Probabilistic Formalism Research Articles

Artificial Broadcasts as Galactic Populations. I. A Point Process Formalism for Extraterrestrial Intelligences and Their Broadcasts

Artificial broadcasts from extraterrestrial intelligences are a hypothetical class of celestial phenomena. Unlike known astrophysical objects, the societies that generate them may be able to replicate on galactic scales through interstellar travel. Different galaxies could thus have drastically different populations, with variations in abundance of many orders of magnitude. I present a probabilistic formalism to treat this shared history, in which societies and their broadcasts are described by distributions over basic properties like lifespan and energy released. The framework contains a hierarchy of objects related by a tree structure. Discrete societies, the sources of broadcasts, are organized into potentially interstellar metasocieties. The population of each type of object is represented by a random point process in an abstract parameter hyperspace, a haystack. When a selection like an observation draws a sample, the point process is thinned. Given assumptions of interchangeability and independence, observables are modeled with compound Poisson random variables. I present an example of how selection bias can favor sampling longer-lived objects. I rederive the Drake equation for societies in the limit of no expansion. When interstellar replication is present, however, the mean number of detected broadcasts can depend quadratically on stellar mass, suggesting a search strategy favoring large galaxies.

Modeling and Simulation of Shared Electric Automated and Connected Mobility Systems with Autonomous Repositioning: Performance Evaluation and Deployment

The boom seen in artificial intelligence in recent years has led to a revolution in the automotive industry. Numerous automakers around the world, such as Tesla, Toyota, Honda, and BMW, have achieved giant strides in the development of e-autonomous vehicles. Consequently, shared electric automated vehicle mobility (SEAVM) systems, which are a crucial part of future innovative transportation solutions, have attracted significant attention from the research community, particularly from a design perspective. However, the flexibility of shared automated mobility systems may lead to a self-operating technology issue (unequal distribution of vehicles), since users in these systems can pick up and drop off electric vehicles wherever they like. With this in mind, this paper addressed the issues of autonomous repositioning and the assignment of shared autonomous electric vehicle systems to balance a system’s network and fulfill its demand. Modeling, analysis and assessment of the system’s performance were carried out using stochastic Petri nets formalism, which included determining the average time areas were empty/congested and the number of unserved consumers, and estimating the redistribution service launch moment. Furthermore, many simulation scenarios were analyzed, including repositioning and without repositioning scenarios, in order to evaluate the efficiency of the model and to show the potential of using Petri nets as a probabilistic formalism approach for the modeling of e-automated mobility systems.

Effect of Fiber-matrix Interface Decohesion on the Behavior of Thermoset and Thermoplastic Composites Reinforced with Natural Fibers: A Comparative Study

In this article, a comparative study was carried out on two types of thermosetting and thermoplastic matrices to study the effect of the fiber-matrix interface damage on the behavior of thermosetting and thermoplastic composites reinforced by the same natural alfa and wood fibers. The genetic modeling was based on the probabilistic formalism of Weibull. The results have been compared with those obtained by the nonlinear acoustic technique, the two results found to coincide perfectly. The numerical simulation also shows a good concordance with the real behavior of the materials studied, and shows that thermosetting composites are the most resistant to applied thermal stress by 21% compared to thermoplastic composites. Statistical analysis demonstrates that the correlation coefficient values found are very close to 1 (0.964 and 0.973), these values are very satisfactory, and confirm that the results obtained by the genetic model and the nonlinear acoustic technique are in very good agreement with the statistical analysis data. The experimental work presented by Antoine Le Duigou et al. and the work of Bodros et al. have shown that the use of natural fibers greatly improves the mechanical properties of composite materials.

A probabilistic approach for determining Monte Carlo beam source parameters: I. Modeling of a CyberKnife M6 unit

Objective. During Monte Carlo modeling of external radiotherapy beams, models must be adjusted to reproduce the experimental measurements of the linear accelerator being considered. The aim of this work is to propose a new method for the determination of the energy and spot size of the electron beam incident on the target of a linear accelerator using a maximum likelihood estimation. Approach. For that purpose, the method introduced by Francescon et al (2008 Med. Phys. 35 504–13) is expanded upon in this work. Simulated tissue-phantom ratios and uncorrected output factors using a set of different detector models are compared to experimental measurements. A probabilistic formalism is developed and a complete uncertainty budget, which includes a detailed simulation of positioning errors, is evaluated. The method is applied to a CyberKnife M6 unit using four detectors (PTW 60012, PTW 60019, Exradin A1SL and IBA CC04), with simulations being performed using the EGSnrc suite. Main results. The likelihood distributions of the electron beam energy and spot size are evaluated, leading to and . Using these results and a 95% confidence region, simulations reproduce measurements in 13 out of the 14 considered setups. Significance. The proposed method allows an accurate beam parameter optimization and uncertainty evaluation during the Monte Carlo modeling of a radiotherapy unit.

