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International audience; The extraction of cooccurrences between two events, A and B, is a central learning mechanism shared by all species capable of associative learning. Formally, the cooccurrence of events A and B appearing in a sequence is measured by the transitional probability (TP) between these events, and it corresponds to the probability of the second stimulus given the first (i.e., p(B|A)). In the present study, nonhuman primates (Guinea baboons, Papio papio) were exposed to a serial version of the XOR (i.e., exclusive-OR), in which they had to process sequences of three stimuli: A, B, and C. In this manipulation, first-order TPs (i.e., AB and BC) were uninformative due to their transitional probabilities being equal to .5 (i.e., p(B|A) = p(C|B) = .5), while secondorder TPs were fully predictive of the upcoming stimulus (i.e., p(C|AB) = 1). In Experiment 1, we found that baboons were able to learn second-order TPs, while no learning occurred on first-order TPs. In Experiment 2, this pattern of results was replicated, and a final test ruled out an alternative interpretation in terms of proximity to the reward. These results indicate that a non-human primate species can learn a nonlinearly separable problem such as the XOR. They also provide fine-grained empirical data to test models of statistical learning on the interaction between the learning of different orders of TPs. Recent bioinspired models of associative learning are also introduced as promising alternatives to the modeling of statistical learning mechanisms.

Decision makers are often faced with making single hard decisions, without having any knowledge of the amount of uncertainties contained in them, and taking the risk of making damaging, if not dramatic, mistakes. In such situations, where the uncertainty is higher due to imperfect information, it may be useful to provide set-valued but more reliable decisions. This works thus focuses on making distributionally robust, skeptical inferences (or decisions) in supervised classification problems using imprecise probabilities. By distributionally robust, we mean that we consider a set of possible probability distributions, i.e. imprecise probabilities, and by skeptical we understand that we consider as valid only those inferences that are true for every distribution within this set. Specifically, we focus on extending the Gaussian discriminant analysis and multilabel classification approaches to the imprecise probabilistic setting. Regarding to Gaussian discriminant analysis, we extend it by proposing a new imprecise classifier, considering the imprecision as part of its basic axioms, based on robust Bayesian analysis and near-ignorance priors. By including an imprecise component in the model, our proposal highlights those hard instances on which the precise model makes mistakes in order to provide cautious decisions in the form of set-valued class, instead. Regarding to multi-label classification, we first focus on reducing the time complexity of making a cautious decision over its output space of exponential size by providing theoretical justifications and efficient algorithms applied to the Hamming loss. Relaxing the assumption of independence on labels, we obtain partial decisions, i.e. not classifying at all over some labels, which generalize the binary relevance approach by using imprecise marginal distributions. Secondly, we extend the classifierchains approach by proposing two different strategies to handle imprecise probabilityestimates, and a new dynamic, context-dependent label ordering which dynamically selects the labels with low uncertainty as the chain moves forwards.; Les décideurs sont souvent confrontés au défi de prendre des décisions précises, sans avoir aucune connaissance de la quantité d’incertitudes que celles-ci peuvent contenir, et en prenant le risque de commettre des erreurs dommageables, voire dramatiques. Dans de telles situations, où l’incertitude est plus élevée due à des informations imparfaites, il peut être plutôt utile de fournir des décisions prudentes, sous la forme d’un ensemble de solutions possibles, plus fiables. Ce travail se concentre donc sur la prise de décisions (ou inférences) sceptiques (ou prudentes) et robustes dans des problèmes de classification supervisée en utilisant des probabilités imprécises. Par robuste, nous voulons dire que nous considérons un ensemble des distributions de probabilités possibles, c'est-à-dire des probabilités imprécises, et par sceptique, nous voulons dire que nous ne considérons comme valides que les décisions étant vraies pour chaque distribution dans cet ensemble. Plus précisément, nous nous concentrons sur l'extension d’approches basée sur l'analyse discriminante gaussienne et la classification multi-étiquettes au cadre probabiliste imprécis. Concernant l'analyse discriminante gaussienne, nous proposons un nouveau classifieur imprécis qui généralise celui-ci et qui est basé sur l’inférence bayésienne robuste et un ensemble des lois de probabilités a priori. L’inclusion d’un composant imprécis dans notre approche met en évidence les décisions difficiles à prendre (c.-à-d. les observations difficiles à classifier), sur lesquelles les modèles précis font des erreurs, et permet de fournir à la place des décisions prudentes. Concernant la classification multi-étiquettes, nous nous concentrons d’abord sur la réduction de la complexité calculatoire de prendre une décision prudente sur son espace de sortie combinatoire. Pour cela, nous fournissons des justifications théoriques et des algorithmes efficaces appliqués à la fonction de coût Hamming. En outre, en relâchant l’hypothèse d’indépendance sur les étiquettes, on obtient de décisions partielles (c.-à-d. ne pas décider sur certaines étiquettes), qui généralisent l’approche classique précise (nommé « binary relevance ») en utilisant des distributions marginales imprécises. D’autre part, nous proposons aussi d’étendre le chaînage multi-étiquette classique au cadre probabiliste imprécis en fournissant deux stratégies différentes pour gérer les estimations imprécises sous la forme d’intervalles, et une nouvelle procédure d’ordre des étiquettes qui dépend des incertitudes associées aux étiquettes sélectionnées au fur et à mesure que la chaîne avance.

