A Diagramatic Analysis of Duality in Supersymmetric Gauge Theories

We introduce a diagramatic notation for supersymmetric gauge theories. The notation is a tool for exploring duality and helps to present the field content of more complicated models in a simple visual way. We introduce the notation with a few examples from the literature. The power of the formalism allows us to study new models with gauge group $(SU(N))^k$ and their duals. Amongst these are models which, contrary to a naive analysis, possess no conformal phase.Comment: 20 pages, LaTeX, figures include

Hiding State in CλaSH Hardware Descriptions

Synchronous hardware can be modelled as a mapping from input and state to output and a new state, such mappings are referred to as transition functions. It is natural to use a functional language to implement transition functions. The CaSH compiler is capable of translating transition functions to VHDL. Modelling hardware using multiple components is convenient. Components in CaSH can be considered as instantiations of functions. To avoid packing and unpacking state when composing components, functions are lifted to arrows. By using arrows the chance of making errors will decrease as it is not required to manually (un)pack the state. Furthermore, the Haskell do-syntax for arrows increases the readability of hardware designs. This is demonstrated using a realistic example of a circuit which consists of multiple components

Modelos Bayesianos gráficos jerárquicos en psicología

El mejoramiento de los métodos gráficos en la investigación en psicología puede promover su uso y una mejor compresión de su poder de expresión. La aplicación de modelos Bayesianos gráficos jerárquicos se ha vuelto más frecuente en la investigación en psicología. El objetivo de este trabajo es introducir sugerencias para el mejoramiento de los modelos Bayesianos gráficos jerárquicos en psicología. Este conjunto de sugerencias se apoya en la descripción y comparación entre los dos enfoques principales con el uso de notación y pictogramas de distribución. Se concluye que la combinación de los aspectos relevantes de ambos puede mejorar el uso de los modelos Bayesianos gráficos jerárquicos en psicología.The improvement of graphical methods in psychological research can promote their use and a better comprehension of their expressive power. The application of hierarchical Bayesian graphical models has recently become more frequent in psychological research. The aim of this contribution is to introduce suggestions for the improvement of hierarchical Bayesian graphical models in psychology. This novel set of suggestions stems from the description and comparison between two main approaches concerned with the use of plate notation and distribution pictograms. It is concluded that the combination of relevant aspects of both models might improve the use of powerful hierarchical Bayesian graphical models in psychology.Fil: Campitelli, Guillermo Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Edith Cowan University; AustraliaFil: Macbeth, Guillermo Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ciencias de la Educación; Argentin

A calculus for bordered Floer homology

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complete description of slopes giving rise to L-space Dehn fillings as well as necessary and sufficient conditions for L-spaces resulting from identifying two such manifolds along their boundaries. As an application, we show that Seifert fibered spaces with torus boundary fall into this class, leading to a proof that, among graph manifolds containing a single JSJ torus, the property of being an L-space is equivalent to non-left-orderability of the fundamental group and to the non-existence of a coorientable taut foliation.Comment: 79 pages, 14 figures, uses tik

Characterization of combinatorially independent permutation separability criteria

The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of at least one of the resulting operators is greater than one. If it is greater than one then the state is necessarily entangled. A shortcoming of the permutation separability criteria is that many permutations give rise to dependent separability criteria. Therefore, we introduce a necessary condition for two permutations to yield independent criteria called combinatorical independence. This condition basically means that the map corresponding to one permutation cannot be obtained by concatenating the map corresponding to the second permutation with a norm-preserving map. We characterize completely combinatorically independent criteria, and determine simple permutations that represent all independent criteria. The representatives can be visualized by means of a simple graphical notation. They are composed of three basic operations: partial transpose, and two types of so-called reshufflings. In particular, for a four-partite system all criteria except one are composed of partial transpose and only one type of reshuffling; the exceptional one requires the second type of reshuffling. Furthermore, we show how to obtain efficiently for every permutation a simple representative. This method allows to check easily if two permutations are combinatorically equivalent or not.Comment: 9 pages, corrected proof of rule