Decomposição em valores singulares aplicada a dados de campo magnético

Neste trabalho, a decomposição em valores singulares (DVS) de uma matriz A, n x m, que representa a anomalia magnética, é vista como um método de filtragem bidimensional de coerência que separa informações correlacionáveis e não correlacionáveis contidas na matriz de dados magnéticos A. O filtro DVS é definido através da expansão da matriz A em autoimagens e valores singulares. Cada autoimagem é dada pelo produto escalar dos vetores de base, autovetores, associados aos problemas de autovalor e autovetor das matrizes de covariância A^TA e AA^T. Este método de filtragem se baseia no fato de que as autoimagens associadas a grandes valores singulares concentram a maior parte da informação correlacionável presente nos dados, enquanto que a parte não correlacionada, presumidamente constituída de ruídos causados por fontes magnéticas externas, ruídos introduzidos pelo processo de medida, estão concentrados nas autoimagens restantes. Utilizamos este método em diferentes exemplos de dados magnéticos sintéticos. Posteriormente, o método foi aplicado a dados do aerolevantamento feito pela PETROBRÁS no Projeto Carauari-Norte (Bacia do Solimões), para analisarmos a potencialidade deste na identificação, eliminação ou atenuação de ruídos e como um possível método de realçar feições particulares da anomalia geradas por fontes profundas e rasas. Este trabalho apresenta também a possibilidade de introduzir um deslocamento estático ou dinâmico nos perfis magnéticos, com a finalidade de aumentar a correlação (coerência) entre eles, permitindo assim concentrar o máximo possível do sinal correlacionável nas poucas primeiras autoimagens. Outro aspecto muito importante desta expansão da matriz de dados em autoimagens e valores singulares foi o de mostrar, sob o ponto de vista computacional, que a armazenagem dos dados contidos na matriz, que exige uma quantidade n x m de endereços de memória, pode ser diminuída consideravelmente utilizando p autoimagens. Assim o número de endereços de memória cai para p x (n + m + 1), sem alterar a anomalia, na reprodução praticamente perfeita. Dessa forma, concluímos que uma escolha apropriada do número e dos índices das autoimagens usadas na decomposição mostra potencialidade do método no processamento de dados magnéticos.

Singular Value Decomposition and Ligand Binding Analysis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A graphical tool for the tomographic characterisation of microstructural features on metal matrix composites

Research on the micro-structural characterization of metal-matrix composites uses X-ray computed tomography to collect information about the interior features of the samples, in order to elucidate their exhibited properties. The tomographic raw data needs several steps of computational processing in order to eliminate noise and interference. Our experience with a program (Tritom) that handles these questions has shown that in some cases the processing steps take a very long time and that it is not easy for a Materials Science specialist to interact with Tritom in order to define the most adequate parameter values and the proper sequence of the available processing steps. For easing the use of Tritom, a system was built which addresses the aspects described before and that is based on the OpenDX visualization system. OpenDX visualization facilities constitute a great benefit to Tritom. The visual programming environment of OpenDX allows an easy definition of a sequence of processing steps thus fulfilling the requirement of an easy use by non-specialists on Computer Science. Also the possibility of incorporating external modules in a visual OpenDX program allows the researchers to tackle the aspect of reducing the long execution time of some processing steps. The longer processing steps of Tritom have been parallelized in two different types of hardware architectures (message-passing and shared-memory); the corresponding parallel programs can be easily incorporated in a sequence of processing steps defined in an OpenDX program. The benefits of our system are illustrated through an example where the tool is applied in the study of the sensitivity to crushing – and the implications thereof – of the reinforcements used in a functionally graded syntactic metallic foam.

