Analysis and Synthesis of Digital Dyadic Sequences

We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a complete characterization of the design space and count the possible number of constructions with and without considering possible reorderings of the point set. Based on this analysis, we then show that every digital dyadic net can be reordered into a sequence, together with a corresponding algorithm. Finally, we present a novel family of self-similar digital dyadic sequences, to be named $\xi$-sequences, that spans a subspace with fewer degrees of freedom. Those $\xi$-sequences are extremely efficient to sample and compute, and we demonstrate their advantages over the classic Sobol (0, 2)-sequence.Comment: 17 pages, 11 figures. Minor improvement of exposition; references to earlier proofs of Theorems 3.1 and 3.3 adde

Domótica e a requalificação de edifícios

Para a elaboração deste artigo técnico foi necessário adoptar uma estrutura que possibilitasse fornecer um estudo teóricoprático, transversal e equilibrado, das diferentes tecnologias domóticas. Inicialmente realizou-se um pequeno estudo teórico das tecnologias domóticas mais relevantes, de uma forma transversal e resumida (Capítulo 2). Em função do estudo teórico do capítulo anterior, no Capítulo 3 realizou-se uma análise mais prática, em que ao invés de abordar um caso prático existente, de grandes instalações com o seu valor emblemático, optou-se por utilizar como modelo o edifício F do Instituto Superior de Engenharia do Porto e apresentar uma das soluções possíveis de implementação de tecnologias domóticas em edifícios já existentes (aplicação do conceito de requalificação de edifícios). Depois da exposição do caso prático, expôs-se o futuro e oportunidades de mercado da domótica ou sistema de gestão técnica centralizada, mais focalizado para o mundo académico (Capítulo 4). Por fim, são tecidas as conclusões e considerações finais do artigo (capitulo 5). Esse artigo foi elaborado sob o ponto de vista de integrador. Por outras palavras, procurou-se realizar uma aproximação da realidade prática a nível de implementação das tecnologias domóticas em edifícios, ao dar uma linha de conhecimento abrangente e ao mesmo acessível aos leitores, que muitas das vezes esse tema acaba por transmitir conceitos errados

Eutactic quantum codes

We consider sets of quantum observables corresponding to eutactic stars. Eutactic stars are systems of vectors which are the lower dimensional ``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases. Although these vector systems are not comeasurable, they represent redundant coordinate bases with remarkable properties. One application is quantum secret sharing.Comment: 6 page

On the multiple Borsuk numbers of sets

The Borsuk number of a set S of diameter d >0 in Euclidean n-space is the smallest value of m such that S can be partitioned into m sets of diameters less than d. Our aim is to generalize this notion in the following way: The k-fold Borsuk number of such a set S is the smallest value of m such that there is a k-fold cover of S with m sets of diameters less than d. In this paper we characterize the k-fold Borsuk numbers of sets in the Euclidean plane, give bounds for those of centrally symmetric sets, smooth bodies and convex bodies of constant width, and examine them for finite point sets in the Euclidean 3-space.Comment: 16 pages, 3 figure

Multi-interaction mean-field renormalization group

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.JkComment: Tex file and three macros appended at the end. Five figures available upon request to: [email protected], Fax: [+]39-40-224-60

Concentration of the intrinsic volumes of a convex body

The intrinsic volumes are measures of the content of a convex body. This paper applies probabilistic and information-theoretic methods to study the sequence of intrinsic volumes. The main result states that the intrinsic volume sequence concentrates sharply around a specific index, called the central intrinsic volume. Furthermore, among all convex bodies whose central intrinsic volume is fixed, an appropriately scaled cube has the intrinsic volume sequence with maximum entropy

Tomosyn inhibits synaptic vesicle priming in Caenorhabditis elegans

Caenorhabditis elegans TOM-1 is orthologous to vertebrate tomosyn, a cytosolic syntaxin-binding protein implicated in the modulation of both constitutive and regulated exocytosis. To investigate how TOM-1 regulates exocytosis of synaptic vesicles in vivo, we analyzed C. elegans tom-1 mutants. Our electrophysiological analysis indicates that evoked postsynaptic responses at tom-1 mutant synapses are prolonged leading to a two-fold increase in total charge transfer. The enhanced response in tom-1 mutants is not associated with any detectable changes in postsynaptic response kinetics, neuronal outgrowth, or synaptogenesis. However, at the ultrastructural level, we observe a concomitant increase in the number of plasma membrane-contacting vesicles in tom-1 mutant synapses, a phenotype reversed by neuronal expression of TOM-1. Priming defective unc-13 mutants show a dramatic reduction in plasma membrane-contacting vesicles, suggesting these vesicles largely represent the primed vesicle pool at the C. elegans neuromuscular junction. Consistent with this conclusion, hyperosmotic responses in tom-1 mutants are enhanced, indicating the primed vesicle pool is enhanced. Furthermore, the synaptic defects of unc-13 mutants are partially suppressed in tom-1 unc-13 double mutants. These data indicate that in the intact nervous system, TOM-1 negatively regulates synaptic vesicle priming. © 2006 Gracheva et al

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the set of 3-subsets of J is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio

Loss of Dictyostelium HSPC300 causes a scar-like phenotype and loss of SCAR protein

<p>Abstract</p> <p>Background</p> <p>SCAR/WAVE proteins couple signalling to actin polymerization, and are thus fundamental to the formation of pseudopods and lamellipods. They are controlled as part of a five-membered complex that includes the tiny HSPC300 protein. It is not known why SCAR/WAVE is found in such a large assembly, but in <it>Dictyostelium </it>the four larger subunits have different, clearly delineated functions.</p> <p>Results</p> <p>We have generated <it>Dictyostelium </it>mutants in which the HSPC300 gene is disrupted. As has been seen in other regulatory complex mutants, SCAR is lost in these cells, apparently by a post-translational mechanism, though PIR121 levels do not change. HSPC300 knockouts resemble <it>scar </it>mutants in slow migration, roundness, and lack of large pseudopods. However <it>hspc300</it>-colonies on bacteria are larger and more similar to wild type, suggesting that some SCAR function can survive without HSPC300. We find no evidence for functions of HSPC300 outside the SCAR complex.</p> <p>Conclusion</p> <p>HSPC300 is essential for most SCAR complex functions. The phenotype of HSPC300 knockouts is most similar to mutants in <it>scar</it>, not the other members of the SCAR complex, suggesting that HSPC300 acts most directly on SCAR itself.</p