Notes on the Sum-Rank Weight of a Matrix with Restricted Rank

These notes cover a few calculations regarding the sum-rank weight of a matrix in relation to its rank. In particular, a formula and lower bounds are given on the probability that a matrix of rank $t$ consisting of $\ell$ blocks has sum-rank weight $\ell t$

Withdrawal-induced delirium associated with a benzodiazepine switch: a case report

<p>Abstract</p> <p>Introduction</p> <p>Introduced in the early 1960s, diazepam remains among the most frequently prescribed benzodiazepine-type sedatives and hypnotics. Patients with chronic use of short-acting benzodiazepines are frequently switched to diazepam because the accumulating, long-acting metabolite, N-desmethyl-diazepam, prevents benzodiazepine-associated withdrawal symptoms, which can occur during trough plasma levels of short-acting benzodiazepines. Although mild to moderate withdrawal symptoms are frequently observed during benzodiazepine switching to diazepam, severe medical complications associated with this treatment approach have thus far not been reported.</p> <p>Case presentation</p> <p>A 64-year-old female Caucasian with major depression, alcohol dependence and benzodiazepine dependence was successfully treated for depression and, after lorazepam-assisted alcohol detoxification, was switched from lorazepam to diazepam to facilitate benzodiazepine discontinuation. Subsequent to the benzodiazepine switch, our patient unexpectedly developed an acute delirious state, which quickly remitted after re-administration of lorazepam. A newly diagnosed early form of mixed dementia, combining both vascular and Alzheimer-type lesions, was found as a likely contributing factor for the observed vulnerability to benzodiazepine-induced withdrawal symptoms.</p> <p>Conclusion</p> <p>Chronic use of benzodiazepines is common in the elderly and a switch to diazepam often precedes benzodiazepine discontinuation trials. However, contrary to common clinical practice, benzodiazepine switching to diazepam may require cross-titration with slow tapering of the first benzodiazepine to allow for the build-up of N-desmethyl-diazepam, in order to safely prevent severe withdrawal symptoms. Alternatively, long-term treatment with low doses of benzodiazepines may be considered, especially in elderly patients with chronic use of benzodiazepines and proven vulnerability to benzodiazepine-associated withdrawal symptoms.</p

Chronic benzodiazepine use in general practice patients with depression: an evaluation of controlled treatment and taper-off: report on behalf of the Dutch Chronic Benzodiazepine Working Group.

BACKGROUND: Many patients with depression take benzodiazepine drugs long term despite the absence of continuing therapeutic value. AIMS: To evaluate a treatment programme involving gradual discontinuation with or without simultaneous selective serotonin reuptake inhibitor (SSRI) prescribing and to determine the long-term outcome after benzodiazepine withdrawal. METHOD: Patients went through three phases - change to an equivalent dose of diazepam; subsequent randomisation to either 20 mg of paroxetine or placebo; and gradual reduction of diazepam in depression-free patients - with a follow-up after 2 or 3 years. RESULTS: A total of 230 patients were recruited and 75% in the paroxetine group and 61% in the placebo group were successfully treated after 6 weeks (P:=0.067). After 2 or 3 years 13% of patients were still benzodiazepine free: 26% of those who had successfully tapered off benzodiazepine and 6% of the total group. CONCLUSIONS: Transfer to diazepam followed by gradual withdrawal is an effective way of discontinuing chronic benzodiazepine use. The addition of SSRI treatment is of limited value

The long-term outcome of a benzodiazepine discontinuation programme in depressed outpatients.

Item does not contain fulltextOBJECTIVE: To assess longitudinally the prescription of psychotropic drugs in depressed patients after they participated in a benzodiazepine discontinuation programme. METHODS: Two hundred and thirty depressed patients on chronic benzodiazepine therapy took part in a discontinuation programme conducted in 36 general practices. After 2.3 years (S.D.=0.65, range 0.1-3.6) medical records were reviewed. RESULTS: Follow-up was achieved for 207 (90%) patients. Twenty-five (12%) patients remained benzodiazepine free during the full follow-up period. The majority (n=181, 87%) was prescribed benzodiazepines at an average of 13 (+/-14) mg of diazepam equivalents for 537 (+/-375) days. Fifty-five (74% of 74) of the successfully discontinued patients restarted benzodiazepine therapy. Sixty-eight (33%) patients were prescribed benzodiazepines during the whole follow-up period. Successful taper predicted no or lower subsequent benzodiazepine prescription rates (OR=7.3; 95% CI: 2-16). No influence of GP policy towards benzodiazepine prescription could be detected (P=0.275). Antidepressants were prescribed in 115 (55%) patients for an average duration of 476 (+/-360) days. There was no difference in benzodiazepine prescription (dosage, duration) between patients who had or had not been prescribed an antidepressant. LIMITATIONS: Patients were not been diagnosed systematically during the follow-up period. CONCLUSIONS: If measured longitudinally, the rate of benzodiazepine prescription after discontinuation is much higher than reported in previous studies that have measured this cross-sectionally. Successful discontinuation is a strong predictor of modest or no future benzodiazepine prescription. Two-thirds of patients altered their benzodiazepine usage after taking part in a discontinuation programme. Treatment with antidepressants does not seem to influence benzodiazepine prescription. Patients' request (not GPs'policy) seems to be an important factor in continuing or resuming benzodiazepine prescription