Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Large-scale dust jets in the coma of 67P/Churyumov-Gerasimenko as seen by the OSIRIS instrument onboard Rosetta

Context. During the most recent perihelion passage in 2009 of comet 67P/Churyumov-Gerasimenko (67P), ground-based observations showed an anisotropic dust coma where jet-like features were detected at similar to 1.3 AU from the Sun. The current perihelion passage is exceptional as the Rosetta spacecraft is monitoring the nucleus activity since March 2014, when a clear dust coma was already surrounding the nucleus at 4.3 AU from the Sun. Subsequently, the OSIRIS camera also witnessed an outburst in activity between April 27 and 30, and since mid-July, the dust coma at rh similar to 3.7-3.6 AU preperihelion is clearly non-isotropic, pointing to the existence of dust jet-like features. Aims. We aim to ascertain on the nucleus surface the origin of the dust jet-like features detected as early as in mid-July 2014. This will help to establish how the localized comet nucleus activity compares with that seen in previous apparitions and will also help following its evolution as the comet approaches its perihelion, at which phase most of the jets were detected from ground-based observations. Determining these areas also allows locating them in regions on the nucleus with spectroscopic or geomorphological distinct characteristics. Methods. Three series of dust images of comet 67P obtained with the Wide Angle Camera (WAC) of the OSIRIS instrument onboard the Rosetta spacecraft were processed with different enhancement techniques. This was made to clearly show the existence of jet-like features in the dust coma, whose appearance toward the observer changed as a result of the rotation of the comet nucleus and of the changing observing geometry from the spacecraft. The position angles of these features in the coma together with information on the observing geometry, nucleus shape, and rotation, allowed us to determine the most likely locations on the nucleus surface where the jets originate from. Results. Geometrical tracing of jet sources indicates that the activity of the nucleus of 67P gave rise during July and August 2014 to large-scale jet-like features from the Hapi, Hathor, Anuket, and Aten regions, confirming that active regions may be present on the nucleus localized at 60. northern latitude as deduced from previous comet apparitions. There are also hints that large-scale jets observed from the ground are possibly composed, at their place of origin on the nucleus surface, of numerous small-scale features.

Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^

Dissolved organic matter molecular composition and concentrations from a large scale mesocosm study KOSMOS 2013 Kristineberg) on ocean acidification

Marine dissolved organic matter (DOM) represents one of the largest active carbon reservoirs on Earth. Changes in pool size or composition could have major impacts on the global carbon cycle. Ocean acidification is a potential driver for these changes because it influences marine primary production and heterotrophic respiration. Here we show that ocean acidification as expected for a 'business-as-usual' emission scenario in the year 2100 (900 µatm) does not affect the DOM pool with respect to its size and molecular composition. We applied ultrahigh-resolution mass spectrometry to monitor the production and turnover of 7,360 distinct molecular DOM features in an unprecedented long-term mesocosm study in a Swedish Fjord, covering a full cycle of marine production. DOM concentration and molecular composition did not differ significantly between present-day and year 2100 CO2 levels. Our findings are likely applicable to other coastal and productive marine ecosystems in general.

A non-perturbative Kolmogorov turbulence approach to the cosmic web structure

The Kolmogorov approach to turbulence is applied to the Burgers turbulence in the stochastic adhesion model of large-scale structure formation. As the perturbative approach to this model is unreliable, here a new, non-perturbative approach, based on a suitable formulation of Kolmogorov's scaling laws, is proposed. This approach suggests that the power-law exponent of the matter density two-point correlation function is in the range 1–1.33, but it also suggests that the adhesion model neglects important aspects of the gravitational dynamics.

Use of Feynman diagrams in large-scale neural networks with nonlinear behaviour

A new proposal to the study of large-scale neural networks is reported. It is based on the use of similar graphs to the Feynman diagrams. A first general theory is presented and some interpretations are given. A propagator, based on the Green's function of the neuron, is the basis of the method. Application to a simple case is reported.

