A Class of Non-Parametric Statistical Manifolds modelled on Sobolev Space

We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on Rd. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports the Fisher-Rao metric as a weak Riemannian metric. Densities are expressed in terms of a deformed exponential function having linear growth. Unusually for the Sobolev context, and as a consequence of its linear growth, this "lifts" to a nonlinear superposition (Nemytskii) operator that acts continuously on a particular class of mixed-norm model spaces, and on the fixed norm space W²'¹ i.e. it maps each of these spaces continuously into itself. It also maps continuously between other fixed-norm spaces with a loss of Lebesgue exponent that increases with the number of derivatives. Some of the results make essential use of a log-Sobolev embedding theorem. Each manifold contains a smoothly embedded submanifold of probability measures. Applications to the stochastic partial differential equations of nonlinear filtering (and hence to the Fokker-Planck equation) are outlined

Matrix metalloproteinases (MMP-2,9) and their tissue inhibitors (TIMP-1,2) as novel markers of stress response and atherogenesis in children with chronic kidney disease (CKD) on conservative treatment

The system of matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs) may play a key role in atherogenesis of chronic kidney disease (CKD) patients by its impact on matrix accumulation. Connections with inflammation, stress, or endothelial dysfunction are also probable. However, the data on correlations between these parameters in CKD patients are scarce in adults and absent in children. The aim of our study was to evaluate serum concentrations of MMP-2, MMP-9, TIMP-1, and TIMP-2, as well as their correlations with markers of stress response (Hsp90-α, anti-Hsp60), endothelial dysfunction (sE-selectin), and inflammation (high-sensitivity C-reactive protein) in CKD children treated conservatively. Thirty-seven patients were divided into two groups according to the CKD stage (gr.CKDI, 19 children with CKD stages 2–3; gr.CKDII, 18 subjects with CKD stages 4–5). Twenty-four age-matched healthy subjects served as controls. Serum concentrations of MMP-2, MMP-9, TIMP-1, TIMP-2, Hsp90-α, anti-Hsp60, and sE-selectin were assessed by ELISA. Median values of MMP-2, MMP-9, TIMP-1, and TIMP-2 were significantly higher in all CKD children vs. controls and were increased in patients with CKD stages 4–5 vs. CKD stages 2–3. Hsp90-α, anti-Hsp60, sE-selectin, and glomerular filtration rate predicted the values of MMPs and TIMPs. Chronic kidney disease in children is characterized by MMP/TIMP system dysfunction, aggravated by the progression of renal failure. Correlations between examined parameters, heat shock proteins, and markers of endothelial damage suggest the possibility of MMP/TIMP application as indicators of stress response and atherogenesis in children with CKD on conservative treatment

Characterizing flow zones in a fractured and karstified limestone aquifer through integrated interpretation of geophysical and hydraulic data

A detailed and integrated geologic–hydraulic–geophysical–geochemical study of groundwater flow in the near-vicinity of a borehole drilled into fractured and karstified limestone demonstrates the power of such an integrated approach in localising and characterising preferential groundwater flow pathways and ambient borehole flow. The study, conducted in the vicinity of a 100-m-deep research borehole on the island of Mallorca, achieves such characterisation on a scale from millimetres to tens of metres in scale. More specifically, it adds single packer and open-hole pumping test interpretations to the results obtained during fluid logging, impeller flowmeter testing, borehole imaging, core descriptions and an innovative fracture analysis. This approach allows the delineation of the main flowing features and showed that such features are directly or indirectly linked to karst phenomena. Understanding this complex flow system is critical for an appropriate assessment of groundwater resources and the design of sustainable groundwater production schemes

Angiotensin-converting enzyme inhibition but not angiotensin II receptor blockade regulates matrix metalloproteinase activity in patients with glomerulonephritis

Equivalent long-term effects on the kidney are attributed to angiotensin-converting enzyme inhibitors (ACEI) and angiotensin II type 1 receptor blockers (ARB). Nevertheless, it is unknown to which degree effects of these compounds on individual inflammatory mediators, including matrix metalloproteinases (MMP), are comparable. On the basis of structural and functional differences, it was hypothesized that ACEI and ARB differentially regulate MMP activity. In a randomized, prospective crossover trial, the effect of an ACEI (fosinopril; 20 mg/d) and of an ARB (irbesartan; 150 mg/d) on MMP activity was evaluated. Ten hypertensive patients with glomerulonephritis and normal or mildly reduced creatinine clearance were studied. MMP activity and tissue inhibitors of metalloproteinase (TIMP) levels were analyzed in serum and urine: without therapy, with ACEI, with ARB, and with both agents combined. Treatment periods continued for 6 wk separated by periods of 4 wk each without therapy. Untreated patients with glomerulonephritis displayed distinctively higher serum levels of MMP-2 but much lower MMP-1/-8/-9 concentrations compared with healthy control subjects. Immunohistology of MMP-2 and MMP-9 in kidney biopsy specimen was accordingly. However, these patients excreted higher amounts of MMP-2 and MMP-9 in urine than healthy control subjects, possibly reflecting ongoing glomerular inflammation. In patients with glomerulonephritis, ACEI significantly reduced overall MMP serum activity to 25%, whereas ARB did not show any effect. Activities of MMP-1/-2/-8/-9 were also significantly inhibited by fosinopril but not by irbesartan. Levels of TIMP-1/-2 remained unaffected. In conclusion, ACEI and ARB differentially regulate MMP activity, which may ultimately have consequences in certain types of MMP-dependent glomerulonephritis

Differential regulation of metzincins in experimental chronic renal allograft rejection: potential markers and novel therapeutic targets

Chronic renal allograft rejection is characterized by alterations in the extracellular matrix compartment and in the proliferation of various cell types. These features are controlled, in part by the metzincin superfamily of metallo-endopeptidases, including matrix metalloproteinases (MMPs), a disintegrin and metalloproteinase (ADAM) and meprin. Therefore, we investigated the regulation of metzincins in the established Fisher to Lewis rat kidney transplant model. Studies were performed using frozen homogenates and paraffin sections of rat kidneys at day 0 (healthy controls) and during periods of chronic rejection at day +60 and day +100 following transplantation. The messenger RNA (mRNA) expression was examined by Affymetrix Rat Expression Array 230A GeneChip and by real-time Taqman polymerase chain reaction analyses. Protein expression was studied by zymography, Western blot analyses, and immunohistology. mRNA levels of MMPs (MMP-2/-11/-12/-14), of their inhibitors (tissue inhibitors of metalloproteinase (TIMP)-1/-2), ADAM-17 and transforming growth factor (TGF)-beta1 significantly increased during chronic renal allograft rejection. MMP-2 activity and immunohistological staining were augmented accordingly. The most important mRNA elevation was observed in the case of MMP-12. As expected, Western blot analyses also demonstrated increased production of MMP-12, MMP-14, and TIMP-2 (in the latter two cases as individual proteins and as complexes). In contrast, mRNA levels of MMP-9/-24 and meprin alpha/beta had decreased. Accordingly, MMP-9 protein levels and meprin alpha/beta synthesis and activity were downregulated significantly. Members of metzincin families (MMP, ADAM, and meprin) and of TIMPs are differentially regulated in chronic renal allograft rejection. Thus, an altered pattern of metzincins may represent novel diagnostic markers and possibly may provide novel targets for future therapeutic interventions