Modern graphics accelerators have embedded programmable components in the form of vertex and fragment shading units. Current APIs permit specification of the programs for these components using an assembly-language level interface. Compilers for high-level shading languages are available but these read in an external string specification, which can be inconvenient. It is possible, using standard C++, to define an embedded high-level shading language. Such a language can be nearly indistinguishable from a special-purpose shading language, yet permits more direct interaction with the specification of textures and parameters, simplifies implementation, and enables on-the-fly generation, manipulation, and specification of shader programs. An embedded shading language also permits the lifting of C++ host language type, modularity, and scoping constructs into the shading language without any additional implementation effort.

A snake (coil) is an induced path (cycle) in a hypercube. They are well known from the snake-in-the-box (coil-in-the-box) problem which asks for the longest snake (coil) in a hypercube. They have been generalized to k-snakes (k-coils) which preserve distances between their every two vertices at distance at most k − 1 in hypercube. We study them as a variant of Locke's hypothesis. It states that a balanced set F ⊆ V (Qn) of cardinality 2m can be avoided by a Hamiltonian cycle if n ≥ m + 2 and m ≥ 1. We show that if S is a k-snake (k-coil) in Qn for n ≥ k ≥ 6 (n ≥ k ≥ 7), then Qn − V (S) is Hamiltonian laceable. For a fixed k the number of vertices of a k-coil may even be exponential with n. We introduce a dragon, which is an induced tree in a hypercube, and its generalization a k-dragon which preserves distances between its every two vertices at distance at most k−1 in hypercube. By proving a specific lemma from my Bachelor thesis that was previously verified by a computer, we finish the proof of the theorem regarding Hamiltonian laceability of hypercubes without n-dragons.

