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Land-use intensification is a major driver of biodiversity loss(1,2). Alongside reductions in local species diversity, biotic homogenization at larger spatial scales is of great concern for conservation. Biotic homogenization means a decrease in beta-diversity (the compositional dissimilarity between sites). Most studies have investigated losses in local (alpha)-diversity(1,3) and neglected biodiversity loss at larger spatial scales. Studies addressing beta-diversity have focused on single or a few organism groups (for example, ref. 4), and it is thus unknown whether land-use intensification homogenizes communities at different trophic levels, above-and belowground. Here we show that even moderate increases in local land-use intensity (LUI) cause biotic homogenization across microbial, plant and animal groups, both above- and belowground, and that this is largely independent of changes in alpha-diversity. We analysed a unique grassland biodiversity dataset, with abundances of more than 4,000 species belonging to 12 trophic groups. LUI, and, in particular, high mowing intensity, had consistent effects on beta-diversity across groups, causing a homogenization of soil microbial, fungal pathogen, plant and arthropod communities. These effects were nonlinear and the strongest declines in beta-diversity occurred in the transition from extensively managed to intermediate intensity grassland. LUI tended to reduce local alpha-diversity in aboveground groups, whereas the alpha-diversity increased in belowground groups. Correlations between the alpha-diversity of different groups, particularly between plants and their consumers, became weaker at high LUI. This suggests a loss of specialist species and is further evidence for biotic homogenization. The consistently negative effects of LUI on landscape-scale biodiversity underscore the high value of extensively managed grasslands for conserving multitrophic biodiversity and ecosystem service provision. Indeed, biotic homogenization rather than local diversity loss could prove to be the most substantial consequence of land-use intensification.
Species diversity promotes the delivery of multiple ecosystem functions (multifunctionality). However, the relative functional importance of rare and common species in driving the biodiversity multifunctionality relationship remains unknown. We studied the relationship between the diversity of rare and common species (according to their local abundances and across nine different trophic groups), and multifunctionality indices derived from 14 ecosystem functions on 150 grasslands across a land use intensity (LUI) gradient. The diversity of above- and below-ground rare species had opposite effects, with rare above-ground species being associated with high levels of multifunctionality, probably because their effects on different functions did not trade off against each other. Conversely, common species were only related to average, not high, levels of multifunctionality, and their functional effects declined with LUI. Apart from the community level effects of diversity, we found significant positive associations between the abundance of individual species and multifunctionality in 6% of the species tested. Species specific functional effects were best predicted by their response to LUI: species that declined in abundance with land use intensification were those associated with higher levels of multifunctionality. Our results highlight the importance of rare species for ecosystem multifunctionality and help guiding future conservation priorities.
Although temporal heterogeneity is a well-accepted driver of biodiversity, effects of interannual variation in land-use intensity (LUI) have not been addressed yet. Additionally, responses to land use can differ greatly among different organisms; therefore, overall effects of land-use on total local biodiversity are hardly known. To test for effects of LUI (quantified as the combined intensity of fertilization, grazing, and mowing) and interannual variation in LUI (SD in LUI across time), we introduce a unique measure of whole-ecosystem biodiversity, multidiversity. This synthesizes individual diversity measures across up to 49 taxonomic groups of plants, animals, fungi, and bacteria from 150 grasslands. Multidiversity declined with increasing LUI among grasslands, particularly for rarer species and aboveground organisms, whereas common species and belowground groups were less sensitive. However, a high level of interannual variation in LUI increased overall multidiversity at low LUI and was even more beneficial for rarer species because it slowed the rate at which the multidiversity of rare species declined with increasing LUI. In more intensively managed grasslands, the diversity of rarer species was, on average, 18% of the maximum diversity across all grasslands when LUI was static over time but increased to 31% of the maximum when LUI changed maximally over time. In addition to decreasing overall LUI, we suggest varying LUI across years as a complementary strategy to promote biodiversity conservation.
