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Benford's law is a statement about the frequency that each digit arises as the leading digit of numbers in a dataset. It is satisfied by various common integer sequences, such as the Fibonacci numbers, the factorials, and the powers of most integers. In this paper, we prove that integer sequences resulting from a random integral decomposition process (which we model as discrete "stick breaking") subject to a certain congruence stopping condition approach Benford distribution asymptotically. We also show that our requirement on the number of congruence classes defining the congruence stopping condition is necessary for Benford behavior to occur and is a critical point; deviation from that would result in drastically different behavior. [ABSTRACT FROM AUTHOR]

We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the " ballot sequences ", variant to which Catalan numbers offer a solution. Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final goal, the rule he elaborated allowed him to carry on calculating them as long as he wanted. As such, it is possible this was the first time such numbers were determined. • Giovanni Rizzetti (1675–1751) probability scholar in the group of Jacopo Riccati. • The historical work of Igor Pak and the birth of Catalan numbers. • The denomination "Catalan numbers" (from Igor Pak). • Catalan numbers as a solution to a probability problem in a manuscript of Rizzetti. • Rizzetti's solution and the first calculation of Catalan numbers. [ABSTRACT FROM AUTHOR]

For a finite group G , we study the probability sp (G) that, given two elements x , y ∈ G , the cyclic subgroup 〈 x 〉 is subnormal in the subgroup 〈 x , y 〉. This can be seen as an intermediate invariant between the probability that two elements generate a nilpotent subgroup and the probability that two elements generate a solvable subgroup. We prove that sp (G) ≤ 1 / 6 for every nonsolvable group G. Moreover, this bound is best possible. [ABSTRACT FROM AUTHOR]

We study the irreducibility and Galois group of random polynomials over function fields. We prove that a random polynomial f = y n + ∑ i = 0 n − 1 a i (x) y i ∈ F q [ x ] [ y ] with i.i.d. coefficients a i taking values in the set { a (x) ∈ F q [ x ] : deg ⁡ a ≤ d } with uniform probability, is irreducible with probability tending to 1 − 1 q d as n → ∞ , where d and q are fixed. We also prove that with the same probability, the Galois group of this random polynomial contains the alternating group A n. Moreover, we prove that if we assume a version of the polynomial Chowla conjecture over F q [ x ] , then the Galois group of this polynomial is actually equal to the symmetric group S n with probability tending to 1 − 1 q d . We also study the other possible Galois groups occurring with positive limit probability. Finally, we study the same problems with n fixed and d → ∞. [ABSTRACT FROM AUTHOR]

The main goal of the paper is to present a general model theoretic framework to understand a result of Shalev on probabilistically finite nilpotent groups. We prove that a suitable group where the equation [ x 1 , ... , x k ] = 1 holds on a wide set, in a model theoretic sense, is an extension of a nilpotent group of class less than k by a uniformly locally finite group. In particular, this result applies to amenable groups, as well as to suitable model-theoretic families of definable groups such as groups in simple theories and groups with finitely satisfiable generics. [ABSTRACT FROM AUTHOR]

• Integer lattice. • Discrepancy. • Annuli. • Gauss circle problem. Given a domain Ω ⊆ R 2 , let D (Ω , x , R) be the number of lattice points from Z 2 in R Ω − x , for R ≥ 1 and x : = (x 1 , x 2) ∈ T 2 , minus the area of R Ω: D (Ω , x , R) = # { (j , k) ∈ Z 2 : (j − x 1 , k − x 2) ∈ R Ω } − R 2 | Ω |. We call ∫ T 2 | D (Ω , x , R) | p d x the p -th moment of the discrepancy function D. In 2014, Huxley showed that for convex domains with sufficiently smooth boundary, the fourth moment of D is bounded by O (R 2 log ⁡ R) , and in 2019, Colzani, Gariboldi, and Gigante extended this result to higher dimensions. In this paper, our contribution is twofold: first, we present a simple direct proof of Huxley's 2014 result; second, we establish new estimates for the p -th moments of lattice point discrepancy of annuli of radius R , and any fixed thickness 0 < t < 1 for p ≥ 2. For a video summary of this paper, please visit https://youtu.be/YWIe1IBIi9Q. [ABSTRACT FROM AUTHOR]

Histology restricted genetic predisposition testing of ovarian carcinoma patients is a topic of debate as the prevalence of BRCA1/2 pathogenic variants (PVs) in various histological subtypes is ambiguous. Our primary aim was to investigate the proportion of germline BRCA1/2 PVs per histological subtype. Additionally, we evaluated (i) proportion of somatic BRCA1/2 PVs and (ii) proportion of germline PVs in other ovarian carcinoma risk genes. PubMed, EMBASE and Web of Science were systematically searched and we included all studies reporting germline BRCA1/2 PVs per histological subtype. Pooled proportions were calculated using a random-effects meta-analysis model. Subsets of studies were used for secondary analyses. Twenty-eight studies were identified. The overall estimated proportion of germline BRCA1/2 PVs was 16.8% (95% CI 14.6 to 19.2). Presence differed substantially among patients with varying histological subtypes of OC; proportions being highest in high-grade serous (22.2%, 95% CI 19.6 to 25.0) and lowest in clear cell (3.0%, 95% CI 1.6 to 5.6) and mucinous (2.5%, 95% CI 0.6 to 9.6) carcinomas. Somatic BRCA1/2 PVs were present with total estimated proportion of 6.0% (95% CI 5.0 to 7.3), based on a smaller subset of studies. Germline PVs in BRIP1 , RAD51C , RAD51D , PALB2 , and ATM were present in approximately 3%, based on a subset of nine studies. Germline BRCA1/2 PVs are most frequently identified in high-grade serous ovarian carcinoma patients, but are also detected in patients having ovarian carcinomas of other histological subtypes. Limiting genetic predisposition testing to high-grade serous ovarian carcinoma patients will likely be insufficient to identify all patients with a germline PV. • Probability of finding germline BRCA1/2 PVs varies widely among histological subtypes of ovarian carcinoma (OC). • Germline BRCA1/2 PVs are most frequently detected in high-grade serous OC patients. • Limiting testing to high-grade serous histology will be insufficient to identify all OC patients with germline BRCA1/2 PVs. [ABSTRACT FROM AUTHOR]

