Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Error and uncertainty of adult age estimation of the pubic symphysis in an Australian sub-population using computed tomography

After attending this presentation, attendees will gain awareness of: (1) the error and uncertainty associated with the application of the Suchey-Brooks (S-B) method of age estimation of the pubic symphysis to a contemporary Australian population; (2) the implications of sexual dimorphism and bilateral asymmetry of the pubic symphysis through preliminary geometric morphometric assessment; and (3) the value of three-dimensional (3D) autopsy data acquisition for creating forensic anthropological standards. This presentation will impact the forensic science community by demonstrating that, in the absence of demographically sound skeletal collections, post-mortem autopsy data provides an exciting platform for the construction of large contemporary ‘virtual osteological libraries’ for which forensic anthropological research can be conducted on Australian individuals. More specifically, this study assesses the applicability and accuracy of the S-B method to a contemporary adult population in Queensland, Australia, and using a geometric morphometric approach, provides an insight to the age-related degeneration of the pubic symphysis. Despite the prominent use of the Suchey-Brooks (1990) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations1-4. Australian forensic anthropology is constrained by a paucity of population specific standards due to a lack of repositories of documented skeletons. Consequently, in Australian casework proceedings, standards constructed from predominately American reference samples are applied to establish a biological profile. In the global era of terrorism and natural disasters, more specific population standards are required to improve the efficiency of medico-legal death investigation in Queensland. The sample comprises multi-slice computed tomography (MSCT) scans of the pubic symphysis (slice thickness: 0.5mm, overlap: 0.1mm) on 195 individuals of caucasian ethnicity aged 15-70 years. Volume rendering reconstruction of the symphyseal surface was conducted in Amira® (v.4.1) and quantitative analyses in Rapidform® XOS. The sample was divided into ten-year age sub-sets (eg. 15-24) with a final sub-set of 65-70 years. Error with respect to the method’s assigned means were analysed on the basis of bias (directionality of error), inaccuracy (magnitude of error) and percentage correct classification of left and right symphyseal surfaces. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface and micro-architectural assessment of cortical and trabecular bone composition were quantified using novel automated engineering software capabilities. The results of this study demonstrated correct age classification utilizing the mean and standard deviations of each phase of the S-B method of 80.02% and 86.18% in Australian males and females, respectively. Application of the S-B method resulted in positive biases and mean inaccuracies of 7.24 (±6.56) years for individuals less than 55 years of age, compared to negative biases and mean inaccuracies of 5.89 (±3.90) years for individuals greater than 55 years of age. Statistically significant differences between chronological and S-B mean age were demonstrated in 83.33% and 50% of the six age subsets in males and females, respectively. Asymmetry of the pubic symphysis was a frequent phenomenon with 53.33% of the Queensland population exhibiting statistically significant (χ2 - p<0.01) differential phase classification of left and right surfaces of the same individual. Directionality was found in bilateral asymmetry, with the right symphyseal faces being slightly older on average and providing more accurate estimates using the S-B method5. Morphometric analysis verified these findings, with the left surface exhibiting significantly greater circumference and surface area than the right (p<0.05). Morphometric analysis demonstrated an increase in maximum height and width of the surface with age, with most significant changes (p<0.05) occurring between the 25-34 and 55-64 year age subsets. These differences may be attributed to hormonal components linked to menopause in females and a reduction in testosterone in males. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal surfaces of the pubic symphysis. This study recommends that the S-B method be applied with caution in medico-legal death investigations of unknown skeletal remains in Queensland. Age estimation will always be accompanied by error; therefore this study demonstrates the potential for quantitative morphometric modelling of age related changes of the pubic symphysis as a tool for methodological refinement, providing a rigor and robust assessment to remove the subjectivity associated with current pelvic aging methods.

Axial spondyloarthritis: A new disease entity, not necessarily early ankylosing spondylitis

New classification criteria for axial spondyloarthritis have been developed with the goal of increasing sensitivity of criteria for early inflammatory spondyloarthritis. However these criteria substantially increase heterogeneity of the resulting disease group, reducing their value in both research and clinical settings. Further research to establish criteria based on better knowledge of the natural history of non-radiographic axial spondyloarthritis, its aetiopathogenesis and response to treatment is required. In the meantime the modified New York criteria for ankylosing spondylitis remain a very useful classification criteria set, defining a relatively homogenous group of cases for clinical use and research studies.