Matrix Support in Mental Health: Achievements and Limits in Primary Health Care

Changes in mental health care in the city of Fortaleza (Northeastern Brazil) have a recent historical and political process. Compared to other municipalities of the State of Ceara, which in the early 1990s were already pioneers in the process, Fortaleza has not implemented the changes due to the interests of psychiatric hospitals, of psychiatric outpatient clinics of the public network, and because of the difficulty in managing the new mental health devices and equipment present in Primary Care. In the municipality, the reorganization of mental health actions and services has required that the Primary Care Network faces the challenge of assisting mental health problems with the implementation of Matrix Support. In light of this context, we aimed to evaluate Matrix Support in mental health in Primary Care Units and to identify achievements and limitations in the Primary Care Units with Matrix Support. This study used a qualitative approach and was carried out by means of a case study. We interviewed twelve professionals from the Family Health Teams of four Units with implemented Matrix Support. The analysis of the information reveals that access, decision making, participation and the challenges of implementing Matrix Support are elements that are, in a dialectic way, weak and strong in the reorganization of services and practices. The presence of Matrix Support in Primary Care highlights the proposal of dealing with mental health within the network in the municipality. The process has not ended. Mobilization, awareness-raising and qualification of Primary Care have to be enhanced constantly, but implementation has enabled, to the service and professionals, greater acceptance of mental health in Primary Care.

ACTIVE NETWORKS THAT MAXIMIZE THE AMOUNT OF INFORMATION TRANSMISSION

This work clarifies the relationship between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e. g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

A generalization of the Moore-Penrose inverse related to matrix subspaces of C(nxm)

[EN]A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m x n complex matrix A, denoted by As, is defined for any linear subspace S of the matrix vector space Cnxm. The S-Moore-Penrose inverse As is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with respect to the Frobenius inner product. These results are applied to the preconditioning of linear systems based on Frobenius norm minimization and to the linearly constrained linear least squares problem.

Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

Misleading Population Estimates: Biases and Consistency of Visual Surveys and Matrix Modelling in the Endangered Bearded Vulture

Conservation strategies for long-lived vertebrates require accurate estimates of parameters relative to the populations' size, numbers of non-breeding individuals (the “cryptic” fraction of the population) and the age structure. Frequently, visual survey techniques are used to make these estimates but the accuracy of these approaches is questionable, mainly because of the existence of numerous potential biases. Here we compare data on population trends and age structure in a bearded vulture (Gypaetus barbatus) population from visual surveys performed at supplementary feeding stations with data derived from population matrix-modelling approximations. Our results suggest that visual surveys overestimate the number of immature (<2 years old) birds, whereas subadults (3–5 y.o.) and adults (>6 y.o.) were underestimated in comparison with the predictions of a population model using a stable-age distribution. In addition, we found that visual surveys did not provide conclusive information on true variations in the size of the focal population. Our results suggest that although long-term studies (i.e. population matrix modelling based on capture-recapture procedures) are a more time-consuming method, they provide more reliable and robust estimates of population parameters needed in designing and applying conservation strategies. The findings shown here are likely transferable to the management and conservation of other long-lived vertebrate populations that share similar life-history traits and ecological requirements.

Phylogenetic analysis of the gag region encoding the matrix protein of small ruminant lentiviruses: comparative analysis and molecular epidemiological applications

Little sequence information exists on the matrix-protein (MA) encoding region of small ruminant lentiviruses (SRLV). Fifty-two novel sequences were established and permitted a first phylogenetic analysis of this region of the SRLV genome. The variability of the MA encoding region is higher compared to the gag region encoding the capsid protein and surprisingly close to that reported for the env gene. In contrast to primate lentiviruses, the deduced amino acid sequences of the N- and C-terminal domains of MA are variable. This permitted to pinpoint a basic domain in the N-terminal domain that is conserved in all lentiviruses and likely to play an important functional role. Additionally, a seven amino acid insertion was detected in all MVV strains, which may be used to differentiate CAEV and MVV isolates. A molecular epidemiology analysis based on these sequences indicates that the Italian lentivirus strains are closely related to each other and to the CAEV-CO strain, a prototypic strain isolated three decades ago in the US. This suggests a common origin of the SRLV circulating in the monitored flocks, possibly related to the introduction of infected goats in a negative population. Finally, this study shows that the MA region is suitable for phylogenetic studies and may be applied to monitor SRLV eradication programs.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Steady-state diffusion imaging for MR in-vivo evaluation of reparative cartilage after matrix-associated autologous chondrocyte transplantation at 3 tesla--preliminary results