Managing the Risk Is Not Enough

Standard portfolio construction models are based on the implicit assumption that all information relevant to making investment choices is probabilizable. However, both empirical behaviors of market participants and the increased success of approaches like risk parity underly an implicit rejection of this paradigm. This rejection is caused by uncertainty about metrics from a probabilistic formalization, induced by the fundamental nature of financial dynamics. It is concretely expressed through research into a balanced distribution of sources of risk rather than the minimization of a risk measure, and by the mobilization of knowledge that escapes pure probabilistic logic. The present paper aims to extract the substance of these ways of considering uncertainty in order to reconcile the taking into account of the uncertainty about metrics from a probabilistic formalization, while preserving the advantages of the risk/return approach which is the basis of the modern portfolio theory. The thrust of the approach taken is that reducing uncertainty involves limiting the importance of financial bets as a function of the uncertainty associated with the premises on which they are based. In order to attribute a value to the uncertainty of the premises, the angle of analysis adopted here is the stability of risk factor relations on which the relevance of probabilistic metrics depends. Consequently, the first part focuses on the risk decomposition of a portfolio with respect to risk factors and analyze the impact of estimation errors of inputs related to risk factors on the risk measure. Based on this analysis, the second part of the paper defines a framework for the construction of a coherent uncertainty measure of a portfolio. The third part presents a model of portfolio construction including a coherent uncertainty measure of a portfolio: the Uncertainty-Risk-Return optimization. A general method to solve this non-convex program is then exposed. Finally, the properties of this new method of portfolio optimization incorporating the management of uncertainty are analyzed through concrete examples.

Quantum Theory of EEG with Application to the Single-Trial ERP Analysis

The probabilistic formalism of quantum mechanics is used to quantitatively link the electroencephalogram (EEG) with the underlying microscale activity of cortical neurons. Previous approaches applied methods of classic physics to reconstruct the EEG in terms of explicit physical models of cortical neurons and the volume conductor. However, the multiplicity of cellular processes with extremely intricate mixtures of deterministic and random factors prevented the creation of consistent biophysical parameter sets. To avoid the uncertainty surrounding the physical attributes of the neuronal ensembles, we undertake here a radical departure from deterministic equations of classical physics to the probabilistic reasoning of quantum mechanics. The crucial step is the relocation of the elementary bioelectric sources from cellular to molecular level. Using a novel method of time-frequency analysis with adaptive segmentation for digital processing of empirical EEG and single trial event related potentials (ERPs), we found universal “building blocks” of these cortical processes both in the frequency and time domains. This result is qualified as a phenomenon known in statistical physics and quantum mechanics as universality. Therationale is that despite dramatic differences in the cellular machineries, the statistical factors governed by the central limit theorem produce the EEG waveform as a statistical aggregate of the synchronized activities of large ensembles of closely located cortical neurons. Using these theoretical and empirical findings the probabilistic laws that control the microscale machinery generating the EEG are deduced.

The Manifold Of Variations: hazard assessment of short-term impactors

When an asteroid has a few observations over a short time span the information contained in the observational arc could be so little that a full orbit determination may be not possible. One of the methods developed in recent years to overcome this problem is based on the systematic ranging and combined with the Admissible Region theory to constrain the poorly-determined topocentric range and range-rate. The result is a set of orbits compatible with the observations, the Manifold Of Variations, a two-dimensional compact manifold parametrised over the Admissible Region. Such a set of orbits represents the asteroid confidence region and is used for short-term hazard predictions. In this paper we present the Manifold Of Variations method and make a detailed analysis of the related probabilistic formalism.

Understanding the operation of general composite detector for gamma-ray spectroscopy

We have presented a probabilistic formalism for predicting the response of the series and parallel combination of gamma-ray detectors arranged in the form of a matrix. Assuming isotropic scattering of incident gamma-rays and considering up to four detector hit events, we have obtained expressions for the addback factor and the peak-to-total ratio (in the addback mode) in terms of only one probability. Using the experimental data of the HHS spectrometer, we have predicted the addback factor for four composite detectors. Predicted values of addback factor and fold distribution show a reasonable agreement with the experimental ones for the clover detector.

