The existence problem for dynamics of dissipative systems in quantum probability

Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $\delta$ is densely defined in a unital $C^{\ast}$-algebra $\mathfrak{A}$. The identity element in ${\frak A}$ is also in the domain of $\delta$. Completely dissipative maps $\delta$ are defined by the requirement that the induced maps, $(a_{ij})\to (\delta (a_{ij}))$, are dissipative on the $n$ by $n$ complex matrices over ${\frak A}$ for all $n$. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of ${\frak A}$ is injective, we show the existence of an extension of $\delta$ which is the infinitesimal generator of a quantum dynamical semigroup of completely positive maps in the von Neumann algebra. If $\delta$ is a given well-behaved *-derivation, then we show that each of the maps $\delta$ and $-\delta$ is completely dissipative.Comment: 24 pages, LaTeX/REVTeX v. 4.0, submitted to J. Math. Phys.; PACS 02., 02.10.Hh, 02.30.Tb, 03.65.-w, 05.30.-

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

Background: Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936. Findings: Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79). Interpretation: In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research

Tocilizumab in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Background: In this study, we aimed to evaluate the effects of tocilizumab in adult patients admitted to hospital with COVID-19 with both hypoxia and systemic inflammation. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. Those trial participants with hypoxia (oxygen saturation <92% on air or requiring oxygen therapy) and evidence of systemic inflammation (C-reactive protein ≥75 mg/L) were eligible for random assignment in a 1:1 ratio to usual standard of care alone versus usual standard of care plus tocilizumab at a dose of 400 mg–800 mg (depending on weight) given intravenously. A second dose could be given 12–24 h later if the patient's condition had not improved. The primary outcome was 28-day mortality, assessed in the intention-to-treat population. The trial is registered with ISRCTN (50189673) and ClinicalTrials.gov (NCT04381936). Findings: Between April 23, 2020, and Jan 24, 2021, 4116 adults of 21 550 patients enrolled into the RECOVERY trial were included in the assessment of tocilizumab, including 3385 (82%) patients receiving systemic corticosteroids. Overall, 621 (31%) of the 2022 patients allocated tocilizumab and 729 (35%) of the 2094 patients allocated to usual care died within 28 days (rate ratio 0·85; 95% CI 0·76–0·94; p=0·0028). Consistent results were seen in all prespecified subgroups of patients, including those receiving systemic corticosteroids. Patients allocated to tocilizumab were more likely to be discharged from hospital within 28 days (57% vs 50%; rate ratio 1·22; 1·12–1·33; p<0·0001). Among those not receiving invasive mechanical ventilation at baseline, patients allocated tocilizumab were less likely to reach the composite endpoint of invasive mechanical ventilation or death (35% vs 42%; risk ratio 0·84; 95% CI 0·77–0·92; p<0·0001). Interpretation: In hospitalised COVID-19 patients with hypoxia and systemic inflammation, tocilizumab improved survival and other clinical outcomes. These benefits were seen regardless of the amount of respiratory support and were additional to the benefits of systemic corticosteroids. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research

Development of predator defences in fishes

A variety of development characteristics, morphological, behavioural, and experiential, contribute to the extreme vulnerability of young fishes to predation. The influence of these characteristics is complicated by the fact that the larval period is one of substantial and rapid change. Yet survival is the ultimate goal;-it is only by reaching maturity that individual fish have the opportunity to reproduce. With such high stakes it is not surprising that predator defences are of major importance during all phases of life. Developmental constraints may limit the defensive options for young fishes. Avoidance behaviours, which reduce the likelihood of encountering a predator or of being attacked by it, are particulaly evident in the youngest stages. Here size, coloration and dispersal are used to help elude the predator's attention. As fishes grow and acquire greater morphological and behavioural sophistication, there is more scope for predator evasion when avoidance fails. Older fishes are increasingly able to respond to external stimuli and can detect and react to predators or join conspecifics in common defence (schooling). Behavioural development is not simply a consequence of growth and the concomitant physical alterations of the body; it is also mediated by experience that comes through interaction with the physical and biotic environment. Predispositions to respond to experience may be a product of evolutionary history. Although mortality rates decline markedly with development and maturity, changes in size or behaviour can render fishes vulnerable to new suites of predators. Effective predator avoidance can compromise other activities, such as foraging, and individuals may be forced to reconcile conflicting demands. Developmental niche shifts that occur, for example, when certain size classes take refuge in less profitable feeding habitats, represent one such trade-off. Niche shifts may also be mediated by the influence of the programme for morphological development on sensory or behavioural capabilities. In addition to all of these developmental consderations, natural variations in environmental conditions - such as temperature, photoperiod, predator density and variety, and presence of alternative prey - represent additional challenges to predator defences during the rite of passage from birth to reproduction.</p