OBJECTIVES: To demonstrate the feasibility of time-reversed fast imaging with steady-state precession (FISP) called PSIF for diffusion-weighted imaging of cartilage and cartilage transplants in a clinical study. MATERIAL AND METHODS: In a cross-sectional study 15 patients underwent MRI using a 3D partially balanced steady-state gradient echo pulse sequence with and without diffusion weighting at two different time points after matrix-associated autologous cartilage transplantation (MACT). Mean diffusion quotients (signal intensity without diffusion-weighting divided by signal intensity with diffusion weighting) within the cartilage transplants were compared to diffusion quotients found in normal cartilage. RESULTS: The global diffusion quotient found in repair cartilage was significantly higher than diffusion values in normal cartilage (p<0.05). There was a decrease between the earlier and the later time point after surgery. CONCLUSIONS: In-vivo diffusion-weighted imaging based on the PSIF technique is possible. Our preliminary results show follow-up of cartilage transplant maturation in patients may provide additional information to morphological assessment.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

Multimodal approach in the use of clinical scoring, morphological MRI and biochemical T2-mapping and diffusion-weighted imaging in their ability to assess differences between cartilage repair tissue after microfracture therapy and matrix-associated autologous chondrocyte transplantation: a pilot study

OBJECTIVE: The aim of the present pilot study is to show initial results of a multimodal approach using clinical scoring, morphological magnetic resonance imaging (MRI) and biochemical T2-relaxation and diffusion-weighted imaging (DWI) in their ability to assess differences between cartilage repair tissue after microfracture therapy (MFX) and matrix-associated autologous chondrocyte transplantation (MACT). METHOD: Twenty patients were cross-sectionally evaluated at different post-operative intervals from 12 to 63 months after MFX and 12-59 months after MACT. The two groups were matched by age (MFX: 36.0+/-10.4 years; MACT: 35.1+/-7.7 years) and post-operative interval (MFX: 32.6+/-16.7 months; MACT: 31.7+/-18.3 months). After clinical evaluation using the Lysholm score, 3T-MRI was performed obtaining the MR observation of cartilage repair tissue (MOCART) score as well as T2-mapping and DWI for multi-parametric MRI. Quantitative T2-relaxation was achieved using a multi-echo spin-echo sequence; semi-quantitative diffusion-quotient (signal intensity without diffusion-weighting divided by signal intensity with diffusion weighting) was prepared by a partially balanced, steady-state gradient-echo pulse sequence. RESULTS: No differences in Lysholm (P=0.420) or MOCART (P=0.209) score were observed between MFX and MACT. T2-mapping showed lower T2 values after MFX compared to MACT (P=0.039). DWI distinguished between healthy cartilage and cartilage repair tissue in both procedures (MFX: P=0.001; MACT: P=0.007). Correlations were found between the Lysholm and the MOCART score (Pearson: 0.484; P=0.031), between the Lysholm score and DWI (Pearson:-0.557; P=0.011) and a trend between the Lysholm score and T2 (Person: 0.304; P=0.193). CONCLUSION: Using T2-mapping and DWI, additional information could be gained compared to clinical scoring or morphological MRI. In combination clinical, MR-morphological and MR-biochemical parameters can be seen as a promising multimodal tool in the follow-up of cartilage repair.

T1(Gd) gives comparable information as Delta T1 relaxation rate in dGEMRIC evaluation of cartilage repair tissue

