Hot new directions for quasi-Monte Carlo research in step with applications

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when $s$ is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications

Successive Coordinate Search and Component-by-Component Construction of Rank-1 Lattice Rules

The (fast) component-by-component (CBC) algorithm is an efficient tool for the construction of generating vectors for quasi-Monte Carlo rank-1 lattice rules in weighted reproducing kernel Hilbert spaces. We consider product weights, which assigns a weight to each dimension. These weights encode the effect a certain variable (or a group of variables by the product of the individual weights) has. Smaller weights indicate less importance. Kuo (2003) proved that the CBC algorithm achieves the optimal rate of convergence in the respective function spaces, but this does not imply the algorithm will find the generating vector with the smallest worst-case error. In fact it does not. We investigate a generalization of the component-by-component construction that allows for a general successive coordinate search (SCS), based on an initial generating vector, and with the aim of getting closer to the smallest worst-case error. The proposed method admits the same type of worst-case error bounds as the CBC algorithm, independent of the choice of the initial vector. Under the same summability conditions on the weights as in [Kuo,2003] the error bound of the algorithm can be made independent of the dimension $d$ and we achieve the same optimal order of convergence for the function spaces from [Kuo,2003]. Moreover, a fast version of our method, based on the fast CBC algorithm by Nuyens and Cools, is available, reducing the computational cost of the algorithm to $O(d \, n \log(n))$ operations, where $n$ denotes the number of function evaluations. Numerical experiments seeded by a Korobov-type generating vector show that the new SCS algorithm will find better choices than the CBC algorithm and the effect is better when the weights decay slower.Comment: 13 pages, 1 figure, MCQMC2016 conference (Stanford

Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

S100A6 (Calcyclin) is a prostate basal cell marker absent in prostate cancer and its precursors

S100A6 (Calcyclin) is a calcium-binding protein that has been implicated in a variety of biological functions as well as tumorigenesis. The aim of our study was to investigate the involvement of S100A6 during prostate cancer development and progression. Using immunohistochemistry, the expression of S100A6 was examined in benign (n ¼ 66), premalignant (n ¼ 10), malignant (n ¼ 66) and metastatic prostate (n ¼ 5) tissues arranged in a tissue-microarray or whole sections as well as in prostate cancer cell lines. The S100A6 immunostaining pattern in tissues was compared with that of cytokeratin 5 (a basal cell marker) and 18 (a benign luminal cell marker). In all cases of benign epithelium, intense S100A6 expression was seen in the basal cell layer with absent staining in luminal cells. In all cases of prostatic adenocarcinoma (matched), metastatic lesions and 3/10 high-grade prostatic intraepithelial neoplasia lesions, an absence of S100A6 was seen. Western blotting and RT–PCR analysis of cell lines showed S100A6 expression to be absent in LNCaP, LNCaP-LN3 and LNCaP-Pro5 but present in Du145, PC3, PC-3M and PC-3M-LN4. LNCaP cells treated with 5- Azacytidine, caused re-expression of S100A6 mRNA. Sequencing of bisulphite modified DNA showed CpG methylation within the S100A6 promoter region and exon 1 of LNCaP, LNCaP-LN3 and LNCaP-Pro5 cell lines but not in Du145 cells. Our data suggest that loss of S100A6 protein expression is common in prostate cancer development and may occur at an early stage. The mechanism of loss of expression may involve hypermethylation of CpG sites. The finding of intense S100A6 expression in the basal cells of benign glands but loss of expression in cancer could be useful as a novel diagnostic marker for prostate cancer

Do Neutrophils Play a Role in Establishing Liver Abscesses and Distant Metastases Caused by Klebsiella pneumoniae?