Here, we present results on the intrinsic collision probabilities, $ P_I$, and range of collision speeds, $V_I$, as a function of the heliocentric distance, $r$, in the trans-Neptunian region. The collision speed is one of the parameters, that serves as a proxy to a collisional outcome e.g., complete disruption and scattering of fragments, or formation of crater, where both processes are directly related to the impact energy. We utilize an improved and de-biased model of the trans-Neptunian object (TNO) region from the "Outer Solar System Origins Survey" (OSSOS). It provides a well-defined orbital distribution model of TNOs, based on multiple opposition observations of more than 1000 bodies. In this work we compute collisional probabilities for the OSSOS models of the main classical, resonant, detached+outer and scattering TNO populations. The intrinsic collision probabilities and collision speeds are computed using the ��pik's approach, as revised and modified by Wetherill for non-circular and inclined orbits. The calculations are carried out for each of the dynamical TNO groups, allowing for inter-population collisions as well as collisions within each TNO population, resulting in 28 combinations in total. Our results indicate that collisions in the trans-Neptunian region are possible over a wide range in ($r, V_I$) phase space. Although collisions are calculated to happen within $r\sim 20 - 200$~AU and $V_I \sim 0.1$~km/s to as high as $V_I\sim9$~km/s, most of the collisions are likely to happen at low relative velocities $V_I, 13 pages, 6 figures

Fission and gamma-emission probabilities induced by transfer or inelastic scattering reactions with light projectile nuclei are very valuable quantities for constraining the models that describe the de-excitation of heavy nuclei. We have developed an experimental set-up that allows us to simultaneously measure fission and gamma-emission probabilities. The measurement of the gamma-emission probability at excitation energies where the fission channel is open is challenging due to the intense background of gamma rays emitted by the fission fragments. We discuss the procedure to subtract such a background and the constraints that this subtraction and other experimental conditions put on the set up. We show that our set-up complies with these constraints., 18 pages, 10 figures

International audience; Expert judgment plays an essential role in assessing the safety of levees,since these very long structures are generally old, few data are availablefor them, and they are subject to complex failure mechanisms. Expertjudgement is required to assess the failure probabilities of levees when car-rying out risk analysis studies. However, expert judgement is subject tobiases that are highly likely to impair the quality of the probabilistic assess-ments obtained. This article presents a method for reducing biases inexpert opinion, illustrated by its application to the case of an existinglevee. Initially, the method comprises the calibration of the opinions of apanel of six experts based on the results of a quantitative analysis appliedto 30 levee cross-sections for which numerical calculations were performed.It then proposes a procedure to debias expert assessments using bias cor-rection coefficients. Regarding its application, the assessments made by theexperts were debiased for 30 calibration variables. The correction coeffi-cients obtained were then applied for the assessment of 10 variables ofinterest. The results show a significant reduction of biases, associated witha readjustment of the uncertainty intervals given by the experts.

International audience; Since speech is a continuous stream with no systematic boundaries between words, how do pre-verbal infants manage to discover words? A proposed solution is that they might use the transitional probability between adjacent syllables, which drops at word boundaries. Here, we tested the limits of this mechanism by increasing the size of the word-unit to four syllables, and its automaticity by testing asleep neonates. Using markers of statistical learning in neonates' EEG, compared to adult behavioral performances in the same task, we confirmed that statistical learning is automatic enough to be efficient even in sleeping neonates. We also revealed that: (1) Successfully tracking transition probabilities (TP) in a sequence is not sufficient to segment it. (2) Prosodic cues, as subtle as subliminal pauses, enable to recover words segmenting capacities. (3) Adults' and neonates' capacities to segment streams seem remarkably similar despite the difference of maturation and expertise. Finally, we observed that learning increased the overall similarity of neural responses across infants during exposure to the stream, providing a novel neural marker to monitor learning. Thus, from birth, infants are equipped with adult-like tools, allowing them to extract small coherent word-like units from auditory streams, based on the combination of statistical analyses and auditory parsing cues. RESEARCH HIGHLIGHTS: Successfully tracking transitional probabilities in a sequence is not always sufficient to segment it. Word segmentation solely based on transitional probability is limited to bi- or tri-syllabic elements. Prosodic cues, as subtle as subliminal pauses, enable to recover chunking capacities in sleeping neonates and awake adults for quadriplets.

The distinction between two origins of uncertainty has become standard practice in risk analysis, namely random uncertainty (representing variability) and epistemic uncertainty (related to imperfect knowledge). While the former can be adequately represented using classical probabilities, there is no simple, single answer for the latter. New theories of uncertainty based on "imprecise probabilities" have been developed in recent years to go beyond the systematic use of a single probabilistic law. In this tutorial we analyse the advantages and disadvantages for the assessment of natural hazards (e.g. earthquakes, marine floods, landslides, etc.) with a comparison to the traditional probabilistic approach. We discuss the problems that have been solved and the interesting open questions and challenges that remain, in particular how to appropriately support decision making under uncertainty, how to provide guidance for future actions and how to deal with multiple forms of uncertainty along the assessment chain.

Symbolic protocol verification generally abstracts probabilities away, considering computations that succeed only with negligible probability, such as guessing random numbers or breaking an encryption scheme, as impossible. This abstraction, sometimes referred to as the perfect cryptography assumption, has shown very useful as it simplifies automation of the analysis. However, probabilities may also appear in the control flow where they are generally not negligible. In this paper we consider a framework for symbolic protocol analysis with a probabilistic choice operator: the probabilistic applied pi calculus. We define and explore the relationships between several behavioral equivalences. In particular we show the need to require randomized schedulers-indeed we exhibit a counterexample to one of the main results in a previous work that relied on non-randomized ones. As in other frameworks that mix both non-deterministic and probabilistic choices, schedulers may sometimes be unrealistically powerful. We therefore consider two subclasses of processes that avoid this problem. When considering purely non-deterministic protocols, as is done in classical symbolic verification, we show that a probabilistic adversary has-maybe surprisingly-a strictly superior distinguishing power for may testing, which, when the number of sessions is bounded, we show to coincide with purely possibilistic similarity. Finally, we consider fully probabilistic protocols and show that trace equivalence corresponds to a notion of may testing with purely probabilistic attackers. We also briefly discuss complexity and automation for these subclasses when the number of sessions is bounded.

