Choi matrices revisited, II

In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between $k$-superpositivity and Schmidt number $\le k$ as well as $k$-positivity and $k$-block-positivity. We also compare de Pillis' definition [Pacific J. Math. 23 (1967), 129--137] and Choi's definition [Linear Alg. Appl. 10 (1975), 285--290], which arise from different bilinear forms.Comment: 17 page

Infinite dimensional analogues of Choi matrices

For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor is completely positive. They are also useful to characterize positivity of maps as well as complete positivity. It turns out that such correspondences are possible for every normal completely bounded map if and only if the factor is of type I. As an application, we provide criteria for Schmidt numbers of normal positive functionals in terms of Choi matrices of $k$-positive maps, in infinite dimensional cases. We also define the notion of $k$-superpositive maps, which turns out to be equivalent to the property of $k$-partially entanglement breaking.Comment: 20 page

Association between volume status assessed by bioelectrical impedance analysis, lung ultrasound, or weight change and mortality in patients with sepsis-associated acute kidney injury receiving continuous kidney replacement therapy

Background Fluid overload is an independent risk factor of mortality in patients with acute kidney injury (AKI) receiving continuous kidney replacement therapy (CKRT). However, the association between fluid status, as assessed by bioelectrical impedance analysis (BIA) or lung ultrasound, and survival in patients with AKI requiring CKRT has not been established. Methods We analyzed 36 participants with sepsis-associated AKI who received CKRT at a tertiary hospital. The main exposures were volume surrogates: 1) overhydration normalized by extracellular water (OH/ECW, L/L) assessed by BIA, 2) the number of B-lines measured by lung ultrasound, and 3) weight change ([body weight at CKRT initiation – body weight at admission] × 100/body weight at admission). The primary outcome was the 28-day mortality. Results Seventeen participants (47.2%) died within 28 days. There were no significant correlations between OH/ECW and weight change (R2 = 0.040, p = 0.24), number of B-lines and OH/ECW (R2 = 0.056, p = 0.16), or weight change and number of B-lines (R2 = 0.014, p = 0.49). Kaplan-Meier analyses revealed that patients in the highest tertile of OH/ECW showed a significantly lower cumulative 28-day survival probability than the others (the lowest + middle tertiles). The survival probability of participants in the highest tertile of the number of B-lines or weight change did not differ from that of their counterparts. In a multivariate Cox proportional hazard model, the hazard ratio for the highest tertile of OH/ECW was 3.83 (95% confidence interval, 1.04–14.03). Conclusion Volume overload assessed using BIA (OH/ECW) was associated with the 28-day survival rate in patients with sepsis-associated AKI who received CKRT