In order to predict which ecosystem functions are most at risk from biodiversity loss, meta-analyses have generalised results from biodiversity experiments over different sites and ecosystem types. In contrast, comparing the strength of biodiversity effects across a large number of ecosystem processes measured in a single experiment permits more direct comparisons. Here, we present an analysis of 418 separate measures of 38 ecosystem processes. Overall, 45 % of processes were significantly affected by plant species richness, suggesting that, while diversity affects a large number of processes not all respond to biodiversity. We therefore compared the strength of plant diversity effects between different categories of ecosystem processes, grouping processes according to the year of measurement, their biogeochemical cycle, trophic level and compartment (above- or belowground) and according to whether they were measures of biodiversity or other ecosystem processes, biotic or abiotic and static or dynamic. Overall, and for several individual processes, we found that biodiversity effects became stronger over time. Measures of the carbon cycle were also affected more strongly by plant species richness than were the measures associated with the nitrogen cycle. Further, we found greater plant species richness effects on measures of biodiversity than on other processes. The differential effects of plant diversity on the various types of ecosystem processes indicate that future research and political effort should shift from a general debate about whether biodiversity loss impairs ecosystem functions to focussing on the specific functions of interest and ways to preserve them individually or in combination.
Land-use intensification is a key driver of biodiversity change. However, little is known about how it alters relationships between the diversities of different taxonomic groups, which are often correlated due to shared environmental drivers and trophic interactions. Using data from 150 grassland sites, we examined how land-use intensification (increased fertilization, higher livestock densities, and increased mowing frequency) altered correlations between the species richness of 15 plant, invertebrate, and vertebrate taxa. We found that 54% of pairwise correlations between taxonomic groups were significant and positive among all grasslands, while only one was negative. Higher land-use intensity substantially weakened these correlations(35% decrease in rand 43% fewer significant pairwise correlations at high intensity), a pattern which may emerge as a result of biodiversity declines and the breakdown of specialized relationships in these conditions. Nevertheless, some groups (Coleoptera, Heteroptera, Hymenoptera and Orthoptera) were consistently correlated with multidiversity, an aggregate measure of total biodiversity comprised of the standardized diversities of multiple taxa, at both high and lowland-use intensity. The form of intensification was also important; increased fertilization and mowing frequency typically weakened plant-plant and plant-primary consumer correlations, whereas grazing intensification did not. This may reflect decreased habitat heterogeneity under mowing and fertilization and increased habitat heterogeneity under grazing. While these results urge caution in using certain taxonomic groups to monitor impacts of agricultural management on biodiversity, they also suggest that the diversities of some groups are reasonably robust indicators of total biodiversity across a range of conditions.
Bottom-up effects of plant diversity on multitrophic interactions in a biodiversity experiment
(2010)
We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22].
Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues
(2005)
We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types
Consider the operator T = -d(2)/dx(2) + x(2) + q(x) in L-2 (R), where q is a real function with q' and integral(0)(x) q(s) ds bounded. The spectrum of T is purely discrete and consists of simple eigenvalues. We determine their asymptotics mu(n) = (2n + 1) + (2 pi)(-1) integral(-pi)(pi) q(root 2n+1 sin theta)d theta + O(n(-1/3)) and we extend these results for complex q.
Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times
(2004)
We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form -epsilonDelta+ delF(.) del on R-d or subsets of R-d, where F is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as epsilon down arrow 0, to the capacities of suitably constructed sets. We show that these capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring - Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes
Biodiversity-multifunctionality relationships depend on identity and number of measured functions
(2017)
Biodiversity ensures ecosystem functioning and provisioning of ecosystem services, but it remains unclear how biodiversity-ecosystem multifunctionality relationships depend on the identity and number of functions considered. Here, we demonstrate that ecosystem multifunctionality, based on 82 indicator variables of ecosystem functions in a grassland biodiversity experiment, increases strongly with increasing biodiversity. Analysing subsets of functions showed that the effects of biodiversity on multifunctionality were stronger when more functions were included and that the strength of the biodiversity effects depended on the identity of the functions included. Limits to multifunctionality arose from negative correlations among functions and functions that were not correlated with biodiversity. Our findings underline that the management of ecosystems for the protection of biodiversity cannot be replaced by managing for particular ecosystem functions or services and emphasize the need for specific management to protect biodiversity. More plant species from the experimental pool of 60 species contributed to functioning when more functions were considered. An individual contribution to multifunctionality could be demonstrated for only a fraction of the species.