It is well known that multiple representations can enhance students' conceptual understanding, but only if (potentially superficial) translation activities are deepened by making the connections explicit. But what exactly does that mean? In our qualitative analysis of a design experiment with two twelfth graders from vocational school on conditional probabilities, we show that explicating connections between multiple representations requires processes of unfolding a highly compacted concept into its concept elements (in our case, part, whole and part-whole-relationship) and articulating them in a decontextualized meaning-related language. By this, we intend to contribute to the research identifying conditions of success for working with multiple representations also for high school students.

This paper builds upon the work of Professor Marley, who, since the beginning of his long research career, has proposed rigorous axiomatics in the area of probabilistic choice models. Our study concentrates on models that can be applied to best and worst choice scaling experiments. We focus on those among these models that are based on strong assumptions about the underlying ranking of the alternatives with which the individual is assumed to be endowed when making the choice. Taking advantage of an inclusion-exclusion identity that we showed a few years ago, we propose a variety of best-worst choice probability models that could be implemented in software packages that are flourishing in this field.

International audience; Neutron transfer reaction measurements, relevant to the neutrinoless double β decay candidate Sn124 and its daughter Te124, have been performed. Precise measurements of both neutron addition [(d,p),(He4,He3)] and removal [(p,d),(He3,He4)] cross sections have been used to determine the occupation of valence orbitals pertinent to neutrinoless double β decay in these two nuclei. This information could be used to constrain calculations of the nuclear matrix element for the neutrinoless double β decay of Sn124. The change in the ground-state neutron vacancies in proceeding from Sn124 to Te124 is mainly found in the d3/2,5/2 and h11/2 orbitals. The occupancies of states near the Fermi level are in reasonable agreement with shell model calculations.

Proceedings of the 21st International Conference on Radionuclide Metrology and its Applications (ICRM), 15-19 May 2017, Buenos Aires, Argentina. Organizer: Argentinian Comis Nacl Energia Atomica; International audience; The ratios of the electron capture probabilities P-K, P-L and P-M of Fe-55 have been measured with a metallic magnetic calorimeter, a specific type of cryogenic detector. The Fe-55 source was enclosed in the detector absorber, whose dimensions were chosen such that the detection efficiency for Mn K X-rays was larger than 99.99%. Since all electrons and photons emitted by the source are absorbed in the detector, the detection efficiency is virtually 100% for K, L and M captures. The energy threshold was low enough to allow for clear separation of the M captures (similar to 80 eV) from noise. The capture probability ratios were translated to capture probabilities using the recommended value for the probability of the undetected N captures. The resulting values are in agreement both with the recommended values of P-K, P-L and P-M and with the experimental data of Pengra and coworkers.

International audience; Studies carried out to analyse the risks of levees must include an evaluation of the probabilities of occurrence of different failure mechanisms (overflow, internal erosion, sliding and scouring). The probabilistic quantitative evaluation of these mechanisms remains difficult due to often insufficient input data, the natural variability of the materials, structures of very long length, the availability of mechanical models for certain failure mechanisms, and the random nature of the stresses involved. This makes it necessary to call for expert judgement to evaluate the probabilities of failure. However, expert judgement is generally associated with a qualitative and subjective dimension, and it comprises biases liable to impair the capacities of an expert to elicit their evaluations. This article proposes an approach to processing expert judgement that includes the modalities of Individual expert Elicitation, Calibration, Aggregation, and Debiasing of expert judgement (IeCAD). This IeCAD approach has been developed for river levees in view to correcting biased expert evaluations in the case of evaluating the failure probability of structures.

One remedy to the misuse of p-values transforms them to bounds on Bayes factors. With a prior probability of the null hypothesis, such a bound gives a lower bound on the posterior probability. Unfortunately, knowing a posterior probability is above some number cannot ensure that the null hypothesis is improbable enough to warrant its rejection. For example, if the lower bound is 0.0001, that implies that the posterior probability is at least 0.0001 but does not imply it is lower than 0.05 or even 0.9. A fiducial argument suggests an alternative estimate of the posterior probability that the null hypothesis is true. In the case that the prior probability of the null hypothesis is 50%, the estimated posterior probability is about p (ln p)^2 for low p. In other cases, p in the formula is the p-value calibrated by multiplying it by the prior odds of the null hypothesis. Since the fiducial estimate of the posterior probability is greater than the lower bounds, its use in place of a bound leads to more stringent hypothesis testing. Making that replacement in a rationale for 0.005 as the significance level reduces the level to 0.001.

International audience; We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the classical logistic model Verhulst (Corresp Math Phys 10:113–121, 1838) when the carrying capacity is large. Being discrete and stochastic, however, our population nonetheless goes extinct in finite time. We present results concerning the maximum of the population prior to extinction in the large population limit, from which we obtain establishment probabilities and upper bounds for the process, as well as estimates for the waiting time to establishment and extinction. As a consequence, we show that conditional upon establishment, the stochastic logistic process will with high probability greatly exceed carrying capacity an arbitrary number of times prior to extinction.

International audience; In this paper, we investigate spectrum sensing in cooperative networks. Hence, in order to enhance cooperative sensing, we propose a novel model based on multiple-input multiple-output (MIMO) relaying broadcast channels with direct link and cognitive radio technology. Despite their efficiency in increasing transmission rates and networks capacities, MIMO relays have not yet been exploited for enhancing spectrum sensing. In this case, each relay is equipped with many antennas and the primary signal samples are collected by both MIMO relays and secondary user. Furthermore, we derive new expressions for the false alarm and detection probabilities as well as the detection threshold. Performance analysis are made for both soft and hard cooperative spectrum sensing schemes. Considering Gaussian and impulsive noise environments, simulations show that the proposed model allows a significant detection performance gain compared to non-cooperative cognitive MIMO models.