The dynamics of ecological communities in nature are typically characterized by probabilistic processes involving invasion dynamics. Because of technical challenges, however, the majority of theoretical and experimental studies have focused on coexistence dynamics. Therefore, it has become central to understand the extent to which coexistence outcomes can be used to predict analogous invasion outcomes relevant to systems in nature. Here, we study the limits to this predictability under a geometric and probabilistic Lotka–Volterra framework. We show that while individual survival probability in coexistence dynamics can be fairly closely translated into invader colonization probability in invasion dynamics, the translation is less precise between community persistence and community augmentation, and worse between exclusion probability and replacement probability. These results provide a guiding and testable theoretical framework regarding the translatability of outcomes between coexistence and invasion outcomes when communities are represented by Lotka–Volterra dynamics under environmental uncertainty. [ABSTRACT FROM AUTHOR]

A policy maker faces a sequence of unknown outcomes. At each stage two (self-proclaimed) experts provide probabilistic forecasts on the outcome in the next stage. A comparison test is a protocol for the policy maker to (eventually) decide which of the two experts is better informed. The protocol takes as input the sequence of pairs of forecasts and actual outcomes and (weakly) ranks the two experts. We focus on anonymous and non-counterfactual comparison tests and propose two natural properties to which such a comparison test must adhere. We show that these determine the test in an essentially unique way. The resulting test is a function of the derivative of the induced pair of measures at the realized outcomes. [ABSTRACT FROM AUTHOR]

In this study, the probability of occurrence of fumonisins in corn in the states of greatest production in Brazil was determined. The data were analyzed through quantitative risk analysis using the Monte Carlo simulation. The results indicated that there is a strong correlation between fumonisins contamination levels and the geographical region due to the influence of climatic characteristics, with temperature having the main influence. The Southern states presented higher risks of occurrence and concentration levels of fumonisins in corn due to the temperate climate with lower average temperature and higher relative humidity and precipitation indices. Cultivation in the best season indicates a significant reduction in the production of fumonisins when this period was evaluated, with average concentration levels up to 42% lower. The generated data are important for regulatory agencies and the agricultural sector, which needs to be aware that the chance of success in grain production depends on efficient planning of the growing season, mainly concerning the climatic conditions to which it is subject to minimize the risks. • Risk of fumonisins in corn was assessed using quantitative risk assessment; • Temperature plays a critical role in fumonisin incidence and level in corn; • Reduction in fumonisin of up to 42% when cultivation at the best time was assessed; • Strong correlation between fumonisins levels and the geographical region was found; • Low temperatures and high humidity increased the probability of fumonisin in corn. [ABSTRACT FROM AUTHOR]

A great deal of current research on moral judgments centers on moral dilemmas concerning tradeoffs between one and five lives. Whether one considers killing one innocent person to save five others to be morally required or impermissible has been taken to determine whether one is appealing to consequentialist or non-consequentialist reasoning. But this focus on tradeoffs between one and five may obscure more nuanced commitments involved in moral decision-making that are revealed when the numbers and ratio of lives to be traded off are varied, and when the probabilities of each outcome occurring are less than certain. Four studies examine participants' reactions to scenarios that diverge in these ways from the standard ones. Study 1 examines the extent to which people are sensitive to the ratio of lives saved to lives ended by a particular action. Study 2 verifies that the ratio rather than the difference between the two values is operative. Study 3 examines whether participants treat probabilistic harm to some as equivalent to certainly harming fewer, holding expected ratio constant. Study 4 explores an analogous issue regarding the sensitivity of probabilistic saving. Participants are remarkably sensitive to expected ratio for probabilistic harms while deviating from expected value for probabilistic saving. Collectively, the studies provide evidence that people's moral judgments are consistent with the principle of threshold deontology. [ABSTRACT FROM AUTHOR]

Recent research has identified three invariants or identities that appear to hold in people’s probabilistic reasoning: the QQ identity, the addition law identity, and the Bayes rule identity (Costello and Watts, 2014, 2016a, Fisher and Wolfe, 2014, Wang and Busemeyer, 2013, Wang et al., 2014). Each of these identities represent specific agreement with the requirements of normative probability theory; strikingly, these identities seem to hold in people’s judgements despite the presence of strong and systematic biases against the requirements of normative probability theory in those very same judgements. These results suggest that the systematic biases seen in people’s probabilistic reasoning follow mathematical rules: for these particular identities, these rules cause an overall cancellation of biases and so produce agreement with normative requirements. We assess two competing mathematical models of probabilistic reasoning (the ‘probability theory plus noise’ model and the ‘quantum probability’ model) in terms of their ability to account for this pattern of systematic biases and invariant identities. [ABSTRACT FROM AUTHOR]