Interruptions of (CG)n sequences by GG, TG and CA need not prevent B to Z transition in solution

Oligonucleotides containing alternating purines-pyrimidines with AT base pairs have been shown to exist in the Z-form preferably in solid state. We report that oligodeoxyribonucleotides with GG, TG and CA interruptions in their alternating CG sequences can undergo B to Z transition in solution in the absence of any chemical modification or topological constraint. The sequences, d(CGCGCGGCGCGC) and d(CGTGCGCACG) have been synthesised and shown to adopt Z- conformation in presence of millimolar concentrations of Ni2+ under low water activity conditions. Significance of GG, TG and CA interruptions in the B to Z transition is discussed.

A Matroidal Framework for Network-Error Correcting Codes

Matroidal networks were introduced by Dougherty et al. and have been well studied in the recent past. It was shown that a network has a scalar linear network coding solution if and only if it is matroidal associated with a representable matroid. A particularly interesting feature of this development is the ability to construct (scalar and vector) linearly solvable networks using certain classes of matroids. Furthermore, it was shown through the connection between network coding and matroid theory that linear network coding is not always sufficient for general network coding scenarios. The current work attempts to establish a connection between matroid theory and network-error correcting and detecting codes. In a similar vein to the theory connecting matroids and network coding, we abstract the essential aspects of linear network-error detecting codes to arrive at the definition of a matroidal error detecting network (and similarly, a matroidal error correcting network abstracting from network-error correcting codes). An acyclic network (with arbitrary sink demands) is then shown to possess a scalar linear error detecting (correcting) network code if and only if it is a matroidal error detecting (correcting) network associated with a representable matroid. Therefore, constructing such network-error correcting and detecting codes implies the construction of certain representable matroids that satisfy some special conditions, and vice versa. We then present algorithms that enable the construction of matroidal error detecting and correcting networks with a specified capability of network-error correction. Using these construction algorithms, a large class of hitherto unknown scalar linearly solvable networks with multisource, multicast, and multiple-unicast network-error correcting codes is made available for theoretical use and practical implementation, with parameters, such as number of information symbols, number of sinks, number of coding nodes, error correcting capability, and so on, being arbitrary but for computing power (for the execution of the algorithms). The complexity of the construction of these networks is shown to be comparable with the complexity of existing algorithms that design multicast scalar linear network-error correcting codes. Finally, we also show that linear network coding is not sufficient for the general network-error correction (detection) problem with arbitrary demands. In particular, for the same number of network errors, we show a network for which there is a nonlinear network-error detecting code satisfying the demands at the sinks, whereas there are no linear network-error detecting codes that do the same.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

Photosynthesis of Saussurea superba and Gentiana straminea is not reduced after long-term enhancement of UV-B radiation

Experiments were conducted in an alpine Kobresia humilis meadow near Haibei Alpine Meadow Ecosystem Research Station (37degrees29'-37degrees45'N, 101degrees12'-101degrees33'E; altitude 3200 m). Effects of enhanced ultraviolet-B (UV-B) radiation on photosynthesis of the alpine plants of Saussurea superba and Gentiana straminea were investigated. Both species were exposed to a UV-B-BE density at 15.80 kJ m(-2) per day, simulating nearly 14% ozone (O-3) reduction during the plant growing season. Neither photosynthetic CO2 uptake rate nor photosynthetic O-2 evolution rate were decreased after a long period of enhanced UV-B radiation treatment. On the contrary, there was a tendency to increase of both parameters in both species. The photosynthetic pigments were also increased, when expressed on a leaf area basis. UV-B absorbing compounds, detected by the absorbance values at 300 mm, had a tendency to increase in both species after enhanced UV-B radiation. After long-term exposure of plants to enhanced UV-B radiation, leaf morphology was also affected. Leaf thickness in both S. superba and G. straminea were increased significantly (P < 0.001). This supports our hypothesis that the increase of leaf thickness in both species after long-term exposure of enhanced UV-B radiation could compensate for the photodestruction of photosynthetic pigments when light passes through the leaf. Therefore, photosynthesis is not reduced in either species when expressed on leaf area basis. (C) 2003 Elsevier B.V. All rights reserved.

