A Recursive Algorithm for Computing Inferences in Imprecise Markov Chains

We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other types of model uncertainty. The class of inferences that we consider contains, as special cases, tight lower and upper bounds on expected hitting times, on hitting probabilities and on expectations of functions that are a sum or product of simpler ones. Our algorithm exploits the specific structure that is inherent in all these inferences: they admit a general recursive decomposition. This allows us to achieve a computational complexity that scales linearly in the number of time points on which the inference depends, instead of the exponential scaling that is typical for a naive approach

Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with Imprecision

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed - smaller - state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality.Comment: 9th International Conference on Soft Methods in Probability and Statistics (SMPS 2018

An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations

Irregular screening participation increases advanced stage breast cancer at diagnosis:A population-based study

Objective: To evaluate the effect of irregular screening behaviour on the risk of advanced stage breast cancer at diagnosis in Flanders. Methods: All women aged 50–69 who were invited to the organized breast cancer screening and diagnosed with breast cancer before age 72 from 2001 to 2018 were included. All prevalent screen and interval cancers within 2 years of a prevalent screen were excluded. Screening behaviour was categorized based on the number of invitations and performed screenings. Four groups were defined: regular, irregular, only-once, and never attenders. Advanced stage cancer was defined as a stage III + breast cancer. The association between screening regularity and breast cancer stage at diagnosis was evaluated in multivariable logistic regression models, taking age of diagnosis and socio-economic status into account. Results: In total 13.5% of the 38,005 breast cancer cases were diagnosed at the advanced stage. Compared to the regular attenders, the risk of advanced stage breast cancer for the irregular attenders, women who participated only-once, and never attenders was significantly higher with ORadjusted:1.17 (95%CI:1.06–1.29) and ORadjusted:2.18 (95%CI:1.94–2.45), and ORadjusted:5.95 (95%CI:5.33–6.65), respectively. Conclusions: In our study, never attenders were nearly six times more likely to be diagnosed with advanced stage breast cancer than regular attenders, which was much higher than the estimates published thus far. An explanation for this is that the ever screened women is a heterogeneous group regarding the participation profiles which also includes irregular and only-once attenders. The benefit of regular screening should be informed to all women invited for screening

Modest effect of p53, EGFR and HER-2/neu on prognosis in epithelial ovarian cancer: a meta-analysis

Background: P53, egfr and her-2/neu are the most frequently studied molecular biological parameters in epithelial ovarian cancer, but their prognostic impact is still unequivocal. We performed a meta-analysis to more precisely estimate their prognostic significance. Methods: Published studies that investigated the association between p53, egfr and her-2/neu status and survival were identified. Meta-analysis was performed using a dersimonian-laird model. Publication bias was investigated using funnel plots and sources of heterogeneity were identified using meta-regression analysis. Results: A total of 62 studies were included for p53, 15 for egfr and 20 for her-2/neu. P53, egfr and her-2/neu status had a modest effect on overall survival (Pooled hr 1.47, 95% Ci 1.33-1.61 For p53; Hr 1.65, 95% Ci 1.25-2.19 For egfr and hr 1.67, 95% Ci 1.34-2.08 For her-2/neu). Meta-regression analysis for p53 showed that figo stage distribution influenced study outcome. For egfr and her-2/neu, considerable publication bias was present. Conclusions: Although p53, egfr and her-2/neu status modestly influences survival, these markers are, by themselves, unlikely to be useful as prognostic markers in clinical practice. Our study highlights the need for well-defined, prospective clinical trials and more complete reporting of results of prognostic factor studies. British journal of cancer ( 2009) 101, 149-159. Doi: 10.1038/Sj.Bjc.6605112 Www.Bjcancer.Com published online 9 june 2009 (C) 2009 Cancer research uk

Satisfaction with cosmetic outcomes of breast reconstruction:Investigations into the correlation between the patients' Breast-Q outcome and the judgment of panels

Objectives: We aimed to determine the relation between breast reconstruction method, patient satisfaction, and surgeon reported cosmetic outcome among women who underwent breast reconstruction after mastectomy. Study Design: A cross-sectional study of patients treated between 2006 and 2010. Main Outcome: Women's satisfaction with cosmetic outcomes after breast reconstruction. Measures: Cosmetic outcomes were evaluated by (1) women using the Breast-Q to rate satisfaction with breasts outcomes, and (2) an independent panel using the Strasser score. The relationships between the Breast-Q rating, Strasser scores, and breast reconstruction methods, including laterality and timing, were evaluated by Mann-Whitney U tests, Spearman's rank correlations, and Wilcoxon signed-rank tests. Results: Ninety-four women were included. Patients were more satisfied with their breasts if they had undergone autologous, unilateral, or secondary breast reconstruction compared with those who underwent alloplastic, bilateral, or primary breast reconstruction (p-values 0.008, 0.011, and 0.001, respectively). The Strasser system did not reveal significant cosmetic differences, with all breast reconstructions graded as mediocre or poor. Conclusions: Patient satisfaction with breast outcomes, as measured by the Breast-Q, was described as mediocre or poorly reflected by the Strasser score. If doctors are to support patients to make informed decisions on the optimal method of breast reconstruction, we need a more sensitive, comprehensive tool reflecting patients' cosmetic outcomes

The Evaluation of More Lymph Nodes in Colon Cancer Is Associated with Improved Survival in Patients of All Ages

BACKGROUND:Improvement in survival of patients with colon cancer is reduced in elderly patients compared to younger patients. The aim of this study was to investigate whether the removal of ≥ 12 lymph nodes can explain differences in survival rates between elderly and younger patients diagnosed with colon cancer. METHODS:In a population-based cohort study, all patients (N = 41,074) diagnosed with colon cancer stage I to III from 2003 through 2010 from the Netherlands Cancer Registry were included. Age groups were defined as < 66, 66-75 and > 75 years of age. Main outcome measures were overall and relative survival, the latter as a proxy for disease specific survival. RESULTS:Over an eight years time period there was a 41.2% increase in patients with ≥ 12 lymph nodes removed, whereas the percentage of patients with the presence of lymph node metastases remained stable (35.7% to 37.5%). After adjustment for patient and tumour characteristics and adjuvant chemotherapy, it was found that for patients in which ≥ 12 lymph nodes were removed compared to patients with < 12 lymph nodes removed, there was a statistically significant higher overall survival (< 66: HR: 0.858 (95% CI, 0.789-0.933); 66-75: HR: 0.763 (95% CI, 0.714-0.814); > 75: HR: 0.734 (95% CI, 0.700-0.771)) and relative survival (< 66: RER: 0.783 (95% CI, 0.708-0.865); 66-75: RER: 0.672 (95% CI, 0.611-0.739); > 75: RER: 0.621 (95% CI, 0.567-0.681)) in all three age groups. CONCLUSIONS:The removal of ≥ 12 lymph nodes is associated with an improvement in both overall and relative survival in all patients. This association was stronger in the elderly patient. The biology of this association needs further clarification