Sinc-Galerkin method for solving nonlinear boundary-value problems

AbstractThe sinc-Galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second-, fourth-, and sixth-order differential equations with homogeneous and nonhomogeneous boundary conditions. The scheme is tested on four nonlinear problems. The results demonstrate the reliability and efficiency of the algorithm developed

A system of ODEs for a Perturbation of a Minimal Mass Soliton

We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify a system of ODEs similar to those from Comech and Pelinovsky (2003), which model the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, which is in accord with the conclusions of Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a soliton structure, a generic initial perturbation oscillates around the stable family of solitons. For initial data which is expected to disperse, the finite dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit

Minimum follow-up time required for the estimation of statistical cure of cancer patients: verification using data from 42 cancer sites in the SEER database

BACKGROUND: The present commonly used five-year survival rates are not adequate to represent the statistical cure. In the present study, we established the minimum number of years required for follow-up to estimate statistical cure rate, by using a lognormal distribution of the survival time of those who died of their cancer. We introduced the term, threshold year, the follow-up time for patients dying from the specific cancer covers most of the survival data, leaving less than 2.25% uncovered. This is close enough to cure from that specific cancer. METHODS: Data from the Surveillance, Epidemiology and End Results (SEER) database were tested if the survival times of cancer patients who died of their disease followed the lognormal distribution using a minimum chi-square method. Patients diagnosed from 1973–1992 in the registries of Connecticut and Detroit were chosen so that a maximum of 27 years was allowed for follow-up to 1999. A total of 49 specific organ sites were tested. The parameters of those lognormal distributions were found for each cancer site. The cancer-specific survival rates at the threshold years were compared with the longest available Kaplan-Meier survival estimates. RESULTS: The characteristics of the cancer-specific survival times of cancer patients who died of their disease from 42 cancer sites out of 49 sites were verified to follow different lognormal distributions. The threshold years validated for statistical cure varied for different cancer sites, from 2.6 years for pancreas cancer to 25.2 years for cancer of salivary gland. At the threshold year, the statistical cure rates estimated for 40 cancer sites were found to match the actuarial long-term survival rates estimated by the Kaplan-Meier method within six percentage points. For two cancer sites: breast and thyroid, the threshold years were so long that the cancer-specific survival rates could yet not be obtained because the SEER data do not provide sufficiently long follow-up. CONCLUSION: The present study suggests a certain threshold year is required to wait before the statistical cure rate can be estimated for each cancer site. For some cancers, such as breast and thyroid, the 5- or 10-year survival rates inadequately reflect statistical cure rates, and highlight the need for long-term follow-up of these patients

Survival of patients with metastatic breast cancer: twenty-year data from two SEER registries

BACKGROUND: Many researchers are interested to know if there are any improvements in recent treatment results for metastatic breast cancer in the community, especially for 10- or 15-year survival. METHODS: Between 1981 and 1985, 782 and 580 female patients with metastatic breast cancer were extracted respectively from the Connecticut and San Francisco-Oakland registries of the Surveillance, Epidemiology, and End Results (SEER) database. The lognormal statistical method to estimate survival was retrospectively validated since the 15-year cause-specific survival rates could be calculated using the standard life-table actuarial method. Estimated rates were compared to the actuarial data available in 2000. Between 1991 and 1995, further 752 and 632 female patients with metastatic breast cancer were extracted respectively from the Connecticut and San Francisco-Oakland registries. The data were analyzed to estimate the 15-year cause-specific survival rates before the year 2005. RESULTS: The 5-year period (1981–1985) was chosen, and patients were followed as a cohort for an additional 3 years. The estimated 15-year cause-specific survival rates were 7.1% (95% confidence interval, CI, 1.8–12.4) and 9.1% (95% CI, 3.8–14.4) by the lognormal model for the two registries of Connecticut and San Francisco-Oakland respectively. Since the SEER database provides follow-up information to the end of the year 2000, actuarial calculation can be performed to confirm (validate) the estimation. The Kaplan-Meier calculation for the 15-year cause-specific survival rates were 8.3% (95% CI, 5.8–10.8) and 7.0% (95% CI, 4.3–9.7) respectively. Using the 1991–1995 5-year period cohort and followed for an additional 3 years, the 15-year cause-specific survival rates were estimated to be 9.1% (95% CI, 3.8–14.4) and 14.7% (95% CI, 9.8–19.6) for the two registries of Connecticut and San Francisco-Oakland respectively. CONCLUSIONS: For the period 1981–1985, the 15-year cause-specific survival for the Connecticut and the San Francisco-Oakland registries were comparable. For the period 1991–1995, there was not much change in survival for the Connecticut registry patients, but there was an improvement in survival for the San Francisco-Oakland registry patients

