Compressed sensing magnetic resonance imaging (CS-MRI) is a technique aimed at accelerating the data acquisition of MRI. While down-sampling in k-space proportionally reduces the data acquisition time, it results in images corrupted by aliasing artifacts and blur. To reconstruct images from the down-sampled k-space, recent deep-learning based methods have shown better performance compared with classical optimization-based CS-MRI methods. However, they usually use deep neural networks as a black-box, which directly maps the corrupted images to the target images from fully-sampled k-space data. This lack of transparency may impede practical usage of such methods. In this work, we propose a deep reinforcement learning based method to reconstruct the corrupted images with meaningful pixel-wise operations (e.g. edge enhancing filters), so that the reconstruction process is transparent to users. Specifically, MRI reconstruction is formulated as Markov Decision Process with discrete actions and continuous action parameters. We conduct experiments on MICCAI dataset of brain tissues and fastMRI dataset of knee images. Our proposed method performs favorably against previous approaches. Our trained model learns to select pixel-wise operations that correspond to the anatomical structures in the MR images. This makes the reconstruction process more interpretable, which would be helpful for further medical analysis.

Effectively utilizing temporal information is critical for human pose estimation in videos. Recent methods either neglect the displacements of keypoints in the video frames, or rely on time-consuming optical flow estimation when fusing temporal information. By contrast, we propose a flow-free and displacement-aware algorithm for pose estimation in videos. Our method is based on the observation that the appearance of the body keypoints remains almost unchanged throughout a video. This motivates us to exploit temporal visual consistency of keypoints via temporal feature correlation to establish sparse correspondences between the keypoints in neigh-boring frames. Specifically, we first extract keypoint features from the previous frame, which can be treated as exemplars to search on the intermediate feature map of the current frame. Then we conduct temporal feature correlation for the keypoint search, and the obtained correlation maps are combined with the convolutional features to further guide heatmap estimation. Extensive experiments demonstrate that the proposed method compares favorably against state-of-the-art approaches on both sub-JHMDB and Penn Action datasets. More importantly, our method is robust to large keypoint displacements and could be applied to videos under fast motion.

BACKGROUND: The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a longer read is more likely to be uniquely mapped to the reference genome, a quantitative analysis of the influence of read lengths on mappability has been lacking. To address this question, we evaluate the k-mer distribution of the human reference genome. The k-mer frequency is determined for k ranging from 20 bp to 1000 bp. RESULTS: We observe that the proportion of non-singletons k-mers decreases slowly with increasing k, and can be fitted by piecewise power-law functions with different exponents at different ranges of k. A slower decay at greater values for k indicates more limited gains in mappability for read lengths between 200 bp and 1000 bp. The frequency distributions of k-mers exhibit long tails with a power-law-like trend, and rank frequency plots exhibit a concave Zipf's curve. The most frequent 1000-mers comprise 172 regions, which include four large stretches on chromosomes 1 and X, containing genes of biomedical relevance. Comparison with other databases indicates that the 172 regions can be broadly classified into two types: those containing LINE transposable elements and those containing segmental duplications. CONCLUSION: Read mappability as measured by the proportion of singletons increases steadily up to the length scale around 200 bp. When read length increases above 200 bp, smaller gains in mappability are expected. Moreover, the proportion of non-singletons decreases with read lengths much slower than linear. Even a read length of 1000 bp would not allow the unique alignment of reads for many coding regions of human genes. A mix of techniques will be needed for efficiently producing high-quality data that cover the complete human genome.

BACKGROUND: Several features are known to correlate with the GC-content in the human genome, including recombination rate, gene density and distance to telomere. However, by testing for pairwise correlation only, it is impossible to distinguish direct associations from indirect ones and to distinguish between causes and effects. RESULTS: We use partial correlations to construct partially directed graphs for the following four variables: GC-content, recombination rate, exon density and distance-to-telomere. Recombination rate and exon density are unconditionally uncorrelated, but become inversely correlated by conditioning on GC-content. This pattern indicates a model where recombination rate and exon density are two independent causes of GC-content variation. CONCLUSION: Causal inference and graphical models are useful methods to understand genome evolution and the mechanisms of isochore evolution in the human genome.

BACKGROUND: Regions with copy number variations (in germline cells) or copy number alteration (in somatic cells) are of great interest for human disease gene mapping and cancer studies. They represent a new type of mutation and are larger-scaled than the single nucleotide polymorphisms. Using genotyping microarray for copy number variation detection has become standard, and there is a need for improving analysis methods. RESULTS: We apply the cumulative plot to the detection of regions with copy number variation/alteration, on samples taken from a chronic lymphocytic leukemia patient. Two sets of whole-genome genotyping of 317 k single nucleotide polymorphisms, one from the normal cell and another from the cancer cell, are analyzed. We demonstrate the utility of cumulative plot in detecting a 9 Mb (9 x 10(6) bases) hemizygous deletion and 1 Mb homozygous deletion on chromosome 13. We also show the possibility to detect smaller copy number variation/alteration regions below the 100 kb range. CONCLUSION: As a graphic tool, the cumulative plot is an intuitive and a scale-free (window-less) way for detecting copy number variation/alteration regions, especially when such regions are small.