International audience; The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on an accurate knowledge of the galaxy mean redshift ⟨z⟩. We investigate the possibility of measuring ⟨z⟩ with an accuracy better than 0.002 (1 + z) in ten tomographic bins spanning the redshift interval 0.2 99.8%. The zPDF approach can also be successful if the zPDF is de-biased using a spectroscopic training sample. This approach requires deep imaging data but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the de-biasing method and confirm our finding by applying it to real-world weak-lensing datasets (COSMOS and KiDS+VIKING-450).

International audience; Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment - the basic quantum interference experiment. In this paper, we report on an economics experiment based on a three-slit experiment design, where the slits are menus of alternatives from which one can choose. The test of nonclassicality is based on the Sorkin equality (which was only recently tested in quantum physics). Each alternative is a voucher to buy products in one or more stores. The alternatives are obtained from all disjunctions including one, two or three stores. The participants have to reveal the amount for which they are willing to sell the chosen voucher. Interference terms are computed by comparing the willingness to sell a voucher built as a disjunction of stores and the willingness to sell the vouchers corresponding to the singleton stores. These willingness to sell amounts are used to estimate probabilities and to test both the law of total probabilities and the Born Rule. Results reject neither classical nor quantum probability. We discuss this initial experiment and our results and provide guidelines for future studies.

International audience; In the standard definition of the classical gambler's ruin game, a persistent player enters in a stochastic process with an initial budget b 0 , which is, round after round, either increased by 1 with probability p, or decreased by 1 with probability 1 − p. The player wins the game if the budget reaches a given objective value g, and loses the game if the budget drops to zero (the gambler is ruined). This article introduces the decisional gambling process, where the parameter p is hidden, and the player has the possibility to stop the game at any round keeping earnings. In this case, the best a player can do is to maintain an estimate of p based on the observed outcomes, and use it to decide whether is better to stay or quit the game. The main contribution of this article is to bring the question of finding the optimal stopping time to the gambler's ruin game. Different heuristics are analyzed and evaluated according to their performance in maximizing the gambler's expected final budget.

In this work, we present direct regression analysis for the transition probabilities in the possibly non-Markov progressive illness-death model. The method is based on binomial regression, where the response is the indicator of the occupancy for the given state along time. Randomly weighted score equations that are able to remove the bias due to censoring are introduced. By solving these equations, one can estimate the possibly time-varying regression coefficients, which have an immediate interpretation as covariate effects on the transition probabilities. The performance of the proposed estimator is investigated through simulations. We apply the method to data from the Registry of Systematic Lupus Erythematosus RELESSER, a multicenter registry created by the Spanish Society of Rheumatology. Specifically, we investigate the effect of age at Lupus diagnosis, sex, and ethnicity on the probability of damage and death along time. Copyright © 2017 John WileySons, Ltd.

We consider an obliquely reflected Brownian motion $Z$ with positive drift in a quadrant stopped at time $T$, where $T:=\inf \{ t>0 : Z(t)=(0,0) \}$ is the first hitting time of the origin. Such a process can be defined even in the non-standard case where the reflection matrix is not completely-$\mathcal{S}$. We show that in this case the process has two possible behaviors: either it tends to infinity or it hits the corner (origin) in a finite time. Given an arbitrary starting point $(u,v)$ in the quadrant, we consider the escape (resp. absorption) probabilities $\mathbb{P}_{(u,v)}[T=\infty]$ (resp. $\mathbb{P}_{(u,v)}[T, Comment: 33 pages

International audience

Optimal Control, Differential Games, Mean Field Games, and Pontryagin and Hamilton-Jacobi equations on probabilities The talk will be a short introduction to the emerging topic of Mean Field Games in connection with optimal control and differential games. I will present what is in general a Mean-Field Game and how to translate it into a coupled system of a forward continuity (or Fokker-Planck) equation on the density of players and of a backward Hamilton-Jacobi equation on their value function. Then I will focus on the case where this system has a variational origin and I will explain how this system actually corresponds to Pontryagin’s maximum principle in the space of measures... wait, wait : if thys system, which includes a Hamilton-Jacobi equation, is Pontryagin, what is the Hamilton-Jacobi equation in this case? the talk will finish evoking some answers to this question, for control problem in the space of measures and also for differential games, thus arriving up to the so-called “Master equation” introduced by P.-L. Lions, which will be sketched.

Background Bayesian methods, with the predictive probability (PredP), allow multiple interim analyses with interim posterior probability (PostP) computation, without the need to correct for multiple looks at the data. The objective of this paper was to illustrate the use of PredP by simulating a sequential analysis of a clinical trial. Methods We used data from the Laryngobloc trial that planned to include 480 patients to demonstrate the equivalence of success between a laryngoscopy performed with the Laryngobloc® device and a control device. A crossover Bayesian design was used. The success rates of the two laryngoscopy devices were compared. Interim analyses, computed from random numbers of subjects, were simulated. Results The PostP of equivalence rapidly reached the predefined bound of 0.95. The PredP computed with an equivalence margin of 10% reached the efficacy bound between 352 and 409 of the 480 included patients. If a frequentist analysis had been made on the basis of 217 out of 480 subjects, the study would have been prematurely stopped for equivalence. The PredP indicated that this result was nonetheless unstable and that the equivalence was, thus far, not guaranteed. Conclusions Based on these interim analyses, we can conclude with a sufficiently high probability that the equivalence would have been met on the primary outcome before the predetermined end of this particular trial. If a Bayesian approach using PredP had been used, it would have allowed an early termination of the trial by reducing the calculated sample size by 15–20%.

