Expertise and the perception of kinematic and situational probability information

Two experiments were conducted on the nature of expert perception in the sport of squash. In the first experiment, ten expert and fifteen novice players attempted to predict the direction and force of squash strokes from either a film display (occluded at variable time periods before and after the opposing player had struck the ball) or a matched point-light display (containing only the basic kinematic features of the opponent's movement pattern). Experts outperformed the novices under both display conditions, and the same basic time windows that characterised expert and novice pick-up of information in the film task also persisted in the point-light task. This suggests that the experts' perceptual advantage is directly related to their superior pick-up of essential kinematic information. In the second experiment, the vision of six expert and six less skilled players was occluded by remotely triggered liquid-crystal spectacles at quasi-random intervals during simulated match play. Players were required to complete their current stroke even when the display was occluded and their prediction performance was assessed with respect to whether they moved to the correct half of the court to match the direction and depth of the opponent's stroke. Consistent with experiment 1, experts were found to be superior in their advance pick-up of both directional and depth information when the display was occluded during the opponent's hitting action. However, experts also remained better than chance, and clearly superior to less skilled players, in their prediction performance under conditions where occlusion occurred before any significant pre-contact preparatory movement by the opposing player was visible. This additional source of expert superiority is attributable to their superior attunement to the information contained in the situational probabilities and sequential dependences within their opponent's pattern of play.

Probability backflow for a Dirac particle

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is known that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown thar the maximum possible amount of probability that can flow backwards, over a given time interval of duration T, depends on the dimensionless parameter epsilon = root 4h/mc(2)T, where m is the mass of the particle and c is the speed of light. At epsilon = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as epsilon increases from 0, and show that it depends on the size of m, h, and T, unlike the nonrelativistic case.

The velocity of probability transport in quantum mechanics

In his study of the 'time of arrival' problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.

Probability of axillary node involvement in patients with tubular carcinoma of the breast

The aim of this study was to investigate the frequency of axillary metastasis in women with tubular carcinoma (TC) of the breast. Women who underwent axillary dissection for TC in the Western Sydney area (1984-1995) were identified retrospectively through a search of computerized records. A centralized pathology review was performed and tumours were classified as pure tubular (22) or mixed tubular (nine), on the basis of the invasive component containing 90 per cent or more, or 75-90 per cent tubule formation respectively. A Medline search of the literature was undertaken to compile a collective series (20 studies with a total of 680 patients) to address the frequency of nodal involvement in TC. A quantitative meta-analysis was used to combine the results of these studies. The overall frequency of nodal metastasis was five of 31 (16 per cent); one of 22 pure tubular and four of nine mixed tumours (P = 0.019). None of the tumours with a diameter of 10 mm or less (n = 16) had nodal metastasis compared with five of 15 larger tumours (P = 0.018). The meta-analysis of 680 women showed an overall frequency of nodal metastasis in TC of 13.8 (95 per cent confidence interval 9.3-18.3) per cent. The frequency of nodal involvement was 6.6 (1.7-11.4) per cent in pure TC (n = 244) and 25.0 (12.5-37.6) per cent in mixed TC (n = 149). A case may be made for observing the clinically negative axilla in women with a small TC (10 mm or less in diameter).

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve

Background and aim of the study: Results of valve re-replacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. Methods: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. Results: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. Conclusion: Younger patient age and root versus non-root replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.

Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure

The acceptance-probability-controlled simulated annealing with an adaptive move generation procedure, an optimization technique derived from the simulated annealing algorithm, is presented. The adaptive move generation procedure was compared against the random move generation procedure on seven multiminima test functions, as well as on the synthetic data, resembling the optical constants of a metal. In all cases the algorithm proved to have faster convergence and superior escaping from local minima. This algorithm was then applied to fit the model dielectric function to data for platinum and aluminum.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c)

Local Utility Functions and Local Probability Transformations

This note shows that, under appropriate conditions, preferences may be locally approximated by the linear utility or risk-neutral preference functional associated with a local probability transformation.

