Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Glomus intraradices induces changes in root system architecture of rice independently of common symbiosis signaling

? Arbuscular mycorrhizal fungi colonize the roots of most monocotyledons and dicotyledons despite their different root architecture and cell patterning. Among the cereal hosts of arbuscular mycorrhizal fungi, Oryza sativa (rice) possesses a peculiar root system composed of three different types of roots: crown roots; large lateral roots; and fine lateral roots. Characteristic is the constitutive formation of aerenchyma in crown roots and large lateral roots and the absence of cortex from fine lateral roots. Here, we assessed the distribution of colonization by Glomus intraradices within this root system and determined its effect on root system architecture. ? Large lateral roots are preferentially colonized, and fine lateral roots are immune to arbuscular mycorrhizal colonization. Fungal preference for large lateral roots also occurred in sym mutants that block colonization of the root beyond rhizodermal penetration. ? Initiation of large lateral roots is significantly induced by G. intraradices colonization and does not require a functional common symbiosis signaling pathway from which some components are known to be needed for symbiosis-mediated lateral root induction in Medicago truncatula. ? Our results suggest variation of symbiotic properties among the different rice root-types and induction of the preferred tissue by arbuscular mycorrhizal fungi. Furthermore, signaling for arbuscular mycorrhizal-elicited alterations of the root system differs between rice and M. truncatula.

Genetic architecture of ambulatory blood pressure in the general population: insights from cardiovascular gene-centric array.

Genetic determinants of blood pressure are poorly defined. We undertook a large-scale, gene-centric analysis to identify loci and pathways associated with ambulatory systolic and diastolic blood pressure. We measured 24-hour ambulatory blood pressure in 2020 individuals from 520 white European nuclear families (the Genetic Regulation of Arterial Pressure of Humans in the Community Study) and genotyped their DNA using the Illumina HumanCVD BeadChip array, which contains ≈50 000 single nucleotide polymorphisms in >2000 cardiovascular candidate loci. We found a strong association between rs13306560 polymorphism in the promoter region of MTHFR and CLCN6 and mean 24-hour diastolic blood pressure; each minor allele copy of rs13306560 was associated with 2.6 mm Hg lower mean 24-hour diastolic blood pressure (P=1.2×10(-8)). rs13306560 was also associated with clinic diastolic blood pressure in a combined analysis of 8129 subjects from the Genetic Regulation of Arterial Pressure of Humans in the Community Study, the CoLaus Study, and the Silesian Cardiovascular Study (P=5.4×10(-6)). Additional analysis of associations between variants in gene ontology-defined pathways and mean 24-hour blood pressure in the Genetic Regulation of Arterial Pressure of Humans in the Community Study showed that cell survival control signaling cascades could play a role in blood pressure regulation. There was also a significant overrepresentation of rare variants (minor allele frequency: <0.05) among polymorphisms showing at least nominal association with mean 24-hour blood pressure indicating that a considerable proportion of its heritability may be explained by uncommon alleles. Through a large-scale gene-centric analysis of ambulatory blood pressure, we identified an association of a novel variant at the MTHFR/CLNC6 locus with diastolic blood pressure and provided new insights into the genetic architecture of blood pressure.

Bone mineral density (BMD), micro-architecture estimation (TBS) and vertebral fracture assessment (VFA) extracted from a single DXA device in combination with clinical risk factors improve significantly the identification of women at high risk of fracture

