistic properties. Noise effects on responses are shown via a generalized Melnikov criterion and the probability density function. It is found that the presence of noise may expand the chaotic domain in the parameter space and also cause transitions between coexisting responses. ABSTRACT: Nonlinear responses of a submerged moored structure are investigated taking into account the presence of environment random noise. Sources of nonlinearity of the system include a quadratic Morison hydrodynamic damping and a geometrically nonlinear restoring force. The random perturbations are modeled by a white-noise process to examine their effects on nonlinear responses analytically and numerically. The analysis procedure includes a generalized Melnikov process to study response stabilities in a global sense and the Fokker-Planck equation to demonstrate response characteristics from a probabilistic perspective. Rich non­ linear phenomena including bifurcations. coexistence of attractors. and chaos are identified and demonstrated. Probability density functions solved from the Fokker-Planck equation are used to depict (co)existing response attractors on the Poincare section and demonstrate their probabilistic properties. Noise effects on responses are shown via a generalized Melnikov criterion and the probability density function. It is found that the presence of noise may expand the chaotic domain in the parameter space and also cause transitions between coexisting responses.

Self-Affine Carpets on the Square Lattice

We explore the ‘Hausdorff dimension at infinity’ for self-affine carpets defined on the square lattice. This notion of dimension (due to Barlow and Taylor), which is the correct notion from a probabilistic perspective, differs for these sets from more ‘naive’ indices of fractal dimension.

Simple Genetic Algorithms with Linear Fitness

A general form of stochastic search is described (random heuristic search), and some of its general properties are proved. This provides a framework in which the simple genetic algorithm (SGA) is a special case. The framework is used to illuminate relationships between seemingly different probabilistic perspectives of SGA behavior. Next, the SGA is formalized as an instance of random heuristic search. The formalization then used to show expected population fitness is a Lyapunov function in the infinite population model when mutation is zero and fitness is linear. In particular, the infinite population algorithm must converge, and average population fitness increases from one generation to the next. The consequence for a finite population SGA is that the expected population fitness increases from one generation to the next. Moreover, the only stable fixed point of the expected next population operator corresponds to the population consisting entirely of the optimal string. This result is then extended by way of a perturbation argument to allow nonzero mutation.

The 1993 Midwest Extreme Precipitation in Historical and Probabilistic Perspective

Extreme rainfall amounts that resulted in severe flooding during the spring and summer of 1993 along the Missouri and Mississippi Rivers are examined from a historical and probabilistic viewpoint. Long-term average precipitation amounts and the departures of the 1993 summer rainfall from these averages are presented. Also, climatic regionalization and precipitation probabilities developed for the National Drought Atlas using L-moment techniques have been applied to the drainage area that contributed to the flooding. The exceedance probabilities of monthly and multiple-month observed precipitation amounts have been calculated. The results show that the three-month period May–July experienced unusually heavy rainfall when compared to prior years, and that July was particularly wet. Recurrence intervals for the rainfall events vary widely depending on the specific time period and locality, but the observed precipitation was an extreme event.

The Importance of a Game

Organized play for many of major sports that are popular around world (baseball, basketball, hockey, tennis, and volleyball, for example) involves a contest between two opponents in which victor is team or individual that is first to win a prescribed number of subcontests. Often during these contests one will hear in conversation or on a broadcast a statement such as This game is most important game of series. Why are some games perceived as being more important than others, when each game counts same toward total number of victories required to win contest? The purpose of this article to analyze meaning and validity of such statements from a probabilistic perspective and to provide a means of quantifying importance, in order that comparative significance of games can be measured. In this paper, word game will refer to subcontests that comprise a contest, and one participant in contest will be arbitrarily denoted the contestant, or C. The key observation is that importance of a game depends on context. Two distinct versions of importance, developed below, are therefore appropriate. It will be assumed that outcome of each game in a contest is independent of all other outcomes. Participants in such contests frequently dispute reasonableness of this supposition, citing effects of momentum and other factors, primarily psychological; however, evidence from statistical analysis of contests [2] suggests that actual experience is quite compatible with independence assumption.

More on the Uneasy Case for Using Mill-Type Methods in Small-N Comparative Studies

The methods of agreement and difference are outdated and inappropriate procedures for comparative or historical analysis based on a small number of cases. The methods cannot employ a probabilistic perspective, deal with data errors, use multivariate analyses, or take into account interaction effects. All of these are critical features in contemporary ways of thinking about social processes. Although Savolainen (1994) accepts the importance of having a method that can cope with these matters, he argues that Mill's methods permit such steps. However, he provides neither specific examples of where these methods actually address these issues nor does he present a formal set of rules whereby the methods of difference or agreement can estimate them. This is not surprising since Mill himself recognized that these methods were inappropriate for the kinds of problems addressed in most social research.