Understanding the operation of gamma-ray detectors arranged in the shape of a pyramid

Motivated by the various shapes and configurations of detectors used in modern gamma arrays, for the first time in literature, we have investigated the operation of a composite detector comprising of elements arranged in the shape of a pyramid. A probabilistic formalism is introduced to predict the response of two, three and four level pyramid shaped composite detector in terms of only one probability amplitude. Considering up to four detector hit events, expressions for the addback factor and the peak-to-total ratio have been obtained. The general trend of predicted values of the addback factor, the peak-to-total ratio and the fold distribution match with the available experimental data for other composite detectors. Our novel phenomenological approach could provide a guidance in designing new detectors for gamma-ray spectroscopy.

Fokker-Planck representations of non-Markov Langevin equations: application to delayed systems.

Noise and time delays, or history-dependent processes, play an integral part in many natural and man-made systems. The resulting interplay between random fluctuations and time non-locality are essential features of the emerging complex dynamics in non-Markov systems. While stochastic differential equations in the form of Langevin equations with additive noise for such systems exist, the corresponding probabilistic formalism is yet to be developed. Here we introduce such a framework via an infinite hierarchy of coupled Fokker-Planck equations for the n-time probability distribution. When the non-Markov Langevin equation is linear, we show how the hierarchy can be truncated at n = 2 by converting the time non-local Langevin equation to a time-local one with additive coloured noise. We compare the resulting Fokker-Planck equations to an earlier version, solve them analytically and analyse the temporal features of the probability distributions that would allow to distinguish between Markov and non-Markov features. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Analytical and Numerical Investigations of Probabilistic Monochromatic Problem

A probabilistic formalism, relying on Bayes’ theorem and linear Gaussian inversion, is adapted, so that a monochromatic problem can be investigated. The formalism enables an objective test in probabilistic terms of the quantities and model concepts involved in the problem at hand. With this formalism, an amplitude (linear parameter), a frequency (non-linear parameter) and a hyperparameter of the Gaussian amplitude prior are inferred jointly given simulated data sets with Gaussian noise contributions. For the amplitude, an analytical normal posterior follows which is conditional on the frequency and the hyperparameter. The remaining posterior estimates the frequency with an uncertainty of MHz, while the convolution of a standard approach would achieve an uncertainty of some GHz. This improvement in the estimation is investigated analytically and numerically, revealing for instance the positive effect of a high signal-to-noise ratio and/or a large number of data points. As a fixed choice of the hyperparameter imposes certain results on the amplitude and frequency, this parameter is estimated and, thus, tested for plausibility as well. From abstract point of view, the model posterior is investigated as well.

Distributed diagnosis based on distributed probability propagation nets

This paper addresses the problem of modelling uncertainty in the distributed context. It is situated in the field of diagnosis; more precisely, model-based diagnosis of distributed systems. A special focus is given to modelling uncertainty and probabilistic reasoning. Thus, this work is based on a probabilistic modelling formalism called: 'probability propagation nets' (PPNs), which are designed for centralised systems. Hence, an extension of this model is proposed to suit the distributed context. Distributed probability propagation nets (DPPNs), the proposed extension, were conceived to consider the distributed systems' particularities. So, the set we consider is a set of interacting subsystems, each of which is modelled by a DPPN. The interaction among the subsystems is modelled through the firing of common transitions belonging to more than one subsystem. All of that is logically supported by means of probabilistic Horn abductions (PHAs). Furthermore, the diagnostic process is done by exploiting transition-invariants, a diagnostic technique developed for Petri nets. The proposed extension is illustrated through a real life example.