We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure μ ( Ω ) of (not necessarily compact) basic semi-algebraic sets Ω ⊂ R n . We obtain two monotone (non-increasing and non-decreasing) sequences of upper and lower bounds ( ω ‾ d ) , ( ω _ d ) , d ∈ N , each converging to μ ( Ω ) as d → ∞ . For each d , computing ω ‾ d or ω _ d reduces to solving a semidefinite program whose size increases with d . Some preliminary (small dimension) computational experiments are encouraging and illustrate the potential of the method. The method also works for any measure whose moments are known and which satisfies Carleman's condition. [ABSTRACT FROM AUTHOR]

This paper investigates belief revision with uncertainty. Normally, this kind of revision is processed in the framework of possibilistic logic, which is good at processing incomplete and imprecise information. However, the possibilistic logic based revision does not provide a probabilistic explanation for uncertainty. To solve this problem, it is necessary to express this problem from a perspective of probability. This paper proposes the definitions of formula probability and model probability, and then derives the conversion equation between them. To deal with uncertain belief revision, a probabilistic estimation is used. The approaches for revision with a reliable input and an uncertain input are discussed respectively. At last, differences between our approach and the existing ones for uncertain revision are explored. [ABSTRACT FROM AUTHOR]

Methods of measuring differentiation in archaeological assemblages have long been based on attribute-level analyses of assemblages. This paper considers a method of comparing assemblages as probability distributions via the Hellinger distance, as calculated through a Dirichlet-categorical model of inference using Monte Carlo methods of approximation. This method has application within practice-theory traditions of archaeology, an approach which seeks to measure and associate different factors that comprise the habitus of society. It is implemented here focusing on the question of regional food consumption habits in Republican Italy in the last two centuries BCE, toward informing a perspective on mass social change. [ABSTRACT FROM AUTHOR]

How does probability affect attributions of intentionality? In five experiments (total N = 1410), we provide evidence for a probability raising account holding that people are more likely to see the outcome of an agent's action as intentional if the agent does something to increase the odds of that outcome. Experiment 1 found that high probability without probability raising does not suffice for strong attributions of intentionality. Participants were more likely to conclude a girl intentionally obtained a desired gumball from a single gumball machine when it offered favorable odds for getting that kind of gumball compared with when it offered poor odds, but their attributions of intentionality were lukewarm. Experiments 2 and 3 then found stronger attributions of intentionality when the girl raised her probability of success by choosing to use machines offering favorable odds over machines offering poor odds. Finally, Experiments 4 and 5 examined whether these effects of probability raising might reduce to consideration of agents' beliefs and expectations. We found that although these mental states do matter, probability raising matters too—people attribute intentional actions to agents who increase their odds of success, rather than to agents who merely become convinced that success is likely. We discuss the implications of these findings for claims that control and skill contribute to attributions of intentional action. [ABSTRACT FROM AUTHOR]

We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von Neumann entropy. These quantities allow us to find new proofs of some standard results in quantum information theory, such as the concavity of von Neumann entropy and Holevo's theorem. The existence of an underlying probability distribution helps shed light on the conceptual underpinnings of these results. • New forms of quantum conditional entropy and mutual information defined using underlying quantum conditional probability. • New proofs for quantum information theoretic identities. • Additional relationships explored involving system–subsystem relationships. • Generalizations of conditional probabilities discussed. [ABSTRACT FROM AUTHOR]

Babai and Pak proved that the product replacement algorithm (a widely used heuristic algorithm intended to rapidly generate nearly uniformly distributed random elements in a finite group G ) has a flaw. Indeed the projection of the uniform distribution on generating n -tuples onto the first component may not give the uniform distribution on elements of G . In this paper we examine the difference between this distribution and the uniform one, in the particular case when G is a finitely generated prosoluble group. Under some additional hypotheses (for example if the derived subgroup is pronilpotent), this bias is bounded away from 1. However even for soluble groups, the problem pointed out by Babai and Pak is unavoidable. We construct a sequence of finite soluble groups of derived length 4 for which the bias is close to 1. [ABSTRACT FROM AUTHOR]

A common view in current psychology is that people estimate probabilities using various ‘heuristics’ or rules of thumb that do not follow the normative rules of probability theory. We present a model where people estimate conditional probabilities such as P ( A | B ) (the probability of A given that B has occurred) by a process that follows standard frequentist probability theory but is subject to random noise. This model accounts for various results from previous studies of conditional probability judgment. This model predicts that people’s conditional probability judgments will agree with a series of fundamental identities in probability theory whose form cancels the effect of noise, while deviating from probability theory in other expressions whose form does not allow such cancellation. Two experiments strongly confirm these predictions, with people’s estimates on average agreeing with probability theory for the noise-cancelling identities, but deviating from probability theory (in just the way predicted by the model) for other identities. This new model subsumes an earlier model of unconditional or ‘direct’ probability judgment which explains a number of systematic biases seen in direct probability judgment (Costello & Watts, 2014). This model may thus provide a fully general account of the mechanisms by which people estimate probabilities. [ABSTRACT FROM AUTHOR]

