Probabilistic Conditions Research Articles

Hamilton Jacobi Isaacs equations for differential games with asymmetric information on probabilistic initial condition

We investigate Hamilton Jacobi Isaacs equations associated to a two-players zero-sum differential game with incomplete information. The first player has complete information on the initial state of the game while the second player has only information of a – possibly uncountable – probabilistic nature: he knows a probability measure on the initial state. Such differential games with finite type incomplete information can be viewed as a generalization of the famous Aumann–Maschler theory for repeated games. The main goal and novelty of the present work consists in obtaining and investigating a Hamilton Jacobi Isaacs Equation satisfied by the upper and the lower values of the game. Since we obtain a uniqueness result for such Hamilton Jacobi equation, as a byproduct, this gives an alternative proof of the existence of a value of the differential game (which has been already obtained in the literature by different technics). Since the Hamilton Jacobi equation is naturally stated in the space of probability measures, we use the Wasserstein distance and some tools of optimal transport theory.

A Gift-Exchange with Probabilistic Payoffs

Ample experimental evidence demonstrates a positive wage-effort relationship in which the results from the employee’s effort lead to deterministic firm’ payoffs. We thus investigate a reframed version of the gift-exchange game by Fehr et al. (1998) in which the firms’ payoffs can take two values and one of them is randomly determined by an external process after the effort choice has been made. We find that effort levels are significantly lower when payoffs are probabilistic than when they are deterministic. As a consequence, high waging is profitable in the deterministic, but not in the probabilistic condition. Moreover, the treatment effect is strongest among firms which offer high wages.

A novel architecture with scalable security having expandable computational complexity for stream ciphers

Stream cipher designs are difficult to implement since they are prone to weaknesses based on usage, with properties being similar to one-time pad besides keystream is subjected to very strict requirements. Contemporary stream cipher designs are highly vulnerable to algebraic cryptanalysis based on linear algebra, in which the inputs and outputs are formulated as multivariate polynomial equations. Solving a nonlinear system of multivariate equations will reduce the complexity, which in turn yields the targeted secret information. Recently, Addition Modulo has been suggested over logic XOR as a mixing operator to guard against such attacks. However, it has been observed that the complexity of Modulo Addition can be drastically decreased with the appropriate formulation of polynomial equations and probabilistic conditions. A new design for Addition Modulo is proposed. The framework for the new design is characterized by user-defined expandable security for stronger encryption and does not impose changes in existing layout for any stream cipher such as SNOW 2.0, SOSEMANUK, CryptMT, Grain Family, etc. The structure of the proposed design is highly scalable, which boosts the algebraic degree and thwarts the probabilistic conditions by maintaining the original hardware complexity without changing the integrity of the Addition Modulo.

Inverse acoustic scattering problem in half-space with anisotropic random impedance

We study an inverse acoustic scattering problem in half-space with a probabilistic impedance boundary value condition. The Robin coefficient (surface impedance) is assumed to be a Gaussian random function with a pseudodifferential operator describing the covariance. We measure the amplitude of the backscattered field averaged over the frequency band and assume that the data is generated by a single realization of λ. Our main result is to show that under certain conditions the principal symbol of the covariance operator of λ is uniquely determined. Most importantly, no approximations are needed and we can solve the full non-linear inverse problem. We concentrate on anisotropic models for the principal symbol, which leads to the analysis of a novel anisotropic spherical Radon transform and its invertibility.

Eye movements are captured by a perceptually simple conditioned stimulus in the absence of explicit contingency knowledge.

Past reports suggest that threatening materials can impact the efficiency of goal-directed behavior. However, questions remain about whether a conditional stimulus (CS) can capture attention as previous results may have been influenced by voluntary prioritization of a to-be-ignored CS. In 2 experiments, eye tracking was used to evaluate whether neutral, perceptually simple materials capture attention when they take on aversive properties via probabilistic fear conditioning with strict methods in place to eliminate voluntary CS prioritization. During training, participants attempted to fixate search targets (i.e., horizontally or vertically oriented rectangles) as quickly as possible to avoid shock. In reality, shock administration was related to rectangle orientation so that 1 rectangle (CS+) predicted shock more often than the other (CS-). Subsequently rectangles became distractors and were to be ignored. At this point, participants were instructed to fixate a new target and incidences of CS capture were examined. Results showed that saccades were made more quickly to the CS+ than the CS- as training progressed, and that oculomotor capture by irrelevant rectangles occurred more often for the CS+ than the CS-. An independent physiological index (skin conductance response) confirmed that contingencies had been learned, as SCR magnitude was greater for CS+ than CS- trials early in the test phase. These effects were documented despite the absence of explicit contingency knowledge, assessed using a postexperimental questionnaire. Collectively, these outcomes indicate that a CS can capture attention despite being task-irrelevant, and that these effects do not depend on conscious awareness of learned contingencies. (PsycINFO Database Record

