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Supercuspidal unipotent representations: L-packets and formal degrees
Let K be a non-archimedean local field and let G be a connected reductive
K-group which splits over an unramified extension of K. We investigate
supercuspidal unipotent representations of the group G(K). We establish a
bijection between the set of irreducible G(K)-representations of this kind and
the set of cuspidal enhanced L-parameters for G(K), which are trivial on the
inertia subgroup of the Weil group of K. The bijection is characterized by a
few simple equivariance properties and a comparison of formal degrees of
representations with adjoint -factors of L-parameters.
This can be regarded as a local Langlands correspondence for all
supercuspidal unipotent representations. We count the ensueing L-packets, in
terms of data from the affine Dynkin diagram of G. Finally, we prove that our
bijection satisfies the conjecture of Hiraga, Ichino and Ikeda about the formal
degrees of the representations.Comment: Version 2: minor corrections and additions, mainly in section 1
Recycling BiCGSTAB with an Application to Parametric Model Order Reduction
Krylov subspace recycling is a process for accelerating the convergence of
sequences of linear systems. Based on this technique, the recycling BiCG
algorithm has been developed recently. Here, we now generalize and extend this
recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving
sequences of dual linear systems, while the focus here is on efficiently
solving sequences of single linear systems (assuming non-symmetric matrices for
both recycling BiCG and recycling BiCGSTAB).
As compared with other methods for solving sequences of single linear systems
with non-symmetric matrices (e.g., recycling variants of GMRES), BiCG based
recycling algorithms, like recycling BiCGSTAB, have the advantage that they
involve a short-term recurrence, and hence, do not suffer from storage issues
and are also cheaper with respect to the orthogonalizations.
We modify the BiCGSTAB algorithm to use a recycle space, which is built from
left and right approximate invariant subspaces. Using our algorithm for a
parametric model order reduction example gives good results. We show about 40%
savings in the number of matrix-vector products and about 35% savings in
runtime.Comment: 18 pages, 5 figures, Extended version of Max Planck Institute report
(MPIMD/13-21
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Use of Antihypertensive Agents and Association With Risk of Adverse Outcomes in Chronic Kidney Disease: Focus on Angiotensin-Converting Enzyme Inhibitors and Angiotensin Receptor Blockers.
Background Our objective was to determine patterns of antihypertensive agent use by stage of chronic kidney disease (CKD) and to evaluate the association between different classes of antihypertensive agents with nonrenal outcomes, especially in advanced CKD . Methods and Results We studied 3939 participants of the CRIC (Chronic Renal Insufficiency Cohort) study. Predictors were time-dependent angiotensin-converting enzyme inhibitor or angiotensin receptor blocker , β-blocker, and calcium channel blocker use (versus nonuse of agents in each class). Outcomes were adjudicated heart failure events or death. Adjusted Cox models were used to determine the association between predictors and outcomes. We also examined whether the associations differed based on the severity of CKD (early [stage 2-3 CKD ] versus advanced disease [stage 4-5 CKD ]). During median follow-up of 7.5 years, renin-angiotensin-aldosterone system inhibitor use plateaued during CKD stage 3 (75%) and declined to 37% by stage 5, while β-blocker, calcium channel blocker, and diuretic use increased steadily with advancing CKD . Renin-angiotensin-aldosterone system inhibitor use was associated with lower risk of heart failure (hazard ratio, 0.79; 95% confidence interval, 0.67-0.97) and death (hazard ratio, 0.78; 95% confidence interval, 0.67-0.90), regardless of severity of CKD . Calcium channel blocker use was not associated with risk of heart failure or death, regardless of the severity of CKD . β-Blocker use was associated with higher risk of heart failure (hazard ratio, 1.62; 95% confidence interval, 1.29-2.04) and death (hazard ratio, 1.22; 95% confidence interval, 1.03-1.43), especially during early CKD ( P<0.05 for interaction). Conclusions Angiotensin-converting enzyme inhibitor and angiotensin receptor blocker use decreased, while use of other agents increased with advancing CKD . Use of agents besides angiotensin-converting enzyme inhibitors or angiotensin receptor blockers may be associated with suboptimal outcomes in patients with CKD
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