A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Scheduling batches with simultaneous job processing for two-machine shop problems

We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn-in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem.

A robust tri-state election algorithm for scalable applications

Existing election algorithms suffer limited scalability. This limit stems from the communication design which in turn stems from their fundamentally two-state behaviour. This paper presents a new election algorithm specifically designed to be highly scalable in broadcast networks whilst allowing any processing node to become coordinator with initially equal probability. To achieve this, careful attention has been paid to the communication design, and an additional state has been introduced. The design of the tri-state election algorithm has been motivated by the requirements analysis of a major research project to deliver robust scalable distributed applications, including load sharing, in hostile computing environments in which it is common for processing nodes to be rebooted frequently without notice. The new election algorithm is based in-part on a simple 'emergent' design. The science of emergence is of great relevance to developers of distributed applications because it describes how higher-level self-regulatory behaviour can arise from many participants following a small set of simple rules. The tri-state election algorithm is shown to have very low communication complexity in which the number of messages generated remains loosely-bounded regardless of scale for large systems; is highly scalable because nodes in the idle state do not transmit any messages; and because of its self-organising characteristics, is very stable.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

The Ocean Colour Climate Change Initiative: III. A round-robin comparison on in-water bio-optical algorithms

Satellite-derived remote-sensing reflectance (Rrs) can be used for mapping biogeochemically relevant variables, such as the chlorophyll concentration and the Inherent Optical Properties (IOPs) of the water, at global scale for use in climate-change studies. Prior to generating such products, suitable algorithms have to be selected that are appropriate for the purpose. Algorithm selection needs to account for both qualitative and quantitative requirements. In this paper we develop an objective methodology designed to rank the quantitative performance of a suite of bio-optical models. The objective classification is applied using the NASA bio-Optical Marine Algorithm Dataset (NOMAD). Using in situRrs as input to the models, the performance of eleven semi-analytical models, as well as five empirical chlorophyll algorithms and an empirical diffuse attenuation coefficient algorithm, is ranked for spectrally-resolved IOPs, chlorophyll concentration and the diffuse attenuation coefficient at 489 nm. The sensitivity of the objective classification and the uncertainty in the ranking are tested using a Monte-Carlo approach (bootstrapping). Results indicate that the performance of the semi-analytical models varies depending on the product and wavelength of interest. For chlorophyll retrieval, empirical algorithms perform better than semi-analytical models, in general. The performance of these empirical models reflects either their immunity to scale errors or instrument noise in Rrs data, or simply that the data used for model parameterisation were not independent of NOMAD. Nonetheless, uncertainty in the classification suggests that the performance of some semi-analytical algorithms at retrieving chlorophyll is comparable with the empirical algorithms. For phytoplankton absorption at 443 nm, some semi-analytical models also perform with similar accuracy to an empirical model. We discuss the potential biases, limitations and uncertainty in the approach, as well as additional qualitative considerations for algorithm selection for climate-change studies. Our classification has the potential to be routinely implemented, such that the performance of emerging algorithms can be compared with existing algorithms as they become available. In the long-term, such an approach will further aid algorithm development for ocean-colour studies.

Ocean Net Heat Flux Influences Seasonal to Interannual Patterns of Plankton Abundance

Changes in the net heat flux (NHF) into the ocean have profound impacts on global climate. We analyse a long-term plankton time-series and show that the NHF is a critical indicator of ecosystem dynamics. We show that phytoplankton abundance and diversity patterns are tightly bounded by the switches between negative and positive NHF over an annual cycle. Zooplankton increase before the transition to positive NHF in the spring but are constrained by the negative NHF switch in autumn. By contrast bacterial diversity is decoupled from either NHF switch, but is inversely correlated (r=-0.920) with the magnitude of the NHF. We show that the NHF is a robust mechanistic tool for predicting climate change indicators such as spring phytoplankton bloom timing and length of the growing season.

Uncertainty estimates of remote sensing reflectance derived from comparison of ocean color satellite data sets

Assigning uncertainty to ocean-color satellite products is a requirement to allow informed use of these data. Here, uncertainty estimates are derived using the comparison on a 12th-degree grid of coincident daily records of the remote-sensing reflectance RRS obtained with the same processing chain from three satellite missions, MERIS, MODIS and SeaWiFS. The approach is spatially resolved and produces σ, the part of the RRS uncertainty budget associated with random effects. The global average of σ decreases with wavelength from approximately 0.7– 0.9 10−3 sr−1 at 412 nm to 0.05–0.1 10−3 sr−1 at the red band, with uncertainties on σ evaluated as 20–30% between 412 and 555 nm, and 30–40% at 670 nm. The distribution of σ shows a restricted spatial variability and small variations with season, which makes the multi-annual global distribution of σ an estimate applicable to all retrievals of the considered missions. The comparison of σ with other uncertainty estimates derived from field data or with the support of algorithms provides a consistent picture. When translated in relative terms, and assuming a relatively low bias, the distribution of σ suggests that the objective of a 5% uncertainty is fulfilled between 412 and 490 nm for oligotrophic waters (chlorophyll-a concentration below 0.1 mg m−3). This study also provides comparison statistics. Spectrally, the mean absolute relative difference between RRS from different missions shows a characteristic U-shape with both ends at blue and red wavelengths inversely related to the amplitude of RRS. On average and for the considered data sets, SeaWiFS RRS tend to be slightly higher than MODIS RRS, which in turn appear higher than MERIS RRS. Biases between mission-specific RRS may exhibit a seasonal dependence, particularly in the subtropical belt.