Replacement of https://hal.archives-ouvertes.fr/hal-01386163; There seems to be nothing short of a {\it double whammy} hitting the users of probability, and among them physicists, especially those involved in the foundations of quanta. First is the instant instinctual reaction that phenomena which interest one do sharply and clearly divide into the {\it dichotomy} of {\it two and only two} alternatives of being {\it either} ``deterministic", {\it or} on the contrary, being ``probabilistic". However, there is also a second, prior and yet deeper trouble, namely, the ``probabilistic" case is strongly believed to be equally clear and well-founded as is the ``deterministic" one. And the only difference seen between the two is that the latter can talk also about ``individual" phenomena, while the former can only do so about large enough ``ensembles" for which, however, it is believed to be equally clear, precise and rigorous with the ``deterministic" approach. Or briefly, ``probabilistic'' is seen as nothing else but the ``deterministic'' on the level of ``ensembles" ... \\The fact, however, is that there is a {\it deep gap} between the empirical world of ``random" phenomena, and on the other hand, theories of ``probability". Furthermore, any attempt to bridge that gap does inevitably involve {\it infinity}, thus aggravating the situation to the extent that even today, and even if not quite realized by many, theories of ``probabilities" have a {\it shaky} foundation. \\This paper tries to bring to the awareness of various users of ``probabilities", and among them, to physicists involved in quanta, the fact that - seemingly unknown to them - they are self-inflicted victims of the mentioned double whammy.

International audience; Cascading failures seriously threat the reliability/availability of power transmission networks. In fact, although rare, their consequences may be catastrophic, including large-scale blackouts affecting the economics and the social safety of entire regions. In this context, the quantification of the probability of occurrence of these events, as a consequence of the operating and environmental uncertain conditions, represents a fundamental task. To this aim, the classical simulation-based Monte Carlo (MC) approaches may be impractical, due to the fact that (i) power networks typically have very large reliabilities, so that cascading failures are rare events and (ii) very large computational expenses are required for the resolution of the cascading failure dynamics of real grids. In this work we originally propose to resort to two MC variance reduction techniques based on metamodeling for a fast approximation of the probability of occurrence of cascading failures leading to power losses. A new algorithm for properly initializing the variance reduction methods is also proposed, which is based on a smart Latin Hypercube search of the events of interest in the space of the uncertain inputs. The combined methods are demonstrated with reference to the realistic case study of a modified RTS 96 power transmission network of literature.

Part 1: Full Papers; International audience; Clock-dependent probabilistic timed automata extend classical timed automata with discrete probabilistic choice, where the probabilities are allowed to depend on the exact values of the clocks. Previous work has shown that the quantitative reachability problem for clock-dependent probabilistic timed automata with at least three clocks is undecidable. In this paper, we consider the subclass of clock-dependent probabilistic timed automata that have one clock, that have clock dependencies described by affine functions, and that satisfy an initialisation condition requiring that, at some point between taking edges with non-trivial clock dependencies, the clock must have an integer value. We present an approach for solving in polynomial time quantitative and qualitative reachability problems of such one-clock initialised clock-dependent probabilistic timed automata. Our results are obtained by a transformation to interval Markov decision processes.

Reliable neutron-induced reaction cross sections of unstable nuclei are essential for nuclear astrophysics and applications but their direct measurement is often impossible. The surrogate-reaction method is one of the most promising alternatives to access these cross sections. However, its use is hampered by the need to account for the differences between the angular momenta and parities populated by the surrogate and the neutron-induced reactions. Here we show that it is possible to overcome this limitation and infer for the first time both the neutron-induced fission and radiative-capture cross sections of 239Pu. This was achieved by combining simultaneously-measured fission and gamma-emission probabilities for the 240Pu(4He,4He') surrogate reaction with a calculation of the angular-momentum and parity distributions populated in this reaction.

International audience; Background: The formation of superheavy nuclei in fusion reactions is suppressed by a competing quasifission process. The competition between the formation of the compound nucleus and the quasifission depends strongly on the reaction entrance channel. Purpose: The investigation of fission and quasifission processes in the formation of Z=120 superheavy composite systems in the Cr52,54+Cm248 and Zn68+Th232 reactions, and their comparison with the Ni64+U238 reaction at energies in the vicinity of the Coulomb barrier. Methods: Mass-energy distributions of fissionlike fragments formed in the reactions Cr52,54+Cm248 and Zn68+Th232 at energies near the Coulomb barrier were measured using the double-arm time-of-flight spectrometer CORSET. Results: Capture cross sections for the reactions under investigation were measured. The most probable fragment masses and total kinetic energies as well as their variances in dependence on the interaction energy were studied for asymmetric and symmetric fragments. The fusion probabilities were estimated from the analysis of mass-energy distributions. Conclusions: The estimated fusion probability drops down by a factor of 103 in the Cr54+Cm248 reaction compared to the reactions of Ca48 ions with actinides. Among the studied reactions, the Cr54+Cm248 is the most favorable one for the production of the superheavy element with Z=120.

Cumulative reaction probability plays a central role in the calculation of reaction rate constant of any bimolecular chemical reaction of interest. In order to give meaningful results, these calculations should be performed for chemical systems with a large number of degrees of freedom leadingto expensive and often infeasible simulations. In this work, a new computational scheme is proposed to allow high dimensional quantum reactive simulations. This scheme is based on the Green’s function operator technics combined to absorbing boundary conditions, a powerful approach introduced by W.H. Miller, T. Seideman and U. Manthe many years ago [1,2]. The new implementation takes benefit that the initial quantum reactive scattering problem can be cast into an eigenvalue problem [2] and uses the high efficiency and accuracy of Smolyak algorithm [3] to build very compact basis for eigenvalue problems [4]. Using this new computational framework, it is now possible to perform quantum dynamics simulations for multidimensional systems pushing away the curse of dimensionality problem. Some preliminary results will be presented [5] using this new powerful scheme