Hierarchical Bayesian approach for estimating physical properties in nearby galaxies: Age Maps (Paper II)

One of the fundamental goals of modern astrophysics is to estimate the physical parameters of galaxies. We present a hierarchical Bayesian model to compute age maps from images in the \Ha\ line (taken with Taurus Tunable Filter, TTF), ultraviolet band (GALEX far UV, FUV), and infrared bands (Spitzer 24, 70, and 160 $\mu$m). We present the burst ages for young stellar populations in a sample of nearby and nearly face-on galaxies. The \Ha\ to FUV flux ratio is a good relative indicator of the very recent star formation history (SFH). As a nascent star-forming region evolves, the \Ha\ line emission declines earlier than the UV continuum, leading to a decrease in the \Ha/FUV ratio. Using star-forming galaxy models, sampled with a probabilistic formalism, and allowing for a variable fraction of ionizing photons in the clusters, we obtain the corresponding theoretical ratio \Ha/FUV to compare with our observed flux ratios, and thus to estimate the ages of the observed regions. We take into account the mean uncertainties and the interrelationships between parameters when computing \Ha/FUV. We propose a Bayesian hierarchical model where a joint probability distribution is defined to determine the parameters (age, metallicity, IMF) from the observed data (the observed flux ratios \Ha/FUV). The joint distribution of the parameters is described through independent and identically distributed (i.i.d.) random variables generated through MCMC (Markov Chain Monte Carlo) techniques.

O Argumento do Milagre comete a Falácia da Taxa-base? Apresentação, Estado da Arte e Questões de Formalização

Objetivamos discutir a crítica, avançada por Colin Howson em Hume's problem, segundo a qual o argumento do milagre (doravante, AM) comete a falácia da taxa-base. Por falácia da taxa-base, entende-se a negligência do valor da probabilidade prévia de determinada hipótese ou teoria T, P(T). Por sua vez, em uma de suas versões, AM assere que apenas assumindo que uma teoria científica madura T é aproximadamente verdadeira não faz de seu sucesso preditivo um milagre. Formalizado probabilisticamente, Howson argumenta que a conclusão de AM, a probabilidade de que a teoria T seja aproximadamente verdadeira é grande, apenas se segue se assumirmos para T um valor não-negligenciável. Tal crítica de Howson despertou duas categorias de reação na literatura especializada: supondo que AM comete a falácia da taxa base, alguns autores propuseram abandonar AM enquanto um argumento para a tese epistemológica do realismo científico, ao passo que outros defenderam que apenas uma versão de AM comete a falácia da taxa-base; defendendo que AM não comete a falácia da taxa base, certos autores alegaram alguns problemas na formalização probabilística de AM, enquanto outros buscaram refinar tal formalização de modo que a nova evite a falácia em questão. Tendo apresentado esse estado da arte, investigaremos se a formalização probabilística do argumento do milagre é razoável. Discutiremos se ela acomoda a natureza de inferência à melhor explicação pressuposta no AM. Por fim, indicaremos, brevemente, algumas dificuldades para a crítica de Howson ao assumir-se que AM instancia, na verdade, uma abdução Peirceana.

Quantum theory of mass potentials.

Probabilistic formalism of quantum mechanics is used to quantitatively link the global scale mass potential with the underlying electrical activity of excitable cells. Previous approaches implemented methods of classical physics to reconstruct the mass potential in terms of explicit physical models of participating cells and the volume conductor. However, the multiplicity of cellular processes with extremely intricate mixtures of deterministic and random factors prevents the creation of consistent biophysical parameter sets. To avoid the uncertainty inherent in physical attributes of cell ensembles, we undertake here a radical departure from deterministic equations of classical physics, instead applying the probabilistic reasoning of quantum mechanics. Crucial steps include: (1) the relocation of the elementary bioelectric sources from a cellular to a molecular level; (2) the creation of microscale particle models in terms of a non-homogenous birth-and-death process. To link the microscale processes with macroscale potentials, time-frequency analysis was applied for estimation of the empirical characteristic functions for component waveforms of electroencephalogram (EEG), eye-blink electromyogram (EMG), and electrocardiogram (ECG). We describe universal models for the amplitude spectra and phase functions of functional components of mass potentials. The corresponding time domain relationships disclose the dynamics of mass potential components as limit distribution functions produced by specific microscale transients. The probabilistic laws governing the microscale machinery, founded on an empirical basis, are presented. Computer simulations of particle populations with time dependent transition probabilities reveal that hidden deterministic chaos underlies development of the components of mass potentials. We label this kind of behaviour “transient deterministic chaos”.

