Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

Interpretation of Resistivity Piezocone Tests in a Contaminated Municipal Solid Waste Disposal Site

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Diatom stratigraphy of the lower Pliocene part of the Sisquoc Formation, Harris Grade section, California

Lower Pliocene diatoms were studied from the Sisquoc Formation and lowermost Foxen Mudstone, exposed along Hams Grade north of Lompoc, California, to refine the diatom biostratigraphy of post-Monterey Formation sediments in California. Sixty-seven diatom taxa were identified in the 25 samples examined from the 790-m thick (2950-ft) section. The diatoms are assignable to the uppermost Nitzschia reinholdii Zone and Thalassiosira oestrupii Zone of Damn (1981), and five tentative subzones for local correlation are proposed. Regional correlations and taxon occurrence are discussed, and the base of the Nitzschia reinholdii Zone is redefined as at the last occurrence of Thalassionema schraderi.

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

A Systems-Level Approach to Human Epileptic Seizures

Epileptic seizures are due to the pathological collective activity of large cellular assemblies. A better understanding of this collective activity is integral to the development of novel diagnostic and therapeutic procedures. In contrast to reductionist analyses, which focus solely on small-scale characteristics of ictogenesis, here we follow a systems-level approach, which combines both small-scale and larger-scale analyses. Peri-ictal dynamics of epileptic networks are assessed by studying correlation within and between different spatial scales of intracranial electroencephalographic recordings (iEEG) of a heterogeneous group of patients suffering from pharmaco-resistant epilepsy. Epileptiform activity as recorded by a single iEEG electrode is determined objectively by the signal derivative and then subjected to a multivariate analysis of correlation between all iEEG channels. We find that during seizure, synchrony increases on the smallest and largest spatial scales probed by iEEG. In addition, a dynamic reorganization of spatial correlation is observed on intermediate scales, which persists after seizure termination. It is proposed that this reorganization may indicate a balancing mechanism that decreases high local correlation. Our findings are consistent with the hypothesis that during epileptic seizures hypercorrelated and therefore functionally segregated brain areas are re-integrated into more collective brain dynamics. In addition, except for a special sub-group, a highly significant association is found between the location of ictal iEEG activity and the location of areas of relative decrease of localised EEG correlation. The latter could serve as a clinically important quantitative marker of the seizure onset zone (SOZ).

Benthic foraminifera of the Labrador Sea and Buffin Bay

Trigger weight (TWC) and piston (PC) cores obtained from surveys of the three sites drilled during Ocean Drilling Program (ODP) Leg 105 were studied in detail for benthic foraminiferal assemblages, total carbonate (all sites), planktonic foraminiferal abundances (Sites 645 and 647), and stable isotopes (Sites 646 and 647). These high-resolution data provide the link between modern environmental conditions represented by the sediment in the TWC and the uppermost cores of the ODP holes. This link provides essential control data for interpretating late Pleistocene paleoceanographic records from these core holes. At Site 645 in Baffin Bay, local correlation is difficult because the area is dominated by ice-rafted deposits and by debris flows and/or turbidite sedimentation. At the two Labrador Sea sites (646 and 647), the survey cores and uppermost ODP cores can be correlated. High-resolution data from the site survey cores also provide biostratigraphic data that refine the interpretations compiled from core-catcher samples at each ODP site.

Paleocene radiolarian distribution and biostratigraphy from offshore eastern New Zealand

A 100-m-thick Paleocene sequence of mainly pelagic sediments at ODP Site 1121, on the eastern flanks of the Campbell Plateau, contains few to common radiolarians of relatively low diversity in the lower 40 m (Early to early Late Paleocene) and abundant, diverse radiolarian assemblages in the upper 60 m (mid-Late Paleocene). The 150 taxa recorded from the entire Paleocene interval are thought to under-represent the actual species diversity by at least one half as many morphotypes have not been differentiated below the level of genus. Assemblages in the lower 40 m are similar to those described from onland New Zealand and DSDP Site 208 (northern Lord Howe Rise); they are correlated with South Pacific radiolarian zones RP4 and RP5. Assemblages in the upper 60 m differ from other known Late Paleocene assemblages in the great abundance of plagiacanthids and cycladophorids. Similarities are noted with later Cenozoic cool-water assemblages. This upper interval is correlated with South Pacific zone RP6, as revised herein, based on comparison with faunas from Site 208 and Marlborough, New Zealand. The interval is also correlated with the upper part of North Atlantic zone RP6 (RP6b-c) based on the presence of Aspis velutochlamydosaurus, Plectodiscus circularis and Pterocodon poculum. Other species, such as Buryella tetradica and Buryella pentadica, are valuable for local correlation but exhibit considerable diachroneity between the Pacific, Indian and Atlantic Oceans. An age model for the Paleocene interval at Site 1121, based on well-constrained nannofossil and radiolarian datums, indicates that the rate of compacted sediment accumulation doubles from 15 to 30 mm/ka at the RP5/RP6 zonal boundary. In large part this is due to a sudden and pronounced increase in accumulation rates for all siliceous fossils; radiolarians and larger diatoms increase from <100 to >10 000 specimens/cm2/ka. This apparent increase in biosiliceous productivity is age-equivalent to a mid-Paleocene cooling event (57-59 Ma) identified from global stable isotope records that is associated with the heaviest delta13C values for the entire Cenozoic.