Childhood-Diagnosed ADHD, Symptom Progression, and Reversal Learning in Adulthood

Objective: ADHD persists in up to 60% into adulthood, and the reasons for persistence are not fully understood. The objective of this study was to characterize the neurofunctional basis of decision making in those with a childhood diagnosis of ADHD with either persistent or remitted symptoms in adulthood versus healthy control participants. Method: Thirty-two adults diagnosed with ADHD as children were split into persistent (n = 18) or remitted (n = 14) ADHD groups. Their neural activity and neurofunctional connectivity during a probabilistic reversal learning task were compared with 32 healthy controls. Results: Remitters showed significantly higher neural connectivity in final reversal error and probabilistic error conditions, and persisters depict higher neural connectivity in reversal errors than controls at a family-wise error (FWE) corrected whole-brain corrected threshold. Conclusion: Remitters may have utilized higher neural connectivity than controls to make successful decisions. Also, remitters may have utilized compensatory strategies to override any potential underlying ADHD deficits.

Design of multi-step LC compensator for time-varying nonlinear loads based on genetic algorithm

Summary This article presents a method to consider the probabilistic nature of load impedance and harmonic currents by designing a multi-step inductive-capacitive (LC) compensator consisting of switchable units thus assuming that a single unit is not sufficient to ensure satisfactory results. The proposed algorithm divides the time period into sub-regions according to the scheduled number of switchable units over which the multi-step LC compensator is optimized through different performance criteria; maximizing the power factor (PF), minimizing the transmission loss (TL) or minimizing the voltage total harmonic distortion (VTHD); as objective function resulting in lower variance, and hence, the more accurate expectation is obtained. Genetic algorithm (GA) is used to estimate that steps while holding the performance quantities at the corresponding desired values and constraining the compensator values which would create resonance. Also, the manufacturer's standard values for power shunt capacitors with/without equal steps are considered. GA is a search mechanism based on the principle of natural selection and population genetics. The contribution of the proposed procedure is demonstrated in examples taken from previous publications. Finally, simulated results show that the multi-step LC compensator provides a considerable improvement in the performance in case of the probabilistic condition. Copyright © 2016 John Wiley & Sons, Ltd.

A Comparative Study on Probabilistic Optimization Methods for Electromagnetic Design

A reliability-based robust design optimization (RBRDO) is developed to ensure the product quality as well as the confidence in product reliability of electromagnetic devices. In the method, the first two statistical moments, mean and variance, of a quality loss function are estimated by the univariate dimension reduction method, while desired probabilistic constraint conditions are assessed by one of the first-order reliability analysis methods, called performance measure approach. For a better understanding between probabilistic design optimization methods, three different formulations of reliability-based design optimization, robust design optimization (RDO), and RBRDO are compared with one another. A simple mathematical model and a brushless direct current (BLDC) motor design problem are tested to demonstrate the features of the three methods and to examine their numerical efficiency.

Enriched Serial-Loop Optimization Method for Efficient Reliability-Based Electromagnetic Designs

An enriched serial-loop method for reliability-based design optimization is presented to substantially improve computational efficiency as well as numerical accuracy when applied to electromagnetic design problems in the presence of uncertainties. Two numerical improvements are made over the original serial-loop optimization method, which employs a series of cycles of an equivalent deterministic optimization and reliability analysis. One is a feasibility check technique for the probabilistic constraints conducted only at the first design cycle. It identifies inactive constraints, which need not be considered after the next design cycles. The other is a reliability improvement scheme for slightly violated probabilistic constraints, which is performed at the end of iterative design cycles. When an obtained optimum is unsatisfactory to all probabilistic constraint conditions prescribed, the design point is slightly shifted toward a feasible design region by utilizing probabilistic information obtained. Finally, the TEAM Workshop Problem 22 is tested to compare the proposed method with the existing ones from a numerical efficiency and accuracy point of view.