We analyze a general class of difference operators Hε=Tε+Vε on ℓ2((εZ)d), where Vε is a multi-well potential and ε is a small parameter. We derive full asymptotic expansions of the prefactor of the exponentially small eigenvalue splitting due to interactions between two “wells” (minima) of the potential energy, i.e., for the discrete tunneling effect. We treat both the case where there is a single minimal geodesic (with respect to the natural Finsler metric induced by the leading symbol h0(x,ξ) of Hε) connecting the two minima and the case where the minimal geodesics form an ℓ+1 dimensional manifold, ℓ≥1. These results on the tunneling problem are as sharp as the classical results for the Schrödinger operator in Helffer and Sjöstrand (Commun PDE 9:337–408, 1984). Technically, our approach is pseudo-differential and we adapt techniques from Helffer and Sjöstrand [Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique), Mémoires de la S.M.F., 2 series, tome 34, pp 1–113, 1988)] and Helffer and Parisse (Ann Inst Henri Poincaré 60(2):147–187, 1994) to our discrete setting.
In the semiclassical limit (h) over bar -> 0, we analyze a class of self-adjoint Schrodinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V center dot id(E) acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m(1),... m(r) is an element of M, called potential wells. Using quasimodes of WKB-type near m(j) for eigenfunctions associated with the low lying eigenvalues of H-(h) over bar, we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations. Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic (with respect to the associated Agmon metric) connecting two potential wells and the case of a submanifold of minimal geodesics of dimension l + 1. This dimension l determines the polynomial prefactor for exponentially small eigenvalue splitting.
In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.
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For a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2) ((epsilon Z)(d)), where V- epsilon is a multi-well potential and a is a small parameter. we analyze the asymptotic behavior as epsilon -> 0 of the (low-lying) eigenvalues and eigenfunctions. We show that the first it eigenvalues of H converge to the first it eigenvalues of the direct suns of harmonic oscillators oil R-d located at the several wells. Our proof is microlocal.
Objective:To investigate the effects of linagliptin alone and in combination with the angiotensin II receptor blocker (ARB), telmisartan on blood pressure (BP), kidney function, heart morphology and oxidative stress in rats with renovascular hypertension.Methods:Fifty-seven male Wistar rats underwent unilateral surgical stenosis of the renal artery [2-kidney-1-clip (2k1c) method]. Animals were randomly divided into four treatment groups (n=14-18 per group) receiving: telmisartan (10mg/kg per day in drinking water), linagliptin (89ppm in chow), combination (linagliptin 89ppm+telmisartan 10mg/kg per day) or placebo. An additional group of 12 rats underwent sham surgery. BP was measured one week after surgery. Hypertensive animals entered a 16-week dosing period. BP was measured 2, 4, 8, 12 and 16 weeks after the initiation of treatment. Blood and urine were tested for assessment of kidney function and oxidative stress 6, 10, 14 and 18 weeks after surgery. Blood and urine sampling and organ harvesting were finally performed.Results:Renal stenosis caused an increase in meanSD systolic BP as compared with the sham group (157.7 +/- 29.3 vs. 106.2 +/- 20.5mmHg, respectively; P<0.001). Telmisartan alone and in combination with linagliptin, normalized SBP (111.1 +/- 24.3mmHg and 100.4 +/- 13.9mmHg, respectively; P<0.001 vs. placebo). Telmisartan alone and in combination with linagliptin significantly prevented cardiac hypertrophy, measured by heart weight and myocyte diameter. Renal function measured by cystatin C was not affected by 2k1c surgery. Telmisartan significantly increased plasma concentration of cystatin C. 2k1c surgery initiated fibrosis in both kidneys. Telmisartan promoted further fibrotic changes in the clipped kidney, as measured by protein expression of Col1a1 and histology for interstitial fibrosis and glomerulosclerosis. In non-clipped kidneys, telmisartan demonstrated antifibrotic properties, reducing Col1a1 protein expression. Plasma levels of oxidized low-density lipoprotein were higher in the placebo-treated 2k1c rats as compared to sham-operated animals. The increase was abolished by linagliptin alone (P=0.03 vs. placebo) and in combination with telmisartan (P=0.02 vs. placebo). Combination therapy also significantly reduced plasma concentration of carbonyl proteins (P=0.04 vs. placebo).Conclusion:Inhibition of type 4 dipeptidyl peptidase with linagliptin did not counter BP-lowering effects of ARB in 2k1c rats. Linagliptin reduced lipid and protein oxidation in 2k1c rats, and this effect was BP-independent.
