On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Sensor Location Problem for a Multigraph

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Eigenvalue computations in the context of data-sparse approximations of integral operators

In this work, we consider the numerical solution of a large eigenvalue problem resulting from a finite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. The numerical tests are performed using an astrophysics application. Results show the benefits of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.

Implementation of zonal control algorithms in adaptive optical systems with sparse control matrices

Miralls deformables més i més grans, amb cada cop més actuadors estan sent utilitzats actualment en aplicacions d'òptica adaptativa. El control dels miralls amb centenars d'actuadors és un tema de gran interès, ja que les tècniques de control clàssiques basades en la seudoinversa de la matriu de control del sistema es tornen massa lentes quan es tracta de matrius de dimensions tan grans. En aquesta tesi doctoral es proposa un mètode per l'acceleració i la paral.lelitzacó dels algoritmes de control d'aquests miralls, a través de l'aplicació d'una tècnica de control basada en la reducció a zero del components més petits de la matriu de control (sparsification), seguida de l'optimització de l'ordenació dels accionadors de comandament atenent d'acord a la forma de la matriu, i finalment de la seva posterior divisió en petits blocs tridiagonals. Aquests blocs són molt més petits i més fàcils de fer servir en els càlculs, el que permet velocitats de càlcul molt superiors per l'eliminació dels components nuls en la matriu de control. A més, aquest enfocament permet la paral.lelització del càlcul, donant una com0onent de velocitat addicional al sistema. Fins i tot sense paral. lelització, s'ha obtingut un augment de gairebé un 40% de la velocitat de convergència dels miralls amb només 37 actuadors, mitjançant la tècnica proposada. Per validar això, s'ha implementat un muntatge experimental nou complet , que inclou un modulador de fase programable per a la generació de turbulència mitjançant pantalles de fase, i s'ha desenvolupat un model complert del bucle de control per investigar el rendiment de l'algorisme proposat. Els resultats, tant en la simulació com experimentalment, mostren l'equivalència total en els valors de desviació després de la compensació dels diferents tipus d'aberracions per als diferents algoritmes utilitzats, encara que el mètode proposat aquí permet una càrrega computacional molt menor. El procediment s'espera que sigui molt exitós quan s'aplica a miralls molt grans.

A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

An orthogonal forward regression technique for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the desired response, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density (SKD) estimates. The proposed algorithm incrementally minimises a leave-one-out test score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights of the selected sparse model are finally updated using the multiplicative nonnegative quadratic programming algorithm, which ensures the nonnegative and unity constraints for the kernel weights and has the desired ability to reduce the model size further. Except for the kernel width, the proposed method has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Several examples demonstrate the ability of this simple regression-based approach to effectively construct a SKID estimate with comparable accuracy to that of the full-sample optimised PW density estimate. (c) 2007 Elsevier B.V. All rights reserved.

A W-matrix methodology for solving sparse network equations on multiprocessor computers

This paper describes a methodology for solving efficiently the sparse network equations on multiprocessor computers. The methodology is based on the matrix inverse factors (W-matrix) approach to the direct solution phase of A(x) = b systems. A partitioning scheme of W-matrix , based on the leaf-nodes of the factorization path tree, is proposed. The methodology allows the performance of all the updating operations on vector b in parallel, within each partition, using a row-oriented processing. The approach takes advantage of the processing power of the individual processors. Performance results are presented and discussed.

Treatment of multiple adjacent Miller class I and II gingival recessions with a Modified Coronally Advanced Tunnel (MCAT) technique and a collagen matrix or palatal connective tissue graft: a randomized, controlled clinical trial

BACKGROUND A newly developed collagen matrix (CM) of porcine origin has been shown to represent a potential alternative to palatal connective tissue grafts (CTG) for the treatment of single Miller Class I and II gingival recessions when used in conjunction with a coronally advanced flap (CAF). However, at present it remains unknown to what extent CM may represent a valuable alternative to CTG in the treatment of Miller Class I and II multiple adjacent gingival recessions (MAGR). The aim of this study was to compare the clinical outcomes following treatment of Miller Class I and II MAGR using the modified coronally advanced tunnel technique (MCAT) in conjunction with either CM or CTG. METHODS Twenty-two patients with a total of 156 Miller Class I and II gingival recessions were included in this study. Recessions were randomly treated according to a split-mouth design by means of MCAT + CM (test) or MCAT + CTG (control). The following measurements were recorded at baseline (i.e. prior to surgery) and at 12 months: Gingival Recession Depth (GRD), Probing Pocket Depth (PD), Clinical Attachment Level (CAL), Keratinized Tissue Width (KTW), Gingival Recession Width (GRW) and Gingival Thickness (GT). GT was measured 3-mm apical to the gingival margin. Patient acceptance was recorded using a Visual Analogue Scale (VAS). The primary outcome variable was Complete Root Coverage (CRC), secondary outcomes were Mean Root Coverage (MRC), change in KTW, GT, patient acceptance and duration of surgery. RESULTS Healing was uneventful in both groups. No adverse reactions at any of the sites were observed. At 12 months, both treatments resulted in statistically significant improvements of CRC, MRC, KTW and GT compared with baseline (p < 0.05). CRC was found at 42% of test sites and at 85% of control sites respectively (p < 0.05). MRC measured 71 ± 21% mm at test sites versus 90 ± 18% mm at control sites (p < 0.05). Mean KTW measured 2.4 ± 0.7 mm at test sites versus 2.7 ± 0.8 mm at control sites (p > 0.05). At test sites, GT values changed from 0.8 ± 0.2 to 1.0 ± 0.3 mm, and at control sites from 0.8 ± 0.3 to 1.3 ± 0.4 mm (p < 0.05). Duration of surgery and patient morbidity was statistically significantly lower in the test compared with the control group respectively (p < 0.05). CONCLUSIONS The present findings indicate that the use of CM may represent an alternative to CTG by reducing surgical time and patient morbidity, but yielded lower CRC than CTG in the treatment of Miller Class I and II MAGR when used in conjunction with MCAT.