OBJECTIVES: To evaluate the relationship between T1 after intravenous contrast administration (T1Gd) and Delta relaxation rate (DeltaR1) = (1/T1(Gd) - 1/T1o) in the delayed Gadolinium-Enhanced MRI of cartilage (dGEMRIC) evaluation of cartilage repair tissue. MATERIALS AND METHODS: Thirty single MR examinations from 30 patients after matrix-associated autologous chondrocyte transplantations of the knee joint with different postoperative intervals were examined using an 8-channel knee-coil at 3T. T1 mapping using a 3D GRE sequence with a 35/10 degrees flip angle excitation pulse combination was performed before and after contrast administration (dGEMRIC technique). T1 postcontrast (T1(Gd)) and the DeltaR1 (relative index of pre- and postcontrast R1 value) were calculated for repair tissue and the weight-bearing normal appearing control cartilage. For evaluation of the different postoperative intervals, MR exams were subdivided into 3 groups (up to 12 months, 12-24 months, more than 24 months). For statistical analysis Spearman correlation coefficients were calculated. RESULTS: The mean value for T1 postcontrast was 427 +/- 159 ms, for DeltaR1 1.85 +/- 1.0; in reference cartilage 636 +/- 181 ms for T1 postcontrast and 0.83 +/- 0.5 for DeltaR1.The correlation coefficients were highly significant between T1 (Gd) and DeltaR1 for repair tissue (0.969) as well as normal reference cartilage (0.928) in total, and for the reparative cartilage in the early, middle postoperative, and late postoperative interval after surgery (R values: -0.986, -0.970, and -0.978, respectively). Using either T1(Gd) or DeltaR1, the 2 metrics resulted in similar conclusions regarding the time course of change of repair tissue and control tissue, namely that highly significant (P > 0.01) differences between cartilage repair tissue and reference cartilage were found for all follow-up groups. Additionally, for both metrics highly significant differences (P < 0.01) between early follow up and the 2 later postoperative groups for cartilage repair tissue were found. No statistical differences were found between the 2 later follow-up groups of reparative cartilage either for T1 (Gd) or DeltaR1. CONCLUSION: The high correlation between T1 (Gd) and DeltaR1 and the comparable conclusions reached utilizing metric implies that T1 mapping before intravenous administration of MR contrast agent is not necessary for the evaluation of repair tissue. This will help to reduce costs, inconvenience for the patients, simplifies the examination procedure, and makes dGEMRIC more attractive for follow-up of patients after cartilage repair surgeries.

Initial results of in vivo high-resolution morphological and biochemical cartilage imaging of patients after matrix-associated autologous chondrocyte transplantation (MACT) of the ankle

OBJECTIVE: The aim of this study was to use morphological as well as biochemical (T2 and T2* relaxation times and diffusion-weighted imaging (DWI)) magnetic resonance imaging (MRI) for the evaluation of healthy cartilage and cartilage repair tissue after matrix-associated autologous chondrocyte transplantation (MACT) of the ankle joint. MATERIALS AND METHODS: Ten healthy volunteers (mean age, 32.4 years) and 12 patients who underwent MACT of the ankle joint (mean age, 32.8 years) were included. In order to evaluate possible maturation effects, patients were separated into short-term (6-13 months) and long-term (20-54 months) follow-up cohorts. MRI was performed on a 3.0-T magnetic resonance (MR) scanner using a new dedicated eight-channel foot-and-ankle coil. Using high-resolution morphological MRI, the magnetic resonance observation of cartilage repair tissue (MOCART) score was assessed. For biochemical MRI, T2 mapping, T2* mapping, and DWI were obtained. Region-of-interest analysis was performed within native cartilage of the volunteers and control cartilage as well as cartilage repair tissue in the patients subsequent to MACT. RESULTS: The overall MOCART score in patients after MACT was 73.8. T2 relaxation times (approximately 50 ms), T2* relaxation times (approximately 16 ms), and the diffusion constant for DWI (approximately 1.3) were comparable for the healthy volunteers and the control cartilage in the patients after MACT. The cartilage repair tissue showed no significant difference in T2 and T2* relaxation times (p > or = 0.05) compared to the control cartilage; however, a significantly higher diffusivity (approximately 1.5; p < 0.05) was noted in the cartilage repair tissue. CONCLUSION: The obtained results suggest that besides morphological MRI and biochemical MR techniques, such as T2 and T2* mapping, DWI may also deliver additional information about the ultrastructure of cartilage and cartilage repair tissue in the ankle joint using high-field MRI, a dedicated multichannel coil, and sophisticated sequences.