The purpose of this review is to focus on the three most important themes in genetic association studies using randomly selected patients (case, affected) and normal samples (control, unaffected), so that students and researchers alike who are new to this field may quickly grasp the key issues and command basic analysis methods. These three themes are: elementary categorical analysis; disease mutation as an unobserved entity; and the importance of homogeneity in genetic association analysis.

To many biologists, geneticists and bioinformaticians, the excitement of genomics comes from systematic analyses of large amounts of information, such as complete end-to-end DNA sequences, densely packed genetic markers on chromosomes, and sometimes, comprehensive population genetics history in places like Iceland and Finland where extensive genealogical data are available. Also, realizing the importance of sample sizes in mapping susceptibility genes in complex and common diseases, various national and international consortiums were established, and meta analyses were frequently in use on pooled data. Almost everybody agrees that ‘the more (information), the better’. There are two senses in the word ‘more’ used here. One concerns the search space, and another concerns the sample size. It is easy to understand why one would like to see both or either one of them to be large. The reason for demanding a complete search space is that we do not want to miss anything. If we fail to detect a genetic linkage or association signal for a human disease, could it be that we have not covered all genomic regions with enough markers, or is it because we have not compiled a complete list of all coding genes? Having a complete search space will remove these doubts. The reason for larger sample size is well-known in statistics: if the statistical signal is weak, only a larger dataset has a chance to uncover it with confidence. Also, if the sample size is much smaller than the number of variables, such as the ‘large p (number of genes), small n (sample size)’ situation in microarray data, the variable space is not adequately explored, and degenerate fitting models are possible. The ‘large p, even larger n’ situation is preferable. ‘The more, the better’ trend is a natural byproduct of the genomic era, and will undoubtedly continue as ever more advanced biotechnology produces bioinformation faster and cheaper. However, for a specific biology project or a particular human disease study, not all genes are involved and not all chromosomal regions are relevant. An equally important process of removing the irrelevant information allows us to focus on the key areas. A cartoon in Weiss and Terwilliger (2000) compared the search of human disease genes with finding a needle in a haystack. In this example, reducing the haystack size instead of increasing it helps the chance of finding the needle. This principle might be called ‘the less, the better’. ‘The less, the better’ is a recurring theme in many other fields: Occam's razor and the principle of parsimony in philosophy, signal-to-noise ratio and the curse of dimensionality in engineering, simplicity of fundamental laws in physics, minimum length description and lossy data compression in computer science, Morgan's Canon in animal psychology, and so on. The topic of model and variable selection (Burnham and Anderson, 2002) in statistical learning is aimed at simplifying description of data without sacrificing the quality of description. In genomics, genetics and bioinformatics, the parsimony principle has been actually practiced often. The whole point of filtering out low-density and non-differentially-expressed genes in a microarray discriminant analysis is to remove genes that are unlikely to contribute to the phenotype difference. For some microarray datasets, classifiers with extremely small number of genes are able to distinguish normal and diseased samples or samples of different types. In the leukemia data from Golub et al. (1999), for example, the expressions of zyxin, a component of cell adhesion plaques which may play a role in signal transduction, are thoroughly higher in all 11 acute myeloid leukemia (AML) samples than in all 27 acute lymphoblastic leukemia (ALL) samples (Li and Yang, 2002). Even if such a perfect classification rate is not achieved in a larger dataset, this single-gene classifier should still perform well in distinguishing AML and ALL. Similar observation on classification successes with smaller classifiers was also made in Xiong et al. (2001). Rare Mendelian diseases provide another, somewhat trivial, example for requiring fewer genes in describing the data. In most cases, only one gene is behind a rare Mendelian disease. The genetic heterogeneity is probably the only source of complication. As for complex diseases, the number of genes involved in the disease surely increases. But the increase is not without a limit and only a very small proportion of the total ∼25 000 human genes is expected to be the susceptibility genes. The idea of exclusion mapping (Edwards, 1987) is to delete signal-less chromosome region from further investigation. One may also apply the variable selection technique to narrow down the marker list as well as the chromosome regions (Li and Nyholt, 2001). Interestingly, there is a similar debate in statistics on whether the best statistical model should contain fewer variables and parameters. According to the late professor Leo Breiman (Breiman, 2001), the majority of traditional statisticians prefer simple models that have simple explanation and perhaps tractable mathematics; whereas machine-learning-inspired statisticians prefer ‘black box’ and complicated algorithm with better prediction performance. As for the latter category, a new breed of predictors has appeared under the names such as ensembles methods, model aggregation and model averaging. These approaches can achieve excellent prediction rates even when no particular care is taken to reduce the variable list to a minimum. In the example of ‘random forest’ (Amit and Geman, 1997), when it was applied to microarray classification datasets, it performed comparatively well as with other predictors without tree pruning (Díaz-Uriarte and Alvarez de Andrés, 2006). Does using multiple models violate the principle of ‘the less, the better’? In machine learning and statistics literature, there were discussions on two different interpretations of Occam's razor: one being ‘simplicity is a goal in itself’, and the other is ‘simplicity leads to greater accuracy’. Some people expressed reservation on the second interpretation (Domingos, 1999). Another argument for ensemble methods is that owing to bias-variance trade-off (Hastie et al., 2001), a single model either overfits the data (small bias and large variance) or underfits the data (large bias and small variance). Having many models somehow reduce the variance, reminiscent of the variance reduction by having many samples. We can view this issue more intuitively. First, are the irrelevant variables and parameters kept in an aggregation model really contributing to the prediction? In Bayesian subset selection (George and McCulloch, 1993) for example, all variables are kept but some of them have zero weight and others only contribute to the data marginally. This may lead us to the concept of ‘effective number of variables/parameters’. Second, what is the nature of variation among samples that cause a prediction failure? Is it because of some true biological and genetic heterogeneity? If so, then using multiple models indeed makes sense. Suppose a human disease is caused by (say) three genes and one environmental factor, a model or a classifier with these four variables should be the optimal model. Rather than ‘the more, the better’ or ‘the less, the better’, the answer is ‘number four is the best’. Unfortunately, this number and the nature of the disease etiology is often unknown to us. If the disease is heterogeneous, caused by these four factors in some patients but by different genes in others, then an extra layer of complexity is introduced to the data. Perhaps the new principle should be stated as follows: keep the appropriate level of model complexity that matches that of the data and at least throw away the irrelevant information.

