On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model

The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP criterion value to its infimum will exhibit the features of a so-called “degeneracy”. That is, the parameter matrices become nearly rank deficient and the Euclidean norm of some factors tends to infinity. We also show that the CP criterion function does attain its infimum if one of the parameter matrices is constrained to be column-wise orthonormal

Mitral valve surgery for mitral regurgitation caused by Libman-Sacks endocarditis: a report of four cases and a systematic review of the literature

Libman-Sacks endocarditis of the mitral valve was first described by Libman and Sacks in 1924. Currently, the sterile verrucous vegetative lesions seen in Libman-Sacks endocarditis are regarded as a cardiac manifestation of both systemic lupus erythematosus (SLE) and the antiphospholipid syndrome (APS). Although typically mild and asymptomatic, complications of Libman-Sacks endocarditis may include superimposed bacterial endocarditis, thromboembolic events, and severe valvular regurgitation and/or stenosis requiring surgery. In this study we report two cases of mitral valve repair and two cases of mitral valve replacement for mitral regurgitation (MR) caused by Libman-Sacks endocarditis. In addition, we provide a systematic review of the English literature on mitral valve surgery for MR caused by Libman-Sacks endocarditis. This report shows that mitral valve repair is feasible and effective in young patients with relatively stable SLE and/or APS and only localized mitral valve abnormalities caused by Libman-Sacks endocarditis. Both clinical and echocardiographic follow-up after repair show excellent mid- and long-term results

Silver Ring Splints Improve Dexterity in Patients with Rheumatoid Arthritis.

Objective: To study the effect of Silver Ring Splints (SRSs) on hand function in patients with rheumatoid arthritis (RA). - Methods: RA patients with stable disease and finger deformities eligible for splinting received 1 or more SRSs. Primary outcome was dexterity, which was measured with the Sequential Occupational Dexterity Assessment (SODA). Secondary outcome measures were self-reported hand function (Dutch Arthritis Impact Measurement Scales 2), hand pain, grip and pinch strength, Disease Activity Score in 28 joints (DAS28), and patient satisfaction. - Results: Seventeen patients (median age 65 years; median disease duration 21 years) received a total of 72 SRSs. After 1 year, 48 SRSs were regularly used. Two patients dropped out because of adverse events related to SRSs. In the remaining 15 patients, SODA dexterity scores increased significantly (median 71 at baseline, 81 at 3 months, and 85 at 12 months), Wilcoxon signed ranks test P = 0.005 and P = 0.026. DAS28 scores did not change at 3 months and improved slightly after 12 months (-0.5; P = 0.019). Grip strength, self-reported hand function, and hand pain showed no significant changes. Eleven patients stated they would continue using their splints. - Conclusion: SRSs can improve dexterity in selected patients with rheumatoid hand deformities. For a satisfactory result, careful patient preassessment and optimal adjustment of SRSs are essential

Treating to the target of remission in early rheumatoid arthritis is cost-effective: results of the DREAM registry

Background Where health economic studies are frequently performed using modelling, with input from randomized controlled trials and best guesses, we used real-life data to analyse the costeffectiveness and cost-utility of a treatment strategy aiming to the target of remission compared to usual care in early rheumatoid arthritis (RA). Methods We used real-life data from comparable cohorts in the Dutch Rheumatoid Arthritis Monitoring (DREAM) registry: the DREAM remission induction cohort (treat-to-target, T2T) and the Nijmegen early RA inception cohort (usual care, UC). Both cohorts were followed prospectively using the DREAM registry methodology. All patients fulfilled the American College of Rheumatology criteria for RA and were included in the cohort at the time of diagnosis. The T2T cohort was treated according to a protocolised strategy aiming at remission (Disease Activity Score in 28 joints (DAS28) < 2.6). The UC cohort was treated without DAS28-guided treatment decisions. EuroQol-5D utility scores were estimated from the Health Assessment Questionnaire. A health care perspective was adopted and direct medical costs were collected. The incremental cost effectiveness ratio (ICER) per patient in remission and incremental cost utility ratio (ICUR) per quality-adjusted life year (QALY) gained were calculated over two and three years of follow-up. Results Two year data were available for 261 T2T patients and 213 UC patients; an extended followup of three years was available for 127 and 180 patients, respectively. T2T produced higher remission percentages and a larger gain in QALYs than UC. The ICER was