The Complexity of the Simplex Method

The simplex method is a well-studied and widely-used pivoting method for solving linear programs. When Dantzig originally formulated the simplex method, he gave a natural pivot rule that pivots into the basis a variable with the most violated reduced cost. In their seminal work, Klee and Minty showed that this pivot rule takes exponential time in the worst case. We prove two main results on the simplex method. Firstly, we show that it is PSPACE-complete to find the solution that is computed by the simplex method using Dantzig's pivot rule. Secondly, we prove that deciding whether Dantzig's rule ever chooses a specific variable to enter the basis is PSPACE-complete. We use the known connection between Markov decision processes (MDPs) and linear programming, and an equivalence between Dantzig's pivot rule and a natural variant of policy iteration for average-reward MDPs. We construct MDPs and show PSPACE-completeness results for single-switch policy iteration, which in turn imply our main results for the simplex method

Cannabis affects people differently: inter-subject variation in the psychotogenic effects of Δ9-tetrahydrocannabinol: a functional magnetic resonance imaging study with healthy volunteers

Background Cannabis can induce transient psychotic symptoms, but not all users experience these adverse effects. We compared the neural response to Δ9-tetrahydrocannabinol (THC) in healthy volunteers in whom the drug did or did not induce acute psychotic symptoms. Method In a double-blind, placebo-controlled, pseudorandomized design, 21 healthy men with minimal experience of cannabis were given either 10mg THC or placebo, orally. Behavioural and functional magnetic resonance imaging measures were then recorded whilst they performed a go/no-go task. Results The sample was subdivided on the basis of the Positive and Negative Syndrome Scale positive score following administration of THC into transiently psychotic (TP; n=11) and non-psychotic (NP; n=10) groups. During the THC condition, TP subjects made more frequent inhibition errors than the NP group and showed differential activation relative to the NP group in the left parahippocampal gyrus, the left and right middle temporal gyri and in the right cerebellum. In these regions, THC had opposite effects on activation relative to placebo in the two groups. The TP group also showed less activation than the NP group in the right middle temporal gyrus and cerebellum, independent of the effects of THC. Conclusions In this first demonstration of inter-subject variability in sensitivity to the psychotogenic effects of THC, we found that the presence of acute psychotic symptoms was associated with a differential effect of THC on activation in the ventral and medial temporal cortex and cerebellum, suggesting that these regions mediate the effects of the drug on psychotic symptom

[11C]-l-Methionine positron emission tomography in the management of children and young adults with brain tumors

Only a few Methyl-[11C]-l-methionine (MET) positron emission tomography (PET) studies have focused on children and young adults with brain neoplasm. Due to radiation exposure, long scan acquisition time, and the need for sedation in young children MET-PET studies should be restricted to this group of patients when a decision for further therapy is not possible from routine diagnostic procedures alone, e.g., structural imaging. We investigated the diagnostic accuracy of MET-PET for the differentiation between tumorous and non-tumorous lesions in this group of patients. Forty eight MET-PET scans from 39 patients aged from 2 to 21 years (mean 15 ± 5.0 years) were analyzed. The MET tumor-uptake relative to a corresponding control region was calculated. A receiver operating characteristic (ROC) was performed to determine the MET-uptake value that best distinguishes tumorous from non-tumorous brain lesions. A differentiation between tumorous (n = 39) and non-tumorous brain lesions (n = 9) was possible at a threshold of 1.48 of relative MET-uptake with a sensitivity of 83% and a specificity of 92%, respectively. A differentiation between high grade malignant lesions (mean MET-uptake = 2.00 ± 0.46) and low grade tumors (mean MET-uptake = 1.84 ± 0.31) was not possible. There was a significant difference in MET-uptake between the histologically homogeneous subgroups of astrocytoma WHO grade II and anaplastic astrocytoma WHO grade III (P = 0.02). MET-PET might be a useful tool to differentiate tumorous from non-tumorous lesions in children and young adults when a decision for further therapy is difficult or impossible from routine structural imaging procedures alone