Serotype K1 Klebsiella pneumoniae is a major cause of liver abscesses and endophthalmitis. This study was designed to identify the role of neutrophils in the development of distant metastatic complications that were caused by serotype K1 K. pneumoniae. An in vitro cellular model was used to assess serum resistance and neutrophil-mediated killing. BALB/c mice were injected with neutrophils containing phagocytosed K. pneumoniae. Serotype K1 K. pneumoniae was significantly more resistant to serum killing, neutrophil-mediated phagocytosis and intra-cellular killing than non-K1 isolates (p<0.01). Electron microscopic examination had similar findings as in the bioassay findings. Intraperitoneal injection of neutrophils containing phagocytosed serotype K1 K. pneumoniae led to abscess formation in multiple sites including the subcutaneous tissue, lung, and liver, whereas no abscess formation was observed in mice injected with non-K1 isolates. The resistance of serotype K1 K. pneumoniae to complement- and neutrophil-mediated intracellular killing results in the dissemination of K. pneumoniae via the bloodstream. Escape from neutrophil intracellular killing may contribute to the dissemination and establishment of distant metastases. Thus, neutrophils play a role as a vehicle for helping K. pneumoniae and contributing to the establishment of liver abscess and distant metastatic complications

Direct Binding of pRb/E2F-2 to GATA-1 Regulates Maturation and Terminal Cell Division during Erythropoiesis

Cell differentiation is often coupled with cell cycle arrest. Here, we show that direct binding of the erythroid transcription factor GATA-1 to the retinoblastoma protein and the pRb/E2F transcription factor complex is critical for red blood cell formation

Childhood emotional trauma and cyberbullying perpetration among emerging adults: a multiple mediation model of the role of problematic social media use and psychopathology

Research suggests that a small minority of social media users experience problems as a result of their online use. The purpose of the present study was to examine the association of cyberbullying perpetration and problematic social media use with childhood emotional trauma, Cluster B (narcissistic, histrionic, antisocial, and borderline) personality traits, dissociative experiences (DEs), depression, and self-esteem in a nonclinical undergraduate sample. A total of 344 university students volunteered to complete a questionnaire that included measures on the aforementioned dimensions. Thirty-eight percent of the participants had emotional neglect and 27% had emotional abuse, while 44% of them demonstrated at least one cyberbullying perpetration behavior. Results indicated that cyberbullying perpetrators had higher scores on problematic social media use, dissociative experiences, Cluster B traits, depression and childhood emotional trauma, and lower on self-esteem. Path analysis demonstrated that, while adjusting for gender and age, childhood emotional trauma was directly and indirectly associated with cyberbullying perpetration via Cluster B traits. Moreover, depression and dissociation were directly associated with problematic social media use. The findings of this study emphasize the important direct role of childhood emotional trauma and pathological personality traits on cyberbullying perpetration

Magnetic resonance imaging (MRI) in rectal cancer: a comprehensive review

Magnetic resonance imaging (MRI) has established itself as the primary method for local staging in patients with rectal cancer. This is due to several factors, most importantly because of the ability to assess the status of circumferential resection margin. There are several newer developments being introduced continuously, such as diffusion-weighted imaging and imaging with 3 T. Assessment of loco-regional lymph nodes has also been investigated extensively using different approaches, but more work needs to be done. Finally, evaluation of tumours during or after preoperative treatment is becoming an everyday reality. All these new aspects prompt a review of the most recent advances and opinions. In this review, a comprehensive overview of the current status of MRI in the loco-regional assessment and management of rectal cancer is presented. The findings on MRI and their accuracy are reviewed based on the most up-to-date evidence. Optimisation of MRI acquisition and relevant regional anatomy are also presented, based on published literature and our own experience

Stochastic backgrounds of relic gravitons: a theoretical appraisal

Stochastic backgrounds or relic gravitons, if ever detected, will constitute a prima facie evidence of physical processes taking place during the earliest stages of the evolution of the plasma. The essentials of the stochastic backgrounds of relic gravitons are hereby introduced and reviewed. The pivotal observables customarily employed to infer the properties of the relic gravitons are discussed both in the framework of the $\Lambda$CDM paradigm as well as in neighboring contexts. The complementarity between experiments measuring the polarization of the Cosmic Microwave Background (such as, for instance, WMAP, Capmap, Quad, Cbi, just to mention a few) and wide band interferometers (e.g. Virgo, Ligo, Geo, Tama) is emphasized. While the analysis of the microwave sky strongly constrains the low-frequency tail of the relic graviton spectrum, wide-band detectors are sensitive to much higher frequencies where the spectral energy density depends chiefly upon the (poorly known) rate of post-inflationary expansion.Comment: 94 pages, 32 figure