Modeling energy consumption in error-prone IEEE 802.11-based wireless ad-hoc networks

In the IEEE 802.11 MAC layer protocol, there are different trade-off points between the number of nodes competing for the medium and the network capacity provided to them. There is also a trade-off between the wireless channel condition during the transmission period and the energy consumption of the nodes. Current approaches at modeling energy consumption in 802.11 based networks do not consider the influence of the channel condition on all types of frames (control and data) in the WLAN. Nor do they consider the effect on the different MAC and PHY schemes that can occur in 802.11 networks. In this paper, we investigate energy consumption corresponding to the number of competing nodes in IEEE 802.11's MAC and PHY layers in error-prone wireless channel conditions, and present a new energy consumption model. Analysis of the power consumed by each type of MAC and PHY over different bit error rates shows that the parameters in these layers play a critical role in determining the overall energy consumption of the ad-hoc network. The goal of this research is not only to compare the energy consumption using exact formulae in saturated IEEE 802.11-based DCF networks under varying numbers of competing nodes, but also, as the results show, to demonstrate that channel errors have a significant impact on the energy consumption.

Real-time error detection but not error correction drives automatic visuomotor adaptation

We investigated the role of visual feedback of task performance in visuomotor adaptation. Participants produced novel two degrees of freedom movements (elbow flexion-extension, forearm pronation-supination) to move a cursor towards visual targets. Following trials with no rotation, participants were exposed to a 60A degrees visuomotor rotation, before returning to the non-rotated condition. A colour cue on each trial permitted identification of the rotated/non-rotated contexts. Participants could not see their arm but received continuous and concurrent visual feedback (CF) of a cursor representing limb position or post-trial visual feedback (PF) representing the movement trajectory. Separate groups of participants who received CF were instructed that online modifications of their movements either were, or were not, permissible as a means of improving performance. Feedforward-mediated performance improvements occurred for both CF and PF groups in the rotated environment. Furthermore, for CF participants this adaptation occurred regardless of whether feedback modifications of motor commands were permissible. Upon re-exposure to the non-rotated environment participants in the CF, but not PF, groups exhibited post-training aftereffects, manifested as greater angular deviations from a straight initial trajectory, with respect to the pre-rotation trials. Accordingly, the nature of the performance improvements that occurred was dependent upon the timing of the visual feedback of task performance. Continuous visual feedback of task performance during task execution appears critical in realising automatic visuomotor adaptation through a recalibration of the visuomotor mapping that transforms visual inputs into appropriate motor commands.

Spectacle acceptance among secondary school students in rural China: the Xichang Pediatric Refractive Error Study (X-PRES)--report 5.

PURPOSE: To assess determinants of spectacle acceptance and use among rural Chinese children. METHODS: Children with uncorrected acuity < or = 6/12 in either eye and whose presenting vision could be improved > or = 2 lines with refraction were identified from a school-based sample of 1892 students. Information on obtaining glasses and the benefits of spectacles was provided to children, families, and teachers. Purchase of new spectacles and reasons for nonpurchase were assessed by direct inspection and interview 3 months later. RESULTS: Among 674 (35.6%) children requiring spectacles (mean age, 14.7 +/- 0.8 years), 597 (88.6%) were followed up. Among 339 children with no glasses at baseline, 30.7% purchased spectacles, whereas 43.2% of 258 children with inaccurate glasses replaced them. Most (70%) subjects paid US$13 to $26. Among children with bilateral vision < or = 6/18, 45.6% bought glasses. In multivariate models, presenting vision < 6/12 (P < 0.009), refractive error < -2.0 D (P < 0.001), and amount willing to pay for glasses (P = 0.01) were predictors of purchase. Reasons for nonpurchase included satisfaction with current vision (78% of those with glasses at baseline, 49% of those without), concerns over price or parental refusal (18%), and fear glasses would weaken the eyes (13%). Only 26% of children stated that they usually wore their new glasses. CONCLUSIONS: Many families in rural China will pay for glasses, though spectacle acceptance was < 50%, even among children with poor vision. Acceptance could be improved by price reduction, education showing that glasses will not harm the eyes, and parent-focused interventions.

Strategies to improve the accuracy of vision measurement by teachers in rural Chinese secondary schoolchildren: Xichang Pediatric Refractive Error Study (X-PRES) report no. 6.