Multiple Hashing Integration for Real-Time Large Scale Part-to-Part Video Matching

A real-time large scale part-to-part video matching algorithm, based on the cross correlation of the intensity of motion curves, is proposed with a view to originality recognition, video database cleansing, copyright enforcement, video tagging or video result re-ranking. Moreover, it is suggested how the most representative hashes and distance functions - strada, discrete cosine transformation, Marr-Hildreth and radial - should be integrated in order for the matching algorithm to be invariant against blur, compression and rotation distortions: (R; _) 2 [1; 20]_[1; 8], from 512_512 to 32_32pixels2 and from 10 to 180_. The DCT hash is invariant against blur and compression up to 64x64 pixels2. Nevertheless, although its performance against rotation is the best, with a success up to 70%, it should be combined with the Marr-Hildreth distance function. With the latter, the image selected by the DCT hash should be at a distance lower than 1.15 times the Marr-Hildreth minimum distance.

Large scale multiphysics modeling of neurites

Situado en el límite entre Ingeniería, Informática y Biología, la mecánica computacional de las neuronas aparece como un nuevo campo interdisciplinar que potencialmente puede ser capaz de abordar problemas clínicos desde una perspectiva diferente. Este campo es multiescala por naturaleza, yendo desde la nanoescala (como, por ejemplo, los dímeros de tubulina) a la macroescala (como, por ejemplo, el tejido cerebral), y tiene como objetivo abordar problemas que son complejos, y algunas veces imposibles, de estudiar con medios experimentales. La modelización computacional ha sido ampliamente empleada en aplicaciones Neurocientíficas tan diversas como el crecimiento neuronal o la propagación de los potenciales de acción compuestos. Sin embargo, en la mayoría de los enfoques de modelización hechos hasta ahora, la interacción entre la célula y el medio/estímulo que la rodea ha sido muy poco explorada. A pesar de la tremenda importancia de esa relación en algunos desafíos médicos—como, por ejemplo, lesiones traumáticas en el cerebro, cáncer, la enfermedad del Alzheimer—un puente que relacione las propiedades electrofisiológicas-químicas y mecánicas desde la escala molecular al nivel celular todavía no existe. Con ese objetivo, esta investigación propone un marco computacional multiescala particularizado para dos escenarios respresentativos: el crecimiento del axón y el acomplamiento electrofisiológicomecánico de las neuritas. En el primer caso, se explora la relación entre los constituyentes moleculares del axón durante su crecimiento y sus propiedades mecánicas resultantes, mientras que en el último, un estímulo mecánico provoca deficiencias funcionales a nivel celular como consecuencia de sus alteraciones electrofisiológicas-químicas. La modelización computacional empleada en este trabajo es el método de las diferencias finitas, y es implementada en un nuevo programa llamado Neurite. Aunque el método de los elementos finitos es también explorado en parte de esta investigación, el método de las diferencias finitas tiene la flexibilidad y versatilidad necesaria para implementar mode los biológicos, así como la simplicidad matemática para extenderlos a simulaciones a gran escala con un coste computacional bajo. Centrándose primero en el efecto de las propiedades electrofisiológicas-químicas sobre las propiedades mecánicas, una versión adaptada de Neurite es desarrollada para simular la polimerización de los microtúbulos en el crecimiento del axón y proporcionar las propiedades mecánicas como función de la ocupación de los microtúbulos. Después de calibrar el modelo de crecimiento del axón frente a resultados experimentales disponibles en la literatura, las características mecánicas pueden ser evaluadas durante la simulación. Las propiedades mecánicas del axón muestran variaciones dramáticas en la punta de éste, donde el cono de crecimiento soporta las señales químicas y mecánicas. Bansándose en el conocimiento ganado con el modelo de diferencias finitas, y con el objetivo de ir de 1D a 3D, este esquema preliminar pero de una naturaleza innovadora allana el camino a futuros estudios con el método de los elementos finitos. Centrándose finalmente en el efecto de las propiedades mecánicas sobre las propiedades electrofisiológicas- químicas, Neurite es empleado para relacionar las cargas mecánicas macroscópicas con las deformaciones y velocidades de deformación a escala microscópica, y simular la propagación de la señal eléctrica en las neuritas bajo carga mecánica. Las simulaciones fueron calibradas con resultados experimentales publicados en la literatura, proporcionando, por tanto, un modelo capaz de predecir las alteraciones de las funciones electrofisiológicas neuronales bajo cargas externas dañinas, y uniendo lesiones mecánicas con las correspondientes deficiencias funcionales. Para abordar simulaciones a gran escala, aunque otras arquitecturas avanzadas basadas en muchos núcleos integrados (MICs) fueron consideradas, los solvers explícito e implícito se implementaron en unidades de procesamiento central (CPU) y unidades de procesamiento gráfico (GPUs). Estudios de escalabilidad fueron llevados acabo para ambas implementaciones mostrando resultados prometedores para casos de simulaciones extremadamente grandes