A quasi-Newton method with Cholesky factorization

A quasi-Newton method for unconstrained minimization is presented, which uses a Cholesky factorization of an approximation to the Hessian matrix. In each step a new row and column of this approximation matrix is determined and its Cholesky factorization is updated. This reduces storage requirements and simplifies the calculation of the search direction. Precautions are taken to hold the approximation matrix positive definite. It is shown that under usual conditions the method converges superlinearly or evenn-step quadratic.     

Reversibility of changes in left and right ventricular geometry and hemodynamics in pulmonary hypertension. Echocardiographic characteristics before and after pulmonary thromboendarterectomy

Pulmonary thromboendarterectomy (PTE) leads to an acute decrease of right ventricular (RV) afterload in patients with chronic thromboembolic pulmonary hypertension. We investigated the changes in right and left ventricular (LV) geometry and hemodynamics by means of transthoracic echocardiography. The prospective study was performed in 14 patients (8 female, 6 male; age 55 +/- 20 years) before and 18 +/- 12 days after PTE. Total pulmonary vascular resistance and systolic pulmonary artery pressure were significantly decreased (PVR: preoperative 986 +/- 318, postoperative 323 +/- 280 dyn x s/cm5, p < 0.05; PAP preoperative 71 +/- 40, postoperative 41 +/- 40 mm Hg + right atrial pressure, p < 0.05). End diastolic and end systolic RV area decreased from 33 +/- 12 to 23 +/- 8 cm2, respectively, from 26 +/- 10 to 16 +/- 6 cm2, p < 0.05. There was an increase in systolic RV fractional area change from 20 +/- 12 to 30 +/- 16%, p < 0.05. RV systolic pressure rise remained unchanged (516 +/- 166 vs. 556 +/- 128 mm Hg/sec). LV ejection fraction remained within normal ranges (64 +/- 16 vs. 62 +/- 12%). Echocardiographically determined cardiac index increased from 2.8 +/- 0.74 to 4.1 +/- 1.74 l/min/m2. A decrease in LV excentricity indices (end diastolic: 1.9 +/- 1 vs. 1.1 +/- 0.3, end systolic: 1.7 +/- 0.6 vs. 1.1 +/- 0.4, p < 0.05) proved a normalization of preoperatively altered septum motion. LV diastolic filling returned to normal limits: (E/A ratio: 0.62 +/- 0.34 vs. 1.3 +/- 0.8; p < 0.05); Peak E velocity: 0.51 +/- 0.34 vs. 0.88 +/- 0.28 m/sec, p < 0.05; Peak A velocity: 0.81 +/- 0.36 vs. 0.72 +/- 0.42 m/sec, ns; E deceleration velocity: 299 +/- 328 vs. 582 +/- 294 cm/sec2, p < 0.05; Isovolumic relaxation time: 134 +/- 40 vs. 83 +/- 38 m/sec, p < 0.05). We could show a marked decrease in RV afterload shortly after PTE with a profound recovery of right ventricular systolic function--even in case of severe pulmonary hypertension. A decrease in paradoxic motion of the interventricular septum and normalization of LV diastolic filling pattern resulted in a significant increase of cardiac index.     

An ergonomic evaluation of VDTs“”

Eight VDTs of different trademarks were analysed in relation to the following properties:

( a) Contrasts of luminance between the screens on the one hand and source documents, as well as other surfaces of the VDT, on the other.

(b) Oscillation degree, sharpness and stability of characters.

( c) Face and legibility of characters.

( d) Dimensions, mobility and reflection degrees of the keyboards.

Special equipment was developed and standardized conditions were applied to the measurements.

The eight VDTs showed essential differences for all the parameters, which might be partially responsible for eye strain and postural complaints. It can be concluded that customers should pay more attention to ergonomic qualities when choosing a VDT. But such an endeavour remains useless if the customer does not, at the same time, look for a proper design of the whole workstation including the working environment.     

A quasi-Newton method for minimization under linear constraints without evaluating any derivatives

In this paper a method is described for solving linearly constrained nonlinear programming problems without evaluating any derivatives of the objective function. The algorithm uses the concept of active constraints and avoids the calculation of derivatives by approximating modified gradients and Hessian matrices by the aid of differences of function values. These approximations are calculated in such a way that the same convergence results are obtained as for any Quasi-Newton method.     

Characterization of the HCN Interaction Partner TRIP8b/PEX5R in the Intracardiac Nervous System of TRIP8b-Deficient and Wild-Type Mice

The tetratricopeptide repeat-containing Rab8b-interacting protein (TRIP8b/PEX5R) is an interaction partner and auxiliary subunit of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are key for rhythm generation in the brain and in the heart. Since TRIP8b is expressed in central neurons but not in cardiomyocytes, the TRIP8b-HCN interaction has been studied intensely in the brain, but is deemed irrelevant in the cardiac conduction system. Still, to date, TRIP8b has not been studied in the intrinsic cardiac nervous system (ICNS), a neuronal network located within epicardial fat pads. In vitro electrophysiological studies revealed that TRIP8b-deficient mouse hearts exhibit increased atrial refractory and atrioventricular nodal refractory periods, compared to hearts of wild-type littermates. Meanwhile, heart rate, sino-nodal recovery time, and ventricular refractory period did not differ between genotypes. Trip8b mRNA was detected in the ICNS by quantitative polymerase chain reaction. RNAscope in situ hybridization confirmed Trip8b localization in neuronal somata and nerve fibers. Additionally, we found a very low amount of mRNAs in the sinus node and atrioventricular node, most likely attributable to the delicate fibers innervating the conduction system. In contrast, TRIP8b protein was not detectable. Our data suggest that TRIP8b in the ICNS may play a role in the modulation of atrial electrophysiology beyond HCN-mediated sino-nodal control of the heart.     

A globally and quadratically convergent algorithm for general nonlinear programming problems

This paper presents an algorithm for the minimization of a nonlinear objective function subject to nonlinear inequality and equality constraints. The proposed method has the two distinguishing properties that, under weak assumptions, it converges to a Kuhn-Tucker point for the problem and under somewhat stronger assumptions, the rate of convergence is quadratic. The method is similar to a recent method proposed by Rosen in that it begins by using a penalty function approach to generate a point in a neighborhood of the optimum and then switches to Robinson's method. The new method has two new features not shared by Rosen's method. First, a correct choice of penalty function parameters is constructed automatically, thus guaranteeing global convergence to a stationary point. Second, the linearly constrained subproblems solved by the Robinson method normally contain linear inequality constraints while for the method presented here, only linear equality constraints are required. That is, in a certain sense, the new method “knows” which of the linear inequality constraints will be active in the subproblems. The subproblems may thus be solved in an especially efficient manner. Preliminary computational results are presented.