Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links

We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, and gradient driven transport on networks. Changing the parameters of the distance-dependence, we found a rich phase diagram, with different transient and recurrent phases in the context of random walks on networks. We performed the calculations in two limiting cases: in the annealed case, where the rearrangement of the random links is fast, and in the quenched case, where the link rearrangement is slow compared to the motion of the random walker or the surface. It has been well-established that in a large class of interacting systems, adding an arbitrarily small density of, possibly long-range, quenched random links to a regular lattice interaction topology, will give rise to mean-field (or annealed) like behavior. In some cases, however, mean-field scaling breaks down, such as in diffusion or in the Edwards-Wilkinson process in "low-dimensional" small-world networks. This break-down can be understood by treating the random links perturbatively, where the mean-field (or annealed) prediction appears as the lowest-order term of a naive perturbation expansion. The asymptotic analytic results are also confirmed numerically by employing exact numerical diagonalization of the network Laplacian. Further, we construct a finite-size scaling framework for the relevant observables, capturing the cross-over behaviors in finite networks. This work provides a detailed account of the self-consistent-perturbative and renormalization approaches briefly introduced in two earlier short reports.Comment: 36 pages, 27 figures. Minor revisions in response to the referee's comments. Furthermore, some typos were fixed and new references were adde

Non-deterministic Boolean Proof Nets

16 pagesInternational audienceWe introduce Non-deterministic Boolean proof nets to study the correspondence with Boolean circuits, a parallel model of computation. We extend the cut elimination of Non-deterministic Multiplicative Linear logic to a parallel procedure in proof nets. With the restriction of proof nets to Boolean types, we prove that the cut-elimination procedure corresponds to Non-deterministic Boolean circuit evaluation and reciprocally. We obtain implicit characterization of the complexity classes NP and NC (the efficiently parallelizable functions)

Evaluating predictive pharmacogenetic signatures of adverse events in colorectal cancer patients treated with fluoropyrimidines

The potential clinical utility of genetic markers associated with response to fluoropyrimidine treatment in colorectal cancer patients remains controversial despite extensive study. Our aim was to test the clinical validity of both novel and previously identified markers of adverse events in a broad clinical setting. We have conducted an observational pharmacogenetic study of early adverse events in a cohort study of 254 colorectal cancer patients treated with 5-fluorouracil or capecitabine. Sixteen variants of nine key folate (pharmacodynamic) and drug metabolising (pharmacokinetic) enzymes have been analysed as individual markers and/or signatures of markers. We found a significant association between TYMP S471L (rs11479) and early dose modifications and/or severe adverse events (adjusted OR = 2.02 [1.03; 4.00], p = 0.042, adjusted OR = 2.70 [1.23; 5.92], p = 0.01 respectively). There was also a significant association between these phenotypes and a signature of DPYD mutations (Adjusted OR = 3.96 [1.17; 13.33], p = 0.03, adjusted OR = 6.76 [1.99; 22.96], p = 0.002 respectively). We did not identify any significant associations between the individual candidate pharmacodynamic markers and toxicity. If a predictive test for early adverse events analysed the TYMP and DPYD variants as a signature, the sensitivity would be 45.5 %, with a positive predictive value of just 33.9 % and thus poor clinical validity. Most studies to date have been under-powered to consider multiple pharmacokinetic and pharmacodynamic variants simultaneously but this and similar individualised data sets could be pooled in meta-analyses to resolve uncertainties about the potential clinical utility of these markers

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

A study of the distribution of phylogenetically conserved blocks within clusters of mammalian homeobox genes

Genome sequencing efforts of the last decade have produced a large amount of data, which has enabled whole-genome comparative analyses in order to locate potentially functional elements and study the overall patterns of phylogenetic conservation. In this paper we present a statistically based method for the characterization of these patterns in mammalian DNA sequences. We have applied this approach to the study of exceptionally well conserved homeobox gene clusters (Hox), based on an alignment of six species, and we have constructed a map of Hox cataloguing the conserved fragments, along with their locations in relation to the genes and other landmarks, sometimes showing unexpected layouts

Molecular markers of response and toxicity to FOLFOX chemotherapy in metastatic colorectal cancer

BACKGROUND: To investigate three genetic alterations (TP53 mutation, Kras mutation and microsatellite instability (MSI)) and three polymorphisms (methylene tetrahydrofolate reductase (MTHFR) C677T, excision repair cross complementing group 1 (ERCC1)-118 and X-ray repair cross complementing group 1 (XRCC1)-399) for their ability to predict response, survival and toxicity to FOLFOX first line chemotherapy in the treatment of metastatic colorectal cancer (mCRC). METHODS: Tumour tissues from 118 mCRC patients who underwent FOLFOX treatment from three successive phase II trials were evaluated for mutations in TP53 (exons 5–8) and Kras (codons 12 and 13) and for MSI using PCR-based analysis. Genotyping for common single nucleotide polymorphisms in the MTHFR (codon 677), ERCC1 (codon 118) and XRCC1 (codon 399) genes was also carried out using PCR techniques. These genetic markers were correlated with clinical response, survival and toxicity to treatment. RESULTS: Patients with the T allele of ERCC1-118 showed significantly worse progression-free survival in univariate analysis (HR 2.62; 95 % CI 1.14–6.02; P 0.02). None of the genetic alterations or polymorphisms showed significant association with clinical response to FOLFOX. The MTHFR, ERCC1 and XRCC1 polymorphisms showed no associations with overall haematological, gastrointestinal or neurological toxicity to FOLFOX, although MTHFR 677 TT genotype patients showed a significantly higher incidence of grade 3 or 4 diarrhoea (26%) compared with CC or CT genotype patients (6%, P 0.02). CONCLUSIONS: The ERCC1-118 and MTHFR C677T polymorphisms were associated with progression and severe diarrhoea

On Uniformity and Circuit Lower Bounds

Abstract—We explore relationships between circuit complexity, the complexity of generating circuits, and algorithms for analyzing circuits. Our results can be divided into two parts: 1. Lower Bounds Against Medium-Uniform Circuits. Informally, a circuit class is “medium uniform ” if it can be generated by an algorithmic process that is somewhat complex (stronger than LOGTIME) but not infeasible. Using a new kind of indirect diagonalization argument, we prove several new unconditional lower bounds against medium uniform circuit classes, including: • For all k, P is not contained in P-uniform SIZE(n k). That is, for all k there is a language Lk ∈ P that does not have O(n k)-size circuits constructible in polynomial time. This improves Kannan’s lower bound from 1982 that NP is not in P-uniform SIZE(n k) for any fixed k