This paper provides the second term in the small time asymptotic expansion of the spectral heat content of a rotationally invariant α -stable process, 0 < α ≤ 2 , for the bounded interval ( a , b ) . The small time behavior of the spectral heat content turns out to be linked to the distribution of the supremum and infimum processes. [ABSTRACT FROM AUTHOR]

Cardiac electrophysiology models have been developed for over 50 years, and now include detailed descriptions of individual ion currents and sub-cellular calcium handling. It is commonly accepted that there are many uncertainties in these systems, with quantities such as ion channel kinetics or expression levels being difficult to measure or variable between samples. Until recently, the original approach of describing model parameters using single values has been retained, and consequently the majority of mathematical models in use today provide point predictions, with no associated uncertainty. In recent years, statistical techniques have been developed and applied in many scientific areas to capture uncertainties in the quantities that determine model behaviour, and to provide a distribution of predictions which accounts for this uncertainty. In this paper we discuss this concept, which is termed uncertainty quantification, and consider how it might be applied to cardiac electrophysiology models. We present two case studies in which probability distributions, instead of individual numbers, are inferred from data to describe quantities such as maximal current densities. Then we show how these probabilistic representations of model parameters enable probabilities to be placed on predicted behaviours. We demonstrate how changes in these probability distributions across data sets offer insight into which currents cause beat-to-beat variability in canine APs. We conclude with a discussion of the challenges that this approach entails, and how it provides opportunities to improve our understanding of electrophysiology. [ABSTRACT FROM AUTHOR]

Blackbox algorithms for linear algebra problems start with projection of the sequence of powers of a matrix to a sequence of vectors (Lanczos), a sequence of scalars (Wiedemann) or a sequence of smaller matrices (block methods). Such algorithms usually depend on the minimal polynomial of the resulting sequence being that of the given matrix. Here exact formulas are given for the probability that this occurs. They are based on the generalized Jordan normal form (direct sum of companion matrices of the elementary divisors) of the matrix. Sharp bounds follow from this for matrices of unknown elementary divisors. The bounds are valid for all finite field sizes and show that a small blocking factor can give high probability of success for all cardinalities and matrix dimensions. [ABSTRACT FROM AUTHOR]

Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. However, given the fundamentally different 'representational currency' underlying these approaches—models of the world versus linguistic co-occurrence—their unification has proven extremely difficult. Here, we define Distributional Formal Semantics, which integrates distributionality into a formal semantic system on the level of formal models. This approach offers probabilistic, distributed meaning representations that are inherently compositional, and that naturally capture fundamental semantic notions such as quantification and entailment. Furthermore, we show how the probabilistic nature of these representations allows for probabilistic inference, and how the information-theoretic notion of "information" (measured in Entropy and Surprisal) naturally follows from it. Finally, we illustrate how meaning representations can be derived incrementally from linguistic input using a recurrent neural network model, and how the resultant incremental semantic construction procedure intuitively captures key semantic phenomena, including negation, presupposition, and anaphoricity. [ABSTRACT FROM AUTHOR]

Model updating method has received increasing attention in damage detection of structures based on measured modal parameters. In this article, a probability-based damage detection procedure is presented, in which the random factor method for non-homogeneous random field is developed and used as the forward propagation to analytically evaluate covariance matrices in each iteration step of stochastic model updating. An improved optimization algorithm is introduced to guarantee the convergence and reduce the computational effort, in which the design variables are restricted in search region by region truncation of each iteration step. The developed algorithm is illustrated by a simulated 25-bar planar truss structure and the results have been compared and verified with those obtained from Monte Carlo simulation. In order to assess the influences of uncertainty sources on the results of model updating and damage detection of structures, a comparative study is also given under different cases of uncertainties, that is, structural uncertainty only, measurement uncertainty only and combination of the two. The simulation results show the proposed method can perform well in stochastic model updating and probability-based damage detection of structures with less computational effort. [ABSTRACT FROM AUTHOR]

Most existing route discovery schemes in MANETs are based on probabilistic models by which MANETs usually deploy broadcast mechanisms to discover routes between nodes. This is implemented by flooding the network with routing requests (RREQ) packets which usually result in the well-known broadcast storm problem. Due to the high mobility, frequent breakages are more likely to occur, leading to re-discovering the same routes frequently uncontrolled RREQ packets. Thus, the network may incur more channel contention and high packets collision rate. Existing solutions cannot accommodate the desired performance levels, especially in high mobility. Thus, this paper is the first that considers the velocity vector probabilistic route discovery in MANETs. Two new velocity-aware probabilistic route discovery models are presented to exclude unstable nodes while constructing routes between the source and its destination. The simulation experiments confirm the superiority of the proposed schemes in terms of RREQ packet overhead and link stability. [ABSTRACT FROM AUTHOR]

