Algebraic-graph method for identification of islanding in power system grids

In this paper, a new algebraic-graph method for identification of islanding in power system grids is proposed. The proposed method identifies all the possible cases of islanding, due to the loss of a equipment, by means of a factorization of the bus-branch incidence matrix. The main features of this new method include: (i) simple implementation, (ii) high speed, (iii) real-time adaptability, (iv) identification of all islanding cases and (v) identification of the buses that compose each island in case of island formation. The method was successfully tested on large-scale systems such as the reduced south Brazilian system (45 buses/72 branches) and the south-southeast Brazilian system (810 buses/1340 branches). (C) 2011 Elsevier Ltd. All rights reserved.

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

Automatic code generation: from process algebraic architectural descriptions to multithreaded java programs

Process algebraic architectural description languages provide a formal means for modeling software systems and assessing their properties. In order to bridge the gap between system modeling and system im- plementation, in this thesis an approach is proposed for automatically generating multithreaded object-oriented code from process algebraic architectural descriptions, in a way that preserves – under certain assumptions – the properties proved at the architectural level. The approach is divided into three phases, which are illustrated by means of a running example based on an audio processing system. First, we develop an architecture-driven technique for thread coordination management, which is completely automated through a suitable package. Second, we address the translation of the algebraically-specified behavior of the individual software units into thread templates, which will have to be filled in by the software developer according to certain guidelines. Third, we discuss performance issues related to the suitability of synthesizing monitors rather than threads from software unit descriptions that satisfy specific constraints. In addition to the running example, we present two case studies about a video animation repainting system and the implementation of a leader election algorithm, in order to summarize the whole approach. The outcome of this thesis is the implementation of the proposed approach in a translator called PADL2Java and its integration in the architecture-centric verification tool TwoTowers.

The meccano method for automatic 3-d triangulation and volume parametrization of complex solids

[EN]In this paper we review the novel meccano method. We summarize the main stages (subdivision, mapping, optimization) of this automatic tetrahedral mesh generation technique and we concentrate the study to complex genus-zero solids. In this case, our procedure only requires a surface triangulation of the solid. A crucial consequence of our method is the volume parametrization of the solid to a cube. We construct volume T-meshes for isogeometric analysis by using this result. The efficiency of the proposed technique is shown with several examples. A comparison between the meccano method and standard mesh generation techniques is introduced.-1…

Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.

Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Perhaps Triangulation Isn’t Enough: a Call for Crystallization as a Methodological Referent in NOS Research

This research compares the methodological tools employed in NOS research, with analysis of what the comparison implies about the structure of nature of science knowledge. Descriptions of practicing teachers’ nature of science conceptions were compared based on data collected from forced choice responses, responses to a qualitative survey, and course writing samples. Participants’ understandings were scored differently on the Views of Nature of Science Questionnaire (VNOS) than the forced-choice measure, Scientific Thinking and Internet Learning Technologies (STILT). In addition, analysis of the writing samples and observations combined with interviews portrayed more sophisticated, but more variable, understandings of the nature of science than was evidenced by either the survey or the forced-choice measure. The differences between data collection measures included the degree to which they drew upon context bound or context general reasoning, the degree to which they required students to move beyond the simple intelligibility of their responses and allowed students to explore the fruitfulness of the constructs, as well as the degree to which they revealed the interconnection of participants NOS conceptions. In light of the different portrayals of a participants NOS conceptions yielded by these different measures, we call for the use of crystallization as a methodological referent in research.

Pathway Semantics: An Algebraic Data Driven Algorithm to Generate Hypotheses about Molecular Patterns Underlying Disease Progression

The overarching goal of the Pathway Semantics Algorithm (PSA) is to improve the in silico identification of clinically useful hypotheses about molecular patterns in disease progression. By framing biomedical questions within a variety of matrix representations, PSA has the flexibility to analyze combined quantitative and qualitative data over a wide range of stratifications. The resulting hypothetical answers can then move to in vitro and in vivo verification, research assay optimization, clinical validation, and commercialization. Herein PSA is shown to generate novel hypotheses about the significant biological pathways in two disease domains: shock / trauma and hemophilia A, and validated experimentally in the latter. The PSA matrix algebra approach identified differential molecular patterns in biological networks over time and outcome that would not be easily found through direct assays, literature or database searches. In this dissertation, Chapter 1 provides a broad overview of the background and motivation for the study, followed by Chapter 2 with a literature review of relevant computational methods. Chapters 3 and 4 describe PSA for node and edge analysis respectively, and apply the method to disease progression in shock / trauma. Chapter 5 demonstrates the application of PSA to hemophilia A and the validation with experimental results. The work is summarized in Chapter 6, followed by extensive references and an Appendix with additional material.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Improving shortest paths in the Delaunay triangulation

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s; t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t in the Delaunay triangulation of P u{p} improves as much as possible. We study properties of the problem and give efficient algorithms to find such a point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.