Treatment of multiple adjacent Miller Class I and II gingival recessions with collagen matrix and the modified coronally advanced tunnel technique

OBJECTIVE To clinically evaluate the treatment of Miller Class I and II multiple adjacent gingival recessions using the modified coronally advanced tunnel technique combined with a newly developed bioresorbable collagen matrix of porcine origin. METHOD AND MATERIALS Eight healthy patients exhibiting at least three multiple Miller Class I and II multiple adjacent gingival recessions (a total of 42 recessions) were consecutively treated by means of the modified coronally advanced tunnel technique and collagen matrix. The following clinical parameters were assessed at baseline and 12 months postoperatively: full mouth plaque score (FMPS), full mouth bleeding score (FMBS), probing depth (PD), recession depth (RD), recession width (RW), keratinized tissue thickness (KTT), and keratinized tissue width (KTW). The primary outcome variable was complete root coverage. RESULTS Neither allergic reactions nor soft tissue irritations or matrix exfoliations occurred. Postoperative pain and discomfort were reported to be low, and patient acceptance was generally high. At 12 months, complete root coverage was obtained in 2 out of the 8 patients and 30 of the 42 recessions (71%). CONCLUSION Within their limits, the present results indicate that treatment of Miller Class I and II multiple adjacent gingival recessions by means of the modified coronally advanced tunnel technique and collagen matrix may result in statistically and clinically significant complete root coverage. Further studies are warranted to evaluate the performance of collagen matrix compared with connective tissue grafts and other soft tissue grafts.

Novel fast random search clustering approach for mixing matrix identification in MIMO linear blind inverse problems with sparse inputs

In this paper we propose a novel fast random search clustering (RSC) algorithm for mixing matrix identification in multiple input multiple output (MIMO) linear blind inverse problems with sparse inputs. The proposed approach is based on the clustering of the observations around the directions given by the columns of the mixing matrix that occurs typically for sparse inputs. Exploiting this fact, the RSC algorithm proceeds by parameterizing the mixing matrix using hyperspherical coordinates, randomly selecting candidate basis vectors (i.e. clustering directions) from the observations, and accepting or rejecting them according to a binary hypothesis test based on the Neyman–Pearson criterion. The RSC algorithm is not tailored to any specific distribution for the sources, can deal with an arbitrary number of inputs and outputs (thus solving the difficult under-determined problem), and is applicable to both instantaneous and convolutive mixtures. Extensive simulations for synthetic and real data with different number of inputs and outputs, data size, sparsity factors of the inputs and signal to noise ratios confirm the good performance of the proposed approach under moderate/high signal to noise ratios. RESUMEN. Método de separación ciega de fuentes para señales dispersas basado en la identificación de la matriz de mezcla mediante técnicas de "clustering" aleatorio.

A technique for detecting matrix proteins in the crystalline spicule of the sea urchin embryo.

The presence of proteins associated with the CaCO3-containing biocrystals found in a wide variety of marine organisms is well established. In these organisms, including the primitive skeleton (spicule) of the sea urchin embryo, the structural and functional role of these proteins either in the biomineralization process or in control of the structural features of the biocrystals is unclear. Recently, one of the matrix proteins of the sea urchin spicule, SM 30, has been shown to contain a carbohydrate chain (the 1223 epitope) that has been implicated in the process whereby Ca2+ is deposited as CaCo3. Because an understanding of the localization of this protein, as well as other proteins found within the spicule, is central to understanding their function, we undertook to develop methods to localize spicule matrix proteins in intact spicules, using immunogold techniques and scanning electron microscopy. Gold particles indicative of this matrix glycoprotein could not be detected on the surface of spicules that had been isolated from embryo homogenates and treated with alkaline hypochlorite to remove any associated membranous material. However, when isolated spicules were etched for 2 min with dilute acetic acid (10 mM) to expose more internal regions of the crystal, SM 30 and perhaps other proteins bearing the 1223 carbohydrate epitope were detected in the calcite matrix. These results, indicating that these two antigens are widely distributed in the spicule, suggest that this technique should be applicable to any matrix protein for which antibodies are available.

Binary sparse nonnegative matrix factorization

This paper presents a fast part-based subspace selection algorithm, termed the binary sparse nonnegative matrix factorization (B-SNMF). Both the training process and the testing process of B-SNMF are much faster than those of binary principal component analysis (B-PCA). Besides, B-SNMF is more robust to occlusions in images. Experimental results on face images demonstrate the effectiveness and the efficiency of the proposed B-SNMF.