A hybrid mathematical model was devised to obtain optimal values for bacterial doubling time and initial phage/bacteria multiplicity of infection for the purpose of reaching the highest possible phage titers in steady-state exponentially growing cultures. The computational model consists of an initial probabilistic stage, followed by a second one processed by a system of delayed differential equations. The model’s approach can be used in any phage/bacteria system for which the relevant parameters have been measured. Results of a specific case, based on the detailed, known information about the interactions between virulent T4 phage and its host bacterium Escherichia coli , display a range of possible such values along a highlighted strip of parameter values in the relevant parameter plane. In addition, times to achieve these maxima and gains in phage concentrations are evaluated. [ABSTRACT FROM AUTHOR]

In the present study, we examined 15 years (1993–2007) of satellite altimeter and coastal tide-gauge records in the Bay of Bengal and demonstrate that satellite altimetry can be a useful complementary dataset for the study of storm surges. We first examined the performance of X-TRACK-processed altimeter data. During the period of study (1993–2007), 30 (19), 21 (09), 09 (07), and 07 (01) storm surge events were identified from tide gauges (altimetry) at Hiron Point, Paradip, Visakhapatnam and Chennai respectively. The magnitudes of surges observed by altimeters are comparable to those recorded in tide gauges. Though observing storm surges by altimeters rely purely on a chance, the presence of multiple satellite tracks in a region considerably enhances the chances of capturing the signals of an extreme event. Moreover, information on cross-shelf variations of storm surges is useful for model validation. [ABSTRACT FROM AUTHOR]

We prove a number of limiting distributions for statistics for unimodal sequences of positive integers by adapting a probabilistic framework for integer partitions introduced by Fristedt. The difficulty in applying the direct analogue of Fristedt's techniques to unimodal sequences lies in the fact that the generating function for partitions is an infinite product, while that of unimodal sequences is not. Essentially, we get around this by conditioning on the size of the largest part and working uniformly on contributing summands. Our framework may be used to derive many distributions, and our results include joint distributions for largest parts and multiplicities of small parts. We discuss ranks as well. We further obtain analogous results for strongly unimodal sequences. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new probabilistic gait representation to characterize human walking for recognition by gait. The approach obtains the binomial distribution of every pixel in a gait cycle. Organizing the binomial distribution of all pixels in the gait image, we obtain the gait signature, which we denote as the Gait Probability Image (GPI). In the recognition stage, symmetric Kullback–Leibler divergence is used to measure the information theoretical distance between gait signatures. The experimental results reveal that GPI achieves promising recognition rates. Besides that, experiments on different walking speeds demonstrate that GPI is robust to slight variation in walking speed. [ABSTRACT FROM AUTHOR]

Abstract: Let B be a finite, separable von Neumann algebra. We prove that a B-valued distribution μ that is the weak limit of an infinitesimal array is infinitely divisible. The proof of this theorem utilizes the Steinitz lemma and may be adapted to provide a nonstandard proof of this type of theorem for various other probabilistic categories. We also develop weak topologies for this theory and prove the corresponding compactness and convergence results. [Copyright &y& Elsevier]

Abstract: Preparatory attention (PA) is the ability to allocate attention to a stimulus prior to its occurrence and is a crucial component of attentional control. We investigated the role of brain hemispheres in PA using an experimental test in which normal participants responded to a target that could appear in the right or the left visual fields, thus projecting to the left or the right hemispheres, while ignoring a central distractor that could appear in the preparatory phase preceding the target. This experimental test measures the ability of participants to modulate PA directed to a target location when the probability of a distractor occurrence varies across three blocks of trials (0%, 33%, 67%). The competition between distractors and target for PA should produce slower response times when the probability of distractors is high. Three experiments were conducted varying the temporal predictability of the target occurrence within a trial (high predictability in Experiments 1 and 3, and low predictability in Experiment 2), and the task used (location in Experiments 1 and 2, and detection in Experiment 3). We found that the modulation of PA by the expected probability of events was different in each visual field/hemisphere. Whereas the left hemisphere PA was influenced by the mere probability of events in each block of trials, the right hemisphere PA was mainly influenced by events with high temporal predictability. These results suggest that each hemisphere uses a different strategy to modulate PA when directed to a target location at the perceptual level of visual processing. [Copyright &y& Elsevier]

[Display omitted] • A stochastic virtual track inspection method for track-viaduct system is proposed. • TSI affect the dynamic irregularity signal greatly at characteristic wavelength. • Without reliability assessment the regularity of the line is often overestimated. To evaluate the reliability of the dynamic irregularity of a track structure in satisfying the safety requirements, a stochastic virtual track inspection (SVTI) system that can be used to predict the time-varying probability distribution of dynamic irregularity was developed by combining virtual track inspection (VTI) system and the generalized probability density evolution method (GPDEM) in this study. A train–track–bridge dynamic interaction model (TTBDIM) was built using the Universal Mechanism platform. The inertial reference method (IRM) was simulated by finding the frequency-domain quadratic integration of the axle box acceleration and filtering it, based on which the deterministic VTI system was established. For the sake of probability analysis, the track geometry irregularities (TGI) was considered as a stochastic variable. A number-theory-based uniform experimental design was used to determine the representative points in the high-dimensional probability space. SVTI was established by coupling the deterministic VTI system and the generalized probability density evolution equation. The probability density evolution function of the dynamic irregularity was solved for using the finite difference method with the total variation diminishing (TVD) format. In this study, floating slab tracks on a U-shaped beam viaduct were taken as an example to analyze the influence of track stiffness irregularity (TSI) on the basic signal characteristics of the dynamic irregularity of the tracks using the deterministic VTI system. Furthermore, the SVTI system was used to analyze the influence of TSI on the time-varying probability distribution and determine whether the dynamic inspection requirements of the dynamic irregularity were satisfied. The research findings suggested that the TSI of the track–viaduct system with a low stiffness had a significant influence on the time-varying characteristics of the dynamic irregularity probability distribution. As the stiffness of the track–viaduct system decreased, the mean probability distribution of the dynamic irregularity extrema shifted to the higher-level area with an increasing standard deviation. When rubber spring floating slab tracks (RSFSTs) and steel spring floating slab tracks (SSFSTs) were laid on the 35-m-span U-shaped beam, the probabilities of dynamic irregularity exceeding the limit were 16.13% and 30.02%, respectively. The deterministic VTI system might not be able to detect irregularities exceeding the limit within the limited simulation mileage, which could lead to misjudgments and track regularity overestimation. In conclusion, the proposed SVTI system will provide direction for the design of track–viaduct systems with low stiffnesses in urban rail transit construction. [ABSTRACT FROM AUTHOR]

