Algebraic Constructions of Toroidal Compactifications

2013 ◽  
Author(s):  
Kai-Wen Lan
Keyword(s):  
General Construction ◽  
Formal Models ◽  
Algebraic Models ◽  
Algebraic Construction ◽  
Algebraic Stacks ◽  
Local Structures ◽  
Correct Formulation ◽  
Toroidal Compactifications ◽  
Multiplicative Type ◽  
Algebraic Constructions

This chapter explains the algebraic construction of toroidal compactifications. For this purpose the chapter utilizes the theory of toroidal embeddings for torsors under groups of multiplicative type. Based on this theory, the chapter begins the general construction of local charts on which degeneration data for PEL structures are tautologically associated. The next important step is the description of good formal models, and good algebraic models approximating them. The correct formulation of necessary properties and the actual construction of these good algebraic models are the key to the gluing process in the étale topology. In particular, this includes the comparison of local structures using certain Kodaira–Spencer morphisms. As a result of gluing, this chapter obtains the arithmetic toroidal compactifications in the category of algebraic stacks. The chapter is concluded by a study of Hecke actions on towers of arithmetic toroidal compactifications.

Algebraic Constructions of Minimal Compactifications

2013 ◽  
Author(s):  
Kai-Wen Lan
Keyword(s):  
Large Class ◽  
Automorphic Forms ◽  
Algebraic Construction ◽  
Local Structures ◽  
Jacobi Expansion ◽  
Integral Bases ◽  
Toroidal Compactifications ◽  
Jacobi Expansions ◽  
Algebraic Constructions ◽  
Moduli Problems

This chapter first studies the automorphic forms that are defined as global sections of certain invertible sheaves on the toroidal compactifications. The local structures of toroidal compactifications lead naturally to the theory of Fourier–Jacobi expansions and the Fourier–Jacobi expansion principle. The chapter also obtains the algebraic construction of arithmetic minimal compactifications (of the coarse moduli associated with moduli problems), which are projective normal schemes defined over the same integral bases as the moduli problems are. As a by-product of codimension counting, we obtain Koecher's principle for arithmetic automorphic forms (of naive parallel weights). Furthermore, this chapter shows the projectivity of a large class of arithmetic toroidal compactifications by realizing them as normalizations of blowups of the corresponding minimal compactifications.

Remarks on the Awarding of the Albert O. Hirschman Prize to Charles Tilly

2010 ◽  
Vol 34 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Joan W. Scott
Keyword(s):  
Social Science ◽  
Political Theory ◽  
Social Science Research ◽  
Science Research ◽  
Academic Excellence ◽  
Grey Zone ◽  
Formal Models ◽  
Local Structures ◽  
Charles Tilly ◽  
The Social

The Albert O. Hirschman Prize is the highest award of the Social Science Research Council (SSRC). It recognizes academic excellence in international, interdisciplinary social science research, theory, and public communication in the tradition of the German-born American economist for whom it is named. It makes sense that the SSRC honors Hirschman in this way, for he was, as one biographical summary puts it, a “maverick economist.” The same biography says that Hirschman lived in “the grey zone between economic and political theory,” forging connections between them in unusual and extremely creative ways (homepage.newschool.edu/het//profiles/ hirschm.htm). His work in development economics insisted on attention to local structures and indigenous resources, arguing against the application of formal models and standard criteria, the dominant approach of modernization theorists. Ever concerned about political democracy, he explored its relationship to economics.

The Multiple Faces of Risk-Taking

2016 ◽  
Vol 32 (1) ◽  
pp. 17-38 ◽  
Author(s):  
Florian Schmitz ◽  
Karsten Manske ◽  
Franzis Preckel ◽  
Oliver Wilhelm
Keyword(s):  
Risk Taking ◽  
Basic Research ◽  
Formal Models ◽  
Experimental Paradigm ◽  
Nomological Network ◽  
Balloon Analogue Risk Task ◽  
Parameter Recovery ◽  
Task Specificity ◽  
Available Information ◽  
Criterion Variables