Economic aspects for multi‐step LC compensator with uncertain load characteristics using genetic algorithm

This study presents a method to consider the probabilistic nature of load impedance and harmonic currents by converting the conventional inductive–capacitive (LC) compensator into a multi-step type consisting of switchable units thus assuming that a single unit is not sufficient to ensure satisfactory results. The compensator steps are optimised based on economic criteria; minimising cost and maximising saving; in addition to cost-constrained performance criteria; maximising the power factor, minimising the transmission loss or minimising the voltage total harmonic distortion. The compensator values which would create resonance are constrained. Also the manufacturer's standard values for power shunt capacitors are considered. Genetic algorithm (GA) is used in the optimisation process plus numerical iterative method. GA is a search mechanism based on the principle of natural selection and population genetics. The contribution of the proposed procedure is demonstrated in examples taken from previous publications. Finally, simulated results show that the multi-step LC compensator provides a considerable improvement in the economics in case of probabilistic condition.

STUDY OF MARKOFF MODELS OF PETROLEUM COMPLEX PUMPING UNITS FAILURE RATE

The article presents a method developed for modeling the petroleum complex pumping units failure rate and reliability based on Markoff stochastic processes. A procedure is offered for determination of the pump unit’s probabilistic condition based on Markoff models. The ability of using Markoff models as a tool necessary for organizing and implementing the pumps repair and maintenance is demonstrated. The perspectives of the developed methodology use are described.

Stochastic fatigue crack growth analysis of metallic structures under multiple thermal–mechanical stress levels

This paper proposes an analytical–empirical framework for stochastic assessment of fatigue crack growth. The study offers solutions for drastic problems in studying fatigue field including dispersion and scarcity of fatigue data, and impact of several factors on fatigue crack growth. The research composes of two complementary phases. The first phase analyses the behavior of fatigue models under probabilistic conditions. The propagation of uncertainty is studied in fatigue models in this phase under cyclic loads. The research is based on two fundamental deterministic fatigue models: Walker and Forman correlations. The second phase employs probabilistic distributions for stochastic assessment of fatigue crack growth. A new approach is introduced to simulate fatigue crack growth stochastically under the effects of different variables through combining lognormal distribution and stress life models. Bayesian approach is applied for parameter estimation. The final presented models offer the ability of predicting fatigue crack length with desirable probability under multiple stress levels. Although the method is examined on an automotive application, the presented approach is universal and applicable for other industries dealing fatigue damage with multiple impacting factors.

Methodology for assessing the probabilistic condition of an asset based in concepts of structural reliability “PCBM - Probabilistic Condition Based Maintenance”

The purpose of this paper is to propose a methodology for assessing the probabilistic condition of an asset with the introduction of the concept of PCBM (Probabilistic Condition Based Maintenance) as an extension of the existing concept CBM (Condition Based Maintenance). The concepts of structural reliability and its methods will be used to evaluate the structural integrity of a mechanical system. The evaluation will be held through the probability of failure of this system and its reliability index. The system will be subject to dynamic loads. From experimental results, simulations will be performed and the correlations between the probabilistic model and the deterministic will be conducted in order to verify the possibility of using this methodology to support the decision-making process.

Robot Task Planning in Deterministic and Probabilistic Conditions Using Semantic Knowledge Base

A new method is proposed to increase the reliability of generating symbolic plans by extending the Semantic-Knowledge Based (SKB) plan generation to take into account the amount of information and uncertainty related to existing objects, their types and properties, as well as their relationships with each other. This approach constructs plans by depending on probabilistic values which are derived from learning statistical relational models such as Markov Logic Networks (MLN). An MLN module is established for probabilistic learning and inference together with semantic information to provide a basis for plausible learning and reasoning services in support of robot task-planning. The MLN module is constructed by using an algorithm to transform the knowledge stored in SKB to types, predicates and formulas which represent the main building block for this module. Following this, the semantic domain knowledge is used to derive implicit expectations of world states and the effects of the action which is nominated for insertion into the task plan. The expectations are matched with MLN output.

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.

The Invisible Hand: Toddlers Connect Probabilistic Events With Agentive Causes.

Children posit unobserved causes when events appear to occur spontaneously (e.g., Gelman & Gottfried, 1996). What about when events appear to occur probabilistically? Here toddlers (M=20.1months) saw arbitrary causal relationships (Cause A generated Effect A; Cause B generated Effect B) in a fixed, alternating order. The relationships were then changed in one of two ways. In the Deterministic condition, the event order changed (Event B preceded Event A); in the Probabilistic condition, the causal relationships changed (Cause A generated Effect B; Cause B generated Effect A). As intended, toddlers looked equally long at both changes (Experiment 1). We then introduced a previously unseen candidate cause. Toddlers looked longer at the appearance of a hand (Experiment 2) and novel agent (Experiment 3) in the Deterministic than the Probabilistic conditions, but looked equally long at novel non-agents (Experiment 4), suggesting that by 2 years of age, toddlers connect probabilistic events with unobserved agents.