Abstract: This paper revisits the fundamental concept of the locality of references and proposes to quantify it as a conditional probability: in an address stream, given the condition that an address is accessed, how likely the same address (temporal locality) or an address within its neighborhood (spatial locality) will be accessed in the near future. Previous works use reuse distance histograms as a measure of temporal locality. For spatial locality, some ad hoc metrics have been proposed as a quantitative measure. In contrast, our conditional probability-based locality measure has a clear mathematical meaning and provides a theoretically sound and unified way to quantify both temporal and spatial locality. We showcase that our quantified locality measure can be used to evaluate compiler optimizations, to analyze the locality at different levels of memory hierarchy, to optimize the cache architecture to effectively leverage the locality, and to examine the effect of data prefetching mechanisms. [Copyright &y& Elsevier]

Abstract: A number of stereo matching algorithms have been developed in the last few years, which also have successfully detected occlusions in stereo images. These algorithms typically fall short of a systematic study of occlusions; they predominantly emphasize matching and regard occlusion filling as a secondary operation. Filling occlusions, however, is useful in many applications such as image-based rendering where 3D models are desired to be as complete as possible. In this paper, we study occlusions in a systematic way and propose two algorithms to fill occlusions reliably by applying statistical modeling, visibility constraints, and scene constraints. We introduce a probabilistic, model-based filling order of the occluded points to maintain consistency in filling. Furthermore, we show how an ambiguity in the interpolation of the disparity value of an occluded point can safely be avoided using color homogeneity when the point’s neighborhood consists of multiple scene surfaces. We perform a comparative study and show that statistically, the new algorithms deliver good quality results compared to existing algorithms. [Copyright &y& Elsevier]

Abstract: Two assumptions, commonly made in risk and reliability studies, have a long history. The first is that uncertainty is either aleatoric or epistemic. The second is that standard probability theory is sufficient to express uncertainty. The purposes of this paper are to provide a conceptual analysis of uncertainty and to compare Bayesian approaches with interval approaches with an example relevant to research on climate change. The analysis reveals that the categorisation of uncertainty as either aleatoric or epistemic is unsatisfactory for practical decision making. It is argued that uncertainty emerges from three conceptually distinctive and orthogonal attributes FIR i.e., fuzziness, incompleteness (epistemic) and randomness (aleatory). Characterisations of uncertainty, such as ambiguity, dubiety and conflict, are complex mixes of interactions in an FIR space. To manage future risks in complex systems it will be important to recognise the extent to which we ‘don't know’ about possible unintended and unwanted consequences or unknown–unknowns. In this way we may be more alert to unexpected hazards. The Bayesian approach is compared with an interval probability approach to show one way in which conflict due to incomplete information can be managed. [Copyright &y& Elsevier]

Abstract: We present an explanation-oriented, domain-specific, visual language for explaining probabilistic reasoning. Explanation-oriented programming is a new paradigm that shifts the focus of programming from the computation of results to explanations of how those results were computed. Programs in this language therefore describe explanations of probabilistic reasoning problems. The language relies on a story-telling metaphor of explanation, where the reader is guided through a series of well-understood steps from some initial state to the final result. Programs can also be manipulated according to a set of laws to automatically generate equivalent explanations from one explanation instance. This increases the explanatory value of the language by allowing readers to cheaply derive alternative explanations if they do not understand the first. The language is composed of two parts: a formal textual notation for specifying explanation-producing programs and the more elaborate visual notation for presenting those explanations. We formally define the abstract syntax of explanations and define the semantics of the textual notation in terms of the explanations that are produced. [Copyright &y& Elsevier]

