Pebbling on Directed Graphs

Consider a finite connected graph G whose vertices are labeled with non-negative integers representing the number of pebbles on each vertex. A pebbling move on a graph G is defined as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number f(G) of a connected graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified but arbitrary vertex. We consider pebbling on directed graphs and study what configurations of directed graphs allow for pebbling to be meaningful. We also obtain the pebbling numbers of certain orientations of directed wheel graphs Wn with odd order where n \u3e 6 and directed complete graphs Kn with odd order where n \u3e 5. G is said to be demonic if f(G) = n where n is the order of G. We demonstrate the existence of demonic directed graphs and establish that the sharp upper bound and sharp lower bound of the pebbling numbers of the directed graphs is the same as that of the undirected graphs: n \u3c f(G) \u3c 2n − 1

Pebbling on Directed Graphs

Consider a finite connected graph G whose vertices are labeled with non-negative integers representing the number of pebbles on each vertex. A pebbling move on a graph G is defined as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number f(G) of a connected graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified but arbitrary vertex. We consider pebbling on directed graphs and study what configurations of directed graphs allow for pebbling to be meaningful. We also obtain the pebbling numbers of certain orientations of directed wheel graphs Wn with odd order where n \u3e 6 and directed complete graphs Kn with odd order where n \u3e 5. G is said to be demonic if f(G) = n where n is the order of G. We demonstrate the existence of demonic directed graphs and establish that the sharp upper bound and sharp lower bound of the pebbling numbers of the directed graphs is the same as that of the undirected graphs: n \u3c f(G) \u3c 2n − 1

A retrospective validation of CanAssist Breast in European early-stage breast cancer patient cohort

Hormone-receptor positive; Chemotherapy; Early-stage breast cancerReceptor de hormonas positivo; Quimioterapia; Cáncer de mama en fase inicialReceptor d'hormones positiu; Quimioteràpia; Càncer de mama en fase inicialCanAssist Breast (CAB), a prognostic test uses immunohistochemistry (IHC) approach coupled with artificial intelligence-based machine learning algorithm for prognosis of early-stage hormone-receptor positive, HER2/neu negative breast cancer patients. It was developed and validated in an Indian cohort. Here we report the first blinded validation of CAB in a multi-country European patient cohort. FFPE tumor samples from 864 patients were obtained from-Spain, Italy, Austria, and Germany. IHC was performed on these samples, followed by recurrence risk score prediction. The outcomes were obtained from medical records. The performance of CAB was analyzed by hazard ratios (HR) and Kaplan Meier curves. CAB stratified European cohort (n = 864) into distinct low- and high-risk groups for recurrence (P 50 years (HR: 2.93 (1.44–5.96), P = 0.0002). CAB had an HR of 2.57 (1.26–5.26), P = 0.01) in women with N1 disease. CAB stratified significantly higher proportions (77%) as low-risk over IHC4 (55%) (P < 0.0001). Additionally, 82% of IHC4 intermediate-risk patients were stratified as low-risk by CAB. Accurate risk stratification of European patients by CAB coupled with its similar performance inIndian patients shows that CAB is robust and functions independent of ethnic differences. CAB can potentially prevent overtreatment in a greater number of patients compared to IHC4 demonstrating its usefulness for adjuvant systemic therapy planning in European breast cancer patients

The usefulness of CanAssist Breast over Ki67 in breast cancer recurrence risk assessment

Abstract Background Assessment of Ki67 by immunohistochemistry (IHC) has limited utility in clinical practice owing to analytical validity issues. According to International Ki67 Working Group (IKWG) guidelines, treatment should be guided by a prognostic test in patients expressing intermediate Ki67 range, >5%–5%–30%). CAB generates two risk groups, low and high risk based on a predefined cutoff. Results In the total cohort, 76% of the patients were low risk (LR) by CAB as against 46% by Ki67 with a similar DRFi of 94%. In the node‐negative sub‐cohort, 87% were LR by CAB with a DRFi of 97% against 49% by Ki67 with a DRFi of 96%. In subgroups of patients with T1 or N1 or G2 tumors, Ki67‐based risk stratification was not significant while it was significant by CAB. In the intermediate Ki67 (>5%–<30%) category up to 89% (N0 sub‐cohort) were LR by CAB and the percentage of LR patients was 25% (p < 0.0001) higher compared to NPI or mAOL. In the low Ki67 (≤5%) group, up to 19% were segregated as high‐risk by CAB with 86% DRFi suggesting the requirement of chemotherapy in these low Ki67 patients. Conclusion CAB provided superior prognostic information in various Ki67 subgroups, especially in the intermediate Ki67 group

Stress-induced apoptosis in Spodoptera frugiperda (S&#402;9) cells: baculovirus p35 mitigates eIF2&#945; phosphorylation

