Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

A g-factor metric for k-t-GRAPPA- and PEAK-GRAPPA-based parallel imaging.

PURPOSE The aim of this work is to derive a theoretical framework for quantitative noise and temporal fidelity analysis of time-resolved k-space-based parallel imaging methods. THEORY An analytical formalism of noise distribution is derived extending the existing g-factor formulation for nontime-resolved generalized autocalibrating partially parallel acquisition (GRAPPA) to time-resolved k-space-based methods. The noise analysis considers temporal noise correlations and is further accompanied by a temporal filtering analysis. METHODS All methods are derived and presented for k-t-GRAPPA and PEAK-GRAPPA. A sliding window reconstruction and nontime-resolved GRAPPA are taken as a reference. Statistical validation is based on series of pseudoreplica images. The analysis is demonstrated on a short-axis cardiac CINE dataset. RESULTS The superior signal-to-noise performance of time-resolved over nontime-resolved parallel imaging methods at the expense of temporal frequency filtering is analytically confirmed. Further, different temporal frequency filter characteristics of k-t-GRAPPA, PEAK-GRAPPA, and sliding window are revealed. CONCLUSION The proposed analysis of noise behavior and temporal fidelity establishes a theoretical basis for a quantitative evaluation of time-resolved reconstruction methods. Therefore, the presented theory allows for comparison between time-resolved parallel imaging methods and also nontime-resolved methods. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

Space-time Reconstruction of Oceanic Sea States via Variational Stereo Methods

We present a remote sensing observational method for the measurement of the spatio-temporal dynamics of ocean waves. Variational techniques are used to recover a coherent space-time reconstruction of oceanic sea states given stereo video imagery. The stereoscopic reconstruction problem is expressed in a variational optimization framework. There, we design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal regularizers. A nested iterative scheme is devised to numerically solve, via 3-D multigrid methods, the system of partial differential equations resulting from the optimality condition of the energy functional. The output of our method is the coherent, simultaneous estimation of the wave surface height and radiance at multiple snapshots. We demonstrate our algorithm on real data collected off-shore. Statistical and spectral analysis are performed. Comparison with respect to an existing sequential method is analyzed.

State space models for multi-setup operational modal analysis

Operational Modal Analysis consists on estimate the modal parameters of a structure (natural frequencies, damping ratios and modal vectors) from output-only vibration measurements. The modal vectors can be only estimated where a sensor is placed, so when the number of available sensors is lower than the number of tested points, it is usual to perform several tests changing the position of the sensors from one test to the following (multiple setups of sensors): some sensors stay at the same position from setup to setup, and the other sensors change the position until all the tested points are covered. The permanent sensors are then used to merge the mode shape estimated at each setup (or partial modal vectors) into global modal vectors. Traditionally, the partial modal vectors are estimated independently setup by setup, and the global modal vectors are obtained in a postprocess phase. In this work we present two state space models that can be used to process all the recorded setups at the same time, and we also present how these models can be estimated using the maximum likelihood method. The result is that the global mode shape of each mode is obtained automatically, and subsequently, a single value for the natural frequency and damping ratio of the mode is computed. Finally, both models are compared using real measured data.

Vivienda y fondo edificatorio: análisis de las consecuencias del parámetro fondo en el edificio de vivienda colectiva