Background: Despite the beneficial effects of type 4 dipeptidyl peptidase (DPP-4) inhibitors on glucose levels, its effects on diabetic nephropathy remain unclear.
Method: This study examined the long-term renoprotective effects of DPP-4 inhibitor linagliptin in db/db mice, a model of type 2 diabetes.
Results were compared with the known beneficial effects of renin-angiotensin system blockade by enalapril. Ten-week-old male diabetic db/db mice were treated for 3 months with either vehicle (n = 10), 3 mg linagliptin/kg per day (n = 8), or 20 mg enalapril/kg per day (n = 10). Heterozygous db/m mice treated with vehicle served as healthy controls (n = 8). Results: Neither linagliptin nor enalapril had significant effects on the parameters of glucose metabolism or blood pressure in diabetic db/db mice. However, linagliptin treatment reduced albuminuria and attenuated kidney injury. In addition, expression of podocyte marker podocalyxin was normalized. We also analysed DPP-4 expression by immunofluorescence in human kidney biopsies and detected upregulation of DPP-4 in the glomeruli of patients with diabetic nephropathy, suggesting that our findings might be of relevance for human kidney disease as well.
Conclusion: Treatment with DPP-4 inhibitor linagliptin delays the progression of diabetic nephropathy damage in a glucose-independent and blood-pressure-independent manner. The observed effects may be because of the attenuation of podocyte injury and inhibition of myofibroblast transformation.
In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t.
In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest.
Background: Uremic cardiomyopathy contributes substantially to mortality in chronic kidney disease (CKD) patients. Glucagon-like peptide-1 (GLP-1) may improve cardiac function, but is mainly degraded by dipeptidyl peptidase-4 (DPP-4).
Methodology/Principal Findings: In a rat model of chronic renal failure, 5/6-nephrectomized [5/6N] rats were treated orally with DPP-4 inhibitors (linagliptin, sitagliptin, alogliptin) or placebo once daily for 4 days from 8 weeks after surgery, to identify the most appropriate treatment for cardiac dysfunction associated with CKD. Linagliptin showed no significant change in blood level AUC(0-infinity) in 5/6N rats, but sitagliptin and alogliptin had significantly higher AUC(0-infinity) values; 41% and 28% (p=0.0001 and p=0.0324), respectively. No correlation of markers of renal tubular and glomerular function with AUC was observed for linagliptin, which required no dose adjustment in uremic rats. Linagliptin 7 mu mol/kg caused a 2-fold increase in GLP-1 (AUC 201.0 ng/l*h) in 5/6N rats compared with sham-treated rats (AUC 108.6 ng/l*h) (p=0.01). The mRNA levels of heart tissue fibrosis markers were all significantly increased in 5/6N vs control rats and reduced/normalized by linagliptin.
Conclusions/Significance: DPP-4 inhibition increases plasma GLP-1 levels, particularly in uremia, and reduces expression of cardiac mRNA levels of matrix proteins and B-type natriuretic peptides (BNP). Linagliptin may offer a unique approach for treating uremic cardiomyopathy in CKD patients, with no need for dose-adjustment.
In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.