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Thesis advisor: Ziqiang Wang / Exotic phases and associated phase transitions in low dimensions have been a fascinating frontier and a driving force in modern condensed matter physics since the 80s. Due to strong correlation effect, they are beyond the description of mean-field theory based on a single-particle picture and Landau's symmetry-breaking theory of phase transitions. These new phases of matter require new physical quantities to characterize them and new languages to describe them. This thesis is devoted to the study on exotic phases of correlated electrons in two spatial dimensions. We present the following efforts in understanding two-dimensional exotic phases: (1) Using Zn vertex algebra, we give a complete classification and characterization of different one-component fractional quantum Hall (FQH) states, including their ground state properties and quasiparticles. (2) In terms of a non-unitary transformation, we obtain the exact form of statistical interactions between composite fermions in the lowest Landau level (LLL) with v=1/(2m), m=1,2... By studying the pairing instability of composite fermions we theoretically explains recently observed FQHE in LLL with v=1/2,1/4. (3) We classify different Z2 spin liquids (SLs) on kagome lattice in Schwinger-fermion representation using projective symmetry group (PSG). We propose one most promising candidate for the numerically discovered SL state in nearest-neighbor Heisenberg model on kagome lattice}. (4) By analyzing different Z2 spin liquids on honeycomb lattice within PSG classification, we find out the nature of the gapped SL phase in honeycomb lattice Hubbard model, labeled sublattice pairing state (SPS) in Schwinger-fermion representation. We also identify the neighboring magnetic phase of SPS as a chiral-antiferromagnetic (CAF) phase and analyze the continuous phase transition between SPS and CAF phase. For the first time we identify a SL called 0-flux state in Schwinger-boson representation with one (SPS) in Schwinger-fermion representation by a duality transformation. (5) We show that when certain non-collinear magnetic order coexists in a singlet nodal superconductor, there will be Majorana bound states in vortex cores/on the edges of the superconductor. This proposal opens a window for discovering Majorana fermions in strongly correlated electrons. (6) Motivated by recent numerical discovery of fractionalized phases in topological flat bands, we construct wavefunctions for spin-polarized fractional Chern insulators (FCI) and time reversal symmetric fractional topological insulators (FTI) by parton approach. We show that lattice symmetries give rise to different FCI/FTI states even with the same filling fraction. For the first time we construct FTI wavefunctions in the absence of spin conservation which preserve all lattice symmetries. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Usamos as regras de soma da QCD para obter a massa dos pentaquarks \" \'teta\' POT.+\"(1540) e \"\'ksi\' POT.--\" (1862), a largura de decaimento da \"\'teta\' POT.+\" e a constante de acoplamento e fator de forma presentes no vertice J/ \'psi\' \"DD POT.*\". No estudo dos pentaquarks, usamos dois tipos de campos interpolantes contendo dois diquarks altamente correlacionados. Obtemos as massas consistentes com os dados experimentais, porém esta regra de soma têm uma grande contribuição do contínuo e a OPE não é muito boa. Obtivemos uma largura de decaimento compatível com os valores experimentais desde que sejam subtraídos diagramas que representam a \" \'teta\' POT.+\" como um estado ligado K - n. No estudo do vértice vertice J/ \'psi\' \"DD POT.*\" calculamos o fator de forma e a constante de acoplamento, considerando três casos: D off-shell, \"D POT.*\" off-shell e J/ \'psi\' off-shell. A constante de acoplamento é a mesma nesses três casos, porém o fator de forma depende da escolha da partícula off-shell, onde para a J/ \'psi\' off-shell o fator de forma é bem mais duro que o fator de forma obtido para os outros casos. Também comparamos os nossos resultados com outros métodos: o modelo de quark méson constituintes e o modelo de quarks relativísticos constituintes / We use the QCD sum rules to obtain the masses of the pentaquarks _+(1540) and _−−(1862), _+ decay width and the coupling constant and the form factor for the J/ DD* vertex.In the study of the pentaquarks, we use two kinds of interpolating fields, containing two highly correlated diquarks. We get the masses in a good agreement with the experimental value, but this sum rule has a large continuuum contribution and the OPE convergence is not so good. We get the decay width compatible with the experimental value, since we subtract the diagrams that represent _+ as a K − n bound state. In the study of J/ DD* vertex, we calculate the form factor and the coupling constant considering three cases: D off-shell, D* off-shell and J/ off-shell. The coupling constant is the same in those three cases, however the form factor depends on the choice of the particle off-shell, where for the J/ off-shell the form factor is much harder than the form factor obtained for the other cases. We also compare our results with other methods: the constituent quark meson model and the relativistic constituent quark model.

Usamos as regras de soma da QCD para obter a massa dos pentaquarks \" \'teta\' POT.+\"(1540) e \"\'ksi\' POT.--\" (1862), a largura de decaimento da \"\'teta\' POT.+\" e a constante de acoplamento e fator de forma presentes no vertice J/ \'psi\' \"DD POT.*\". No estudo dos pentaquarks, usamos dois tipos de campos interpolantes contendo dois diquarks altamente correlacionados. Obtemos as massas consistentes com os dados experimentais, porém esta regra de soma têm uma grande contribuição do contínuo e a OPE não é muito boa. Obtivemos uma largura de decaimento compatível com os valores experimentais desde que sejam subtraídos diagramas que representam a \" \'teta\' POT.+\" como um estado ligado K - n. No estudo do vértice vertice J/ \'psi\' \"DD POT.*\" calculamos o fator de forma e a constante de acoplamento, considerando três casos: D off-shell, \"D POT.*\" off-shell e J/ \'psi\' off-shell. A constante de acoplamento é a mesma nesses três casos, porém o fator de forma depende da escolha da partícula off-shell, onde para a J/ \'psi\' off-shell o fator de forma é bem mais duro que o fator de forma obtido para os outros casos. Também comparamos os nossos resultados com outros métodos: o modelo de quark méson constituintes e o modelo de quarks relativísticos constituintes / We use the QCD sum rules to obtain the masses of the pentaquarks _+(1540) and _−−(1862), _+ decay width and the coupling constant and the form factor for the J/ DD* vertex.In the study of the pentaquarks, we use two kinds of interpolating fields, containing two highly correlated diquarks. We get the masses in a good agreement with the experimental value, but this sum rule has a large continuuum contribution and the OPE convergence is not so good. We get the decay width compatible with the experimental value, since we subtract the diagrams that represent _+ as a K − n bound state. In the study of J/ DD* vertex, we calculate the form factor and the coupling constant considering three cases: D off-shell, D* off-shell and J/ off-shell. The coupling constant is the same in those three cases, however the form factor depends on the choice of the particle off-shell, where for the J/ off-shell the form factor is much harder than the form factor obtained for the other cases. We also compare our results with other methods: the constituent quark meson model and the relativistic constituent quark model.

