Collaborative Change: Environmental Jolt, Network (Re)Design and Firm Performance

Motivated by the need to understand which are the underlying forces that trigger network evolution, we develop a multilevel theoretical and empirically testable model to examine the relationship between changes in the external environment and network change. We refer to network change as the dissolution or replacement of an interorganizational tie, adding also the case of the formation of new ties with new or preexisting partners. Previous research has paid scant attention to the organizational consequences of quantum change enveloping entire industries in favor of an emphasis on continuous change. To highlight radical change we introduce the concept of environmental jolt. The September 11 terrorist attacks provide us with a natural experiment to test our hypotheses on the antecedents and the consequences of network change. Since network change can be explained at multiple levels, we incorporate firm-level variables as moderators. The empirical setting is the global airline industry, which can be regarded as a constantly changing network of alliances. The study reveals that firms react to environmental jolts by forming homophilous ties and transitive triads as opposed to the non jolt periods. Moreover, we find that, all else being equal, firms that adopt a brokerage posture will have positive returns. However, we find that in the face of an environmental jolt brokerage relates negatively to firm performance. Furthermore, we find that the negative relationship between brokerage and performance during an environmental jolt is more significant for larger firms. Our findings suggest that jolts are an important predictor of network change, that they significantly affect operational returns and should be thus incorporated in studies of network dynamics.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Marx Illusion

With “Marx Illusion”, Claudiu Coman recalls sociology - this science of analytic and methodological strictness - to its uncorrupted philosophical dignity. Not only the theorization - that is the seduction of quality essay, Claudiu Coman demonstrating here a single ability - but the philosophy itself: a science, if we want, but as a way of cognitive enclosure of the beings of the world, firstly of those who make the world possible, but of the transcendent world that transcends them making possible - as a 20th century scientist would say - the man’s connection to an existence that is not his own, but that identifies itself with the difference. Being in the world - M. Heidegger writes (in 1928, after the apparition of the work “The Being and Time”) - it is specific only to the man - and here within the Territory of Existence I have the impression that philosophy and sociology responded together. However, working together with philosophy, the sociology extends enveloping the “world less” beings, too. These things would already been in the world as “direct” things (“handy”) being caught by the man by referring to them in the world itself.

Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.

Softening the Lower Crust: Modes of Syn-Transport Transposition Around and Adjacent to a Deep Crustal Granulite Nappe, Parry Sound Domain, Grenville Province, Ontario, Canada

The Parry Sound domain is a granulite nappe-stack transported cratonward during reactivation of the ductile lower and middle crust in the late convergence of the Mesoproterozoic Grenville orogeny. Field observations suggest the following with respect to the ductile sheath: (1) Formation of a carapace of transposed amphibolite facies gneiss derived from and enveloping the western extremity of the Parry Sound domain and separating it from high-strain gneiss of adjacent allochthons. This ductile sheath formed dynamically around the moving granulite nappe through the development of systems of progressively linked shear zones. (2) Transposition initiated by hydration (amphibolization) of granulite facies gneiss by introduction of fluid along cracks accompanying pegmatite emplacement. Shear zones nucleated along pegmatite margins and subsequently linked and rotated. The source of the pegmatites was most likely subjacent migmatitic and pegmatite-rich units or units over which Parry Sound domain was transported. Comparison of gneisses of the ductile sheath with high-strain layered gneiss of adjacent allochthons show the mode of transposition of penetratively layered gneiss depended on whether or not the gneiss protoliths were amphibolite or granulite facies tectonites before initiation of transposition, resulting in, e.g., folding before shearing, no folding before shearing, respectively. Meter-scale truncation along high-strain gradients at the margins of both types of transposition-related shear zones observed within and marginal to Parry Sound domain mimic features at kilometer scales, implying that apparent truncation by transposition originating in a manner similar to the ductile sheath may be a common feature of deep crustal ductile reworking. Citation: Culshaw, N., C. Gerbi, and J. Marsh (2010), Softening the lower crust: Modes of syn-transport transposition around and adjacent to a deep crustal granulite nappe, Parry Sound domain, Grenville Province, Ontario, Canada, Tectonics, 29, TC5013, doi:10.1029/2009TC002537.

A Logical Descriptor for Regular Languages via Stone Duality

In this paper we introduce a class of descriptors for regular languages arising from an application of the Stone duality between finite Boolean algebras and finite sets. These descriptors, called classical fortresses, are object specified in classical propositional logic and capable to accept exactly regular languages. To prove this, we show that the languages accepted by classical fortresses and deterministic finite automata coincide. Classical fortresses, besides being propositional descriptors for regular languages, also turn out to be an efficient tool for providing alternative and intuitive proofs for the closure properties of regular languages.

Admissibility via natural dualities

It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be characterized using natural dualities. In particular, axiomatizations are obtained for the admissible clauses and quasi-identities of bounded distributive lattices, Stone algebras, Kleene algebras and lattices, and De Morgan algebras and lattices.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

Microfossils and chemical elements in bottom sediments of the Ashadze-1 Hydrothermal Field (tropical Mid-Atlantic Ridge)

The first thorough analysis of microfossils from ore-bearing sediments of the Ashadze-1 Hydrothermal Field in the Mid-Atlantic Ridge sampled during Cruise 26 of R/V Professor Logachev in 2005 revealed substantial influence of hydrothermal processes on preservation of planktonic calcareous organisms as well as on preservation and composition of benthic foraminifera. From lateral and vertical distribution patterns and secondary alterations of microfossils it is inferred that the main phase of hydrothermal mineralization occurred in Holocene. Heavy metals (Cu, Co, Cr, and Ag) were accumulated by foraminiferal tests and in their enveloping Fe-Mn crusts. Distribution of authigenic minerals replacing foraminiferal tests demonstrates local zoning related to hydrothermal activity. There are three mineral-geochemical zones defined: sulfide zone, zone with elevated Mg content, and zone of Fe-Mn crusts.

Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Hiord: A type-free higher-order logic programming language with predicate abstraction

A new formalism, called Hiord, for defining type-free higherorder logic programming languages with predicate abstraction is introduced. A model theory, based on partial combinatory algebras, is presented, with respect to which the formalism is shown sound. A programming language built on a subset of Hiord, and its implementation are discussed. A new proposal for defining modules in this framework is considered, along with several examples.

Categorical Structures in Non-Commutative Measure Theory.

In this paper, we investigate effect algebras and base normed spaces from the categorical point of view. We prove that the category of effect algebras is complete and cocomplete as well as the category of base normed spaces is complete, and discuss the contravariant functor from the category of effect algebras to the category of base normed spaces.