A constructive study of the module structure of rings of partial differential operators

The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Dislocation loops in overheated free-standing smectic films

Static and dynamic phenomena in overheated free-standing smectic-A films are studied using a generalization of de Gennes' theory for a confined presmectic liquid. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated films, namely "uniform thinning" vs. nucleation of dislocation loops. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.Comment: 16 pages, 8 figure

Eda haplotypes in three-spined stickleback are associated with variation in immune gene expression

Haplotypes underlying local adaptation and speciation are predicted to have numerous phenotypic effects, but few genes involved have been identified, with much work to date concentrating on visible, morphological, phenotypes. The link between genes controlling these adaptive morphological phenotypes and the immune system has seldom been investigated, even though changes in the immune system could have profound adaptive consequences. The Eda gene in three-spined stickleback is one of the best studied major adaptation genes; it directly controls bony plate architecture and has been associated with additional aspects of adaptation to freshwater. Here, we exposed F2 hybrids, used to separate Eda genotype from genetic background, to contrasting conditions in semi-natural enclosures. We demonstrate an association between the Eda haplotype block and the expression pattern of key immune system genes. Furthermore, low plated fish grew less and experienced higher burdens of a common ectoparasite with fitness consequences. Little is currently known about the role of the immune system in facilitating adaptation to novel environments, but this study provides an indication of its potential importance

Impacts des vers de terre sur les composants et la dynamique du sol (synthèse bibliographique)

Impacts of earthworms on soil components and dynamics. A review. Earthworm populations are important decomposers contributing to aggregate formation and nutrient cycling processes involving nitrogen cycles, phosphorus and carbon. They are known to influence soil fertility by participating to important processes in soil such as soil structure regulation and organic matter dynamics. Earthworms also modify the microbial communities through digestion, stimulation and dispersion in casts. Consequently, changes in the activities of earthworm communities, as a result of soil management practices, can also be used as indicators of soil fertility and quality. It is therefore important to understand how earthworm communities affect soil dynamics. This review adresses the current state of knowledge on earthworm's impacts on soil structure and soil organic matter (carbon, nitrogen, and phosphorus) dynamics, with special emphasis on the effects of land management practices on earthworm communities

Modeling Dipolar and Quadrupolar Defect Structures generated by Chiral Islands in Freely-Suspended Liquid Crystal Films

We report a detailed theoretical analysis of novel quadrupolar interactions observed between islands, which are disk-like inclusions of extra layers, floating in thin, freely suspended smectic C liquid crystal films. Strong tangential anchoring at the island boundaries result in a strength +1 chiral defect in each island and a companion -1 defect in the film, these forming a topological dipole. While islands of the same handedness form linear chains with the topological dipoles pointing in the same direction, as reported in the literature, islands with different handedness form compact quadrupolar structures with the associated dipoles pointing in opposite directions. The interaction between such heterochiral island--defect pairs is complex, with the defects moving to minimize the director field distortion as the distance between the islands changes. The details of the inter-island potential and the trajectories of the -1 defects depend strongly on the elastic anisotropy of the liquid crystal, which can be modified in the experiments by varying the material chirality of the liquid crystal. A Landau model that describes the energetics of freely mobile defects is solved numerically to find equilibrium configurations for a wide range of parameters.Comment: 8 pages, 9 figure

Assessment of the quality of recommendations from 161 clinical practice guidelines using the Appraisal of Guidelines for Research and Evaluation-Recommendations Excellence (AGREE-REX) instrument shows there is room for improvement

To assess the quality of recommendations from 161 clinical practice guidelines (CPGs) using AGREE-REX-D (Appraisal of Guidelines REsearch and Evaluation-Recommendations Excellence Draft). International CPG community. Three hundred twenty-two international CPG developers, users, and researchers. Participants were assigned to appraise one of 161 CPGs selected for the study using the AGREE-REX-D tool Main outcome measures: AGREE-REX-D scores of 161 CPGs (7-point scale, maximum 7). Recommendations from 161 CPGs were appraised by 322 participants using the AGREE-REX-D. CPGs were developed by 67 different organizations. The total overall average score of the CPG recommendations was 4.23 (standard deviation (SD) = 1.14). AGREE-REX-D items that scored the highest were (mean; SD): evidence (5.51; 1.14), clinical relevance (5.95; SD 0.8), and patients/population relevance (4.87; SD 1.33), while the lowest scores were observed for the policy values (3.44; SD 1.53), local applicability (3,56; SD 1.47), and resources, tools, and capacity (3.49; SD 1.44) items. CPGs developed by government-supported organizations and developed in the UK and Canada had significantly higher recommendation quality scores with the AGREE-REX-D tool (p < 0.05) than their comparators. We found that there is significant room for improvement of some CPGs such as the considerations of patient/population values, policy values, local applicability and resources, tools, and capacity. These findings may be considered a baseline upon which to measure future improvements in the quality of CPGs

Reliability and validity of the AGREE instrument used by physical therapists in assessment of clinical practice guidelines

BACKGROUND: The AGREE instrument has been validated for evaluating Clinical Practice Guidelines (CPG) pertaining to medical care. This study evaluated the reliability and validity of physical therapists using the AGREE to assess quality of CPGs relevant to physical therapy practice. METHODS: A total of 69 physical therapists participated and were classified as generalists, specialist or researchers. Pairs of appraisers within each category evaluated independently, a set of 6 CPG selected at random from a pool of 55 CPGs. RESULTS: Reliability between pairs of appraisers indicated low to high reliability depending on the domain and number of appraisers (0.17–0.81 for single appraiser; 0.30–0.96 when score averaged across a pair of appraisers). The highest reliability was achieved for Rigour of Development, which exceeded ICC> 0.79, if scores from pairs of appraisers were pooled. Adding more than 3 appraisers did not consistently improve reliability. Appraiser type did not determine reliability scores. End-users, including study participants and a separate sample of 102 physical therapy students, found the AGREE useful to guide critical appraisal. The construct validity of the AGREE was supported in that expected differences on Rigour of Development domains were observed between expert panels versus those with no/uncertain expertise (differences of 10–21% p = 0.09–0.001). Factor analysis with varimax rotation, produced a 4-factor solution that was similar, although not in exact agreement with the AGREE Domains. Validity was also supported by the correlation observed (Kendall-tao = 0.69) between Overall Assessment and the Rigour of Development domain. CONCLUSION: These findings suggest that the AGREE instrument is reliable and valid when used by physiotherapists to assess the quality of CPG pertaining to physical therapy health services