Categorical formulation of quantum algebras

We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between finite-dimensional C*-algebras and certain types of dagger-Frobenius monoids in the category of Hilbert spaces. Using this technology, we recast the spectral theorems for commutative C*-algebras and for normal operators into an explicitly categorical language, and we examine the case that the results of measurements do not form finite sets, but rather objects in a finite Boolean topos. We describe the relevance of these results for topological quantum field theory.Comment: 34 pages, to appear in Communications in Mathematical Physic

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Effect of neuromuscular electrical stimulation on the recovery of people with COVID-19 admitted to the intensive care unit: A narrative review.

The rehabilitation of patients with COVID-19 after prolonged treatment in the intensive care unit is often complex and challenging. Patients may develop a myriad of long-term multi-organ impairments, affecting the respiratory, cardiac, neurological, digestive and musculoskeletal systems. Skeletal muscle dysfunction of respiratory and limb muscles, commonly referred to as intensive care unit acquired weakness, occurs in approximately 40% of all patients admitted to intensive care. The impact on mobility and return to activities of daily living is severe. Furthermore, many patients experience ongoing symptoms of fatigue, weakness and shortness of breath, in what is being described as "long COVID". Neuromuscular electrical stimulation is a technique in which small electrical impulses are applied to skeletal muscle to cause contractions when voluntary muscle contraction is difficult or impossible. Neuromuscular electrical stimulation can prevent muscle atrophy, improve muscle strength and function, maintain blood flow and reduce oedema. This review examines the evidence, current guidelines, and proposed benefits of using neuromuscular electrical stimulation with patients admitted to the intensive care unit. Practical recommendations for using electrical muscle stimulation in patients with COVID-19 are provided, and suggestions for further research are proposed

Campaign 9 of the K2 Mission: Observational Parameters, Scientific Drivers, and Community Involvement for a Simultaneous Space- and Ground-based Microlensing Survey

K2's Campaign 9 (K2C9) will conduct a ~3.7 deg2 survey toward the Galactic bulge from 2016 April 22 through July 2 that will leverage the spatial separation between K2 and the Earth to facilitate measurement of the microlens parallax ${\pi }_{{\rm{E}}}$ for $\gtrsim 170$ microlensing events. These will include several that are planetary in nature as well as many short-timescale microlensing events, which are potentially indicative of free-floating planets (FFPs). These satellite parallax measurements will in turn allow for the direct measurement of the masses of and distances to the lensing systems. In this article we provide an overview of the K2C9 space- and ground-based microlensing survey. Specifically, we detail the demographic questions that can be addressed by this program, including the frequency of FFPs and the Galactic distribution of exoplanets, the observational parameters of K2C9, and the array of resources dedicated to concurrent observations. Finally, we outline the avenues through which the larger community can become involved, and generally encourage participation in K2C9, which constitutes an important pathfinding mission and community exercise in anticipation of WFIRST

The Spitzer Microlensing Program As A Probe For Globular Cluster Planets: Analysis Of Ogle-2015-BLG-0448

The microlensing event OGLE-2015-BLG-0448 was observed by Spitzer and lay within the tidal radius of the globular cluster NGC 6558. The event had moderate magnification and was intensively observed, hence it had the potential to probe the distribution of planets in globular clusters. We measure the proper motion of NGC 6558 (${{\boldsymbol{\mu }}}_{\mathrm{cl}}(N,E)=(+0.36\pm 0.10,+1.42\pm 0.10)\;{\rm{mas}}\;{{\rm{yr}}}^{-1}$) as well as the source and show that the lens is not a cluster member. Even though this particular event does not probe the distribution of planets in globular clusters, other potential cluster lens events can be verified using our methodology. Additionally, we find that microlens parallax measured using Optical Gravitational Lens Experiment (OGLE) photometry is consistent with the value found based on the light curve displacement between the Earth and Spitzer

NMR studies of glucose and glutamine metabolism in mammalian cells

SIGLEAvailable from British Library Document Supply Centre- DSC:D181942 / BLDSC - British Library Document Supply CentreGBUnited Kingdo