Abstract: The perception of target events presented in a rapid stream of non-targets is impaired for early target positions, but then gradually improves, a phenomenon known as attentional awakening. This phenomenon has been associated with better resource allocation. It is unclear though whether improved resource allocation and attentional awakening are a consequence of the temporal context, that is, the position of the target event in the stimulus stream, or are due to a simple expectancy or foreperiod effect. Expectancy is an alternative explanation of attentional awakening because it depends on the a posteriori probabilities, which will increase with target position when all target positions are equally likely. To differentiate between the expectancy and the temporal context account the a priori (objective) probability of target position was defined such that the a posteriori probability would be high for early and late, and low for intermediate target positions. EEG was collected and the P3 ERP evoked by target events was derived as an indicator of resource allocation. A robust attentional awakening effect was observed. The relationships between measures of performance and P3 amplitude, and respectively target position, a priori, and a posteriori probability were analyzed. Results showed that in contrast to target position, a posteriori probability had little impact on performance and did not moderate the association between P3 amplitude and performance. Results also indicated that in spite of the evident role of target position on resource allocation and the perception of target events in rapid stimulus streams, target position is likely not the only variable these are affected by. Nevertheless, the findings of the present study suggest that whereas the temporal context of a rapid serial event is a key player for resource allocation to and perception of the event, expectancy seems of very little consequence. [Copyright &y& Elsevier]

Abstract: Bayesian inference has taken FMRI methods research into areas that frequentist statistics have struggled to reach. In this article we will consider some of the early forays into Bayes and what motivated its use. We shall see the impact that Bayes has had on haemodynamic modelling, spatial modelling, group analysis, model selection and brain connectivity analysis; and consider how these advancements have spun-off into related areas of neuroscience and some of the challenges that remain. Bayes has brought to the table inference flexibility, incorporation of prior information, adaptive regularisation and model selection. But perhaps more important than these things, is the ability of Bayes to empower the methods researcher with a mathematically principled framework for inferring on any model. [Copyright &y& Elsevier]

Abstract: The methodology of predicting sonication-induced unfolding proteins (SUP) is presented in this study. The methodology bases on: (a) simulation of SUP by the excessive deviations of protein domains in regime of damped forced vibrations caused by critical level of involved acoustic energy, which is associated with temperature rise and acoustic pressure; (b) simulation of stochasticity of SUP by failures in jobs service in the queueing system with Markovian fluxes. The assessments of probability of SUP accounting the complex of parameters of pulsed ultrasound, biophysical properties of tissue and macromolecular crowding of insonated zone of tissue are considered. [Copyright &y& Elsevier]

Abstract: In this paper, a new stochastic variational PDE model is developed, using instead of hard segmentation soft segmentation. In this way, each pixel is allowed to belong to each image pattern with some probability. Our work proposes a functional with variable exponent, which provides a more accurate model for image segmentation and denoising. The diffusion resulting from the proposed model is a combination between TV-based and isotropic smoothing. The modeling procedure, computational implementation and results are explored in detail and numerical examples of real and synthetic images are presented. [Copyright &y& Elsevier]

Abstract: Statistical properties in the visual environment can be used to improve performance on visual working memory (VWM) tasks. The current study examined the ability to incidentally learn that a change is more likely to occur to a particular feature dimension (shape, color, or location) and use this information to improve change detection performance for that dimension (the change probability effect). Participants completed a change detection task in which one change type was more probable than others. Change probability effects were found for color and shape changes, but not location changes, and intentional strategies did not improve the effect. Furthermore, the change probability effect developed and adapted to new probability information quickly. Finally, in some conditions, an improvement in change detection performance for a probable change led to an impairment in change detection for improbable changes. [Copyright &y& Elsevier]

Abstract: J.J. Sylvester''s four-point problem asks for the probability that four points chosen uniformly at random in the plane have a triangle as their convex hull. Using a combinatorial classification of points in the plane due to Goodman and Pollack, we generalize Sylvester''s problem to one involving reduced expressions for the long word in . We conjecture an answer of 1/4 for this new version of the problem. [Copyright &y& Elsevier]

Abstract: This paper presents an integrated hydrodynamic modeling and probability analysis approach to assess the long-term effects of changing river inflows on the estuarine ecosystem. The probability analysis method, which is popularly used in advanced hydrological frequency analysis of river flows and rainfalls, has been applied to analyze the effects of changing inflow on salinity and thus on oyster ecology in Apalachicola Bay. Long-term salinity data were predicted through the application of a calibrated 3D hydrodynamic model under two river inflow conditions over a 10-year period. The first flow represents the historic flow. The 2nd flow condition, called Scenario-1, represents a regulated flow scenario to account for the potential increasing upstream water demands. Two stations, Mid Bay and Dry Bar, in the bay were selected to examine the estuarine responses. Under the historic flow condition, the maximum probability salinity at Dry Bar in the rich oyster reef is near 24ppt, within the optimal salinity range for oyster growth of 16–26 ppt (Harned et al., 1996); the maximum probability salinity at Mid Bay station is 27ppt, beyond the optimal salinity for oyster growth in mid-bay area where there is no oyster reef around. While it is difficult to examine the difference between two scenarios by conventional time series analysis of river flows and salinity, probability analysis reasonably characterizes and quantifies the changes of river flow and salinity patterns over the 10-year period. The Scenario-1 has caused the increase of the probability in low flows. Higher probability of low flows for the regulated flow scenario shortens the period of optimal salinity in the oyster reef, and cause substantial increase of exceedance probability of higher salinity in the oyster reef to the level beyond the optimal salinity range for oyster growth. The probability analysis approach has demonstrated its advantage for the risk assessments of the long-term estuarine ecohydrological effects under various regulated inflow scenarios to support estuarine water resources managements. [Copyright &y& Elsevier]

