Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse-engineering and a colonization-competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co-occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio-temporal samples of assemblages in homogenous environments or environmental gradients.

Healing of two and three wall intrabony periodontal defects following treatment with an enamel matrix derivative combined with autogenous bone

BACKGROUND: There are still limited data on the outcomes of regenerative periodontal surgery using a combination of an enamel matrix protein derivative (EMD) and autogenous bone (AB). AIM: To evaluate the healing of deep intrabony defects treated with either a combination EMD+AB or EMD alone. MATERIALS AND METHODS: Forty patients with advanced chronic periodontitis, with one deep intrabony defect, were randomly treated with either EMD+AB (test) or EMD (control). Clinical assessments were performed at baseline and at 1 year after treatment. The primary outcome variable was relative attachment level (RAL). RESULTS: Healing was uneventful in all patients. The test sites showed a reduction in the mean probing pocket depth (PPD) of 5.6 +/- 0.9 mm (p<0.001), a gain in the mean RAL of 4.2 +/- 1.1 mm (p<0.001) and a gain in the mean probing bone level (PBL) of 3.9 +/- 1.0 mm (p<0.001). The control group displayed a mean PPD reduction of 4.6 +/- 0.4 mm (p<0.001), a mean RAL gain of 3.4 +/- 0.8 mm (p<0.001) and a mean PBL gain of 2.8 +/- 0.8 mm (p<0.001). RAL gains of > or =4 mm were measured in 90% of the test defects and in 55% of the controls. PBL gains of > or =4 mm were obtained in 85% of the test defects and in 25% of the control ones. The test treatment resulted in statistically higher PPD reductions, RAL gains and PBL gains compared with the control (p<0.01). CONCLUSIONS: Within their limits, the present results indicate that: (i) at 1 year after surgery, both therapies resulted in statistically significant clinical improvements compared with baseline and (ii) although the combination of EMD+AB resulted in statistically significant higher soft and hard tissue improvements compared with treatment with EMD, the clinical relevance of this finding is unclear.

Delayed gadolinium-enhanced MRI of cartilage in the ankle at 3 T: feasibility and preliminary results after matrix-associated autologous chondrocyte implantation

To demonstrate the feasibility of delayed gadolinium-enhanced magnetic resonance imaging (MRI) of cartilage (dGEMRIC) in the ankle at 3 T and to obtain preliminary data on matrix associated autologous chondrocyte (MACI) repair tissue.

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.

Investigation of a unique short open reading frame within the 3' untranslated region of the canine distemper virus matrix messenger RNA

Increasing evidence suggest that the long "untranslated" region (UTR) between the matrix (M) and the fusion (F) proteins of morbilliviruses has a functional role. In canine distemper virus (CDV), the F 5' UTR was recently shown to code for a long F signal peptide (Fsp). Subsequently, it was reported that the M/F UTRs combined with the long Fsp were synergistically regulating the F mRNA and protein expression, thereby modulating virulence. Unique to CDV, a short putative open reading frame (ORF) has been identified within the wild-type CDV-M 3' UTR (termed M2). Here, we investigated whether M2 was expressed from the genome of the virulent and demyelinating A75/17-CDV strain. An expression plasmid encoding the M2 ORF tagged both at its N-terminal (HA) and C-terminal domains (RFP), was first constructed. Then, a recombinant virus with its putative M2 ORF replaced by HA-M2-RFP was successfully recovered from cDNA (termed recA75/17(green)-HA-M2-RFP). M2 expression in cells transfected or infected with these mutants was studied by immunoprecipitation, immunofluorescence, immunoblot and flow cytometry analyses. Although fluorescence was readily detected in HA-M2-RFP-transfected cells, absence of red fluorescence emission in several recA75/17(green)-HA-M2-RFP-infected cell types suggested lack of M2 biosynthesis, which was confirmed by the other techniques. Consistent with these data, no functional role of the short polypeptide was revealed by infecting various cell types with HA-M2-RFP over-expressing or M2-knockout recombinant viruses. Thus, in sharp contrast to the CDV-F 5' UTR reported to translate a long Fsp, our data provided evidence that the CDV-M 3' UTR does not express any polypeptides.

