Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.

Set theory and metric spaces. Math. 261, autumn, 1950.

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Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics. Designed for the use of students in the university.

Mode of access: Internet.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

An Inquiry Into The Theory, Causes And Consequences Of Monitoring Indicators Of Health And Safety At Work

This paper engages in an interdisciplinary survey of the current state of knowledge related to the theory, determinants and consequences of occupational safety and health (OSH). First, it synthesizes the available theoretical frameworks used by economists and psychologists to understand the issues related to the optimal provision of OSH in the labour market. Second, it reviews the academic literature investigating the correlates of a comprehensive set of OSH indicators, which portray the state of OSH infrastructure (social security expenditure, prevention, regulations), inputs (chemical and physical agents, ergonomics, working time, violence) and outcomes (injuries, illnesses, absenteeism, job satisfaction) within workplaces. Third, it explores the implications of the lack of OSH in terms of the economic and social costs that are entailed. Finally, the survey identifies areas of future research interests and suggests priorities for policy initiatives that can improve the health and safety of workers.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.

Workshop: ASSIP - Attempted Suicide Short Intervention Program. Theory, Practice, and 24 Months Follow-up RCT.

Background: ASSIP is a manualized brief therapy based on a model of suicide as goal-directed action, aimed at establishing a therapeutic alliance in a patient-oriented, collaborative approach. The main goals of the three-session program ASSIP are for patients to understand, from an observer’s position, patterns leading to a suicidal crisis, recognize triggers and warning signs, and to establish individual safety strategies for future suicidal crises. An ongoing therapeutic support is provided with regular letters over 24 months. Method: The study was conducted in a naturalistic setting. 120 Patients were randomly assigned to an intervention group (60 participants) treated with ASSIP combined with follow-up contact through letters, and a control group (60 participants) receiving a single session of clinical assessment. Both groups had treatment as usual. Patients completed a set of psychosocial and clinical questionnaires every six months over a period of 24 months. Results: In the ASSIP group 5 patients made a total of 5 reattempts, compared to 15 patients with 41 reattempts in the control group. The survival analysis yielded a significant difference with a Wald Chi2 of .000003. The ASSIP group had significantly lower suicidal ideation and fewer days of inpatient treatment compared to the control group. Higher scores in the Penn Helping Alliance Questionnaire were associated with lower suicidal ideation during follow-up. Conclusions: ASSIP is a highly effective brief therapy for patients with recent suicide attempts. Forming a strong therapeutic alliance is considered to be a major factor for outcome. ASSIP can be used with minimal training by experienced therapists. An English version of the manual will be published in May 2015.

Are you a bromide? : or, The sulphitic theory expounded and exemplified according to the most recent researches into the psychology of boredom, including many well-known bromidioms now in use /

"This essay is reprinted, with revisions and additions, from 'The sulphitic theory,' published in 'the Smart set' for April, 1906."

Leading theory: Bourdieu and the field of educational leadership. An introduction and overview to this special issue

Bourdieu … makes it possible to explain how the actions of principals are always contextual, since their interests vary with issue, location, time, school mix, composition of staff and so on. This 'identity' perspective points at a different kind of research about principal practice: to understand the game and its logic requires an analysis of the situated everyday rather than abstractions that claim truth in all instances and places. (Thomson 2001a: 14)

Operators Factoring through Banach Lattices and Ideal Norms

A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.

Fuzzy Set Theory Approach as the Basis of Analysis of Financial Flows in the Economical Security System

The problems of formalization of the process of matching different management subjects’ functioning characteristics obtained on the financial flows analysis basis is considered. Formal generalizations for gaining economical security system knowledge bases elements are presented. One of feedback directions establishment between knowledge base of the system of economical security and financial flows database analysis is substantiated.

The Development of the Generalization Algorithm Based on the Rough Set Theory

This paper considers the problem of concept generalization in decision-making systems where such features of real-world databases as large size, incompleteness and inconsistence of the stored information are taken into account. The methods of the rough set theory (like lower and upper approximations, positive regions and reducts) are used for the solving of this problem. The new discretization algorithm of the continuous attributes is proposed. It essentially increases an overall performance of generalization algorithms and can be applied to processing of real value attributes in large data tables. Also the search algorithm of the significant attributes combined with a stage of discretization is developed. It allows avoiding splitting of continuous domains of insignificant attributes into intervals.