con GPUs. Esta tesis abre la vía para futuros modelos mecánicos con el objetivo de unir las propiedades electrofisiológicas-químicas con las propiedades mecánicas. El objetivo general es mejorar el conocimiento de las comunidades médicas y de bioingeniería sobre la mecánica de las neuronas y las deficiencias funcionales que aparecen de los daños producidos por traumatismos mecánicos, como lesiones traumáticas en el cerebro, o enfermedades neurodegenerativas como la enfermedad del Alzheimer. ABSTRACT Sitting at the interface between Engineering, Computer Science and Biology, Computational Neuron Mechanics appears as a new interdisciplinary field potentially able to tackle clinical problems from a new perspective. This field is multiscale by nature, ranging from the nanoscale (e.g., tubulin dimers) to the macroscale (e.g., brain tissue), and aims at tackling problems that are complex, and sometime impossible, to study through experimental means. Computational modeling has been widely used in different Neuroscience applications as diverse as neuronal growth or compound action potential propagation. However, in the majority of the modeling approaches done in this field to date, the interactions between the cell and its surrounding media/stimulus have been rarely explored. Despite of the tremendous importance of such relationship in several medical challenges—e.g., traumatic brain injury (TBI), cancer, Alzheimer’s disease (AD)—a bridge between electrophysiological-chemical and mechanical properties of neurons from the molecular scale to the cell level is still lacking. To this end, this research proposes a multiscale computational framework particularized for two representative scenarios: axon growth and electrophysiological-mechanical coupling of neurites. In the former case, the relation between the molecular constituents of the axon during its growth and its resulting mechanical properties is explored, whereas in the latter, a mechanical stimulus provokes functional deficits at cell level as a consequence of its electrophysiological-chemical alterations. The computational modeling approach chosen in this work is the finite difference method (FDM), and was implemented in a new program called Neurite. Although the finite element method (FEM) is also explored as part of this research, the FDM provides the necessary flexibility and versatility to implement biological models, as well as the mathematical simplicity to extend them to large scale simulations with a low computational cost. Focusing first on the effect of electrophysiological-chemical properties on the mechanical proper ties, an adaptation of Neurite was developed to simulate microtubule polymerization in axonal growth and provide the axon mechanical properties as a function of microtubule occupancy. After calibrating the axon growth model against experimental results available in the literature, the mechanical characteristics can be tracked during the simulation. The axon mechanical properties show dramatic variations at the tip of the axon, where the growth cone supports the chemical and mechanical signaling. Based on the knowledge gained from the FDM scheme, and in order to go from 1D to 3D, this preliminary yet novel scheme paves the road for future studies with FEM. Focusing then on the effect of mechanical properties on the electrophysiological-chemical properties, Neurite was used to relate macroscopic mechanical loading to microscopic strains and strain rates, and simulate the electrical signal propagation along neurites under mechanical loading. The simulations were calibrated against experimental results published in the literature, thus providing a model able to predict the alteration of neuronal electrophysiological function under external damaging load, and linking mechanical injuries to subsequent acute functional deficits. To undertake large scale simulations, although other state-of-the-art architectures based on many integrated cores (MICs) were considered, the explicit and implicit solvers were implemented for central processing units (CPUs) and graphics processing units (GPUs). Scalability studies were done for both implementations showing promising results for extremely large scale simulations with GPUs. This thesis opens the avenue for future mechanical modeling approaches aimed at linking electrophysiological- chemical properties to mechanical properties. Its overarching goal is to enhance the bioengineering and medical communities knowledge on neuronal mechanics and functional deficits arising from damages produced by direct mechanical insults, such as TBI, or neurodegenerative evolving illness, such as AD.

Neurite, a finite difference large scale parallel program for the simulation of the electrical signal propagation in neurites under mechanical loading

With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, function of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells has only very recently been proposed (Jerusalem et al., 2013). In this paper, we present the implementation details of Neurite: the finite difference parallel program used in this reference. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite-explicit and implicit-were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between lectrophysiology and mechanics (Jerusalem et al., 2013). This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.