Abstract. The Balloon-Analogue Risk Task (BART; Lejuez et al., 2002 ) is one of the most popular behavioral tasks suggested to assess risk-taking in the laboratory. Previous research has shown that the conventionally computed score is predictive, but neglects available information in the data. We suggest a number of alternative scores that are motivated by theories of risk-taking and that exploit more of the available data. These scores can be grouped around (1) risk-taking, (2) task performance, (3) impulsive decision making, and (4) reinforcement sequence modulation. Their theoretical rationale is detailed and their validity is tested within the nomological network of risk-taking, deviance, and scholastic achievement. Two multivariate studies were conducted with youths (n = 435) and with adolescents/young adults (n = 316). Additionally, we tested formal models suggested for the BART that decompose observed behavior into a set of meaningful parameters. A simulation study with parameter recovery was conducted, and the data from the two studies were reanalyzed using the models. Most scores were reliable and differentially predictive of criterion variables and may be used in basic research. However, task specificity and the generally moderate validity do not warrant use of the experimental paradigm for diagnostic purposes.

Constructing and Deconstructing Concepts

2016 ◽  
Vol 63 (5) ◽  
pp. 249-262 ◽  
Author(s):  
Charles A. Doan ◽  
Ronaldo Vigo
Keyword(s):  
Information Theory ◽  
Model Performance ◽  
Unsupervised Classification ◽  
Family Resemblance ◽  
Category Membership ◽  
Formal Models ◽  
Human Beings ◽  
One Dimensional ◽  
Relational Patterns ◽  
Optimal Classification

Abstract. Several empirical investigations have explored whether observers prefer to sort sets of multidimensional stimuli into groups by employing one-dimensional or family-resemblance strategies. Although one-dimensional sorting strategies have been the prevalent finding for these unsupervised classification paradigms, several researchers have provided evidence that the choice of strategy may depend on the particular demands of the task. To account for this disparity, we propose that observers extract relational patterns from stimulus sets that facilitate the development of optimal classification strategies for relegating category membership. We conducted a novel constrained categorization experiment to empirically test this hypothesis by instructing participants to either add or remove objects from presented categorical stimuli. We employed generalized representational information theory (GRIT; Vigo, 2011b , 2013a , 2014 ) and its associated formal models to predict and explain how human beings chose to modify these categorical stimuli. Additionally, we compared model performance to predictions made by a leading prototypicality measure in the literature.

Influential individuals: Approach to modeling

2018 ◽  
pp. 114-131
Author(s):  
O. Yu. Bondarenko
Keyword(s):  
Social Interactions ◽  
Social Status ◽  
Experimental Approach ◽  
Expert Knowledge ◽  
Formal Models ◽  
Leader Influence ◽  
Learning Game ◽  
Game Theoretic ◽  
Asymmetric Interactions ◽  
Influential Individuals

his article explores theoretical and experimental approach to modeling social interactions. Communication and exchange of information with other people affect individual’s behavior in numerous areas. Generally, such influence is exerted by leaders, outstanding individuals who have a higher social status or expert knowledge. Social interactions are analyzed in the models of social learning, game theoretic models, conformity models, etc. However, there is a lack of formal models of asymmetric interactions. Such models could help elicit certain qualities characterizing higher social status and perception of status by other individuals, find the presence of leader influence and analyze its mechanism.

Single Image Dehazing by Predicting Atmospheric Scattering Parameters

2020 ◽  
Vol 2020 (1) ◽  
pp. 74-77
Author(s):  
Simone Bianco ◽  
Luigi Celona ◽  
Flavio Piccoli
Keyword(s):  
Reference Image ◽  
Single Image ◽  
Scattering Parameters ◽  
Image Dehazing ◽  
Atmospheric Scattering ◽  
Local Structures ◽  
Full Reference ◽  
Reconstruction Quality ◽  
Single Image Dehazing

In this work we propose a method for single image dehazing that exploits a physical model to recover the haze-free image by estimating the atmospheric scattering parameters. Cycle consistency is used to further improve the reconstruction quality of local structures and objects in the scene as well. Experimental results on four real and synthetic hazy image datasets show the effectiveness of the proposed method in terms of two commonly used full-reference image quality metrics.

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