Occurence of foraminifera and other microfossils in sediment core CRP-2/2A (Table 1)

Sparse to moderately abundant foraminiferal assemblages from Oligocene and Lower Miocene sediments in the CRP-2/2A drillhole contain C.27 genera and 42 species of calcareous benthic foraminifera. No planktic or agglutinated taxa were observed. On the basis of their faunal characteristics, four Foraminiferal Units are defined in drillhole succession: Foraminiferal Unit I (26.91-193.95 mbsf), mostly sparse assemblages with Elphidium magellanicum and Cribroelphidium sp.; Foraminiferal Unit II (193.95-342.42 mbsf), mostly moderately abundant assemblages with Cassidulinoides aequilatera and Eponides bradyi; Foraminiferal Unit III (342.42-486.19 mbsf), moderately abundant to sparse assemblages characterised by Cassidulinoides chapmani and Stainforthia sp.; and Foraminiferal Unit IV, Improverished (486.19-624.15, total depth, mbsf), with mostly barren residues, but with large Milioliidae recorded in situ at various horizons in the drill core. Foraminiferal Units I-IV lack taxa allowing correlation to standard zonal schemes. Inspection of faunal records from CIROS-1 and DSDP 270 indicates that, although the faunas show an overall similarity, CRP-2/2A Foraminiferal Units I-IV are not identifiable at these sites. The units are therefore most likely to reflect local environmental changes, and probably will prove useful for local correlation, but their lateral extent is undetermined. All four assemblages apparently represent various glacially-influenced shelf environments, and appear to reflect a long term deepening trend from Units IV to II, from perhaps inner to mid or outer-shelf depths, followed by a return to shallower, inner shelf, conditios for Unit I.

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

Esta tese apresenta o desenvolvimento e aplicação de modelos de turbulência, transição laminar-turbulenta e de interações fluido-estrutura ao escoamento externo em cilindro rígido estacionário e em vibrações induzidas por vórtices. Tais desenvolvimentos foram realizados no código ReFRESCO, baseado em técnicas de dinâmica de fluidos computacional (CFD). Realizou-se um estudo quanto ao desempenho do modelo k- SST em extensa faixa de números de Reynolds, segundo o qual se identificaram as deficiências de modelagem para este escoamento. A modelagem adaptativa das escalas (SAS) e o modelo de transição por correlações locais (LCTM), ambos combinados ao SST, melhoraram a aderência aos resultados experimentais para este escoamento, em uma contribuição original deste trabalho. A aplicação de técnicas de verificação e validação possibilitou a estimação de incertezas e erros para os modelos e números de Reynolds e também de identificada como outra contribuição deste trabalho. A combinação da modelagem em SST, SAS e LCTM com movimentos impostos de realizada para números de Reynolds moderados, diferentes frequências e amplitudes de vibração, algo que poucas publicações abordam em detalhes. Com relação aos movimentos livres, este trabalho traz contribuições com a aplicação dos modelos SST e SAS ao estudo de vibrações induzidas por vórtices em dois graus de liberdade, baixa razão de massa e números de Reynolds moderados, mais altos do que normalmente observados na literatura. Por fim, a investigação da importância relativa de efeitos da turbulência aos casos de movimentos livres e impostos, com relação ao caso de cilindro estacionário, comprovou a conjetura formulada na parte inicial deste trabalho, no que tange à escolha do modelo de turbulência em determinadas aplicações. Tal escolha mostrou-se menos decisiva no caso do cilindro em movimento imposto e ainda menos nos movimentos livres, em comparação ao caso estacionário, uma vez que a resposta em movimentos do corpo filtra grande parte dos efeitos turbulentos de ordem superior. Esta observação mostra-se relevante, uma vez que pode permitir simplificações na modelagem e aplicação de ferramentas de CFD em uma classe importante de projetos de engenharia.

Correlation between local structural dynamics of proteins inferred from NMR ensembles and evolutionary dynamics of homologues of known structure

Conformational changes in proteins are extremely important for their biochemical functions. Correlation between inherent conformational variations in a protein and conformational differences in its homologues of known structure is still unclear. In this study, we have used a structural alphabet called Protein Blocks (PBs). PBs are used to perform abstraction of protein 3-D structures into a 1-D strings of 16 alphabets (a-p) based on dihedral angles of overlapping pentapeptides. We have analyzed the variations in local conformations in terms of PBs represented in the ensembles of 801 protein structures determined using NMR spectroscopy. In the analysis of concatenated data over all the residues in all the NMR ensembles, we observe that the overall nature of inherent local structural variations in NMR ensembles is similar to the nature of local structural differences in homologous proteins with a high correlation coefficient of .94. High correlation at the alignment positions corresponding to helical and beta-sheet regions is only expected. However, the correlation coefficient by considering only the loop regions is also quite high (.91). Surprisingly, segregated position-wise analysis shows that this high correlation does not hold true to loop regions at the structurally equivalent positions in NMR ensembles and their homologues of known structure. This suggests that the general nature of local structural changes is unique; however most of the local structural variations in loop regions of NMR ensembles do not correlate to their local structural differences at structurally equivalent positions in homologues.

Diffusing-wave spectroscopy in an inhomogeneous object: Local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation g(2)(tau)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth M(tau)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(tau). The modulation depth M(tau(i)) at any delay time tau(i) can be measured by short-time Fourier transform of g(2)(tau) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(tau) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(omega), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(omega) corresponding to these regions from the measured region specific M(tau(i))vs tau(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of tau, the match was good only in the initial transients in regard to experimental measurements with ultrasound.