A liberation model for comminution based on probability theory

Mineral processing plants use two main processes; these are comminution and separation. The objective of the comminution process is to break complex particles consisting of numerous minerals into smaller simpler particles where individual particles consist primarily of only one mineral. The process in which the mineral composition distribution in particles changes due to breakage is called 'liberation'. The purpose of separation is to separate particles consisting of valuable mineral from those containing nonvaluable mineral. The energy required to break particles to fine sizes is expensive, and therefore the mineral processing engineer must design the circuit so that the breakage of liberated particles is reduced in favour of breaking composite particles. In order to effectively optimize a circuit through simulation it is necessary to predict how the mineral composition distributions change due to comminution. Such a model is called a 'liberation model for comminution'. It was generally considered that such a model should incorporate information about the ore, such as the texture. However, the relationship between the feed and product particles can be estimated using a probability method, with the probability being defined as the probability that a feed particle of a particular composition and size will form a particular product particle of a particular size and composition. The model is based on maximizing the entropy of the probability subject to mass constraints and composition constraint. Not only does this methodology allow a liberation model to be developed for binary particles, but also for particles consisting of many minerals. Results from applying the model to real plant ore are presented. A laboratory ball mill was used to break particles. The results from this experiment were used to estimate the kernel which represents the relationship between parent and progeny particles. A second feed, consisting primarily of heavy particles subsampled from the main ore was then ground through the same mill. The results from the first experiment were used to predict the product of the second experiment. The agreement between the predicted results and the actual results are very good. It is therefore recommended that more extensive validation is needed to fully evaluate the substance of the method. (C) 2003 Elsevier Ltd. All rights reserved.

Heavy tails, importance sampling and cross-entropy

We consider the problem of estimating P(Yi + (...) + Y-n > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a toot for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y-1 + (...) + Y-n > x), n - 1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some specific parametric examples (Pareto and Weibull) how this leads to precise answers which, as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/l and GI/G/l queues are also discussed.

Correlation of non-uniform protein expression with variation in transmitter release probability

The strength of synaptic transmission is highly variable between different synapses. The present study examined some factors that may contribute to this variation in the strength of neurotransmission in sympathetic varicosities of the mouse vas deferens. Transmitter release was measured using a focal macropatch electrode placed over pairs of visualised varicosities. By regulating the calcium concentration of the solutions inside the recording electrode and in the bath independently of each other, transmitter release was restricted to one or two surface varicosities at each recording site. Using this technique, transmitter release probability was shown to be highly variable, even between adjacent varicosities on single axon branches. Very little variation was observed in the calcium influx following single impulse nerve stimulation between adjacent Oregon Green BAPTA-1 loaded varicosities. However, the staining intensities of three vesicular proteins, SV2, synaptophysin, and synaptotagmin 1, showed considerable variation between adjacent varicosities on single axon branches. This variation in staining intensity may be partly explained by variation in the density of synaptic vesicles. However, double staining experiments using two vesicular antigens showed some varicosities staining for one vesicular antigen, but not for the second, suggesting that the expression of these release machinery proteins is regulated locally within the varicosities. The results of the present study strengthen suggestions that synaptic strength is at least in part, regulated by variation in the expression of vesicular proteins. (C) 2004 Wiley-Liss, Inc.

Testing multiple mapping conditioning mixing for Monte Carlo probability density function simulations

Mitarai [Phys. Fluids 17, 047101 (2005)] compared turbulent combustion models against homogeneous direct numerical simulations with extinction/recognition phenomena. The recently suggested multiple mapping conditioning (MMC) was not considered and is simulated here for the same case with favorable results. Implementation issues crucial for successful MMC simulations are also discussed.

Pitch jump probability measures for the analysis of snoring sounds in apnea

Obstructive sleep apnea (OSA) is a highly prevalent disease in which upper airways are collapsed during sleep, leading to serious consequences. The gold standard of diagnosis, called polysomnography (PSG), requires a full-night hospital stay connected to over ten channels of measurements requiring physical contact with sensors. PSG is inconvenient, expensive and unsuited for community screening. Snoring is the earliest symptom of OSA, but its potential in clinical diagnosis is not fully recognized yet. Diagnostic systems intent on using snore-related sounds (SRS) face the tough problem of how to define a snore. In this paper, we present a working definition of a snore, and propose algorithms to segment SRS into classes of pure breathing, silence and voiced/unvoiced snores. We propose a novel feature termed the 'intra-snore-pitch-jump' (ISPJ) to diagnose OSA. Working on clinical data, we show that ISPJ delivers OSA detection sensitivities of 86-100% while holding specificity at 50-80%. These numbers indicate that snore sounds and the ISPJ have the potential to be good candidates for a take-home device for OSA screening. Snore sounds have the significant advantage in that they can be conveniently acquired with low-cost non-contact equipment. The segmentation results presented in this paper have been derived using data from eight patients as the training set and another eight patients as the testing set. ISPJ-based OSA detection results have been derived using training data from 16 subjects and testing data from 29 subjects.