Extremal graphs for the sum of the two largest signless Laplacian eigenvalues

Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q1(G) and q2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S+ n the star graph with an additional edge. It is proved that inequality q1(G)+q2(G) e(G)+3 is tighter for the graph S+ n among all firefly graphs and also tighter to S+ n than to the graphs Kk _ Kn−k recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S+ n minimizes f(G) = e(G) − q1(G) − q2(G) among all graphs G on n vertices.

Spatial neighborhood matrix computation: Inverse distance weighted versus binary contiguity

Paper presented at Geo-Spatial Crossroad GI_Forum, Salzburg, Austria.

A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols

We characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,

Diffusion-weighted imaging for the follow-up of patients after matrix-associated autologous chondrocyte transplantation

To evaluate the use of diffusion-weighted imaging (DWI) for the assessment of cartilage maturation in patients after matrix-associated autologous chondrocyte transplantation (MACT).

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.

Elimination of cross-talk in diffuse optical tomographic reconstructions through a weighted update procedure: results of simulation study - art. no. 61640S

Reconstructions in optical tomography involve obtaining the images of absorption and reduced scattering coefficients. The integrated intensity data has greater sensitivity to absorption coefficient variations than scattering coefficient. However, the sensitivity of intensity data to scattering coefficient is not zero. We considered an object with two inhomogeneities (one in absorption and the other in scattering coefficient). The standard iterative reconstruction techniques produced results, which were plagued by cross talk, i.e., the absorption coefficient reconstruction has a false positive corresponding to the location of scattering inhomogeneity, and vice-versa. We present a method to remove cross talk in the reconstruction, by generating a weight matrix and weighting the update vector during the iteration. The weight matrix is created by the following method: we first perform a simple backprojection of the difference between the experimental and corresponding homogeneous intensity data. The built up image has greater weightage towards absorption inhomogeneity than the scattering inhomogeneity and its appropriate inverse is weighted towards the scattering inhomogeneity. These two weight matrices are used as multiplication factors in the update vectors, normalized backprojected image of difference intensity for absorption inhomogeneity and the inverse of the above for the scattering inhomogeneity, during the image reconstruction procedure. We demonstrate through numerical simulations, that cross-talk is fully eliminated through this modified reconstruction procedure.

Weighted subspace methods and spatial smoothing: analysis and comparison

The effect of using a spatially smoothed forward-backward covariance matrix on the performance of weighted eigen-based state space methods/ESPRIT, and weighted MUSIC for direction-of-arrival (DOA) estimation is analyzed. Expressions for the mean-squared error in the estimates of the signal zeros and the DOA estimates, along with some general properties of the estimates and optimal weighting matrices, are derived. A key result is that optimally weighted MUSIC and weighted state-space methods/ESPRIT have identical asymptotic performance. Moreover, by properly choosing the number of subarrays, the performance of unweighted state space methods can be significantly improved. It is also shown that the mean-squared error in the DOA estimates is independent of the exact distribution of the source amplitudes. This results in a unified framework for dealing with DOA estimation using a uniformly spaced linear sensor array and the time series frequency estimation problems.

Faster algorithms for all-pairs small stretch distances in weighted graphs

Abstract. Let G = (V,E) be a weighted undirected graph, with non-negative edge weights. We consider the problem of efficiently computing approximate distances between all pairs of vertices in G. While many efficient algorithms are known for this problem in unweighted graphs, not many results are known for this problem in weighted graphs. Zwick [14] showed that for any fixed ε> 0, stretch 1 1 + ε distances between all pairs of vertices in a weighted directed graph on n vertices can be computed in Õ(n ω) time, where ω < 2.376 is the exponent of matrix multiplication and n is the number of vertices. It is known that finding distances of stretch less than 2 between all pairs of vertices in G is at least as hard as Boolean matrix multiplication of two n×n matrices. It is also known that all-pairs stretch 3 distances can be computed in Õ(n 2) time and all-pairs stretch 7/3 distances can be computed in Õ(n 7/3) time. Here we consider efficient algorithms for the problem of computing all-pairs stretch (2+ε) distances in G, for any 0 < ε < 1. We show that all pairs stretch (2 + ε) distances for any fixed ε> 0 in G can be computed in expected time O(n 9/4 logn). This algorithm uses a fast rectangular matrix multiplication subroutine. We also present a combinatorial algorithm (that is, it does not use fast matrix multiplication) with expected running time O(n 9/4) for computing all-pairs stretch 5/2 distances in G. 1

Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

Determination of electricity consumers’ load profiles via weighted evidence accumulation clustering using subsampling

With the electricity market liberalization, the distribution and retail companies are looking for better market strategies based on adequate information upon the consumption patterns of its electricity consumers. A fair insight on the consumers’ behavior will permit the definition of specific contract aspects based on the different consumption patterns. In order to form the different consumers’ classes, and find a set of representative consumption patterns we use electricity consumption data from a utility client’s database and two approaches: Two-step clustering algorithm and the WEACS approach based on evidence accumulation (EAC) for combining partitions in a clustering ensemble. While EAC uses a voting mechanism to produce a co-association matrix based on the pairwise associations obtained from N partitions and where each partition has equal weight in the combination process, the WEACS approach uses subsampling and weights differently the partitions. As a complementary step to the WEACS approach, we combine the partitions obtained in the WEACS approach with the ALL clustering ensemble construction method and we use the Ward Link algorithm to obtain the final data partition. The characterization of the obtained consumers’ clusters was performed using the C5.0 classification algorithm. Experiment results showed that the WEACS approach leads to better results than many other clustering approaches.

Weighted input predictive controller

A discrete-time algorithm is presented which is based on a predictive control scheme in the form of dynamic matrix control. A set of control inputs are calculated and made available at each time instant, the actual input applied being a weighted summation of the inputs within the set. The algorithm is directly applicable in a self-tuning format and is therefore suitable for slowly time-varying systems in a noisy environment.

Method validation using weighted linear regression models for quantification of UV filters in water samples

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

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.

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.