Kuhn-Tucker-based stability conditions for systems with saturation

This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods

Prognostic relevance of serum beta2 microglobulin in patients with follicular lymphoma treated with anthracycline-containing regimens. A GISL study.

Background and ObjectivesAlthough serum b2 microglobulin (b2M) is an easy parameter to measure, and overexpressedin a large number of lymphoproliferative diseases, its prognostic value hasbeen largely underestimated. The present study examined the influence of b2M levelson overall survival (OS) of patients with follicular lymphoma (FL).Design and MethodsThe prognostic role of b2M was evaluated in 236 patients with FL identified from thedatabases of the Gruppo Italiano per lo Studio dei Linfomi (GISL) and treated withanthracycline-based regimens from 1993 to 2003.ResultsElevated serum b2M levels were found in 82 patients (35%). According to multivariatelogistic regression analysis, elevated b2M levels were associated with elevatedlactate dehydrogenase (LDH) (p=0.021), age (p=0.029), and number of involvednodal areas (p<0.001). The percentage of elevated b2M levels increased progressivelywith increasing FLIPI scores (17%, 38%, and 63% in the low-, intermediate-, andhigh-risk groups, respectively). Five-year OS was 61% (95% CI, 47-73%) and 89% (95%CI, 82-93%) for patients with elevated vs normal b2M levels respectively (p<0.001).Cox regression analysis showed that b2M level had an independent and stable prognosticvalue (HR=3.0; 95%CI, 1.6-5.7). In a multivariate analysis the impact of b2Mlevel on survival was independent of FLIPI score, with a HR of 2.94 (95% CI, 1.54-5.62).Interpretation and ConclusionsOur results demonstrate that in patients treated in the pre-rituximab era, b2M levelwas an independent prognostic marker in addition to FLIPI score. We thus suggestthat b2M be routinely assessed and tested in future prognostic studies of FL patientstreated with combination chemotherapy and anti-CD20 agents

Amyloid fibrils derived from the apolipoprotein A1 Leu174Ser variant contain elements of ordered helical structure

We recently described a new apolipoprotein A1 variant presenting a Leu174Ser replacement mutation that is associated with a familial form of systemic amyloidosis displaying predominant heart involvement. We have now identified a second unrelated patient with very similar clinical presentation and carrying the identical apolipoprotein A1 mutation. In this new patient the main protein constituent of the amyloid fibrils is the polypeptide derived from the first 93 residues of the protein, the identical fragment to that found in the patient previously described to carry this mutation. The X-ray fiber diffraction pattern obtained from preparations of partially aligned fibrils displays the cross-β reflections characteristic of all amyloid fibrils. In addition to these cross-β reflections, other reflections suggest the presence of well-defined coiled-coil helical structure arranged with a defined orientation within the fibrils. In both cases the fibrils contain a trace amount of full-length apolipoprotein A1 with an apparent prevalence of the wild-type species over the variant protein. We have found a ratio of full-length wild-type to mutant protein in plasma HDL of three to one. The polypeptide 1–93 purified from natural fibrils can be solubilized in aqueous solutions containing denaturants, and after removal of denaturants it acquires a monomeric state that, based on CD and NMR studies, has a predominantly random coil structure. The addition of phospholipids to the monomeric form induces the formation of some helical structure, thought most likely to occur at the C-terminal end of the polypeptide