Spodoptera frugiperda (S&#402;9) ovarian cells, natural hosts for baculovirus, are good model systems to study apoptosis and also heterologous gene expression. We report that uninfected S&#402;9 cells readily undergo apoptosis and show increased phosphorylation of the a subunit of eukaryotic initiation factor 2 (eIF2&#945;) in the presence of agents such as UVB light, etoposide, high concentrations of cycloheximide, and EGTA. In contrast, tunicamycin, A23187, and low concentrations of cycloheximide promoted eIF2&#945; phosphorylation in S&#402;9 cells but without apoptosis. These findings therefore suggest that increased eIF2&#945; phosphorylation does not always necessarily lead to apoptosis, but it is a characteristic hallmark of stressed cells and also of cells undergoing apoptosis. Cell death induced by the above agents was abrogated by infection of S&#402;9 cells with wild-type (wt) AcNPV. In contrast, S&#402;9 cells when infected with vAc&#948;35, a virus carrying deletion of the antiapoptotic p35 gene, showed increased apoptosis and enhanced eIF2&#945; phosphorylation. Further, a recombinant wt virus vAcS51D expressing human S51D, a phosphomimetic form of eIF2&#945;, induced apoptosis in UVB pretreated S&#402;9 cells. However, infection with vAcS51A expressing a nonphosphorylatable form (S51A) of human eIF2&#945; partially reduced apoptosis. Consistent with these findings, it has been observed here that caspase activation has led to increased eIF2&#945; phosphorylation, while caspase inhibition by z-VAD-fmk reduced eIF2&#945; phosphorylation selectively in cells exposed to proapoptotic agents. These findings therefore suggest that the stress signaling pathway determines apoptosis, and caspase activation is a prerequisite for increased eIF2&#945; phosphorylation in S&#402;9 cells undergoing apoptosis. The findings also reinforce the conclusion for the first time that the "pancaspase inhibitor" baculovirus p35 mitigates eIF2&#945; phosphorylation

Analytical validation of CanAssist-Breast: an immunohistochemistry based prognostic test for hormone receptor positive breast cancer patients

Abstract Background CanAssist-Breast is an immunohistochemistry based test that predicts risk of distant recurrence in early-stage hormone receptor positive breast cancer patients within first five years of diagnosis. Immunohistochemistry gradings for 5 biomarkers (CD44, ABCC4, ABCC11, N-Cadherin and pan-Cadherins) and 3 clinical parameters (tumor size, tumor grade and node status) of 298 patient cohort were used to develop a machine learning based statistical algorithm. The algorithm generates a risk score based on which patients are stratified into two groups, low- or high-risk for recurrence. The aim of the current study is to demonstrate the analytical performance with respect to repeatability and reproducibility of CanAssist-Breast. Methods All potential sources of variation in CanAssist-Breast testing involving operator, run and observer that could affect the immunohistochemistry performance were tested using appropriate statistical analysis methods for each of the CanAssist-Breast biomarkers using a total 309 samples. The cumulative effect of these variations in the immunohistochemistry gradings on the generation of CanAssist-Breast risk score and risk category were also evaluated. Intra-class Correlation Coefficient, Bland Altman plots and pair-wise agreement were performed to establish concordance on IHC gradings, risk score and risk categorization respectively. Results CanAssist-Breast test exhibited high levels of concordance on immunohistochemistry gradings for all biomarkers with Intra-class Correlation Coefficient of ≥0.75 across all reproducibility and repeatability experiments. Bland-Altman plots demonstrated that agreement on risk scores between the comparators was within acceptable limits. We also observed > 90% agreement on risk categorization (low- or high-risk) across all variables tested. Conclusions The extensive analytical validation data for the CanAssist-Breast test, evaluating immunohistochemistry performance, risk score generation and risk categorization showed excellent agreement across variables, demonstrating that the test is robust

The usefulness of CanAssist breast in the assessment of recurrence risk in patients of ethnic Indian origin

Accurate recurrence risk assessment in hormone receptor positive, HER2/neu negative breast cancer is critical to plan precise therapy. CanAssist Breast (CAB) assesses recurrence risk based on tumor biology using artificial intelligence-based approach. We report CAB risk assessment correlating with disease outcomes in multiple clinically high- and low-risk subgroups. In this retrospective cohort of 925 patients [median age-54 (22–86)] CAB had hazard ratio (HR) of 3 (1.83–5.21) and 2.5 (1.45–4.29), P = 0.0009) in univariate and multivariate analysis. CAB's HR in sub-groups with the other determinants of outcome, T2 (HR: 2.79 (1.49–5.25), P = 0.0001); age [16% as high-risk with recurrence rates of up to 12%. In clinically high-risk patients (T2N1 tumors (HR: 2.65 (1.31–5.36), P = 0.003; low-risk DMFS: 92.66 ± 1.88) and in women with luminal-B characteristics (HR: 3.24; (1.69–6.22), P 64% as low-risk. Thus, CAB prognostication was significant in women with clinically low- and high-risk disease. The data imply the use of CAB for providing helpful information to stratify tumors based on biology incorporated with clinical features for Indian patients, which can be extrapolated to regions with similarly characterized patients, South-East Asia