O presente trabalho consistiu em investigar os fenômenos da materialidade pelo vértice poético da experiência humana em diálogo com o caso Piggle do pediatra e psicanalista Donald Winnicott a partir de um ponto de vista hermenêutico. Antes de realizarmos a investigação do caso a partir do vértice da materialidade, foram apresentados alguns aspectos de como a materialidade comparece como um elemento importante no cotidiano pessoal de Winnicott assim como também na clínica psicanalítica que Winnicott realizou. Em seguida, foi apresentado e discutido o vértice poético da experiência humana em diálogo com alguns psicanalistas, entre eles Winnicott, Milner e Safra e com alguns artistas, dos quais, William Blake, Adélia Prado e Manoel de Barros foram autores relevantes. Finalmente, foi realizada a investigação da materialidade como evento poético em cada uma das consultas do caso Piggle de Winnicott. Com este percurso realizado, chegamos a alguns pontos fundamentais: 1) a materialidade não é um conceito que pode ser abordado por abstrações, pois ela emerge como experiência poética no espaço do entre o homem e o mundo; 2) a disponibilidade poética do terapeuta é fundamental como condição para que seja possível acolher a materialidade do mundo como evento poético que eclode no cotidiano e no encontro clínico como experiência que revela a condição humana; 3) a compreensão dos fenômenos da materialidade é fundamental na clínica psicanalítica, em uma perspectiva ética, para que o clínico nesta abordagem possa ofertar um trabalho encarnado ao seu paciente e que seu oficio possa ser uma ação resistente e alerta ao esfacelamento da experiência humana no mundo / This paper aims to investigate the phenomena of the materiality by the poetical view of human experience in dialog with case Piggle by the pediatric and psychoanalyst Donald Winnicott through a point of view of the hermeneutics. Before investigating the case through the question of the materiality, we introduced some aspects of how this theme appears in Winnicotts personal way of life and also in the contributions he did in his theories. After that, we discussed and presented the poetical interpretation of the human experience in dialog with relevant authors, some of who were the psychoanalysts Winnicott, Milner and Safra and also with some artists as William Blake, Adélia Prado and Manoel de Barros. Finally, we investigated the materiality as poetical event in all the consultations of the case Piggle by Winnicott. After all, we reached some key points: 1) the materiality is not a concept which could be studied through abstractions, because it emerges as a poetical experience in the space between the human being and the world. 2) the therapists poetical openness is a fundamental condition in order to welcome the materiality of the world as a poetical event which appears in daily life and in the clinical situation as an experience which reveals the human condition; 3) the understanding of these phenomena is crucial to psychoanalytical situation, in an ethical perspective offering to the therapist in his/her work a possibility of working with body presence and an action of resistance to the vanishing experience of the human being in the world

Neste trabalho consideramos extensões do Modelo Padrão contendo vértices quárticos anômalos parametrizados por operadores efetivos de dimensão oito. Estes alteram o comportamento das amplitudes do tipo VV VV , onde V pode ser o fóton, o bóson Z, o bóson W ou o Higgs. Para essa extensão ser consistente, ela tem que obedecer o teorema ótico. Entretanto, as amplitudes geradas por estes operadores efetivos tendem a aumentar conforme a energia do centro de massa aumenta. Estudaremos o comportamento dessas amplitudes e determinaremos se há violação de unitariedade. Para isso utilizamos também o formalismo da base de helicidade. / In this work we consider Standard Model extensions containing anomalous quartic vertex parametrized by effective dimension-eight operators. These modify the behaviour of the scat- tering amplitudes VV VV , where V can be photon, Z boson, W boson and Higgs. To this extension be consistent, it has to obey the optical theorem. However, the amplitudes generated by these effective operators tends to grow as the center of mass energy increase. We will study the behaviour of these amplitudes and we will determine if there is unitarity violation. For this it was also used the helicity base formalism.

