Nystrom Methods in the RKQ Algorithm for Initial-value Problems

We incorporate explicit Nystrom methods into the RKQ algorithm for stepwise global error control in numerical solutions of initial-value problems. The initial-value problem is transformed into an explicitly second-order problem, so as to be suitable for Nystrom integration. The Nystrom methods used are fourth-order, fifth-order and 10th-order. Two examples demonstrate the effectiveness of the algorithm.Comment: This is an extension of ideas published in J. Math. Res. (open access); see refs [1] and [2

An Euler-type method for Volterra integro-differential equations

We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent variable as the required nodes for the integration variable. We have developed an error control device, using Richardson extrapolation, and we have achieved accuracy better than 1e-12 for all numerical examples considered.Comment: 11 page

Stability analysis of an implicit and explicit numerical method for Volterra integro-differential equations with kernel K(x,y(t),t)

We present implicit and explicit versions of a numerical algorithm for solving a Volterra integro-differential equation. These algorithms are an extension of our previous work, and cater for a kernel of general form. We use an appropriate test equation to study the stability of both algorithms,, numerically deriving stability regions. The region for the implicit method appears to be unbounded, while the explicit has a bounded region close to the origin. We perform a few calculations to demonstrate our results.Comment: 10 pages, 1 Figur

Error propagation in an explicit and an implicit numerical method for Volterra integro-differential equations

We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show that the global order for both methods is expected to be first-order. A few numerical examples illustrate our results.Comment: 14p, 5 fig

Range and Domain Partitioning in Piecewise Polynomial Approximation

Abstract: Error control in piecewise polynomial interpolation of a smooth univariate function f requires that the interval of approximation be subdivided into many subintervals, on each of which an interpolating polynomial is determined. The number of such subintervals is often over- estimated through the use of a high-order derivative of f . We report on a partitioning algorithm, in which we attempt to reduce the number of subintervals required, by imposing conditions on f and its relevant higher derivative. One of these conditions facilitates a distinction between the need for absolute or relative error control. Two examples demonstrate the effectiveness of this partitioning algorithm. Key Words: Piecewise Polynomial; Range Partitioning; Domain Partitioning; Error Contro

Validation and clinical application of molecular methods for the identification of molds in tissue

Background. Invasive fungal infections due to less-common molds are an increasing problem, and accurate diagnosis is difficult.Methods. We used our previously established molecular method, which allows species identification of molds in histological tissue sections, to test sequential specimens from 56 patients with invasive fungal infections who were treated at our institution from 1982 to 2000.Results. The validity of the method was demonstrated with the establishment of a molecular diagnosis in 52 cases (93%). Confirmation of the causative organism was made in all cases in which a mold had been cultured from the tissue specimen. Less-common molds were identified in 7% of cases and appear to be an increasing problem.Conclusions. Our previously established method has proven to be of value in determining the incidence of invasive infection caused by less-common molds. Institutions should continue to pursue diagnosis of invasive fungal infections by means of tissue culture and microbiologic analysis

Transformation of stimulus correlations by the retina

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.Comment: author list corrected in metadat

The PML-RAR alpha transcript in long-term follow-up of acute promyelocytic leukemia patients

Background and Objectives. Detection of PML-RAR alpha transcripts by RT-PCR is now established as a rapid and sensitive method for diagnosis of acute promyelocytic leukemia (APL), Although the majority of patients in longterm clinical remission are negative by consecutive reverse transcription polymerase chain reaction (RT-PCR) assays, negative tests are still observed in patients who ultimately relapse. Conversion from negative to positive PCR has been observed after consolidation and found to be a much stronger predictor of relapse. This study reports on 47 APL patients to determine the correlation between minimal residual disease (MRD) status and clinical outcome in our cohort of patients. Design and Methods. The presence of PML-RAR alpha t transcripts was investigated in 47 APL patients (37 adults and 10 children) using a semi-nested reverse transcriptase-polymerase chain reaction to evaluate the prognostic value of RT-PCR tests. Results. All patients achieved complete clinical remission (CCR) following induction treatment with all-trans retinoic acid (ATRA) and chemotherapy (CHT) or ATRA alone. Patients were followed up between 2 and 117.6 months (median: 37 months). Relapses occurred in 11 patients (9 adults and 2 children) between 11.4 and 19 months after diagnosis (median: 15.1 months) while 36 patients (28 adults and 8 children) remained in CCR, Seventy-five percent of patients carried the PML-RARa long isoform (bcr 1/2) which also predominated among the relapsed cases (9 of 11) but did not associate with any adverse outcome (p = 0.37), For the purpose of this analysis, minimal residual disease tests were clustered into four time-intervals: 0-2 months, 3-5 months, 5-9 months and 10-24 months. Interpretation and Conclusions. Children showed persisting disease for longer than adults during the first 2 months of treatment, At 2 months, 10 (50%) of 20 patients who remained in CCR and 4 (80%) of 5 patients who subsequently relapsed were positive. Patients who remained in CCR had repeatedly negative results beyond 5.5 months from diagnosis. A positive MRD test preceded relapse in 3 of 4 tested patients. The ability of a negative test to predict CCR (predictive negative value, PNV) was greater after 6 months (> 83%), while the ability of a positive test to predict relapse (predictive positive value, PPV) was most valuable only beyond 10 months (100%). This study (i) highlights the prognostic value of RT-PCR monitoring after treatment of APL patients but only from the end of treatment, (ii) shows an association between conversion to a positive test and relapse and (iii) suggests that PCR assessments should be carried out at 3-month intervals to provide a more accurate prediction of hematologic relapses but only after the end of treatment, (C) 2001, Ferrata Storti Foundatio