Coalgebras on Measurable Spaces

Thesis (PhD) - Indiana University, Mathematics, 2005Given an endofunctor T in a category C, a coalgebra is a pair (X,c) consisting of an object X and a morphism c:X ->T(X). X is called the carrier and the morphism c is called the structure map of the T-coalgebra. The theory of coalgebras has been found to abstract common features of different areas like computer program semantics, modal logic, automata, non-well-founded sets, etc. Most of the work on concrete examples, however, has been limited to the category Set. The work developed in this dissertation is concerned with the category Meas of measurable spaces and measurable functions. Coalgebras of measurable spaces are of interest as a formalization of Markov Chains and can also be used to model probabilistic reasoning. We discuss some general facts related to the most interesting functor in Meas, Delta, that assigns to each measurable space, the space of all probability measures on it. We show that this functor does not preserve weak pullbacks or omega op-limits, conditions assumed in many theorems about coalgebras. The main result will be two constructions of final coalgebras for many interesting functors in Meas. The first construction (joint work with L. Moss), is based on a modal language that lets us build formulas that describe the elements of the final coalgebra. The second method makes use of a subset of the projective limit of the final sequence for the functor in question. That is, the sequence 1 <- T1 <- T 2 1 <-... obtained by iteratively applying the functor to the terminal element 1 of the category. Since these methods seem to be new, we also show how to use them in the category Set, where they provide some insight on how the structure map of the final coalgebra works. We show as an application how to construct universal Type Spaces, an object of interest in Game Theory and Economics. We also compare our method with previously existing constructions

Estimación de la Huella de Carbono del proceso de panificación en la cadena agroindustrial del trigo

Las cadenas alimentarias son responsables, en todo el mundo, de una gran parte de las emisiones totalesde gases de efecto invernadero. La Huella de Carbono (HC) representa un indicador que pretende cuantificarla cantidad total de emisiones de gases de efecto invernadero -expresada en equivalentes de dióxido de carbono-causadas directa o indirectamente por una actividad o las acumuladas durante la vida o etapas de un producto. El objetivo del presente trabajo fue estimar la HC del proceso de panificación incluyendo las etapas de producción primaria, molienda, panificación, consumo y los transportes del trigo y de la harina y, además,comparar la HC del pan producido en Argentina con respecto al producido en Brasil y China, en función de las matrices energéticas de cada país

Free monadic Tarski and MMI3-algebras

MMI3-algebras are a generalization of the monadic Tarski algebras as defined by A. Monteiro and L. Iturrioz, and a particular case of the MMIn+1-algebras defined by A. Figallo. They can also be seen as monadic three-valued £ukasiewicz algebras without a first element. By using this point of view, and the free monadic extensions, we construct the free MMI3-algebras on a finite number of generators, and indicate the coordinates of the generators. As a byproduct, we also obtain a construction of the free monadic Tarski algebras.Fil: Entizne, Rosana V.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Monteiro, Luiz F.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Savini, Sonia M.. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Viglizzo, Ignacio Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentin

Superrational types

We present a formal analysis of Douglas Hofstadter?s concept of superrationality. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that leads them to different choices than the usual assumption of rationality by restricting the range of conceivable choices. These beliefs are captured in the formal notion of type drawn from epistemic game theory. The theory of coalgebras is used to frame type spaces and to account for the existence of some of them. We find conditions that guarantee superrational outcomes.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Structural relations of symmetry among players in strategic games

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to define partial symmetries in payoff matrices. With this purpose, we introduce the notion of the role a player plays with respect to another one, and combinatorial relations between roles are studied. Building on them, we define relations directly between players, which provide yet another characterization of structural symmetries in the payoff matrices of strategic games.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Economía; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Construction of Nelson Algebras

The Vakarelov construction of Nelson algebras up from Heyting ones is generalized to obtain De Morgan algebras from distributive lattices. Necessary and sufficient conditions for these De Morgan algebras to be Nelson algebras are shown, and a characterization of the join-irreducible elements in the finite case is given.Fil: Monteiro, Luiz F.. Universidad Nacional del Sur; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaXIV Congreso Dr. Antonio A. R. MonteiroBahía BlancaArgentinaUniversidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática de Bahía Blanc

Improving carbon sequestration estimation through accounting carbon stored in grassland soil

Based on international guidelines, the elaboration of national carbon (C) budgets in many countries has tended to set aside the capacity of grazing lands to sequester C as soil organic carbon (SOC). A widely applied simple method assumes a steady state for SOC stocks in grasslands and a long-term equilibrium between annual C gains and losses. This article presents a theoretical method based on the annual conversion of belowground biomass into SOC to include the capacity of grazing-land soils to sequester C in greenhouse gases (GHG) calculations. Average figures from both methods can be combined with land-use/land-cover data to reassess the net C sequestration of the rural sector from a country. The results of said method were validated with empirical values based on peer-reviewed literature that provided annual data on SOC sequestration. This methodology offers important differences over pre-existing GHG landscape approach calculation methods: • improves the estimation about the capacity of grazing-land soils to sequester C assuming these lands are not in a steady state and • counts C gains when considering that grazing lands are managed at low livestock densities.Fil: Ricard, Maria Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Ciencias de la Tierra y Ambientales de La Pampa. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Instituto de Ciencias de la Tierra y Ambientales de La Pampa; ArgentinaFil: Viglizzo, Ernesto Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Ciencias de la Tierra y Ambientales de La Pampa. Universidad Nacional de La Pampa. Facultad de Ciencias Exactas y Naturales. Instituto de Ciencias de la Tierra y Ambientales de La Pampa; Argentin