Una revisión de la Cadena Datos-Información-Conocimiento desde el Pragmatismo de Peirce

La Cadena Datos-Información-Conocimiento (DIC), denominada “Jerarquía de la Información” o “Pirámide del Conocimiento”, es uno de los modelos más importantes en la Gestión de la Información y la Gestión del Conocimiento. Por lo general, la estructuración de la cadena se ha ido definiendo como una arquitectura en la que cada elemento se levanta sobre el elemento inmediatamente inferior; sin embargo no existe un consenso en la definición de los elementos, ni acerca de los procesos que transforman un elemento de un nivel a uno del siguiente nivel. En este artículo se realiza una revisión de la Cadena Datos-Información-Conocimiento examinando las definiciones más relevantes sobre sus elementos y sobre su articulación en la literatura, para sintetizar las acepciones más comunes. Se analizan los elementos de la Cadena DIC desde la semiótica de Peirce; enfoque que nos permite aclarar los significados e identificar las diferencias, las relaciones y los roles que desempeñan en la cadena desde el punto de vista del pragmatismo. Finalmente se propone una definición de la Cadena DIC apoyada en las categorías triádicas de signos y la semiosis ilimitada de Peirce, los niveles de sistemas de signos de Stamper y las metáforas de Zeleny.

On the Diversity-Multiplexing Tradefoff for Wireless Cooperative Multiple Access Systems

A spectrally efficient strategy is proposed for cooperative multiple access (CMA) channels in a centralized communication environment with $N$ users. By applying superposition coding, each user will transmit a mixture containing its own information as well as the other users', which means that each user shares parts of its power with the others. The use of superposition coding in cooperative networks was first proposed in , which will be generalized to a multiple-user scenario in this paper. Since the proposed CMA system can be seen as a precoded point-to-point multiple-antenna system, its performance can be best evaluated using the diversity-multiplexing tradeoff. By carefully categorizing the outage events, the diversity-multiplexing tradeoff can be obtained, which shows that the proposed cooperative strategy can achieve larger diversity/multiplexing gain than the compared transmission schemes at any diversity/multiplexing gain. Furthermore, it is demonstrated that the proposed strategy can achieve optimal tradeoff for multiplexing gains $0leq r leq 1$ whereas the compared cooperative scheme is only optimal for $0leq r leq ({1}/{N})$. As discussed in the paper, such superiority of the proposed CMA system is due to the fact that the relaying transmission does not consume extra channel use and, hence, the deteriorating effect of cooperative communication on the data rate is effectively limited.

Direct Observation of strong coupling in a laser-shock compressed plasma

In this Letter we report on a near collective x-ray scattering experiment on shock-compressed targets. A highly coupled Al plasma was generated and probed by spectrally resolving an x-ray source forward scattered by the sample. A significant reduction in the intensity of the elastic scatter was observed, which we attribute to the formation of an incipient long-range order. This speculation is confirmed by x-ray scattering calculations accounting for both electron degeneracy and strong coupling effects. Measurements from rear side visible diagnostics are consistent with the plasma parameters inferred from x-ray scattering data. These results give the experimental evidence of the strongly coupled ionic dynamics in dense plasmas.

Stochastic protein folding simulation in the three-dimensional HP-model

We present results from three-dimensional protein folding simulations in the HP-model on ten benchmark problems. The simulations are executed by a simulated annealing-based algorithm with a time-dependent cooling schedule. The neighbourhood relation is determined by the pull-move set. The results provide experimental evidence that the maximum depth D of local minima of the underlying energy landscape can be upper bounded by D < n(2/3). The local search procedure employs the stopping criterion (In/delta)(D/gamma) where m is an estimation of the average number of neighbouring conformations, gamma relates to the mean of non-zero differences of the objective function for neighbouring conformations, and 1-delta is the confidence that a minimum conformation has been found. The bound complies with the results obtained for the ten benchmark problems. (c) 2008 Elsevier Ltd. All rights reserved.

The Kitai criterion and backward shifts

It is proved that for any separable infinite dimensional Banach space X, there is a bounded linear operator T on X such that T satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that I + T satisfies the Kitai criterion for certain backward weighted shifts T.

A weighted bilateral shift with cyclic square is supercyclic

It is shown, for a bounded weighted bilateral shift T acting on l(p)(Z), and for 1

Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.