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.

Modelling the Distribution of Ischaemic Stroke-Specific Survival Time Using an EM-based Mixture Approach with Random Effects Adjustment

A two-component survival mixture model is proposed to analyse a set of ischaemic stroke-specific mortality data. The survival experience of stroke patients after index stroke may be described by a subpopulation of patients in the acute condition and another subpopulation of patients in the chronic phase. To adjust for the inherent correlation of observations due to random hospital effects, a mixture model of two survival functions with random effects is formulated. Assuming a Weibull hazard in both components, an EM algorithm is developed for the estimation of fixed effect parameters and variance components. A simulation study is conducted to assess the performance of the two-component survival mixture model estimators. Simulation results confirm the applicability of the proposed model in a small sample setting. Copyright (C) 2004 John Wiley Sons, Ltd.

Improved comparison plot method for pore structure characterization of MCM-41

MCM-41 samples of various pore dimensions are synthesized. Plotting of nitrogen adsorption data at 77 K versus the statistical film thickness (comparison plot) reveals three distinct stages, with a characteristic of two points of inflection. The steep intermediate stage caused by capillary condensation occurred in the highly uniform mesopores. From the slopes of the sections before and after the condensation, the surface area of the mesopores is calculated. The linear portion of the last section is extrapolated to the adsorption axis of the comparison plot, and this intercept is used to obtain the volume of the mesopores. From the surface area and pore volume, average mesopore diameter is calculated, and the value thus obtained is in good agreement with the pore dimension obtained from powder X-ray diffraction measurements. The principle of the calculation as well as problems associated are discussed in detail.

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.

Comparison of HRT-3 glaucoma probability score and subjective stereophotograph assessment for prediction of progression in glaucoma

PURPOSE. To assess whether baseline Glaucoma Probability Score (GPS; HRT-3; Heidelberg Engineering, Dossenheim, Germany) results are predictive of progression in patients with suspected glaucoma. The GPS is a new feature of the confocal scanning laser ophthalmoscope that generates an operator-independent, three-dimensional model of the optic nerve head and gives a score for the probability that this model is consistent with glaucomatous damage. METHODS. The study included 223 patients with suspected glaucoma during an average follow-up of 63.3 months. Included subjects had a suspect optic disc appearance and/or elevated intraocular pressure, but normal visual fields. Conversion was defined as development of either repeatable abnormal visual fields or glaucomatous deterioration in the appearance of the optic disc during the study period. The association between baseline GPS and conversion was investigated by Cox regression models. RESULTS. Fifty-four (24.2%) eyes converted. In multivariate models, both higher values of GPS global and subjective stereophotograph assessment ( larger cup-disc ratio and glaucomatous grading) were predictive of conversion: adjusted hazard ratios (95% CI): 1.31 (1.15 - 1.50) per 0.1 higher global GPS, 1.34 (1.12 - 1.62) per 0.1 higher CDR, and 2.34 (1.22 - 4.47) for abnormal grading, respectively. No significant differences ( P > 0.05 for all comparisons) were found between the c-index values ( equivalent to area under ROC curve) for the multivariate models (0.732, 0.705, and 0.699, respectively). CONCLUSIONS. GPS values were predictive of conversion in our population of patients with suspected glaucoma. Further, they performed as well as subjective assessment of the optic disc. These results suggest that GPS could potentially replace stereophotograph as a tool for estimating the likelihood of conversion to glaucoma.

A critical view on biaxial and short-beam uniaxial flexural strength tests applied to resin composites using Weibull, fractographic and finite element analyses

Objective. To evaluate the biaxial and short-beam uniaxial strength tests applied to resin composites based upon their Weibull parameters, fractographic features and stress distribution. Methods. Disk- (15 mm x 1 mm) and beam-shaped specimens (10 mm x 2 mm x 1 mm) of three commercial composites (Concept/Vigodent, CA; Heliomolar/Ivoclar-Vivadent, HE; Z250/3M ESPE, FZ) were prepared. After 48h dry storage at 37 degrees C, disks and beams were submitted to piston-on-three-balls (BI) and three-point bending (UNI) tests, respectively. Data were analyzed by Weibull statistics. Fractured surfaces were observed under stereomicroscope and scanning electron microscope. Maximum principal stress (sigma(1)) distribution was determined by finite element analysis (FEA). Maximum sigma(1-BI) and sigma(1-UNI) were compared to FZ strengths calculated by applying the average failure loads to the analytical equations (sigma(a-BI) and sigma(a-UNI)). Results. For BI, characteristic strengths were: 169.9a (FZ), 122.4b (CA) and 104.8c (HE), and for UNI were: 160.3a (FZ), 98.2b (CA) and 91.6b (HE). Weibull moduli ( m) were similar within the same test. CA and HE presented statistically higher m for BI. Surface pores ( BI) and edge flaws ( UNI) were the most frequent fracture origins. sigma(1-BI) was 14% lower than sigma(a-BI.) sigma(1-UNI) was 43% higher than sigma(a-UNI). Significance. Compared to the short-beam uniaxial test, the biaxial test detected more differences among composites and displayed less data scattering for two of the tested materials. Also, biaxial strength was closer to the material`s strength estimated by FEA. (C) 2009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Effect of ion exchange on strength and slow crack growth of a dental porcelain