There seems to be nothing short of a {\it double whammy} hitting the users of probability, and among them physicists, especially those involved in the foundations of quanta. First is the instant instinctual reaction that phenomena which interest one do sharply and clearly divide into the {\it dichotomy} of {\it two and only two} alternatives of being {\it either} ``deterministic", {\it or} on the contrary, being ``probabilistic". However, there is also a second, prior and yet deeper trouble, namely, the ``probabilistic" case is strongly believed to be equally clear and well-founded as is the ``deterministic" one. And the only difference seen between the two is that the latter can talk also about ``individual" phenomena, while the former can only do so about large enough ``ensembles" for which, however, it is believed to be equally clear, precise and rigorous with the ``deterministic" approach. Or briefly, ``probabilistic'' is seen as nothing else but the ``deterministic'' on the level of ``ensembles" ... \\The fact, however, is that there is a {\it deep gap} between the empirical world of ``random" phenomena, and on the other hand, theories of ``probability". Furthermore, any attempt to bridge that gap does inevitably involve {\it infinity}, thus aggravating the situation to the extent that even today, and even if not quite realized by many, theories of ``probabilities" have a {\it shaky} foundation. \\This paper tries to bring to the awareness of various users of ``probabilities", and among them, to physicists involved in quanta, the fact that - seemingly unknown to them - they are self-inflicted victims of the mentioned double whammy. \\ \\

Concepts from multiple testing can improve tests of single hypotheses. The proposed definition of the calibrated p value is an estimate of the local false sign rate, the posterior probability that the direction of the estimated effect is incorrect. Interpreting one-sided p values as estimates of conditional posterior probabilities, that calibrated p value is (1 - LFDR) p/2 + LFDR, where p is a two-sided p value and LFDR is an estimate of the local false discovery rate, the posterior probability that a point null hypothesis is true given p. A simple option for LFDR is the posterior probability derived from estimating the Bayes factor to be its e p ln(1/p) lower bound. The calibration provides a continuum between significance testing and traditional Bayesian testing. The former effectively assumes the prior probability of the null hypothesis is 0, as some statisticians argue is the case. Then the calibrated p value is equal to p/2, a one-sided p value, since LFDR = 0. In traditional Bayesian testing, the prior probability of the null hypothesis is at least 50%, which usually results in LFDR >> p. At that end of the continuum, the calibrated p value is close to LFDR.

We consider fractal curves in two-dimensional $Z_N$ spin lattice models. These are N states spin models that undergo a continuous ferromagnetic-paramagnetic phase transition described by the ZN parafermionic field theory. The main motivation here is to investigate the correspondence between Schramm-Loewner evolutions (SLE) and conformal field theories with extended conformal algebras (ECFT). By using Monte-Carlo simulation, we compute the fractal dimension of different spin interfaces for the N=3 and N=4 spin models that correspond respectively to the 3 states Potts model and to the Ashkin-Teller model at the Fateev-Zamolodchikov point. These numerical measures, that improve and complete the ones presented in the previous works, are shown to be consistent with SLE/ECFT predictions. We consider then the crossing probability of spin clusters in a rectangular domain. Using a multiple SLE approach, we provide crossing probability formulas for ZN parafarmionic theories. The parafermionic conformal blocks that enter the crossing probability formula are computed by solving a Knhiznik-Zamolodchikov system of rank 3. In the 3 states Potts model case, where the parafermionic blocks coincide with the Virasoro ones, we rederive the crossing formula found by S.M.Flores et al., that is in good agreement with our measures. For N>=4 where the crossing probability satisfies a third order differential equation instead of a second order one, our formulas are new. The theoretical predictions are compared to Monte-Carlo measures taken at N=4 and a fair agreement is found., 25 pages, 5 figures

ISBN: 9783981926347 - 9781728144689 (Print); International audience; Many memory types are asymmetric with respect to the error vulnerability of stored 0's and 1's. For instance, DRAM, STT-MRAM and NAND flash memories may suffer from asymmetric error rates. A recently proposed errorprotection scheme consists in the inversion of the memory words with too many vulnerable values before they are stored in an asymmetric memory. In this paper, a method is proposed for the optimization of systematic binary linear block error-correcting codes in order to maximize their impact when combined with memory word inversion.

International audience; The main purpose of this paper is to compute the theoretical likelihood of some electoral outcomes under the impartial anonymous culture in four-candidate elections by using the last versions of software like LattE or Normaliz. By comparison with the three-candidate case, our results allow to analyze the impact of the number of candidates on the occurrence of these voting outcomes.

International audience; In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) ⊑ D, whose intuitive meaning is that “normally/typically Cs are also Ds”. This extension is based on a minimal model semantics corresponding to a notion of rational closure, built upon preferential models. We recall the basic concepts underlying preferential Description Logics. We also present two extensions of the preferential semantics: on the one hand, we consider probabilistic extensions, based on a distributed semantics that is suitable for tackling the problem of commonsense concept combination, on the other hand, we consider other strengthening of the rational closure semantics and construction to avoid the so called “blocking of property inheritance problem”.

Midzuno sampling enables to estimate ratios unbiasedly. We prove the asymptotic equivalence between Midzuno sampling and simple random sampling for the main statistical purposes of interest in a survey.

International audience; We report on the Pn measurements of the 82,83,84Ga (N = 51, 52, 53) precursors performed in one single experiment using the 3He neutron-counter TETRA at the ALTO facility in Orsay. Altogether our results for the three A = 82, 83 and 84 Ga isotopes point towards a sizable Pn staggering in the N = 50 region, similar to the one already known in the N = 28 region, hinting at a similar mechanism. We will discuss the possible microscopic origin of this behavior i.e. the existence in the N = 50 region of a low-lying component of the so called Pygmy Gamow-Teller Resonance, already well established at Z = 36, and persisting towards 78Ni.