Background: The need for an improved treatment for diabetic nephropathy is greatest in patients who do not adequately respond to angiotensin II receptor blockers (ARBs). This study investigated the effect of the novel dipeptidyl peptidase-4 inhibitor linagliptin alone and in combination with the ARB telmisartan on the progression of diabetic nephropathy in diabetic endothelial nitric oxide synthase (eNOS) knockout mice. Methods: Sixty male eNOS knockout C57BL/6J mice were divided into four groups after receiving intraperitoneal high-dose streptozotocin: telmisartan (1 mg/kg), linagliptin (3 mg/kg), linagliptin + telmisartan (3 mg/kg + 1 mg/kg) and vehicle. Fourteen mice were used as non-diabetic controls. Results: After 12 weeks, urine and blood were obtained and blood pressure measured. Glucose concentrations were increased and similar in all diabetic groups. Telmisartan alone reduced systolic blood pressure by 5.9 mmHg versus diabetic controls (111.2 +/- 2.3 mmHg vs 117.1 +/- 2.2 mmHg; mean +/- SEM; P = 0.071). Combined treatment significantly reduced albuminuria compared with diabetic controls (71.7 +/- 15.3 mu g/24 h vs 170.8 +/- 34.2 mu g/24 h; P = 0.017), whereas the effects of single treatment with either telmisartan (97.8 +/- 26.4 mu g/24 h) or linagliptin (120.8 +/- 37.7 mu g/24 h) were not statistically significant. DPP-4 inhibition, alone and in combination, led to significantly lower plasma osteopontin levels compared with telmisartan alone. Histological analysis revealed reduced glomerulosclerosis after Linagliptin alone and in combination with telmisartan in comparison to non treated diabetic animals (p < 0.01 and p < 0.05). Kidney malonaldehyde immune-reactivity, a marker of oxidative stress, was significantly lower in animals treated with linagliptin. Conclusions: DPP-4 inhibition on top of ARB treatment significantly reduced urinary albumin excretion and oxidative stress in diabetic eNOS knockout mice. Linagliptin on top of an angiotensin II receptor blocker may offer a new therapeutic approach for patients with diabetic nephropathy.
DPP-4 inhibition with linagliptin delays the progression of diabetic nephropathy in db/db mice
(2012)
We analyze a general class of difference operators on where is a multi-well potential and is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrodinger operator [see Helffer and Sjostrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
We analyze a general class of difference operators H(epsilon) = T(epsilon) + V(epsilon) on l(2)((epsilon Z)(d)), where V(epsilon) is a one-well potential and epsilon is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H(epsilon). These are obtained from eigenfunctions or quasimodes for the operator H(epsilon), acting on L(2)(R(d)), via restriction to the lattice (epsilon Z)(d).
Dipeptidyl peptidase (DPP)-4 inhibitors delay chronic kidney disease (CKD) progression in experimental diabetic nephropathy in a glucose-independent manner. Here we compared the effects of the DPP-4 inhibitor linagliptin versus telmisartan in preventing CKD progression in non-diabetic rats with 5/6 nephrectomy. Animals were allocated to 1 of 4 groups: sham operated plus placebo; 5/6 nephrectomy plus placebo; 5/6 nephrectomy plus linagliptin; and 5/6 nephrectomy plus telmisartan. Interstitial fibrosis was significantly decreased by 48% with linagliptin but a non-significant 24% with telmisartan versus placebo. The urine albumin-to-creatinine ratio was significantly decreased by 66% with linagliptin and 92% with telmisartan versus placebo. Blood pressure was significantly lowered by telmisartan, but it was not affected by linagliptin. As shown by mass spectrometry, the number of altered peptide signals for linagliptin in plasma was 552 and 320 in the kidney. For telmisartan, there were 108 peptide changes in plasma and 363 in the kidney versus placebo. Linagliptin up-regulated peptides derived from collagen type I, apolipoprotein C1, and heterogeneous nuclear ribonucleoproteins A2/B1, a potential downstream target of atrial natriuretic peptide, whereas telmisartan up-regulated angiotensin II. A second study was conducted to confirm these findings in 5/6 nephrectomy wild-type and genetically deficient DPP-4 rats treated with linagliptin or placebo. Linagliptin therapy in wild-type rats was as effective as DPP-4 genetic deficiency in terms of albuminuria reduction. Thus, linagliptin showed comparable efficacy to telmisartan in preventing CKD progression in non-diabetic rats with 5/6 nephrectomy. However, the underlying pathways seem to be different. Copyright (C) 2016, International Society of Nephrology. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
We analyze a general class of difference operators H-epsilon = T-epsilon + V-epsilon on l(2)(((epsilon)Z)(d)), where V-epsilon is a multi-well potential and epsilon is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted l(2)-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.
Existence and semiclassical analysis of the total scattering cross-section for atom-ion collisaions
(2000)
We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.