In AdS/CFT we consider a class of bulk geometric quantities inside the entanglement wedge called reflected minimal surfaces. The areas of these surfaces are dual to the entanglement entropy associated to a canonical purification (the GNS state) that we dub the reflected entropy. From the bulk point of view, we show that half the area of the reflected minimal surface gives a reinterpretation of the notion of the entanglement wedge cross-section. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an explicit holographic construction of the canonical purification, introduced by Engelhardt and Wall; the reflected minimal surfaces are simply RT surfaces in this new spacetime. We contrast our results with the entanglement of purification conjecture, and finally comment on the continuum limit where we find a relation to the split property: the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor introduced by Doplicher and Longo.

Frailty is associated with increased mortality both before and after liver transplantation (LT). There are no standardized exercise programs, in particular home‐based exercise programs (HBEPs), for patients awaiting LT. The aim was to investigate the feasibility of such a program in patients awaiting LT. Patients were randomly selected from the Birmingham LT waiting list and provided with a 12‐week HBEP, including average daily step (ADS) targets and twice‐weekly resistance exercises. Feasibility was based on patient eligibility (≥66% of waiting list), target recruitment (≥90% of n = 20), safety (no related serious adverse events), and adherence (≥66% adherence to 6‐week HBEP). Measures of aerobic (incremental shuttle walk test [ISWT], ADS), functional capacity (short physical performance battery test [SPPBT]), and health‐related quality of life (EuroQol 5‐Dimension 5‐Level (EQ‐5D‐5L) and hospital anxiety and depression score [HADS]) were taken at baseline and at 6 and 12 weeks. 18 patients (50% male; median age, 55 years) were recruited. All domains of the study feasibility criteria were met. ISWT improved after 6 weeks (50 m; P ≤ 0.01) and 12 weeks (210 m; P ≤ 0.01), despite withdrawal of the telephone health calls. Similarly, improvements were seen in ADS (2700/day; P ≤ 0.01) and the SPPBT (2.5; P = 0.02) after 12 weeks. There was no difference in HADS (median difference [MD] –3; P = 0.69), but EQ‐5D‐5L after 12 weeks (17.5%; P = 0.04). In conclusion, a 12‐week HBEP, incorporating both easy‐to‐apply resistance and aerobic exercises, is safe and feasible in patients awaiting LT. Measures of aerobic and functional capacity demonstrate trends toward improvement that warrant further investigation in a randomized controlled trial.

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory.Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

Early surgery to avoid PBD is possible within the NHS. By reducing the time to surgery it appears that more patients undergo potentially curative resection. It is desirable to understand why surgery without PBD is not performed routinely as are the development of strategies to support its more widespread practice.