Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Rational algorithms for the decomposition of Feynman integrals via intersection theory

The decomposition of Feynman integrals into a basis of independent master integrals is an essential ingredient of high-precision theoretical predictions, that often represents a major bottleneck when processes with a high number of loops and legs are involved. In this thesis we present a new algorithm for the decomposition of Feynman integrals into master integrals with the formalism of intersection theory. Intersection theory is a novel approach that allows to decompose Feynman integrals into master integrals via projections, based on a scalar product between Feynman integrals called intersection number. We propose a new purely rational algorithm for the calculation of intersection numbers of differential $n-$forms that avoids the presence of algebraic extensions. We show how expansions around non-rational poles, which are a bottleneck of existing algorithms for intersection numbers, can be avoided by performing an expansion in series around a rational polynomial irreducible over $\mathbb{Q}$, that we refer to as $p(z)-$adic expansion. The algorithm we developed has been implemented and tested on several diagrams, both at one and two loops.

$E_{1}$-Formality of complex algebraic varieties

Let $X$ be a smooth complex algebraic variety. Morgan showed that the rational homotopy type of $X$ is a formal consequence of the differential graded algebra defined by the first term $E_{1}(X,W)$ of its weight spectral sequence. In the present work, we generalize this result to arbitrary nilpotent complex algebraic varieties (possibly singular and/or non-compact) and to algebraic morphisms between them. In particular, our results generalize the formality theorem of Deligne, Griffiths, Morgan and Sullivan for morphisms of compact Kähler varieties, filling a gap in Morgan"s theory concerning functoriality over the rationals. As an application, we study the Hopf invariant of certain algebraic morphisms using intersection theory.

Deriving Deligne-Mumford stacks with perfect obstruction theories

Intersection theory on moduli spaces has lead to immense progress in certain areas of enumerative geometry. For some important areas, most notably counting stable maps and counting stable sheaves, it is important to work with a virtual fundamental class instead of the usual fundamental class of the moduli space. The crucial prerequisite for the existence of such a class is a two-term complex controlling deformations of the moduli space. Kontsevich conjectured in 1994 that there should exist derived version of spaces with this specific property. Another hint at the existence of these spaces comes from derived algebraic geometry. It is expected that for every pair of a space and a complex controlling deformations of the space their exists, under some additional hypothesis, a derived version of the space having the chosen complex as cotangent complex. In this thesis one version of these additional hypothesis is identified. We then show that every space admitting a two-term complex controlling deformations satisfies these hypothesis, and we finally construct the derived spaces.

Gestão democrática caminhos e possibilidades : um estudo de caso em uma escola pública de ensino fundamental em Belém