International audience; The present study manipulates first and second order transitional probabilities during the statistical learning of short sequences. Participants were exposed to four sequences of three stimuli (ABC) repeated during the task, with each stimulus corresponding to the position of a red dot on a touchscreen. Participants were required to touch the dots as quickly as possible and response times were recorded between the first two stimuli (Transition Time 1 or TT1) and between the last two stimuli (TT2). In the first experiment the transition AB of a triplet ABC was fully predictable (p(B|A) = 1) while the second transition BC was unpredictable (p(C|B) = .5). The second experiment was a serial version of the exclusive-or (XOR), all first order transitional probabilities were equally unpredictable (p(B|A) = .5, p(C|B) = .5), while the combination of the first two stimuli fully predicted the last stimulus (p(C|AB) = 1). Results showed that participants were able to learn both type of transitional probabilities. The different evolution patterns of TT1 and TT2 and their implications in term of statistical learning mechanisms are discussed.

International audience; Classification of transient and variable light curves is an essential step in using astronomical observations to develop an understanding of the underlying physical processes from which they arise. However, upcoming deep photometric surveys, including the Large Synoptic Survey Telescope (LSST), will produce a deluge of low signal-to-noise data for which traditional type estimation procedures are inappropriate. Probabilistic classification is more appropriate for such data but is incompatible with the traditional metrics used on deterministic classifications. Furthermore, large survey collaborations like LSST intend to use the resulting classification probabilities for diverse science objectives, indicating a need for a metric that balances a variety of goals. We describe the process used to develop an optimal performance metric for an open classification challenge that seeks to identify probabilistic classifiers that can serve many scientific interests. The Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC) aims to identify promising techniques for obtaining classification probabilities of transient and variable objects by engaging a broader community beyond astronomy. Using mock classification probability submissions emulating realistically complex archetypes of those anticipated of PLAsTiCC, we compare the sensitivity of two metrics of classification probabilities under various weighting schemes, finding that both yield results that are qualitatively consistent with intuitive notions of classification performance. We thus choose as a metric for PLAsTiCC a weighted modification of the cross-entropy because it can be meaningfully interpreted in terms of information content. Finally, we propose extensions of our methodology to ever more complex challenge goals and suggest some guiding principles for approaching the choice of a metric of probabilistic data products.

We study Markov chains generated by iterated Lipschitz functions systems with possibly place dependent probabilities. Under general conditions, we prove uniqueness of the invariant probability measure for the associated Markov chain, by using quasi-compact linear operators technics. We use the same approach to describe the behavior of the Diaconis-Friedman's chain on [0, 1] with possibly place dependent probabilities.

The Borda Effect, first introduced by Colman and Poutney (Behav Sci 23:15–20, 1978), occurs in a preference aggregation process using the Plurality rule if given the (unique) winner there is at least one loser that is preferred to the winner by a majority of the electorate. Colman and Poutney (1978) distinguished two forms of the Borda Effect: the Weak Borda Effect, describing a situation under which the unique winner of the Plurality rule is majority dominated by only one loser; and the Strong Borda Effect, under which the Plurality winner is majority dominated by each of the losers. The Strong Borda Effect is well documented in the literature as the Strong Borda Paradox. Colman and Poutney (1978) showed that the probability of the Weak Borda Effect is not negligible; but they only focused on the Plurality rule. In this note, we extend the work of Colman and Poutney (1978) by providing, for three-candidate elections, representations of the limiting probabilities of the (Weak) Borda Effect for the whole family of scoring rules and scoring runoff rules. Our analysis leads us to highlight that there is a relation between the (Weak) Borda Effect and Condorcet efficiency. We perform our analysis under the assumptions of Impartial Culture and Impartial Anonymous Culture, which are two well-known assumptions often used for such a study.

International audience; The pari-mutuel model is a betting scheme that has its origins in horse racing, and that has been applied in a number of contexts, mostly economics. In this paper, we consider the set of probability measures compatible with a pari-mutuel model, characterize its extreme points, and investigate the properties of the associated lower and upper probabilities. We show that the pari-mutuel model can be embedded within the theory of probability intervals, and prove necessary and sucient conditions for it to be a belief function or a minitive measure. In addition, we also investigate the combination of dierent pari-mutuel models and their denition on product spaces.

International audience We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We introduce a new, very general and effective family of score functions which is designed for these problems. We illustrate its behavior on a series of numerical experiments. In particular, we demonstrate how it can be used to estimate large deviation rate functionals for the longtime limit of temporal averages.

International audience; The Kaplan-Meier nonparametric estimator has become a standard tool for estimating a survival time distribution in a right censoring schema. However, if the censoring rate is high, this estimator does not provide a reliable estimation of the extreme survival probabilities. In this paper we propose to combine the nonparametric Kaplan-Meier estimator and a parametric-based model into one construction. The idea is to t the tail of the survival function with a parametric model while for the remaining to use the Kaplan-Meier estimator. A procedure for the automatic choice of the location of the tail based on a goodness-of- t test is proposed. This technique allows us to improve the estimation of the survival probabilities in the mid and long term. We perform numerical simulations which confirm the advantage of the proposed method.