OBJECTIVE: To assess and improve the accuracy of lay screeners compared with vision professionals in detecting visual impairment in secondary schoolchildren in rural China. METHODS: After brief training, 32 teachers and a team of vision professionals independently measured vision in 1892 children in Xichang. The children also underwent vision measurement by health technicians in a concurrent government screening program. RESULTS: Of 32 teachers, 28 (87.5%) believed that teacher screening was worthwhile. Sensitivity (93.5%) and specificity (91.2%) of teachers detecting uncorrected presenting visual acuity of 20/40 or less were better than for presenting visual acuity (sensitivity, 85.2%; specificity, 84.8%). Failure of teachers to identify children owning but not wearing glasses and teacher bias toward better vision in children wearing glasses explain the worse results for initial vision. Wearing glasses was the student factor most strongly predictive of inaccurate teacher screening (P < .001). The sensitivity and specificity of the government screening program detecting low presenting visual acuity were 86.7% and 28.7%, respectively. CONCLUSIONS: Teacher vision screening after brief training can achieve accurate results in this setting, and there is support among teachers for screening. Screening of uncorrected rather than presenting visual acuity is recommended in settings with a high prevalence of corrected and uncorrected refractive error. Low specificity in the government program renders it ineffective.

Associations between near work, outdoor activity, and myopia among adolescent students in rural China: the Xichang Pediatric Refractive Error Study report no. 2.

OBJECTIVE:

To study the associations between near work, outdoor activity, and myopia among children attending secondary school in rural China.

METHODS:

Among a random cluster sample of 1892 children in Xichang, China, subjects with an uncorrected acuity of 6/12 or less in either eye (n = 984) and a 25% sample of children with normal vision (n = 248) underwent measurement of refractive error. Subjects were administered a questionnaire on parental education, time spent outdoors, and weekly time spent engaged in and preferred working distance for a variety of near-work activities.

RESULTS:

Among 1232 children with refraction data, 998 (81.0%) completed the near-work survey. Their mean age was 14.6 years (SD, 0.8 years), 55.6% were girls, and 83.1% had myopia of -0.5 diopters or less (more myopia) in both eyes. Time and diopter-hours spent on near activities did not differ between children with and without myopia. In regression models, time spent on near activities and time outdoors were unassociated with myopia, adjusting for age, sex, and parental education.

CONCLUSIONS:

These and other recent results raise some doubts about the association between near work and myopia. Additional efforts to identify other environmental factors associated with myopia risk and that may be amenable to intervention are warranted.

Self correction of refractive error among young people in rural China: results of cross sectional investigation.

OBJECTIVE: To compare outcomes between adjustable spectacles and conventional methods for refraction in young people. DESIGN: Cross sectional study. SETTING: Rural southern China. PARTICIPANTS: 648 young people aged 12-18 (mean 14.9 (SD 0.98)), with uncorrected visual acuity ≤ 6/12 in either eye. INTERVENTIONS: All participants underwent self refraction without cycloplegia (paralysis of near focusing ability with topical eye drops), automated refraction without cycloplegia, and subjective refraction by an ophthalmologist with cycloplegia. MAIN OUTCOME MEASURES: Uncorrected and corrected vision, improvement of vision (lines on a chart), and refractive error. RESULTS: Among the participants, 59% (384) were girls, 44% (288) wore spectacles, and 61% (393/648) had 2.00 dioptres or more of myopia in the right eye. All completed self refraction. The proportion with visual acuity ≥ 6/7.5 in the better eye was 5.2% (95% confidence interval 3.6% to 6.9%) for uncorrected vision, 30.2% (25.7% to 34.8%) for currently worn spectacles, 96.9% (95.5% to 98.3%) for self refraction, 98.4% (97.4% to 99.5%) for automated refraction, and 99.1% (98.3% to 99.9%) for subjective refraction (P = 0.033 for self refraction v automated refraction, P = 0.001 for self refraction v subjective refraction). Improvements over uncorrected vision in the better eye with self refraction and subjective refraction were within one line on the eye chart in 98% of participants. In logistic regression models, failure to achieve maximum recorded visual acuity of 6/7.5 in right eyes with self refraction was associated with greater absolute value of myopia/hyperopia (P<0.001), greater astigmatism (P = 0.001), and not having previously worn spectacles (P = 0.002), but not age or sex. Significant inaccuracies in power (≥ 1.00 dioptre) were less common in right eyes with self refraction than with automated refraction (5% v 11%, P<0.001). CONCLUSIONS: Though visual acuity was slightly worse with self refraction than automated or subjective refraction, acuity was excellent in nearly all these young people with inadequately corrected refractive error at baseline. Inaccurate power was less common with self refraction than automated refraction. Self refraction could decrease the requirement for scarce trained personnel, expensive devices, and cycloplegia in children's vision programmes in rural China.