Brain areas involved in medial temporal lobe seizures: a principal component analysis of ictal SPECT data

The study describes brain areas involved in medial temporal lobe (mTL) seizures of 12 patients. All patients showed so-called oro-alimentary behavior within the first 20 s of clinical seizure manifestation characteristic of mTL seizures. Single photon emission computed tomography (SPECT) images of regional cerebral blood flow (rCBF) were acquired from the patients in ictal and interictal phases and from normal volunteers. Image analysis employed categorical comparisons with statistical parametric mapping and principal component analysis (PCA) to assess functional connectivity. PCA supplemented the findings of the categorical analysis by decomposing the covariance matrix containing images of patients and healthy subjects into distinct component images of independent variance, including areas not identified by the categorical analysis. Two principal components (PCs) discriminated the subject groups: patients with right or left mTL seizures and normal volunteers, indicating distinct neuronal networks implicated by the seizure. Both PCs were correlated with seizure duration, one positively and the other negatively, confirming their physiological significance. The independence of the two PCs yielded a clear clustering of subject groups. The local pattern within the temporal lobe describes critical relay nodes which are the counterpart of oro-alimentary behavior: (1) right mesial temporal zone and ipsilateral anterior insula in right mTL seizures, and (2) temporal poles on both sides that are densely interconnected by the anterior commissure. Regions remote from the temporal lobe may be related to seizure propagation and include positively and negatively loaded areas. These patterns, the covarying areas of the temporal pole and occipito-basal visual association cortices, for example, are related to known anatomic paths.

Gelatinase B [matrix metalloproteinase (MMP)-9] and collagenases (MMP-8/-13) are upregulated in cerebrospinal fluid during aseptic and bacterial meningitis in children

We investigated the protein expression of gelatinases [matrix metalloproteinase (MMP)-2 and -9] and collagenases (MMP-8 and -13) in cerebrospinal fluid (CSF) from patients with bacterial (BM, n = 17) and aseptic (AM, n = 14) meningitis. In both, MMP-8 and -9 were increased in 100% of patients, whereas MMP-13 was detectable in 53% and 82% respectively. Three patients with clinical signs of meningitis, without CSF pleocytosis, scored positive for all three MMPs. MMP-8 appeared in two isoforms, granulocyte-type [polymorphonuclear cell (PMN)] and fibroblast/macrophage (F/M) MMP-8. Analysis of kinetic changes from serial lumbar punctures showed that these MMPs are independently regulated, and correlate only partly with CSF cytosis or levels of the endogenous inhibitor, tissue inhibitor of matrix metalloproteinase-1. In vitro, T cells, peripheral blood mononuclear cells (PBMCs) and granulocytes (PMN) release MMP-8 and -9, whereas MMP-13 could be found only in the former two cell types. Using models of exogenous (n-formyl-Met-Leu-Phe, T cell receptor cross-linking) and host-derived stimuli (interleukin-2), the kinetics and the release of the MMP-8, -9 and -13 showed strong variation between these immune cells and suggest release from preformed stocks. In addition, MMP-9 is also synthesized de novo in PBMCs and T cells. In conclusion, invading immune cells contribute only partially to MMPs in CSF during meningitis, and parenchymal cells are an equally relevant source. In this context, in patients with clinical signs of meningitis, but without CSF pleocytosis, MMPs seem to be a highly sensitive marker for intrathecal inflammation. The present data support the concept that broad-spectrum enzyme inhibition targeting gelatinases and collagenases is a potential strategy for adjunctive therapy in infectious meningitis.

Influence of diurnal hyperosmotic loading on the metabolism and matrix gene expression of a whole-organ intervertebral disc model

It is generally agreed that the mechanical environment of intervertebral disc cells plays an important role in maintaining a balanced matrix metabolism. The precise mechanism by which the signals are transduced into the cells is poorly understood. Osmotic changes in the extracellular matrix (ECM) are thought to be involved. Current in-vitro studies on this topic are mostly short-term and show conflicting data on the reaction of disc cells subjected to osmotic changes which is partially due to the heterogenous and often substantially-reduced culture systems. The aim of the study was therefore to investigate the effects of cyclic osmotic loading for 4 weeks on metabolism and matrix gene expression in a full-organ intervertebral disc culture system. Intervertebral disc/endplate units were isolated from New Zealand White Rabbits and cultured either in iso-osmotic media (335 mosmol/kg) or were diurnally exposed for 8 hours to hyper-osmotic conditions (485 mosmol/kg). Cell viability, metabolic activity, matrix composition and matrix gene expression profile (collagen types I/II and aggrecan) were monitored using Live/Dead cell viability assay, tetrazolium reduction test (WST 8), proteoglycan and DNA quantification assays and quantitative PCR. The results show that diurnal osmotic stimulation did not have significant effects on proteoglycan content, cellularity and disc cell viability after 28 days in culture. However, hyperosmolarity caused increased cell death in the early culture phase and counteracted up-regulation of type I collagen gene expression in nucleus and annulus cells. Moreover, the initially decreased cellular dehydrogenase activity recovered with osmotic stimulation after 4 weeks and aggrecan gene down-regulation was delayed, although the latter was not significant according to our statistical criteria. In contrast, collagen type II did not respond to the osmotic changes and was down-regulated in both groups. In conclusion, diurnal hyper-osmotic stimulation of a whole-organ disc/endplate culture partially inhibits a matrix gene expression profile as encountered in degenerative disc disease and counteracts cellular metabolic hypo-activity.