Methods to study splicing from high-throughput RNA Sequencing data

The development of novel high-throughput sequencing (HTS) methods for RNA (RNA-Seq) has provided a very powerful mean to study splicing under multiple conditions at unprecedented depth. However, the complexity of the information to be analyzed has turned this into a challenging task. In the last few years, a plethora of tools have been developed, allowing researchers to process RNA-Seq data to study the expression of isoforms and splicing events, and their relative changes under different conditions. We provide an overview of the methods available to study splicing from short RNA-Seq data. We group the methods according to the different questions they address: 1) Assignment of the sequencing reads to their likely gene of origin. This is addressed by methods that map reads to the genome and/or to the available gene annotations. 2) Recovering the sequence of splicing events and isoforms. This is addressed by transcript reconstruction and de novo assembly methods. 3) Quantification of events and isoforms. Either after reconstructing transcripts or using an annotation, many methods estimate the expression level or the relative usage of isoforms and/or events. 4) Providing an isoform or event view of differential splicing or expression. These include methods that compare relative event/isoform abundance or isoform expression across two or more conditions. 5) Visualizing splicing regulation. Various tools facilitate the visualization of the RNA-Seq data in the context of alternative splicing. In this review, we do not describe the specific mathematical models behind each method. Our aim is rather to provide an overview that could serve as an entry point for users who need to decide on a suitable tool for a specific analysis. We also attempt to propose a classification of the tools according to the operations they do, to facilitate the comparison and choice of methods.Comment: 31 pages, 1 figure, 9 tables. Small corrections adde

Detection of gene orthology from gene co-expression and protein interaction networks

Background Ortholog detection methods present a powerful approach for finding genes that participate in similar biological processes across different organisms, extending our understanding of interactions between genes across different pathways, and understanding the evolution of gene families. Results We exploit features derived from the alignment of protein-protein interaction networks and gene-coexpression networks to reconstruct KEGG orthologs for Drosophila melanogaster, Saccharomyces cerevisiae, Mus musculus and Homo sapiens protein-protein interaction networks extracted from the DIP repository and Mus musculus and Homo sapiens and Sus scrofa gene coexpression networks extracted from NCBI\u27s Gene Expression Omnibus using the decision tree, Naive-Bayes and Support Vector Machine classification algorithms. Conclusions The performance of our classifiers in reconstructing KEGG orthologs is compared against a basic reciprocal BLAST hit approach. We provide implementations of the resulting algorithms as part of BiNA, an open source biomolecular network alignment toolkit

Support Vector Machines and Kernels for Computational Biology

ISSN:1553-734XISSN:1553-735

A quantitative approach to study indirect effects among disease proteins in the human protein interaction network

<p>Abstract</p> <p>Background</p> <p>Systems biology makes it possible to study larger and more intricate systems than before, so it is now possible to look at the molecular basis of several diseases in parallel. Analyzing the interaction network of proteins in the cell can be the key to understand how complex processes lead to diseases. Novel tools in network analysis provide the possibility to quantify the key interacting proteins in large networks as well as proteins that connect them. Here we suggest a new method to study the relationships between topology and functionality of the protein-protein interaction network, by identifying key mediator proteins possibly maintaining indirect relationships among proteins causing various diseases.</p> <p>Results</p> <p>Based on the i2d and OMIM databases, we have constructed (i) a network of proteins causing five selected diseases (DP, disease proteins) plus their interacting partners (IP, non-disease proteins), the DPIP network and (ii) a protein network showing only these IPs and their interactions, the IP network. The five investigated diseases were (1) various cancers, (2) heart diseases, (3) obesity, (4) diabetes and (5) autism. We have quantified the number and strength of IP-mediated indirect effects between the five groups of disease proteins and hypothetically identified the most important mediator proteins linking heart disease to obesity or diabetes in the IP network. The results present the relationship between mediator role and centrality, as well as between mediator role and functional properties of these proteins.</p> <p>Conclusions</p> <p>We show that a protein which plays an important indirect mediator role between two diseases is not necessarily a hub in the PPI network. This may suggest that, even if hub proteins and disease proteins are trivially of great interest, mediators may also deserve more attention, especially if disease-disease associations are to be understood. Identifying the hubs may not be sufficient to understand particular pathways. We have found that the mediators between heart diseases and obesity, as well as heart diseases and diabetes are of relatively high functional importance in the cell. The mediator proteins suggested here should be experimentally tested as products of hypothetical disease-related proteins.</p