Objectives. To determine the effect of ion exchange on slow crack growth (SCG) parameters (n, stress corrosion susceptibility coefficient, and sigma(f0), scaling parameter) and Weibull parameters (m, Weibull modulus, and sigma(0), characteristic strength) of a dental porcelain. Methods. 160 porcelain discs were fabricated according to manufacturer`s instructions, polished through 1 mu m and divided into two groups: GC (control) and GI (submitted to an ion exchange procedure using a KNO(3) paste at 470 degrees C for 15 min). SCG parameters were determined by biaxial flexural strength test in artificial saliva at 37 degrees C using five constant stress rates (n =10). 20 specimens of each group were tested at 1 MPa/s to determine Weibull parameters. The SPT diagram was constructed using the least-squares fit of the strength data versus probability of failure. Results. Mean values of m and sigma(0) (95% confidence interval), n and sigma(f0) (standard deviation) were, respectively: 13.8 (10.1-18.8) and 60.4 (58.5 - 62.2), 24.1 (2.5) and 58.1 (0.01) for GC and 7.4 (5.3 -10.0) and 136.8 (129.1-144.7), 36.7 (7.3) and 127.9 (0.01) for GI. Fracture stresses (MPa) calculated using the SPT diagram for lifetimes of 1 day, 1 year and 10 years (at a 5% failure probability) were, respectively, 31.8, 24.9 and 22.7 for GC and 71.2, 60.6 and 56.9 for GI. Significance. For the porcelain tested, the ion exchange process improved strength and resistance to SCG, however, the material`s reliability decreased. The predicted fracture stress at 5% failure probability for a lifetime of 10 years was also higher for the ion treated group. (C) 009 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Failure modes of Y-TZP crowns at different cusp inclines

Objectives To compare the reliability of the disto-facial (DF) and mesio-lingual (ML) cusps of an anatomically correct zirconia (Y-TZP) crown system The research hypotheses tested were (1) fatigue reliability and failure mode are similar for the ML and DF cusps, (2) failure mode of one cusp does not affect the failure of the other Methods The average dimensions of a mandibular first molar crown were imported into CAD software, a tooth preparation was modelled by 1 5 mm marginal high reduction of proximal walls and occlusal surface by 2 0 mm The CAD-based tooth preparation was milled and used as a die to fabricate crowns (n = 14) with porcelain veneer on a 0 5 mm Y-TZP core. Crowns were cemented on composite reproductions of the tooth preparation The crowns were step-stress mouth motion fatigued with sliding (0 7 mm) a tungsten-carbide indenter of 6 25 mm diameter down on the inclines of either the DF or ML cusps Use level probability Weibull curve with use stress of 200 N and the reliability for completion of a mission of 50,000 cycles at 200 N load were calculated Results Reliability for a 200 N at 50,000 cycles mission was not different between tested cusps SEM imaging showed large cohesive failures within the veneer for the ML and smaller for the DF Fractures originated from the contact area regardless of the cusp loaded Conclusion No significant difference on fatigue reliability was observed between the DF compared to the ML cusp Fracture of one cusp did not affect the other (c) 2010 Elsevier Ltd All rights reserved

Fatigue and damage accumulation of veneer porcelain pressed on Y-TZP

Objectives: This study compared the reliability and fracture patterns of zirconia cores veneered with pressable porcelain submitted to either axial or off-axis sliding contact fatigue. Methods: Forty-two Y-TZP plates (12 mm x 12 mm x 0.5 mm) veneered with pressable porcelain (12 mm x 12 mm x 1.2 mm) and adhesively luted to water aged composite resin blocks (12 mm x 12 mm x 4 mm) were stored in water at least 7 days prior to testing. Profiles for step-stress fatigue (ratio 3:2:1) were determined from single load to fracture tests (n = 3). Fatigue loading was delivered on specimen either on axial (n = 18) or off-axis 30 degrees angulation (n = 18) to simulate posterior tooth cusp inclination creating a 0.7 mm slide. Single load and fatigue tests utilized a 6.25 mm diameter WC indenter. Specimens were inspected by means of polarized-light microscope and SEM. Use level probability Weibull curves were plotted with 2-sided 90% confidence bounds (CB) and reliability for missions of 50,000 cycles at 200 N (90% CB) were calculated. Results: The calculated Weibull Beta was 3.34 and 2.47 for axial and off-axis groups, respectively, indicating that fatigue accelerated failure in both loading modes. The reliability data for a mission of 50,000 cycles at 200 N load with 90% CB indicates no difference between loading groups. Deep penetrating cone cracks reaching the core-veneer interface were observed in both groups. Partial cones due to the sliding component were observed along with the cone cracking for the off-axis group. No Y-TZP core fractures were observed. Conclusions: Reliability was not significantly different between axial and off-axis mouth-motion fatigued pressed over Y-TZP cores, but incorporation of sliding resulted in more aggressive damage on the veneer. (C) 2009 Elsevier Ltd. All rights reserved.

Reliability of Metalloceramic and Zirconia-based Ceramic Crowns

Despite the increasing utilization of all-ceramic crown systems, their mechanical performance relative to that of metal ceramic restorations (MCR) has yet to be determined. This investigation tested the hypothesis that MCR present higher reliability over two Y-TZP all-ceramic crown systems under mouth-motion fatigue conditions. A CAD-based tooth preparation with the average dimensions of a mandibular first molar was used as a master die to fabricate all restorations. One 0.5-mm Pd-Ag and two Y-TZP system cores were veneered with 1.5 mm porcelain. Crowns were cemented onto aged (60 days in water) composite (Z100, 3M/ESPE) reproductions of the die. Mouth-motion fatigue was performed, and use level probability Weibull curves were determined. Failure modes of all systems included chipping or fracture of the porcelain veneer initiating at the indentation site. Fatigue was an acceleration factor for all-ceramic systems, but not for the MCR system. The latter presented significantly higher reliability under mouth-motion cyclic mechanical testing.

Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.