A Probabilistic Formalization of the Appraisal for the OCC Event-Based Emotions

This article presents a logical formalization of the emotional appraisal theory, i.e., it formalizes the cognitive process of evaluation that elicits an emotion. This formalization is psychologically grounded on the OCC cognitive model of emotions. More specifically, we are interested in event-based emotions, i.e., emotions that are elicited by the evaluation of the consequences of an event that either happened or will happen. The formal modelling presented here is based on the AfPL Probabilistic Logic, a BDI-like probabilistic modal logic, which allows our model to verify whether the variables that determine the elicitation of emotions achieved the necessary threshold or not. The proposed logical formalization aims at addressing how the emotions are elicited by the agent cognitive mental states (desires, beliefs and intentions), and how to represent the intensity of the emotions. These are important initial points in the investigation of the dynamic interaction among emotions and other mental states.

Predictive Algorithm for Detection of Microcracks from Macroscale Observables

A probabilistic multiscale based computational scheme is developed to predict locations of microcracks and to estimate the associated macroscopic constitutive material properties for structural systems. The proposed scheme only requires a single realization of the macroscale response field (e.g., strain field, strain energy density field) that is often typically available in practice. Here, the macroscale is associated with structural systems of size of the order of 10--100 $m$, while microcracks are used to refer to micron-scale cracks of size 10--100 $\mu m$ (depending on materials) that have the potential to cause catastrophic failures when they coalesce and form larger cracks. The analysis of such microcracks, before a macrocrack visibly appears (say, at the size of a few $cms$), is beyond the scope of the classical fracture mechanics. The present work addresses this issue in a certain sense by incorporating the effects of microcracks into macroscopic constitutive material properties within a probabilistic formalism which is based on multiscale mechanics, random matrix theory, and the principles of minimum complementary energy and minimum potential energy. Distinct differences are observed in the probabilistic features (not deterministic features) of macrolevel response variables depending on the presence or absence of microcracks. Relying on this distinctive probabilistic features and using macroscale experimental measurements as available in practice, an optimization scheme, which is similar to cyclic seesaw optimization, is proposed (1) to identify the spatial locations of microcracks in macroscopic structural systems and (2) to estimate the weakened (due to the presence of microcracks) macroscopic material properties. In particular, the spatial field of weakened macroscopic constitutive elasticity matrix is estimated. The positive-definite feature of the constitutive elasticity matrix is exploited in this proposed optimization-based predictive analytics to achieve a better convergence rate and to improve the accuracy. This work will be useful in estimating remaining useful life of the structural systems.

The probabilistic no miracles argument.

This paper develops a probabilistic reconstruction of the No Miracles Argument (NMA) in the debate between scientific realists and anti-realists. The goal of the paper is to clarify and to sharpen the NMA by means of a probabilistic formalization. In particular, I demonstrate that the persuasive force of the NMA depends on the particular disciplinary context where it is applied, and the stability of theories in that discipline. Assessments and critiques of “the” NMA, without reference to a particular context, are misleading and should be relinquished. This result has repercussions for recent anti-realist arguments, such as the claim that the NMA commits the base rate fallacy (Howson (2000), Magnus and Callender (Philosophy of Science, 71:320–338, 2004)). It also helps to explain the persistent disagreement between realists and anti-realists.

QBRIX: a quantile-based approach to retinex.

In this paper, we introduce a novel probabilistic version of retinex. It is based on a probabilistic formalization of the random spray retinex sampling and contributes to the investigation of the spatial properties of the model. Various versions available of the retinex algorithm are characterized by different procedures for exploring the image content (so as to obtain, for each pixel, a reference white value), then used to rescale the pixel lightness. Here we propose an alternative procedure, which computes the reference white value from the percentile values of the pixel population. We formalize two versions of the algorithm: one with global and one with local behavior, characterized by different computational costs.

Chance-Constrained Probabilistic Simple Temporal Problems

Scheduling under uncertainty is essential to many autonomous systems and logistics tasks. Probabilistic methods for solving temporal problems exist which quantify and attempt to minimize the probability of schedule failure. These methods are overly conservative, resulting in a loss in schedule utility. Chance constrained formalism address over-conservatism by imposing bounds on risk, while maximizing utility subject to these risk bounds. In this paper we present the probabilistic Simple Temporal Network (pSTN), a probabilistic formalism for representing temporal problems with bounded risk and a utility over event timing. We introduce a constrained optimisation algorithm for pSTNs that achieves compactness and efficiency through a problem encoding in terms of a parameterised STNU and its reformulation as a parameterised STN. We demonstrate through a car sharing application that our chance-constrained approach runs in the same time as the previous probabilistic approach, yields solutions with utility improvements of at least 5% over previous arts, while guaranteeing operation within the specified risk bound.