Nós obtemos o hamiltoniano associado ao modelo de oito vértices simétrico, tomando o limite de tempo contínuo em um modelo equivalente (modelo de Ashkin-Teller). O resultado é um hamiltoniano de Heisenberg com coeficientes Jx , Jy e Jz idênticos àqueles encontrados por Sutherland, na região crítica. A mudança nos operadores é acompanhada explicitamente e a relação entre o operador \"crossover\" do modelo de Ashkin-Teller e o operador energia do modelo de Baxter é obtida de forma transparente. / We obtain the associated Harniltonian for the symmetric eight-vertex model by taking the time-continuous limit in an equivalent Ashkin-Teller model. The result is a Heisenberg Hamiltonian with coefficients Jx , Jy e Jz identical to those found by Sutherland for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form.

O presente trabalho consistiu em investigar os fenômenos da materialidade pelo vértice poético da experiência humana em diálogo com o caso Piggle do pediatra e psicanalista Donald Winnicott a partir de um ponto de vista hermenêutico. Antes de realizarmos a investigação do caso a partir do vértice da materialidade, foram apresentados alguns aspectos de como a materialidade comparece como um elemento importante no cotidiano pessoal de Winnicott assim como também na clínica psicanalítica que Winnicott realizou. Em seguida, foi apresentado e discutido o vértice poético da experiência humana em diálogo com alguns psicanalistas, entre eles Winnicott, Milner e Safra e com alguns artistas, dos quais, William Blake, Adélia Prado e Manoel de Barros foram autores relevantes. Finalmente, foi realizada a investigação da materialidade como evento poético em cada uma das consultas do caso Piggle de Winnicott. Com este percurso realizado, chegamos a alguns pontos fundamentais: 1) a materialidade não é um conceito que pode ser abordado por abstrações, pois ela emerge como experiência poética no espaço do entre o homem e o mundo; 2) a disponibilidade poética do terapeuta é fundamental como condição para que seja possível acolher a materialidade do mundo como evento poético que eclode no cotidiano e no encontro clínico como experiência que revela a condição humana; 3) a compreensão dos fenômenos da materialidade é fundamental na clínica psicanalítica, em uma perspectiva ética, para que o clínico nesta abordagem possa ofertar um trabalho encarnado ao seu paciente e que seu oficio possa ser uma ação resistente e alerta ao esfacelamento da experiência humana no mundo / This paper aims to investigate the phenomena of the materiality by the poetical view of human experience in dialog with case Piggle by the pediatric and psychoanalyst Donald Winnicott through a point of view of the hermeneutics. Before investigating the case through the question of the materiality, we introduced some aspects of how this theme appears in Winnicotts personal way of life and also in the contributions he did in his theories. After that, we discussed and presented the poetical interpretation of the human experience in dialog with relevant authors, some of who were the psychoanalysts Winnicott, Milner and Safra and also with some artists as William Blake, Adélia Prado and Manoel de Barros. Finally, we investigated the materiality as poetical event in all the consultations of the case Piggle by Winnicott. After all, we reached some key points: 1) the materiality is not a concept which could be studied through abstractions, because it emerges as a poetical experience in the space between the human being and the world. 2) the therapists poetical openness is a fundamental condition in order to welcome the materiality of the world as a poetical event which appears in daily life and in the clinical situation as an experience which reveals the human condition; 3) the understanding of these phenomena is crucial to psychoanalytical situation, in an ethical perspective offering to the therapist in his/her work a possibility of working with body presence and an action of resistance to the vanishing experience of the human being in the world