Este estudio ofrece una herramienta de aproximación al espacio morfológico-métrico en el que se formula la ciudad de alta densidad desde la vivienda colectiva. La vivienda colectiva es la célula básica de la ciudad. El estudio configurativo y dimensional del tejido urbano muestra la importancia del fondo edificatorio como parámetro clave a mitad de camino entre la vivienda y la ciudad. El fondo edificatorio traza el margen de la arquitectura en la ciudad y desde él se equipa y cuantifica el territorio urbano. Sus dinámicas van caracterizando los distintos entornos, mientras en su interior se formula el tipo en un ajuste de continua verificación y adaptación. La forma de la ciudad y sus distintas posibilidades configurativas —en cuanto masa construida y espacio público, pero sin perder de vista la relación entre ambos— depende en gran medida del fondo edificatorio. Se trata, por tanto, de un parámetro importante de relación entre las distintas configuraciones del espacio exterior e interior. Al proyectar, una vez establecido un fondo, algunas propiedades se adaptan con facilidad mientras que otras requieren un cierto grado de interpretación o deben ser descartadas. Dada una superficie, la especificación del fondo fuerza la dimensión del frente en las configuraciones posibles. Ambas dimensiones son vitales en el valor del factor de forma del continuo edificado y en su relación se produce el complejo rango de posibilidades. Partiendo de la ciudad, un gran fondo encierra y mezcla en su interior todo tipo de usos sin distinción, repercute un menor coste por unidad de superficie edificada y comparte su frente reduciendo los intercambios térmicos y lumínicos. Sin embargo la ciudad de fondo reducido ajusta la forma al uso y se desarrolla linealmente con repetitividad a lo largo de sus frentes exteriores. En ella, el fuerte intercambio energético se opone a las grandes posibilidades del espacio libre. En cambio desde la casa las distintas medidas del fondo se producen bajo determinados condicionantes: clima, compacidad, ocupación, hibridación, tamaño de casa, etc., mientras que el tipo se desarrolla en base a una métrica afín. Este trabajo parte de esta dialéctica. Estudia la relación de dependencia entre las condiciones del edificio de viviendas y su métrica. Jerarquiza edificios en base al parámetro “fondo” para constituir una herramienta que como un ábaco sea capaz de visibilizar las dinámicas relacionales entre configuración y métrica bajo la condición de alta densidad. Para ello en una primera fase se gestiona una extensa muestra de edificios representativos de vivienda colectiva principalmente europea, extraída de tres prestigiosos libros en forma de repertorio. Se ordenan y categorizan extrayendo datos conmensurables y temas principales que ligan la profundidad de la huella a la morfología y posteriormente, esta información se estudia en diagramas que ponen de manifiesto convergencias y divergencias, acumulaciones y vacíos, límites, intervalos característicos, márgenes y ejes, parámetros y atributos... cuya relación trata de factorizar el lugar morfológico y métrico de la casa como metavivienda y ciudad. La herramienta se establece así como un complejo marco relacional en el que posicionar casos concretos y trazar nexos transversales, tanto de tipo morfológico como cultural, climático o técnico, normativo o tecnológico. Cada nuevo caso o traza añadida produce consonancias y disonancias en el marco que requieren interpretación y verificación. De este modo este instrumento de análisis comparativo se tempera, se especializa, se completa y se perfecciona con su uso. La forma de la residencia en la ciudad densa se muestra así sobre un subsistema morfológico unitario y su entendimiento se hace más fácilmente alcanzable y acumulable tanto para investigaciones posteriores como para el aprendizaje o el ejercicio profesional. ABSTRACT This research study offers a tool to approach the morphometric space in which (multi-family) housing defines high-density cities. Multi-family housing is the basic cell of the city. The configuration and dimension studies of the urban fabric render the importance of building depth as a key parameter half way between the dwelling and the city. The building depth traces de limit of architecture in the city. It qualifies and quantifies the urban territory. Its dynamics characterize the different environments while in its essence, an adjustment process of continuous verification and adaption defines type. The shape of the city and its different configuration possibilities —in terms of built fabric and public space, always keeping an eye on the relationship between them— depend majorly on the building depth. Therefore, it is a relevant parameter that relates the diverse configurations between interior and exterior space. When designing, once the depth is established, some properties are easily adpated. However, others require a certain degree of interpretation or have to be left out of the study. Given a ceratin surface, the establishment of the depth forces the dimensions of the facade in the different configurations. Both depth and facade dimensions are crucial for the form factor of the built mass. Its relationship produces a complex range of possibilities. From an urban point of view, great depth means multiple uses (making no distinction whatsoever,) it presents a lower cost per unit of built area and shares its facade optimizing temperature and light exchange. On the contrary, the city of reduced depth adjusts its shape to the use, and develops linearly and repetitively along its facades. The strong energy exchange opposes to the great possibilities of free space. From the perspective of the dwelling, the different dimensions of depth are produced under certain determinants: climate, compactness, occupancy, hybridization, dwelling size, etc. Meanwhile, the type is developed based on a related meter (as in poetry). This work starts from the previous premise. It studies the dependency relation bewteen the conditions of the dwellings and their meter (dimensions). It organizes buildings hierarchically based on the parameter “depth” to create a tool that, as an abacus, is able to visibilise the relational dynamics between configuration and dimension in high density conditions. For this, in the first stage a large group of representative multi-family housing buildings is managed, mostly from Europe, picked from three prestigious books as a repertoir. They are categorized and ordered drawing commensurable data and key issues that link the depth of the fooprint to its morphology. Later, this information is studied deeply with diagrams that bring out connections and discrepancies, voids and accumulations, limits, charasteristic intervals, margins and axii, parameters, attributes, etc. These relationships try to create factors from a morphological and metrical point of view of the house as a metadwelling. This tool is established as a complex relation frame in which case studies are postitioned and cross-cutting nexii are traced. These can deal with morphology, climate, technique, law or technology. Each new case or nexus produces affinities and discrepancies that require interpretation and verification. Thus, this instrument of comparative analysis is fine-tuned, especialized and completed as its use is improved. The way housing is understood in high density cities is shown as a unitary metric subsystem and its understanding is easy to reach and accumulate for future researchers, students or practicing architects.