National audience; Humans can use an intuitive sense of statistics to make predictions about uncertain future events, a cognitive skill that underpins logical and mathematical reasoning. Recent research shows that some of these abilities for statistical inferences can emerge in preverbal infants and non-human primates such as apes and capuchins. An important question is therefore whether animals share the full complement of intuitive reasoning abilities demonstrated by humans, as well as what evolutionary contexts promote the emergence of such skills. Here, we examined whether free-ranging rhesus macaques (Macaca mulatta) can use probability information to infer the most likely outcome of a random lottery, in the first test of whether primates can make such inferences in the absence of direct prior experience. We developed a novel expectancy-violation looking time task, adapted from prior studies of infants, in order to assess the monkeys' expectations. In Study 1, we confirmed that monkeys (n = 20) looked similarly at different sampled items if they had no prior knowledge about the population they were drawn from. In Study 2, monkeys (n = 80) saw a dynamic ‘lottery’ machine containing a mix of two types of fruit outcomes, and then saw either the more common fruit (expected trial) or the relatively rare fruit (unexpected trial) fall from the machine. We found that monkeys looked longer when they witnessed the unexpected outcome. In Study 3, we confirmed that this effect depended on the causal relationship between the sample and the population, not visual mismatch: monkeys (n = 80) looked equally at both outcomes if the experimenter pulled the sampled item from her pocket. These results reveal that rhesus monkeys spontaneously use information about probability to reason about likely outcomes, and show how comparative studies of nonhumans can disentangle the evolutionary history of logical reasoning capacities.

Different rate theories yielded similar forms of rates constants consistent with the phenomenological Arrhenius law, although they were derived from various branches of physics including classical thermodynamics, statistical and quantum mechanics. This convergence supports the validity of the Arrhenius law but also suggests the existence of an even simpler underlying principle. A reductionnist approach is proposed here in which the energetic exponential factor is a conditional probability of sufficient energy and the pre-exponential factor is the frequency of recurrence of the configuration favorable to the reaction, itself proportional to a configurational probability in a chaotic system. This minimalist while rigorous mathematical approach makes it possible to bypass certain questionable postulates of more sophisticated theories and clarifies the meaning of the different types of energies used: activation energy, threshold energy and chemical energy., 8 pages

TransitData 2019, Paris, FRANCE, 10-/07/2019 - 10/07/2019

To evaluate the profitability of a production before the launch of the manufacturing process, most industrial companies use numerical simulation. This allows to test virtually several configurations of the parameters of a given product and to decide on its performance (defined by the specifications). In order to measure the impact of industrial process fluctuations on product performance, we are particularly interested in estimating the probability of failure of the product. Since each simulation requires the execution of a complex and expensive calculation code, it is not possible to perform a sufficient number of tests to estimate this probability using, for example, a Monte-Carlo method. Under the constraint of a limited number of code calls, we propose two very different estimation methods.The first is based on the principles of Bayesian estimation. Our observations are the results of numerical simulation. The probability of failure is seen as a random variable, the construction of which is based on that of a random process to model the expensive calculation code. To correctly define this model, the Kriging method is used. Conditionally to the observations, the posterior distribution of the random variable, which models the probability of failure, is inaccessible. To learn about this distribution, we construct approximations of the following characteristics: expectation, variance, quantiles... We use the theory of stochastic orders to compare random variables and, more specifically, the convex order. The construction of an optimal experimental design is ensured by the implementation of a sequential experimental planning procedure, based on the principle of the SUR ("Stepwise Uncertainty Reduction") strategies.The second method is an iterative procedure, particularly adapted to the case where the probability of failure is very small, i.e. the redoubt event is rare. The expensive calculation code is represented by a function that is assumed to be Lipschitz continuous. At each iteration, this hypothesis is used to construct approximations, by default and by excess, of the probability of failure. We show that these approximations converge towards the true value with the number of iterations. In practice, they are estimated using the Monte-Carlo method known as splitting method.The proposed methods are relatively simple to implement and the results they provide can be easily interpreted. We test them on various examples, as well as on a real case from STMicroelectronics., Pour évaluer la rentabilité d'une production en amont du lancement du processus de fabrication, la plupart des entreprises industrielles ont recours à la simulation numérique. Cela permet de tester virtuellement plusieurs configurations des paramètres d'un produit donné et de statuer quant à ses performances (i.e. les spécifications imposées par le cahier des charges). Afin de mesurer l'impact des fluctuations des procédés industriels sur les performances du produit, nous nous intéressons en particulier à l'estimation de sa probabilité de défaillance. Chaque simulation exigeant l'exécution d'un code de calcul complexe et coûteux, il n'est pas possible d'effectuer un nombre de tests suffisant pour estimer cette probabilité via, par exemple, une méthode Monte-Carlo. Sous la contrainte d'un nombre limité d'appels au code, nous proposons deux méthodes d'estimation très différentes.La première s'appuie sur les principes de l'estimation bayésienne. Nos observations sont les résultats de simulation numérique. La probabilité de défaillance est vue comme une variable aléatoire, dont la construction repose sur celle d'un processus aléatoire destiné à modéliser le code de calcul coûteux. Pour définir correctement ce modèle, on utilise la méthode de krigeage. Conditionnellement aux observations, la loi a posteriori de la variable aléatoire, qui modélise la probabilité de défaillance, est inaccessible. Pour apprendre sur cette loi, nous construisons des approximations des caractéristiques suivantes: espérance, variance, quantiles... On utilise pour cela la théorie des ordres stochastiques pour la comparaison de variables aléatoires et, plus particulièrement, l'ordre convexe. La construction d'un plan d'expériences optimal est assurée par la mise en place d'une procédure de planificationd'expériences séquentielle, basée sur le principe des stratégies SUR ("Stepwise Uncertainty Reduction").La seconde méthode est une procédure itérative, particulièrement adaptée au cas où la probabilité de défaillance est très petite, i.e. l'événement redouté est rare. Le code de calcul coûteux est représenté par une fonction que l'on suppose lipschitzienne. À chaque itération, cette hypothèse est utilisée pour construire des approximations, par défaut et par excès, de la probabilité de défaillance. Nous montrons que ces approximations convergent vers la valeur vraie avec le nombre d'itérations. En pratique, on les estime grâce à la méthode Monte-Carlo dite de "splitting".Les méthodes que l'on propose sont relativement simples à mettre en œuvre et les résultats qu'elles fournissent peuvent être interprétés sans difficulté. Nous les testons sur divers exemples, ainsi que sur un cas réel provenant de la société STMicroelectronics.