Large-scale protein structure modeling of the Saccharomyces cerevisiae genome

The function of a protein generally is determined by its three-dimensional (3D) structure. Thus, it would be useful to know the 3D structure of the thousands of protein sequences that are emerging from the many genome projects. To this end, fold assignment, comparative protein structure modeling, and model evaluation were automated completely. As an illustration, the method was applied to the proteins in the Saccharomyces cerevisiae (baker’s yeast) genome. It resulted in all-atom 3D models for substantial segments of 1,071 (17%) of the yeast proteins, only 40 of which have had their 3D structure determined experimentally. Of the 1,071 modeled yeast proteins, 236 were related clearly to a protein of known structure for the first time; 41 of these previously have not been characterized at all.

A large-scale overexpression screen in Saccharomyces cerevisiae identifies previously uncharacterized cell cycle genes

We have undertaken an extensive screen to identify Saccharomyces cerevisiae genes whose products are involved in cell cycle progression. We report the identification of 113 genes, including 19 hypothetical ORFs, which confer arrest or delay in specific compartments of the cell cycle when overexpressed. The collection of genes identified by this screen overlaps with those identified in loss-of-function cdc screens but also includes genes whose products have not previously been implicated in cell cycle control. Through analysis of strains lacking these hypothetical ORFs, we have identified a variety of new CDC and checkpoint genes.

Large-scale clustering measurements with photometric redshifts: comparing the dark matter haloes of X-ray AGN, star-forming and passive galaxies at z ≈ 1

We combine multi-wavelength data in the AEGIS-XD and C-COSMOS surveys to measure the typical dark matter halo mass of X-ray selected active galactic nuclei (AGN) [L_X(2–10 keV) > 10^42 erg s^− 1] in comparison with far-infrared selected star-forming galaxies detected in the Herschel/PEP survey (PACS Evolutionary Probe; L_IR > 10^11 L_⊙) and quiescent systems at z ≈ 1. We develop a novel method to measure the clustering of extragalactic populations that uses photometric redshift probability distribution functions in addition to any spectroscopy. This is advantageous in that all sources in the sample are used in the clustering analysis, not just the subset with secure spectroscopy. The method works best for large samples. The loss of accuracy because of the lack of spectroscopy is balanced by increasing the number of sources used to measure the clustering. We find that X-ray AGN, far-infrared selected star-forming galaxies and passive systems in the redshift interval 0.6 < z < 1.4 are found in haloes of similar mass, log M_DMH/(M_⊙ h^−1) ≈ 13.0. We argue that this is because the galaxies in all three samples (AGN, star-forming, passive) have similar stellar mass distributions, approximated by the J-band luminosity. Therefore, all galaxies that can potentially host X-ray AGN, because they have stellar masses in the appropriate range, live in dark matter haloes of log M_DMH/(M_⊙ h^−1) ≈ 13.0 independent of their star formation rates. This suggests that the stellar mass of X-ray AGN hosts is driving the observed clustering properties of this population. We also speculate that trends between AGN properties (e.g. luminosity, level of obscuration) and large-scale environment may be related to differences in the stellar mass of the host galaxies.

Probing large-scale wind structures in Vela X–1 using off-states with INTEGRAL

Vela X–1 is the prototype of the class of wind-fed accreting pulsars in high-mass X-ray binaries hosting a supergiant donor. We have analysed in a systematic way 10 years of INTEGRAL data of Vela X–1 (22–50 keV) and we found that when outside the X-ray eclipse, the source undergoes several luminosity drops where the hard X-rays luminosity goes below ∼3 × 1035 erg s−1, becoming undetected by INTEGRAL. These drops in the X-ray flux are usually referred to as ‘off-states’ in the literature. We have investigated the distribution of these off-states along the Vela X–1 ∼ 8.9 d orbit, finding that their orbital occurrence displays an asymmetric distribution, with a higher probability to observe an off-state near the pre-eclipse than during the post-eclipse. This asymmetry can be explained by scattering of hard X-rays in a region of ionized wind, able to reduce the source hard X-ray brightness preferentially near eclipse ingress. We associate this ionized large-scale wind structure with the photoionization wake produced by the interaction of the supergiant wind with the X-ray emission from the neutron star. We emphasize that this observational result could be obtained thanks to the accumulation of a decade of INTEGRAL data, with observations covering the whole orbit several times, allowing us to detect an asymmetric pattern in the orbital distribution of off-states in Vela X–1.