Abstract: Probabilistic record linkage is a method commonly used to determine whether demographic records refer to the same person. The Fellegi–Sunter method is a probabilistic approach that uses field weights based on log likelihood ratios to determine record similarity. This paper introduces an extension of the Fellegi–Sunter method that incorporates approximate field comparators in the calculation of field weights. The data warehouse of a large academic medical center was used as a case study. The approximate comparator extension was compared with the Fellegi–Sunter method in its ability to find duplicate records previously identified in the data warehouse using different demographic fields and matching cutoffs. The approximate comparator extension misclassified 25% fewer pairs and had a larger Welch’s T statistic than the Fellegi–Sunter method for all field sets and matching cutoffs. The accuracy gain provided by the approximate comparator extension grew as less information was provided and as the matching cutoff increased. Given the ubiquity of linkage in both clinical and research settings, the incremental improvement of the extension has the potential to make a considerable impact. [Copyright &y& Elsevier]

Abstract: A decision may be difficult because complex information processing is required to evaluate choices according to deterministic decision rules and/or because it is not certain which choice will lead to the best outcome in a probabilistic context. Factors that tax decision making such as decision rule complexity and low decision certainty should be disambiguated for a more complete understanding of the decision making process. Previous studies have examined the brain regions that are modulated by decision rule complexity or by decision certainty but have not examined these factors together in the context of a single task or study. In the present functional magnetic resonance imaging study, both decision rule complexity and decision certainty were varied in comparable decision tasks. Further, the level of certainty about which choice to make (choice certainty) was varied separately from certainty about the final outcome resulting from a choice (outcome certainty). Lateral prefrontal cortex, dorsal anterior cingulate cortex, and bilateral anterior insula were modulated by decision rule complexity. Anterior insula was engaged more strongly by low than high choice certainty decisions, whereas ventromedial prefrontal cortex showed the opposite pattern. These regions showed no effect of the independent manipulation of outcome certainty. The results disambiguate the influence of decision rule complexity, choice certainty, and outcome certainty on activity in diverse brain regions that have been implicated in decision making. Lateral prefrontal cortex plays a key role in implementing deterministic decision rules, ventromedial prefrontal cortex in probabilistic rules, and anterior insula in both. [Copyright &y& Elsevier]

Abstract: The theory of quasi-arithmetic means represents a powerful tool in the study of covariance functions across space–time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility criteria. Also, some important inequalities involving covariance functions and preference relations as well as algebraic properties can be derived by means of the proposed approach. In particular, quasi-arithmetic covariances allow for ordering and preference relations, for a Jensen-type inequality and for a minimal and maximal element of their class. The general results shown in this paper are then applied to the study of spatial and spatio-temporal random fields. In particular, we discuss the representation and smoothness properties of a weakly stationary random field with a quasi-arithmetic covariance function. Also, we show that the generator of the quasi-arithmetic means can be used as a link function in order to build a space–time nonseparable structure starting from the spatial and temporal margins, a procedure that is technically sound for those working with copulas. Several examples of new families of stationary covariances obtainable with this procedure are shown. Finally, we use quasi-arithmetic functionals to generalise existing results concerning the construction of nonstationary spatial covariances, and discuss the applicability and limits of this generalisation. [Copyright &y& Elsevier]

Abstract: Randomized libraries are increasingly popular in protein engineering and other biomedical research fields. Statistics of the libraries are useful to guide and evaluate randomized library construction. Previous works only give the mean of the number of unique sequences in the library, and they can only handle equal molar ratio of the four nucleotides at a small number of mutation sites. We derive formulas to calculate the mean and variance of the number of unique sequences in libraries generated by cassette mutagenesis with mixtures of arbitrary nucleotide ratios. Computer program was developed which utilizes arbitrary numerical precision software package to calculate the statistics of large libraries. The statistics of library with mutations in more than amino acids can be calculated easily. Results show that the nucleotide ratios have significant effects on these statistics. The more skewed the ratio, the larger the library size is needed to obtain the same expected number of unique sequences. The program is freely available at http://graphics.med.yale.edu/cgi-bin/lib_comp.pl. [Copyright &y& Elsevier]

A quantitative microbial risk assessment (QMRA) model predicting the listeriosis risk related to the consumption of Ready- To- Eat (RTE) cooked meat products sliced at retail stores in Greece was developed. The probability of illness per serving assessed for 87 products available in the Greek market was found highly related to the nitrite concentration; products having a lower concentration showed a higher risk per serving. The predicted 95th percentiles of the annual listeriosis cases totaled 33 of which 13 cases were <65 years old and 20 cases ≥65 years old. The highest number of cases was predicted for mortadella, smoked turkey, boiled turkey and parizer, which were the most frequently consumed product categories. Two scenarios for assessing potential interventions to reduce the risk were tested: setting a use-by date of 14 days (these products have no use-by date based on current European Union legislation) and improving the temperature control during domestic storage. The two scenarios resulted in a decrease of the 95th and 99th percentiles of the total annual cases by 97% and 88%, respectively. • A quantitative risk assessment model was developed for predicting listeriosis risk. • Listeriosis risk was estimated for Ready-To-Eat retail-sliced cooked meat products. • The probability of illness per serving was assessed for 87 products in Greek market. • Two scenarios for assessing potential interventions to reduce the risk were tested. [ABSTRACT FROM AUTHOR]