A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

Map - Plan of Organization of Conquered Position

A map titled "Plan of Organization of Conquered Position". There is a legend at the top right that reads: "Parallel of Surveillance, Parallel of Resistance, Parallel of the Redoubts, Limit between Bns., Final Objective, Final Line after Counter Attack." The map is dated 17 December 1918

Posttraumatic stress disorder symptoms might be destroying your intimacy : a test of mediational models in a community sample of couples

The present research focused on the pathways through which the symptoms of posttraumatic stress disorder (PTSD) may negatively impact intimacy. Previous research has confirmed a link between self-reported PTSD symptoms and intimacy; however, a thorough examination of mediating paths, partner effects, and secondary traumatization has not yet been realized. With a sample of 297 heterosexual couples, intraindividual and dyadic models were developed to explain the relationships between PTSD symptoms and intimacy in the context of interdependence theory, attachment theory, and models of selfpreservation (e.g., fight-or-flight). The current study replicated the findings of others and has supported a process in which affective (alexithymia, negative affect, positive affect) and communication (demand-withdraw behaviour, self-concealment, and constructive communication) pathways mediate the intraindividual and dyadic relationships between PTSD symptoms and intimacy. Moreover, it also found that the PTSD symptoms of each partner were significantly related; however, this was only the case for those dyads in which the partners had disclosed most everything about their traumatic experiences. As such, secondary traumatization was supported. Finally, although the overall pattern of results suggest a total negative effect of PTSD symptoms on intimacy, a sex difference was evident such that the direct effect of the woman's PTSD symptoms were positively associated with both her and her partner's intimacy. I t is possible that the Tend-andBefriend model of threat response, wherein women are said to foster social bonds in the face of distress, may account for this sex difference. Overall, however, it is clear that PTSD symptoms were negatively associated with relationship quality and attention to this impact in the development of diagnostic criteria and treatment protocols is necessary.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Object-Oriented Genetic Programming for the Automatic Inference of Graph Models for Complex Networks

Complex networks are systems of entities that are interconnected through meaningful relationships. The result of the relations between entities forms a structure that has a statistical complexity that is not formed by random chance. In the study of complex networks, many graph models have been proposed to model the behaviours observed. However, constructing graph models manually is tedious and problematic. Many of the models proposed in the literature have been cited as having inaccuracies with respect to the complex networks they represent. However, recently, an approach that automates the inference of graph models was proposed by Bailey [10] The proposed methodology employs genetic programming (GP) to produce graph models that approximate various properties of an exemplary graph of a targeted complex network. However, there is a great deal already known about complex networks, in general, and often specific knowledge is held about the network being modelled. The knowledge, albeit incomplete, is important in constructing a graph model. However it is difficult to incorporate such knowledge using existing GP techniques. Thus, this thesis proposes a novel GP system which can incorporate incomplete expert knowledge that assists in the evolution of a graph model. Inspired by existing graph models, an abstract graph model was developed to serve as an embryo for inferring graph models of some complex networks. The GP system and abstract model were used to reproduce well-known graph models. The results indicated that the system was able to evolve models that produced networks that had structural similarities to the networks generated by the respective target models.