Secondary metabolites, hormonal homeostasis, and antioxidant enzymes of Moringa oleifera in response to white or violet Light Emitting Diodes (LEDs) combined with cytokinins under tissue culture conditions

The present study was carried out between 2021 and 2022 at the tissue culture lab and experimental station of the vegetable and floriculture department, faculty of agriculture, Mansoura University. Using mature seeds, Moringa oleifera is propagated on a large scale and in rapid succession by in vitro culture. Two types of cytokinin: 6-benzylaminopurin (BAP), and thidiauron (TDZ) singly at three different concentrations (0, 1, or 2 mg/L), were used, as well as light-emitting diode systems (LEDs) (white as control and violet; the combination of red and blue; 1:1). After incubation for 30 days, the obtained results showed that the survival percentage increased by the treatments with the maximum value (85%) by MS medium supplemented with 2 mg/L TDZ, under violet LEDs illumination. However, the addition of thidiazuron (TDZ) to the medium did not propagate shoot, and this treatment recorded 100% callus formation other than BAP. The maximum number of axillary shoots per explant and the number of leaves recorded in the MS medium contained 2 mg/L BAP under violet LEDs. Compared to the control values, all the used treatments generally caused surprisingly stimulating the determined antioxidant enzymes and compounds (peroxidase, polyphenol oxidase &catalase and phenols, flavonoids, anthocyanin& ascorbic acid). Concerning the phytohormone content of the hormone-free medium (control), IAA, kinetin, and zeatin increased. Meanwhile, GA3 and ABA decreased with the used treatments

Short- and long-term cause-specific survival of patients with inflammatory breast cancer

BACKGROUND: Inflammatory breast cancer (IBC) had been perceived to have a poor prognosis. Oncologists were not enthusiastic in the past to give aggressive treatment. Single institution studies tend to have small patient numbers and limited years of follow-up. Most studies do not report 10-, 15- or 20-year results. METHODS: Data was obtained from the population-based database of the Surveillance, Epidemiology, and End Results program of the National Cancer Institute from 1975–1995 using SEER*Stat5.0 software. This period of 21 years was divided into 7 periods of 3 years each. The years were chosen so that there was adequate follow-up information to 2000. ICD-O-2 histology 8530/3 was used to define IBC. The lognormal model was used for statistical analysis. RESULTS: A total of 1684 patients were analyzed, of which 84% were white, 11% were African Americans, and 5% belonged to other races. Age distribution was < 30 years in 1%, 30–40 in 11%, 40–50 in 22%, 50–60 in 24%, 60–70 in 21%, and > 70 in 21%. The lognormal model was validated for 1975–77 and for 1978–80, since the 10-, 15- and 20-year cause-specific survival (CSS) rates, could be calculated using the Kaplan-Meier method with data available in 2000. The data were then used to estimate the 10-, 15- and 20-year CSS rates for the more recent years, and to study the trend of improvement in survival. There were increasing incidences of IBC: 134 patients in the 1975–77 period to 416 patients in the 1993–95 period. The corresponding 20-year CSS increased from 9% to 20% respectively with standard errors of less than 4%. CONCLUSION: The improvement of survival during the study period may be due to introduction of more aggressive treatments. However, there seem to be no further increase of long-term CSS, which should encourage oncologists to find even more effective treatments. Because of small numbers of patients, randomized studies will be difficult to conduct. The SEER population-based database will yield the best possible estimate of the trend in improvement of survival for patients with IBC

Characterization of the innate immune response to chronic aspiration in a novel rodent model