MOTIVATION: Genetic association analysis is based on statistical correlations which do not assign any cause-to-effect arrows between the two correlated variables. Normally, such assignment of cause and effect label is not necessary in genetic analysis since genes are always the cause and phenotypes are always the effect. However, among intermediate phenotypes and biomarkers, assigning cause and effect becomes meaningful, and causal inference can be useful. RESULTS: We show that causal inference is possible by an example in a study of rheumatoid arthritis. With the help of genotypic information, the shared epitope, the causal relationship between two biomarkers related to the disease, anti-cyclic citrullinated peptide (anti-CCP) and rheumatoid factor (RF) has been established. We emphasize the fact that third variable must be a genotype to be able to resolve potential ambiguities in causal inference. Two non-trivial conclusions have been reached by the causal inference: (1) anti-CCP is a cause of RF and (2) it is unlikely that a third confounding factor contributes to both anti-CCP and RF.

An important issue commonly encountered in the analysis of microarray data is to decide which and how many genes should be selected for further studies. For discriminant microarray data analyses based on statistical models, such as the logistic regression model, this gene selection can be accomplished by a comparison of the maximum likelihood of the model given the real data, L(D|M), and the expected maximum likelihood of the model given an ensemble of surrogate data, L(D0|M). Typically, the computational burden for obtaining L(D0|M) is immense, often exceeding the limits of available resources by orders of magnitude. Here, we propose an approach that circumvents such heavy computations by mapping the simulation problem to an extreme value problem, which can be easily solved by numerical simulation. We choose three classification problems from two publicly available microarray datasets to illustrate that approach.

Previous divide-and-conquer segmentation analyses of DNA sequences do not provide a satisfactory stopping criterion for the recursion. This paper proposes that segmentation be considered as a model selection process. Using the tools in model selection, a limit for the stopping criterion on the relaxed end can be determined. The Bayesian information criterion, in particular, provides a much more stringent stopping criterion than what is currently used. Such a stringent criterion can be used to delineate larger DNA domains. A relationship between the stopping criterion and the average domain size is empirically determined, which may aid in the determination of isochore borders.

It is shown that the distribution of word frequencies for randomly generated texts is very similar to Zipf's law observed in natural languages such as English. The facts that the frequency of occurrence of a word is almost an inverse power law function of its rank and the exponent of this inverse power law is very close to 1 are largely due to the transformation from the word's length to its rank, which stretches an exponential function to a power law function.>

A greater number of complicated patterns can be produced by cellular automata rules with next nearest neighbors in the updating, than those with only nearest neighbors couplings. Some patterns can be identified as gliders moving on the background, while other rules have more intriguing configurations called “creatures” which move irregularly on the background. Sometimes, even the distinction between creatures and the background disappears, and the patterns look strikingly similar to those generated by probabilistic rules, even though the rules used are strictly deterministic.