Discrete coding of stimulus value, reward expectation, and reward prediction error in the dorsal striatum.

To investigate how the striatum integrates sensory information with reward information for behavioral guidance, we recorded single-unit activity in the dorsal striatum of head-fixed rats participating in a probabilistic Pavlovian conditioning task with auditory conditioned stimuli (CSs) in which reward probability was fixed for each CS but parametrically varied across CSs. We found that the activity of many neurons was linearly correlated with the reward probability indicated by the CSs. The recorded neurons could be classified according to their firing patterns into functional subtypes coding reward probability in different forms such as stimulus value, reward expectation, and reward prediction error. These results suggest that several functional subgroups of dorsal striatal neurons represent different kinds of information formed through extensive prior exposure to CS-reward contingencies.

Early adversity disrupts the adult use of aversive prediction errors to reduce fear in uncertainty

Early life adversity increases anxiety in adult rodents and primates, and increases the risk for developing post-traumatic disorder (PTSD) in humans. We hypothesized that early adversity impairs the use of learning signals -negative, aversive prediction errors–to reduce fear in uncertainty. To test this hypothesis, we gave adolescent rats a battery of adverse experiences then assessed adult performance in probabilistic Pavlovian fear conditioning and fear extinction. Rats were confronted with three cues associated with different probabilities of foot shock: one cue never predicted shock, another cue predicted shock with uncertainty, and a final cue always predicted shock. Control rats initially acquired fear to all cues, but rapidly reduced fear to the non-predictive and uncertain cues. Early adversity rats were slower to reduce fear to the non-predictive cue and never fully reduced fear to the uncertain cue. In extinction, all cues were presented in the absence of shock. Fear to the uncertain cue in discrimination, but not early adversity itself, predicted the reduction of fear in extinction. These results demonstrate early adversity impairs the use of negative aversive prediction errors to reduce fear, especially in situations of uncertainty.

Probabilistic Seismic Assessment of RC Bridges: Part II — Nonlinear Demand Prediction

One of the most determinant components of any seismic safety assessment procedure is the estimate of the nonlinear seismic demand, particularly if such procedure is probabilistic rather than deterministic. Indeed, the prediction of the seismic demand of RC structures is dictated by a number of variables, related to the seismic action or to the geometrical and material properties, with different relevancy and uncertainty levels. From a macro-viewpoint one can distinguish the different approaches for nonlinear demand prediction in two major groups: nonlinear static and dynamic. Whereas the latter is widely recognised as the most accurate approach, the former, particularly by means of nonlinear static procedures (NSPs), represents a valid alternative tool for performance-based seismic assessment of structures, quite accepted among the scientific community worldwide. Significant effort has therefore been made, over the past few years, to improve those simplified methods and several different proposals in terms of application methodology have come up. Simultaneously, validation studies have thoroughly been carried out, even though focusing mainly on regular, building structures, rather than typically irregular bridges, and have focused the validation through the direct comparison of response prediction. The capability of such procedures within a probabilistic framework that yields the collapse probability of randomly sampled RC viaducts is herein investigated. A commonly employed nonlinear static procedure (N2) is further validated against nonlinear dynamic analysis using two distinct probabilistic procedures, described and tested in a companion paper, which account differently for the uncertainty of the concerned variables (geometry, material properties, earthquake records, intensity level). A case study of seven bridge configurations, with different (ir)regularity levels, is considered together with a relatively large set of real earthquake records and random simulation is carried out using the Latin Hypercube Sampling scheme. The conclusions have further probed the suitability of nonlinear static analysis in estimating seismic demand by leading, under probabilistic conditions, to slightly conservative probabilities of collapse of RC bridges with respect to nonlinear dynamic analysis.

On the global stability of an iterative scheme in a probabilistic Menger space

This paper studies the convergence properties of an iterative process which involves sequences of convergent self-mappings in probabilistic Menger spaces which are used to generate the sequences of interest. The convergent self-mappings under consideration satisfy conditions of either uniform or point-wise convergence, in a probabilistic sense, to a self-mapping on the same abstract space of the considered probabilistic metric space. Furthermore, the self-mappings of the considered sequence satisfy a probabilistic ϕ-contractive condition which is based on the use of a control ϕ-function. Some illustrative examples are also discussed.