Introduction: Osteoporosis (OP) is a systemic skeletal disease characterized by a low bone mineral density (BMD) and a micro-architectural (MA) deterioration. Clinical risk factors (CRF) are often used as a MA approximation. MA is yet evaluable in daily practice by the Trabecular Bone Score (TBS) measure. TBS is a novel grey-level texture measurement reflecting bone micro-architecture based on the use of experimental variograms of 2D projection images. TBS is very simple to obtain, by reanalyzing a lumbar DXA-scan. TBS has proven to have diagnosis and prognosis value, partially independent of CRF and BMD. The aim of the OsteoLaus cohort is to combine in daily practice the CRF and the information given by DXA (BMD, TBS and vertebral fracture assessment (VFA)) to better identify women at high fracture risk. Method: The OsteoLaus cohort (1400 women 50 to 80 years living in Lausanne, Switzerland) started in 2010. This study is derived from the cohort COLAUS who started in Lausanne in 2003. The main goals of COLAUS is to obtain information on the epidemiology and genetic determinants of cardiovascular risk in 6700 men and women. CRF for OP, bone ultrasound of the heel, lumbar spine and hip BMD, VFA by DXA and MA evaluation by TBS are recorded in OsteoLaus. Preliminary results are reported. Results: We included 631 women: mean age 67.4±6.7 y, BMI 26.1±4.6, mean lumbar spine BMD 0.943±0.168 (T-score -1.4 SD), TBS 1.271±0.103. As expected, correlation between BMD and site matched TBS is low (r2=0.16). Prevalence of VFx grade 2/3, major OP Fx and all OP Fx is 8.4%, 17.0% and 26.0% respectively. Age- and BMI-adjusted ORs (per SD decrease) are 1.8 (1.2- 2.5), 1.6 (1.2-2.1), 1.3 (1.1-1.6) for BMD for the different categories of fractures and 2.0 (1.4-3.0), 1.9 (1.4-2.5), 1.4 (1.1-1.7) for TBS respectively. Only 32 to 37% of women with OP Fx have a BMD < -2.5 SD or a TBS < 1.200. If we combine a BMD < -2.5 SD or a TBS < 1.200, 54 to 60% of women with an osteoporotic Fx are identified. Conclusion: As in the already published studies, these preliminary results confirm the partial independence between BMD and TBS. More importantly, a combination of TBS subsequent to BMD increases significantly the identification of women with prevalent OP Fx which would have been miss-classified by BMD alone. For the first time we are able to have complementary information about fracture (VFA), density (BMD), micro- and macro architecture (TBS & HAS) from a simple, low ionizing radiation and cheap device: DXA. Such complementary information is very useful for the patient in the daily practice and moreover will likely have an impact on cost effectiveness analysis.

Task-dependent influence of genetic architecture and mating frequency on division of labour in social insect societies.

Division of labour is one of the most prominent features of social insects. The efficient allocation of individuals to different tasks requires dynamic adjustment in response to environmental perturbations. Theoretical models suggest that the colony-level flexibility in responding to external changes and internal perturbation may depend on the within-colony genetic diversity, which is affected by the number of breeding individuals. However, these models have not considered the genetic architecture underlying the propensity of workers to perform the various tasks. Here, we investigated how both within-colony genetic variability (stemming from variation in the number of matings by queens) and the number of genes influencing the stimulus (threshold) for a given task at which workers begin to perform that task jointly influence task allocation efficiency. We used a numerical agent-based model to investigate the situation where workers had to perform either a regulatory task or a foraging task. One hundred generations of artificial selection in populations consisting of 500 colonies revealed that an increased number of matings always improved colony performance, whatever the number of loci encoding the thresholds of the regulatory and foraging tasks. However, the beneficial effect of additional matings was particularly important when the genetic architecture of queens comprised one or a few genes for the foraging task's threshold. By contrast, a higher number of genes encoding the foraging task reduced colony performance with the detrimental effect being stronger when queens had mated with several males. Finally, the number of genes encoding the threshold for the regulatory task only had a minor effect on colony performance. Overall, our numerical experiments support the importance of mating frequency on efficiency of division of labour and also reveal complex interactions between the number of matings and genetic architecture.

The fine-scale architecture of structural variants in 17 mouse genomes.

BACKGROUND: Accurate catalogs of structural variants (SVs) in mammalian genomes are necessary to elucidate the potential mechanisms that drive SV formation and to assess their functional impact. Next generation sequencing methods for SV detection are an advance on array-based methods, but are almost exclusively limited to four basic types: deletions, insertions, inversions and copy number gains. RESULTS: By visual inspection of 100 Mbp of genome to which next generation sequence data from 17 inbred mouse strains had been aligned, we identify and interpret 21 paired-end mapping patterns, which we validate by PCR. These paired-end mapping patterns reveal a greater diversity and complexity in SVs than previously recognized. In addition, Sanger-based sequence analysis of 4,176 breakpoints at 261 SV sites reveal additional complexity at approximately a quarter of structural variants analyzed. We find micro-deletions and micro-insertions at SV breakpoints, ranging from 1 to 107 bp, and SNPs that extend breakpoint micro-homology and may catalyze SV formation. CONCLUSIONS: An integrative approach using experimental analyses to train computational SV calling is essential for the accurate resolution of the architecture of SVs. We find considerable complexity in SV formation; about a quarter of SVs in the mouse are composed of a complex mixture of deletion, insertion, inversion and copy number gain. Computational methods can be adapted to identify most paired-end mapping patterns.