A linha de pesquisa desenvolvida nesta dissertação não é inédita, todavia, apresenta algumas peculiaridades a respeito da gestão democrática para a educação brasileira, mais especificamente em Belém do Pará, que são no mínimo, um contributo à sociedade. Principalmente porque demonstra sucintamente, no primeiro e segundo capítulos a trajetória sócio histórica e a política-pedagógica da gestão democrática no Brasil a partir dos meados do século XVI, até a implementação da LDB nº 9394/96. No terceiro capítulo trato a respeito das Leis de Diretrizes e Bases da Educação Nacional, nº 5692/71 e da LDB nº 9394/96, esta última objetivou romper com os resquícios deixados pela 5692/71, vale frisar que o primeiro estado a implementar as Leis de Diretrizes e Bases, assentadas na Lei nº 9394/96, foi o estado do Pará. Nos capítulos: quarto e quinto destaco a Metodologia aplicada à pesquisa de campo; às análises dos dados coletados e mensurados, e construo uma triangulação e/ou cruzamento (Teoria-Práxis-Teoria que resultará à práxis), entre a teoria pesquisada e analisada, com as referências bibliográficas e com os dados coletados no campo acerca dos caminhos e possibilidades necessários para articular a gestão democrática no município de Belém. Para construir esse trajeto recorri às leituras bibliográficas de autores que já aprofundaram o assunto como: José Júlio Chiavenato, Luiz Fernando Dourado, Paulo Freire, Moacir Gadotti, Carlos Libâneo, João Monlevad, Vítor Paro, Michel Thiollent, Sofia Lérché Vieira entre outros autores que contribuíram para a construção teórica e prática, e que estão citados na referência. No que concerne a pesquisa de campo foi efetivada uma sondagem prévia e uma apresentação do tema à direção da escola e para a presidente do Conselho Escolar, em seguida foram feitos contatos com os profissionais da educação através de conversas informais a cerca do assunto. Após esse processo foram aplicados questionários com vinte e seis perguntas objetivas e duas perguntas subjetivas, que estão expostas no anexo desta dissertação; outros mecanismos utilizados na pesquisa de campo foram as entrevistas in lócus com alguns profissionais da escola pesquisada, utilizou-se também a observação participante com o viés na abordagem sócio histórica. O trabalho de campo e as referências bibliográficas coadunadas à observação participante, no cotidiano da comunidade escolar, foram essenciais para a consolidação deste trabalho dissertativo que envolveu um tema, que certamente, está em voga na educação brasileira e que serviu como base para o título desta dissertação: Gestão democrática caminhos e possibilidades:. Um estudo de caso em uma escola pública de ensino fundamental em Belém. A dissertação em questão também apresenta no capítulo quinto o tripé básico para a análise científica relacionada a gestão democrática que são: Eleição direta para o Conselho Escolar, eleição direta para o diretor/articulador/social, eleição para o grêmio estudantil, esta sob a direção dos alunos. A base desse tripé deve estar assentada na participação qualitativa de todas as categorias da comunidade escolar, preservando e respeitando a autonomia de cada categoria, bem como demonstra a aproximação e a contribuição da comunidade externa para o processo de ensino-aprendizagem. E, por fim, não menos importante, proponho algumas sugestões que estão expostas nas conclusões e demonstram claramente a necessidade de implementação de alguns caminhos a serem seguidos e implementados para que de fato e de direito se processe a gestão democrática participativa, à luz dos conceitos apresentados nesta dissertação que estão diretamente relacionados à formação, à participação, e à autonomia, para isso é necessário alguns ajustes na lei nº 7.722/94, na resolução nº036/2008 e o conhecimento e domínio da Lei nº 9394/96.__ ABSTRACT: The line of research developed in this thesis is not new, however, presents some peculiarities about the democratic management in Brazilian education, specifically in Belem, which are at least a contribution to society. Mainly because it shows succinctly in the first and second chapters the history and socio-historical political-pedagogical democratic management in Brazil since the mid-sixteenth century through implementation of the LDB 9394/96. ln the third chapter dealing with respect to the Laws of Directives and Bases of National Education, 5692/71 and 9394/96 LDB, the latter aimed to break with the remnants left over from 5692/71, it is worth stressing that the first state to implement the laws Guidelines and Bases, sitting in the Law 9394/96, was the Para The fourth and fifth chapters highlight the Methodology applied to field research, the analysis of data collected and measured and construct a triangulation and I or intersection (Theory-Praxis-Theory resulting praxis), between theory researched and analyzed with the references and the data collected in the field about the ways and possibilities necessary to articulate the democratic management at the education system in the municipality of Belém. To construct this path resorted to reading literature by authors who have explored the subject as: Jose Julio Chiavenato, Luiz Fernando Dourado, Paulo Freire, Moacir Gadotti, Carlos Libâneo John Monlevade, Paro Vítor, Michel Thiollent, Sofia Lerche Vieira and others who contributed to the theoretical and practical construction andare cited in the reference. Regarding the field research, it was carried a survey and a preliminary presentation of the theme to the school principal and to the School Board president, then were made contacts with professionals in education, through informal conversations about the subject. After this procedure were applied questionnaires with twenty-six objective questions and two subjective questions that are exposed in the appendix of this thesis. Other mechanisms used in field research were interviews in locus with some professionals of the surveyed. It was also used participant observation with the bias in the socio-historical approach. The field research and the references link ed to the participant observation in daily school community. were essential for the consolidation of this dissertational work involving a theme, which certainly, is in vogue in the Brazilian education and That served as the basis for this title dissertation: Management democratic ways and possibilities: A in a public elementary school case study in Belém. This dissertation Thesis presents in Its fifth chapter the basic tripod for scientific analysis related to the democratic management which are: Direct election for the School Board, direct election for chief articulator/social, for students union, this last one under the direction of the students. The basis of this tripod must be seated in the qualitative participation of all categories of the school community, preserving and respecting the autonomy of each on and demonstrates the approach and the contribution of the externa! community to the process of teaching and learning. At finally, but not less important propose some suggestions that are exposed on the conclusion and clearly demonstrate the need to implement some ways to be followed and implemented so that actually and by law the participatory democratic management, may be conducted according to Ulrich the concepts of this dissertation, are directly related to education, participation, and autonomy. However, this requires some adjustments in the Law 7.722/94, in its resolution 036/2008, and indeed the knowledge mastery of the Law 9394/96.

