V-cycle optimal convergence for certain (multilevel) structured linear systems

In this paper we are interested in the solution by multigrid strategies of multilevel linear systems whose coefficient matrices belong to the circulant, Hartley, or \u3c4 algebras or to the Toeplitz class and are generated by (the Fourier expansion of) a nonnegative multivariate polynomial f. It is well known that these matrices are banded and have eigenvalues equally distributed as f, so they are ill-conditioned whenever f takes the zero value; they can even be singular and need a low-rank correction. We prove the V-cycle multigrid iteration to have a convergence rate independent of the dimension even in presence of ill-conditioning. If the (multilevel) coefficient matrix has partial dimension nr at level r, r = 1, . . . ,d, then the size of the algebraic system is N(n) = \u3a0r=1 d nr, O(N(n)) operations are required by our technique, and therefore the corresponding method is optimal. Some numerical experiments concerning linear systems arising in applications, such as elliptic PDEs with mixed boundary conditions and image restoration problems, are considered and discussed.cussed

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

Cross-Flow Turbine Design For Energy Production And Discharge Regulation

Cross-flow turbines are very efficient and cheap turbines that allow a very good cost/benefit ratio for energy production located at the end of conduits carrying water from a water source to a tank. In this paper a new design procedure for a cross-flow turbine working with a variable flow rate is proposed. The regulation of the head immediately upstream the turbine is faced by adopting a shaped semicircular segment moving around the impeller. The maximum efficiency of the turbine is attained by setting the velocity of the particles entering the impeller at about twice the velocity of the rotating system at the impeller inlet. If energy losses along the pipe are negligible, the semicircular segment allows always a constant hydraulic head and a constant velocity at the impeller inlet, even with variable flow rate. The decrease of the turbine efficiency along with the inlet surface reduction is first investigated; a design methodology, using also CFD simulations, is then proposed for both the cases of negligible and not negligible energy losses along the pipe

Spectral analysis of the anti-reflective algebra

Anti-reflective boundary conditions have been studied in connection with fast deblurring algorithms, in the case of d-dimensional objects (signals for d=1, images for d=2). Here we study how, under the assumption of strong symmetry of the point spread functions and under mild degree conditions, the associated matrices depend on a symbol and define an algebra homomorphism. Furthermore, the eigenvalues can be exhaustively described in terms of samplings of the symbol and other related functions, and appropriate O(ndlog(n)) arithmetic operations algorithms can be derived for the related computations. These results, in connection with the use of the anti-reflective transform, are of interest when employing filtering type procedures for the reconstruction of noisy and blurred objects

Fast and numerically stable algorithms for discrete Hartley transforms and applications to preconditioning

The discrete Hartley transforms (DHT) of types I \u2013 IV and the related matrix algebras are discussed. We prove that any of these DHTs of length N = 2t can be factorized by means of a divide\u2013and\u2013conquer strategy into a product of sparse, orthogonal matrices where in this context sparse means at most two nonzero entries per row and column. The sparsity joint with orthogonality of the matrix factors is the key for proving that these new algorithms have low arithmetic costs equal to 5 2 N log2 (N)+O(N) arithmetic operations and an excellent normwise numerical stability. Further, we consider the optimal Frobenius approximation of a given symmetric Toeplitz matrix generated by an integrable symbol in a Hartley matrix algebra. We give explicit formulas for computing these optimal approximations and discuss the related preconditioned conjugate gradient (PCG) iterations. By using the matrix approximation theory, we prove the strong clustering at unity of the preconditioned matrix sequences under the sole assumption of continuity and positivity of the generating function. The multilevel case is also briefly treated. Some numerical experiments concerning DHT preconditioning are included

Persistent high MR signal of the posterior pituitary gland in central diabetes insipidus.

We describe three cases of central diabetes insipidus, each with a different pathogenesis, in which unexpected hyperintensity of the posterior pituitary gland was seen on T1-weighted MR images obtained at the time of presentation. In the first case (idiopathic), the posterior pituitary signal persisted more than 10 years; in the second case (Langerhans cell histiocytosis), the signal disappeared within 3 months, despite early specific chemotherapy with etoposide; and in the third case (transient), the posterior signal disappeared within 1 year, but it was documented at the time of spontaneous reversal of polyuria and polydipsia

The 47,XXY karyotype and unrelated malformative patterns. An unusual association

Helv Paediatr Acta. 1987 Jun;42(5-6):457-61. The 47,XXY karyotype and unrelated malformative patterns: an unusual association. Aric\uf2 M, Colombo A, Maserati E, Pasquali F, Burgio GR. Source Clinica Pediatrica dell'Universit\ue0, IRCCS Policlinico S. Matteo, Italia. Abstract 47,XXY chromosome complement is relatively frequent (1/750-1000 male newborns) but has so far not been reported in association with malformative syndromes. Three cases of 47,XXY karyotype associated with an unrelated malformative pattern, the Silver-Russell syndrome in two cases and Noonan syndrome in one case are reported. The possibility of a phenotypic alteration of patients with the XXY karyotype by these malformative syndromes is considered