Defining the role of common variation in the genomic and biological architecture of adult human height.

Using genome-wide data from 253,288 individuals, we identified 697 variants at genome-wide significance that together explained one-fifth of the heritability for adult height. By testing different numbers of variants in independent studies, we show that the most strongly associated ∼2,000, ∼3,700 and ∼9,500 SNPs explained ∼21%, ∼24% and ∼29% of phenotypic variance. Furthermore, all common variants together captured 60% of heritability. The 697 variants clustered in 423 loci were enriched for genes, pathways and tissue types known to be involved in growth and together implicated genes and pathways not highlighted in earlier efforts, such as signaling by fibroblast growth factors, WNT/β-catenin and chondroitin sulfate-related genes. We identified several genes and pathways not previously connected with human skeletal growth, including mTOR, osteoglycin and binding of hyaluronic acid. Our results indicate a genetic architecture for human height that is characterized by a very large but finite number (thousands) of causal variants.

Tumor architecture exerts no bias on nuclear grading in breast cancer diagnosis.

We recently reported that nuclear grading in prostate cancer is subject to a strong confirmation bias induced by the tumor architecture. We now wondered whether a similar bias governs nuclear grading in breast carcinoma. An unannounced test was performed at a pathology conference. Pathologists were asked to grade nuclei in a PowerPoint presentation. Circular high power fields of 27 invasive ductal carcinomas were shown, superimposed over low power background images of either tubule-rich or tubule-poor carcinomas. We found (a) that diagnostic reproducibility of nuclear grades was poor to moderate (weighed kappa values between 0.07 and 0.54, 27 cases, 44 graders), but (b) that nuclear grades were not affected by the tumor architecture. We speculate that the categorized grading in breast cancer, separating tubule formation, nuclear pleomorphism, and mitotic figure counts in a combined three tier score, prevents the bias that architecture exerts on nuclear grades in less well-controlled situations.

VLSI architecture for an Underwater Robot Vision System

It is well known that image processing requires a huge amount of computation, mainly at low level processing where the algorithms are dealing with a great number of data-pixel. One of the solutions to estimate motions involves detection of the correspondences between two images. For normalised correlation criteria, previous experiments shown that the result is not altered in presence of nonuniform illumination. Usually, hardware for motion estimation has been limited to simple correlation criteria. The main goal of this paper is to propose a VLSI architecture for motion estimation using a matching criteria more complex than Sum of Absolute Differences (SAD) criteria. Today hardware devices provide many facilities for the integration of more and more complex designs as well as the possibility to easily communicate with general purpose processors

Proposal of a parallel architecture for a motion detection algorithm

This paper proposes a parallel architecture for estimation of the motion of an underwater robot. It is well known that image processing requires a huge amount of computation, mainly at low-level processing where the algorithms are dealing with a great number of data. In a motion estimation algorithm, correspondences between two images have to be solved at the low level. In the underwater imaging, normalised correlation can be a solution in the presence of non-uniform illumination. Due to its regular processing scheme, parallel implementation of the correspondence problem can be an adequate approach to reduce the computation time. Taking into consideration the complexity of the normalised correlation criteria, a new approach using parallel organisation of every processor from the architecture is proposed

All-Optical Label Stacking: Easing the Trade-offs Between Routing and Architecture Cost in All-Optical Packet Switching

All-optical label swapping (AOLS) forms a key technology towards the implementation of all-optical packet switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the way in which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This paper studies all-optical label stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this paper, an integer lineal program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more

Enterprise Architecture Principles in Research and Practice: Insights from an Exploratory Analysis

Even though architecture principles were first discussed in the 1990s, they are still perceived as an underexplored topic in enterprise architecture management research. By now, there is an increasing consensus about EA principles' nature, as well as guidelines for their formulation. However, the extant literature remains vague about what can be considered suitable EA design and evolution guidance principles. In addition, empirical insights regarding their role and usefulness in practice are still lacking. Accordingly, this research seeks to address three questions: (1) What are suitable principles to guide EA design and evolution? (2) What usage do EA principles have for practitioners? (3) Which propositions can be derived regarding EA principles' role and application? Opting for exploratory research, we apply a research process covering critical analysis of current publications as well as capturing experts' perceptions. Our research ontologically distinguishes between principles from nonprinciples, proposes a validated set of meta-principles, and clarifies principles' application, role, and usefulness in practice. The explored insights can be used as guidelines in defining suitable principles and turning them into an effective bridge between strategy and design and a guide in design decisions.