Biological mediators and periodontal regeneration: a review of enamel matrix proteins at the cellular and molecular levels

BACKGROUND: Despite a large body of clinical and histological data demonstrating beneficial effects of enamel matrix proteins (EMPs) for regenerative periodontal therapy, it is less clear how the available biological data can explain the mechanisms underlying the supportive effects of EMPs. OBJECTIVE: To analyse all available biological data of EMPs at the cellular and molecular levels that are relevant in the context of periodontal wound healing and tissue formation. METHODS: A stringent systematic approach was applied using the key words "enamel matrix proteins" OR "enamel matrix derivative" OR "emdogain" OR "amelogenin". The literature search was performed separately for epithelial cells, gingival fibroblasts, periodontal ligament cells, cementoblasts, osteogenic/chondrogenic/bone marrow cells, wound healing, and bacteria. RESULTS: A total of 103 papers met the inclusion criteria. EMPs affect many different cell types. Overall, the available data show that EMPs have effects on: (1) cell attachment, spreading, and chemotaxis; (2) cell proliferation and survival; (3) expression of transcription factors; (4) expression of growth factors, cytokines, extracellular matrix constituents, and other macromolecules; and (5) expression of molecules involved in the regulation of bone remodelling. CONCLUSION: All together, the data analysis provides strong evidence for EMPs to support wound healing and new periodontal tissue formation.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

Variation of cell and matrix morphologies in articular cartilage among locations in the adult human knee

OBJECTIVE: Understanding of articular cartilage physiology, remodelling mechanisms, and evaluation of tissue engineering repair methods requires reference information regarding normal structural organization. Our goals were to examine the variation of cartilage cell and matrix morphology in different topographical areas of the adult human knee joint. METHODS: Osteochondral explants were acquired from seven distinct anatomical locations of the knee joints of deceased persons aged 20-40 years and prepared for analysis of cell, matrix and tissue morphology using confocal microscopy and unbiased stereological methods. Differences between locations were identified by statistical analysis. RESULTS: Medial femoral condyle cartilage had relatively high cell surface area per unit tissue volume in the superficial zone. In the transitional zone, meniscus-covered lateral tibia cartilage showed elevated chondrocyte densities compared to the rest of the knee while lateral femoral condyle cartilage exhibited particularly large chondrocytes. Statistical analyses indicated highly uniform morphology throughout the radial zone (lower 80% of cartilage thickness) in the knee, and strong similarities in cell and matrix morphologies among cartilage from the femoral condyles and also in the mediocentral tibial plateau. Throughout the adult human knee, the mean matrix volume per chondron was remarkably constant at approximately 224,000 microm(3), corresponding to approximately 4.6 x 10(6) chondrons per cm(3). CONCLUSIONS: The uniformity of matrix volume per chondron throughout the adult human knee suggests that cell-scale biophysical and metabolic constraints may place limitations on cartilage thickness, mechanical properties, and remodelling mechanisms. Data may also aid the evaluation of cartilage tissue engineering treatments in a site-specific manner. Results indicate that joint locations which perform similar biomechanical functions have similar cell and matrix morphologies; findings may therefore also provide clues to understanding conditions under which focal lesions leading to osteoarthritis may occur.

Corrected kriging update formulae for batch-sequential data assimilation

Recently, a lot of effort has been spent in the efficient computation of kriging predictors when observations are assimilated sequentially. In particular, kriging update formulae enabling significant computational savings were derived. Taking advantage of the previous kriging mean and variance computations helps avoiding a costly matrix inversion when adding one observation to the TeX already available ones. In addition to traditional update formulae taking into account a single new observation, Emery (2009) proposed formulae for the batch-sequential case, i.e. when TeX new observations are simultaneously assimilated. However, the kriging variance and covariance formulae given in Emery (2009) for the batch-sequential case are not correct. In this paper, we fix this issue and establish correct expressions for updated kriging variances and covariances when assimilating observations in parallel. An application in sequential conditional simulation finally shows that coupling update and residual substitution approaches may enable significant speed-ups.