The Riesz representation theorem and weak∗ compactness of semimartingales

We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterisation of the strongest topology on the Skorokhod space for which these results are true.

Lipid Headgroup Charge and Acyl Chain Composition Modulate Closure of Bacterial β-Barrel Channels

The outer membrane of Gram-negative bacteria contains β-barrel proteins that form high-conducting ion channels providing a path for hydrophilic molecules, including antibiotics. Traditionally, these proteins have been considered to exist only in an open state so that regulation of outer membrane permeability was accomplished via protein expression. However, electrophysiological recordings show that β-barrel channels respond to transmembrane voltages by characteristically switching from a high-conducting, open state, to a so-called ‘closed’ state, with reduced permeability and possibly exclusion of large metabolites. Here, we use the bacterial porin OmpF from E. coli as a model system to gain insight on the control of outer membrane permeability by bacterial porins through the modulation of their open state. Using planar bilayer electrophysiology, we perform an extensive study of the role of membrane lipids in the OmpF channel closure by voltage. We pay attention not only to the effects of charges in the hydrophilic lipid heads but also to the contribution of the hydrophobic tails in the lipid-protein interactions. Our results show that gating kinetics is governed by lipid characteristics so that each stage of a sequential closure is different from the previous one, probably because of intra- or intermonomeric rearrangements.

Prospective Assessment of the Negative Pressure Wound Therapy of the Open Abdomen

Open abdomen (OA) is a surgical approach, that emerged in last 15 years, with its management being complicated, timely and financially demanding, burdened with high morbidity and mortality. In recent years, several publications proved superiority of usage of negative pressure wound therapy (NPWT) over usage of conventional temporary abdominal closure techniques in treatment of open abdomen. Different aspects of treatment of OA with NPWT remain to be assessed and stated.Authors of the paper prospectively assessed group of 48 patients with OA, managed by one surgeon with NPWT between 2006-2014, assessing mortality and morbidity in the group stratified by indication for OA, type of sequential closure of OA, presence and management of concomitant enteroatmospheric fistula (EAF), maximal values of C-reactive protein (CRP) and Procalcitonine (PCT), and initial body mass index (BMI). Mortality of the whole group was 35.41%, rate of fascial closure 45.83% and rate of the wound closure 83.33%. Incidence of the fistula was 37.5%, of these 66.67% were successfully locally managed. Incidence of fascial closure without use of sequential closure was significantly lower as opposed to use of different techniques of sequential closure.Unsuccessful local management of EAF is significant predictor of mortality. All other data were not found to be statistically significant. Identifying specific aspects of treatment of OA by NPWT, significantly improving outcomes, and adhering to these aspects in clinical practice will further ameliorate outcomes.

C-DENSE INJECTIVITY IN Act-S

To study mathematical notions, such as injectivity with respect to the class [Formula: see text] of (mono)morphisms in a category [Formula: see text], one needs to have some categorical and algebraic information about the pair ([Formula: see text], [Formula: see text]). In this paper, we take [Formula: see text] to be the category Act-S of acts over a semigroup S, C to be an arbitrary closure operator in the category Act-S, and [Formula: see text] to be the class of C-dense monomorphisms resulting from a closure operator C and first study some categorical properties of the pair (Act-S, [Formula: see text]). Then injectivity with respect to the class of C-dense monomorphisms is studied. The class of sequentially dense monomorphisms resulting from a special closure operator (sequential closure operator) and injectivity with respect to this class of monomorphisms have been studied by Giuli, Ebrahimi, Mahmoudi and the author. Some of these results generalize some of the results about the class of sequentially dense monomorphisms.