The determination of orbits using Picard iteration

The determination of orbits by using Picard iteration is reported. This is a direct extension of the classical method of Picard that has been used in finding approximate solutions of nonlinear differential equations for a variety of problems. The application of the Picard method of successive approximations to the initial value and the two point boundary value problems is given

Processing of spatial-frequency altered faces in schizophrenia: Effects of illness phase and duration

Low spatial frequency (SF) processing has been shown to be impaired in people with schizophrenia, but it is not clear how this varies with clinical state or illness chronicity. We compared schizophrenia patients (SCZ, n534), first episode psychosis patients (FEP, n522), and healthy controls (CON, n535) on a gender/facial discrimination task. Images were either unaltered (broadband spatial frequency, BSF), or had high or low SF information removed (LSF and HSF conditions, respectively). The task was performed at hospital admission and discharge for patients, and at corresponding time points for controls. Groups were matched on visual acuity. At admission, compared to their BSF performance, each group was significantly worse with low SF stimuli, and most impaired with high SF stimuli. The level of impairment at each SF did not depend on group. At discharge, the SCZ group performed more poorly in the LSF condition than the other groups, and showed the greatest degree of performance decline collapsed over HSF and LSF conditions, although the latter finding was not significant when controlling for visual acuity. Performance did not change significantly over time for any group. HSF processing was strongly related to visual acuity at both time points for all groups. We conclude the following: 1) SF processing abilities in schizophrenia are relatively stable across clinical state; 2) face processing abnormalities in SCZ are not secondary to problems processing specific SFs, but are due to other known difficulties constructing visual representations from degraded information; and 3) the relationship between HSF processing and visual acuity, along with known SCZ- and medication-related acuity reductions, and the elimination of a SCZ-related impairment after controlling for visual acuity in this study, all raise the possibility that some prior findings of impaired perception in SCZ may be secondary to acuity reductions

Impact of recurrent copy number alterations and cancer gene mutations on the predictive accuracy of prognostic models in clear cell renal cell carcinoma.

Several recently reported recurrent genomic alterations in clear cell renal cell carcinoma are linked to pathological and clinical outcomes. We determined whether any recurrent cancer gene mutations or copy number alterations identified in the TCGA (The Cancer Genome Atlas) clear cell renal cell carcinoma data set could add to the predictive accuracy of current prognostic models. In 413 patients who underwent nephrectomy/partial nephrectomy we investigated whole exome, copy number array analyses and clinical variables. We identified 65 recurrent genomic alterations based on prevalence and combined them into 35 alterations, including 12 cancer gene mutations. Genomic markers were modeled using the elastic net algorithm with preoperative variables (tumor size plus patient age) and in the postoperative setting using the externally validated Mayo Clinic SSIGN (stage, size, grade and necrosis) prognostic scoring system. These models were subjected to internal validation using bootstrap. Median followup in survivors was 45 months. Several markers correlated with adverse cancer specific survival and time to recurrence on univariate analysis. However, most of them lost significance when controlling for tumor size with or without age in the preoperative models or for SSIGN score in the postoperative setting. Adding multiple genomic markers selected by the elastic net algorithm failed to substantially add to the predictive accuracy of any preoperative or postoperative model for cancer specific survival or time to recurrence. While recurrent copy number alterations and cancer gene mutations are biologically significant, they do not appear to improve the predictive accuracy of existing models of clinical cancer specific survival or time to recurrence for clear cell renal cell carcinoma