Building theory at the intersection of ecological sustainability and strategic management

This article builds theory at the intersection of ecological sustainability and strategic management literature—specifically, in relation to dynamic capabilities literature. By combining industrial organization economics–based, resource-based, and dynamic capability–based views, it is possible to develop a better understanding of the strategies that businesses may follow, depending on their managers’ assumptions about ecological sustainability. To develop innovative strategies for ecological sustainability, the dynamic capabilities framework needs to be extended. In particular, the sensing–seizing–maintaining competitiveness framework should operate not only within the boundaries of a business ecosystem but in relation to global biophysical ecosystems; in addition, two more dynamic capabilities should be added, namely, remapping and reaping. This framework can explicate core managerial beliefs about ecological sustainability. Finally, this approach offers opportunities for managers and academics to identify, categorize, and exploit business strategies for ecological sustainability.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Conflict prevention and decentralized governance: some remarks about the state of the art in theory and practice

Is there a link between decentralized governance and conflict prevention? This article tries to answer the question by presenting the state of the art of the intersection of both concepts. Provided that social conflict is inevitable and given the appearance of new threats and types of violence, as well as new demands for security based on people (human security), our societies should focus on promoting peaceful changes. Through an extensive analysis of the existing literature and the study of several cases, this paper suggests that decentralized governance can contribute to these efforts by transforming conflicts, bringing about power-sharing and inclusion incentives of minority groups. Albeit the complexity of assessing its impact on conflict prevention, it can be contended that decentralized governance might have very positive effects on the reduction of causes that bring about conflicts due to its ability to foster the creation of war/violence preventors. More specifically, this paper argues that decentralization can have a positive impact on the so-called triggers and accelerators (short- and medium-term causes).

In the intersection of the angles of a table, there is more truth than in all the tangle of muscles: Futurism as anti-humanist critique

The recent celebrations of the centenary of the publication of the Futurist manifesto led to a renewed discussion of the ideas and artworks of the Italian artists’ group. Jacques Rancière related the Futurist ethos with the modernist project of liberating art from representation. Franco ‘Bifo’ Berardi, in his post-Futurist manifesto, also identified a historical irony at play in the emptying out of Futurism’s promise: a liberated mechanical humanity did indeed materialize, in a global economic system premised on financial servitude to the future via debt. However, these models continue to assess Futurism against an unchallenged humanism, finding it either supporting ideals of freedom and human rights despite itself, or else lacking in these areas. But Futurism is potentially more relevant than ever not in spite of its anti-humanist agenda, precisely because of it. Tom McCarthy annexes not Futurist art but Futurist writing to an emerging object oriented ontology that seeks to challenge the primacy of the human. If Futurism is to be repurposed as a critical concept, it can only do so by countering the humanist myth the liberal subject that underlies the current cultural and political hegemony of neo-liberalism.

PRESENTATION. Experimental and behavioral economics. Theory, tools and topics

This note presents the special issue on Experimental and Behavioral Economics. The volume includes some recent contributions from these correlated disciplines –empirical the former and theoretical the latter– and their potential contribution to the intersection of Economics with Psychology and Sociology. The project “El papel de la comparación social en las decisiones económicas bajo incertidumbre” (Junta de Andalucía, P07-SEJ-03155)” provided us with inspiration and financial support to publish this volume.

Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.