Instability of Loaded Fractal Trees

We analyze the failure strength of loaded structures of the fractal-tree type, from a probabilistic perspective. The consideration of the intrinsic fragilities of the basic elements at each level of the tree makes the tree differ from being equivalent to a mere hierarchically organized bundle of fibers. A simple criterion for having a linear proportionality between the size of the tree and the inverse of the threshold strength for failure is found.

On Detecting Regularity of Functions: A Probabilistic Analysis

We study the problem of detecting the regularity degree deg(ƒ) = max{ k: k ≤ r, ƒ ∈ C k } of functions based on a finite number of function evaluations. Since it is impossible to find deg(ƒ) for any function ƒ, we analyze this problem from a probabilistic perspective. We prove that when the class of considered functions is equipped with a Wiener-type probability measure, one can compute deg(ƒ) exactly with super exponentially small probability of failure. That is, we propose an algorithm which, given n function values at equally spaced points, might propose a value different than deg(ƒ) only with probability O(( n −1 ln n) ( n − r)/4 ). Hence, regularity detection is easy in the probabilistic setting even though it is unsolvable in the worst case setting.

Probabilistic input-output analysis: Modeling directions

Recent developments in probabilistic input-output modeling based on the full-distribution approach demonstrate the relationship between distributional forms of industry aggregates and regionally variant production characteristics. Variables such as market structure, establishment size, prices, labor productivity, technology, product mix, and ages of capital stock, all of which vary regionally, are determinants of the probabilistic structure of interindustry interaction. Two modeling directions are described in this paper. The first concerns formalizing the relationship between key variables at the regional level and particular forms of associated aggregate distributions. Once these relationships are specified, the dynamic character of interindustry structure can be developed. The second modeling direction follows on the first, and concerns the more general implications of the probabilistic perspective for regional economic modeling. One model demonstrated generates a nonlinear output growth path from a linear base-point projection of final demand. This model places the regional cyclical stability issue in a new light, and establishes a method for generating interval estimates of regional economic performance for forecasting purposes.

Aerodynamics of urban transit vehicles

The paper discusses the problems of wind loading of urban transit vehicles in the context of the overturning problem. It is shown that vehicles will respond to gusts of the order of only a few seconds in duration. The available aerodynamic information for vehicle shapes is reviewed, as is the nature of the wind environment in urban areas. The implications of these data are placed in a simplified probabilistic perspective that suggests that the risk of overturning can become very significant if a number of factors are unfavourable. While the details of assessing the risks more precisely are described and have been developed in detail elsewhere, they cannot be applied to this problem until better information for particular cases is developed. Better data on both vehicle aerodynamics and the wind statistics for actual vehicle routes are needed. Key words: urban transit vehicles, overturning, wind loading, aerodynamics, wind engineering.

Plasticity in development: Concepts and issues for intervention

Because of its pertinence both to key theoretical issues and to applied concerns, plasticity is a central concept within developmental psychology. Our concept of plasticity derives from a comparative developmental, probabilistic epigenetic perspective: Plasticity is the relative flexibility, or capacity to modify behavior to fit contextual demands, shown by a species (or individual) at its most advanced level of development. We argue that processes of development should be conceived of as plastic, and that they should be studied in relation to constancies and constraints on change. Finally, we indicate that, for intervenors, plasticity represents a double-edged sword: Processes available to be changed for the better may be also changed for tho worse. As such, we discuss several developmental and contextual issues that must be confronted by intervenors if a person's potential plasticity across life is to be actualized in the service of enhancing or optimizing the life course.

Application of Probabilistic Methods to Engineering Estimates of Speed, Power, Weight, and Cost

The development and growth in the application of probabilistic methods are traced up to the present time and it is concluded that such methods are now widely accepted. The maritime engineering community currently employs probabilistic methods in a few instances, but the opportunity for wider applications seems to be great. Especially promising candidates are those activities that are currently regarded as estimates, such as weight estimates, cost estimates, and speed and power estimates. Example applications to each of these three estimating problems are presented, illustrating both the methods and the advantages of adopting the probabilistic perspective. Including measures of the dispersion in certainty in the estimating process is shown to be simple and useful. It is concluded that the maritime engineering community should give serious consideration to greater use of probabilistic methods.