Self-assembly of large, ordered lamellae from non-bilayer lipids and integral membrane proteins in vitro

In many biological membranes, the major lipids are “non-bilayer lipids,” which in purified form cannot be arranged in a lamellar structure. The structural and functional roles of these lipids are poorly understood. This work demonstrates that the in vitro association of the two main components of a membrane, the non-bilayer lipid monogalactosyldiacylglycerol (MGDG) and the chlorophyll-a/b light-harvesting antenna protein of photosystem II (LHCII) of pea thylakoids, leads to the formation of large, ordered lamellar structures: (i) thin-section electron microscopy and circular dichroism spectroscopy reveal that the addition of MGDG induces the transformation of isolated, disordered macroaggregates of LHCII into stacked lamellar aggregates with a long-range chiral order of the complexes; (ii) small-angle x-ray scattering discloses that LHCII perturbs the structure of the pure lipid and destroys the inverted hexagonal phase; and (iii) an analysis of electron micrographs of negatively stained 2D crystals indicates that in MGDG-LHCII the complexes are found in an ordered macroarray. It is proposed that, by limiting the space available for MGDG in the macroaggregate, LHCII inhibits formation of the inverted hexagonal phase of lipids; in thylakoids, a spatial limitation is likely to be imposed by the high concentration of membrane-associated proteins.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation f(x)+f(2x)+⋯+f(nx)=0,x∈R . The continuity of the solutions depends on the sign of the real part of each zero.

Steerage conditions. Partial report, on behalf of the Immigration commission, on steerage conditions ...

Laws of the United States relating to steerage accommodations: p. 40-46.

Development of a carbon dioxide partial pressure sensor

Photocopy.

BM+-tree: A hyperplane-based index method for high-dimensional metric spaces

In this paper, we propose a novel high-dimensional index method, the BM+-tree, to support efficient processing of similarity search queries in high-dimensional spaces. The main idea of the proposed index is to improve data partitioning efficiency in a high-dimensional space by using a rotary binary hyperplane, which further partitions a subspace and can also take advantage of the twin node concept used in the M+-tree. Compared with the key dimension concept in the M+-tree, the binary hyperplane is more effective in data filtering. High space utilization is achieved by dynamically performing data reallocation between twin nodes. In addition, a post processing step is used after index building to ensure effective filtration. Experimental results using two types of real data sets illustrate a significantly improved filtering efficiency.

Recognizing Decomposition of a Partial Boolean Function

A hard combinatorial problem is investigated which has useful application in design of discrete devices: the two-block decomposition of a partial Boolean function. The key task is regarded: finding such a weak partition on the set of arguments, at which the considered function can be decomposed. Solving that task is essentially speeded up by the way of preliminary discovering traces of the sought-for partition. Efficient combinatorial operations are used by that, based on parallel execution of operations above adjacent units in the Boolean space.

Fragmentability of the Dual of a Banach Space with Smooth Bump

We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.