<p>Abstract</p> <p>Background</p> <p>Although chronic aspiration has been associated with several pulmonary diseases, the inflammatory response has not been characterized. A novel rodent model of chronic aspiration was therefore developed in order to investigate the resulting innate immune response in the lung.</p> <p>Methods</p> <p>Gastric fluid or normal saline was instilled into the left lung of rats (n = 48) weekly for 4, 8, 12, or 16 weeks (n = 6 each group). Thereafter, bronchoalveolar lavage specimens were collected and cellular phenotypes and cytokine concentrations of IL-1alpha, IL-1beta, IL-2, IL-4, IL-6, IL-10, GM-CSF, IFN-gamma, TNF-alpha, and TGF-beta were determined.</p> <p>Results</p> <p>Following the administration of gastric fluid but not normal saline, histologic specimens exhibited prominent evidence of giant cells, fibrosis, lymphocytic bronchiolitis, and obliterative bronchiolitis. Bronchoalveolar lavage specimens from the left (treated) lungs exhibited consistently higher macrophages and T cells with an increased CD4:CD8 T cell ratio after treatment with gastric fluid compared to normal saline. The concentrations of IL-1alpha, IL-1beta, IL-2, TNF-alpha and TGF-beta were increased in bronchoalveolar lavage specimens following gastric fluid aspiration compared to normal saline.</p> <p>Conclusion</p> <p>This represents the first description of the pulmonary inflammatory response that results from chronic aspiration. Repetitive aspiration events can initiate an inflammatory response consisting of macrophages and T cells that is associated with increased TGF-beta, TNF-alpha, IL-1alpha, IL-1beta, IL-2 and fibrosis in the lung. Combined with the observation of gastric fluid-induced lymphocyitic bronchiolitis and obliterative bronchiolitis, these findings further support an association between chronic aspiration and pulmonary diseases, such as obliterative bronchiolitis, pulmonary fibrosis, and asthma.</p

Fibrocytes and the tissue niche in lung repair

Human fibrocytes are bone marrow-derived mesenchymal progenitor cells that express a variety of markers related to leukocytes, hematopoietic stem cells and a diverse set of fibroblast phenotypes. Fibrocytes can be recruited from the circulation to the tissue where they further can differentiate and proliferate into various mesenchymal cell types depending on the tissue niche. This local tissue niche is important because it modulates the fibrocytes and coordinates their role in tissue behaviour and repair. However, plasticity of a niche may be co-opted in chronic airway diseases such as asthma, idiopathic pulmonary fibrosis and obliterative bronchiolitis. This review will therefore focus on a possible role of fibrocytes in pathological tissue repair processes in those diseases

The late radiotherapy normal tissue injury phenotypes of telangiectasia, fibrosis and atrophy in breast cancer patients have distinct genotype-dependent causes

The relationship between late normal tissue radiation injury phenotypes in 167 breast cancer patients treated with radiotherapy and: (i) radiotherapy dose (boost); (ii) an early acute radiation reaction and (iii) genetic background was examined. Patients were genotyped at single nucleotide polymorphisms (SNPs) in eight candidate genes. An early acute reaction to radiation and/or the inheritance of the transforming growth factor-β1 (TGFβ1 −509T) SNP contributed to the risk of fibrosis. In contrast, an additional 15 Gy electron boost and/or the inheritance of X-ray repair cross-complementing 1 (XRCC1) (R399Q) SNP contributed to the risk of telangiectasia. Although fibrosis, telangiectasia and atrophy, all contribute to late radiation injury, the data suggest that they have distinct underlying genetic and radiobiological causes. Fibrosis risk is associated with an inflammatory response (an acute reaction and/or TGFβ1), whereas telangiectasia is associated with vascular endothelial cell damage (boost and/or XRCC1). Atrophy is associated with an acute response, but the genetic predisposing factors that determine the risk of an acute response or atrophy have yet to be identified. A combined analysis of two UK breast cancer patient studies shows that 8% of patients are homozygous (TT) for the TGFβ1 (C-509T) variant allele and have a 15-fold increased risk of fibrosis following radiotherapy (95% confidence interval: 3.76–60.3; P=0.000003) compared with (CC) homozygotes