ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

The effect of high-energy extracorporeal shock waves on hyaline cartilage of adult rats in vivo

The aim of this study was to determine if extracorporeal shock wave therapy (ESWT) in vivo affects the structural integrity of articular cartilage. A single bout of ESWT (1500 shock waves of 0.5 mJ/mm(2)) was applied to femoral heads of 18 adult Sprague-Dawley rats. Two sham-treated animals served as controls. Cartilage of each femoral head was harvested at 1, 4, or 10 weeks after ESWT (n = 6 per treatment group) and scored on safranin-O-stained sections. Expression of tenascin-C and chitinase 3-like protein 1 (Chi3L1) was analyzed by immunohistochemistry. Quantitative real-time polymerase chain reaction (PCR) was used to examine collagen (II)alpha(1) (COL2A1) expression and chondrocyte morphology was investigated by transmission electron microscopy no changes in Mankin scores were observed after ESWT. Positive immunostaining for tenascin-C and Chi3L1 was found up to 10 weeks after ESWT in experimental but not in control cartilage. COL2A1 mRNA was increased in samples 1 and 4 weeks after ESWT. Alterations found on the ultrastructural level showed expansion of the rough-surfaced endoplasmatic reticulum, detachment of the cell membrane and necrotic chondrocytes. Extracorporeal shock waves caused alterations of hyaline cartilage on a molecular and ultrastructural level that were distinctly different from control. Similar changes were described before in the very early phase of osteoarthritis (OA). High-energy ESWT might therefore cause degenerative changes in hyaline cartilage as they are found in initial OA.

The effect of different implant neck configurations on soft and hard tissue healing: a randomized-controlled clinical trial

Objective: To compare the soft and hard tissue healing and remodeling around tissue-level implants with different neck configurations after at least 1 year of functional loading. Material and methods: Eighteen patients with multiple missing teeth in the posterior area received two implants inserted in the same sextant. One test (T) implant with a 1.8 mm turned neck and one control (C) implant with a 2.8 mm turned neck were randomly assigned. All implants were placed transmucosally to the same sink depth of approximately 1.8 mm. Peri-apical radiographs were obtained using the paralleling technique and digitized. Two investigators blinded to the implant type-evaluated soft and hard tissue conditions at baseline, 6 months and 1 year after loading. Results: The mean crestal bone levels and soft tissue parameters were not significantly different between T and C implants at all time points. However, T implants displayed significantly less crestal bone loss than C implants after 1 year. Moreover, a frequency analysis revealed a higher percentage (50%) of T implants with crestal bone levels 1–2 mm below the implant shoulder compared with C implants (5.6%) 1 year after loading. Conclusion: Implants with a reduced height turned neck of 1.8 mm may, indeed, lower the crestal bone resorption and hence, may maintain higher crestal bone levels than do implants with a 2.8 mm turned neck, when sunk to the same depth. Moreover, several factors other than the vertical positioning of the moderately rough SLA surface may influence crestal bone levels after 1 year of function.

Effects of long-term feeding of genetically modified corn (event MON810) on the performance of lactating dairy cows

A long-term study over 25 months was conducted to evaluate the effects of genetically modified corn on performance of lactating dairy cows. Thirty-six dairy cows were assigned to two feeding groups and fed with diets based on whole-crop silage, kernels and whole-crop cobs from Bt-corn (Bt-MON810) or its isogenic not genetically modified counterpart (CON) as main components. The study included two consecutive lactations. There were no differences in the chemical composition and estimated net energy content of Bt-MON810 and CON corn components and diets. CON feed samples were negative for the presence of Cry1Ab protein, while in Bt-MON810 feed samples the Cry1Ab protein was detected. Cows fed Bt-MON810 corn had a daily Cry1Ab protein intake of 6.0 mg in the first lactation and 6.1 mg in the second lactation of the trial. Dry matter intake (DMI) was 18.8 and 20.7 kg/cow per day in the first and the second lactation of the trial, with no treatment differences. Similarly, milk yield (23.8 and 29.0 kg/cow per day in the first and the second lactation of the trial) was not affected by dietary treatment. There were no consistent effects of feeding MON810 or its isogenic CON on milk composition or body condition. Thus, the present long-term study demonstrated the compositional and nutritional equivalence of Bt-MON810 and its isogenic CON.

Open or submerged healing of implants with platform switching: a randomized, controlled clinical trial

The temporal pattern of bone-level alterations in conventionally restored implants is dependent upon healing mode (open or submerged). This study examined the influence of healing on marginal bone levels at implants with a medium-rough surface including the implant collar and a clearance-fit implant-abutment connection restored according to a platform-switching concept.

Gene expression profile of osseointegration of a hydrophilic compared with a hydrophobic microrough implant surface

OBJECTIVES: To compare the gene expression profile of osseointegration associated with a moderately rough and a chemically modified hydrophilic moderately rough surface in a human model. MATERIAL AND METHODS: Eighteen solid screw-type cylindrical titanium implants, 4 mm long and 2.8 mm wide, with either a moderately rough (SLA) or a chemically modified moderately rough (SLActive) surface were surgically inserted in the retromolar area of nine human volunteers. The devices were removed using a trephine following 4, 7 and 14 days of healing. The tissue surrounding the implant was harvested, total RNA was extracted and microarray analysis was carried out to identify the differences in the transcriptome between the SLA and SLActive surfaces at days 4, 7 and 14. RESULTS: There were no functionally relevant gene ontology categories that were over-represented in the list of genes that were differentially expressed at day 4. However, by day 7, osteogenesis- and angiogenesis-associated gene expression were up-regulated on the SLActive surface. Osteogenesis and angiogenesis appeared to be regulated by BMP and VEGF signalling, respectively. By day 14, VEGF signalling remains up-regulated on the SLActive surface, while BMP signalling was up-regulated on the SLA surface in what appeared to be a delayed compensatory response. Furthermore, neurogenesis was a prominent biological process within the list of differentially expressed genes, and it was influenced by both surfaces. CONCLUSIONS: Compared with SLA, SLActive exerts a pro-osteogenic and pro-angiogenic influence on gene expression at day 7 following implant insertion, which may be responsible for the superior osseointegrative properties of this surface.

The role of bone debris in early healing adjacent to hydrophilic and hydrophobic implant surfaces in man

To evaluate morphologically and morphometrically the sequential healing and osseointegration events at moderately rough implant surfaces with and without chemical modification. Particularly the role of bone debris in initiating bone formation was emphasized.

Early osseointegration to hydrophilic and hydrophobic implant surfaces in humans

To evaluate the rate and degree of osseointegration at chemically modified moderately rough, hydrophilic (SLActive) and moderately rough, hydrophobic (SLA) implant surfaces during early phases of healing in a human model.