Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Hypoxic Pulmonary Vasoconstriction in Humans:Tale or Myth

Hypoxic Pulmonary vasoconstriction (HPV) describes the physiological adaptive process of lungs to preserves systemic oxygenation. It has clinical implications in the development of pulmonary hypertension which impacts on outcomes of patients undergoing cardiothoracic surgery. This review examines both acute and chronic hypoxic vasoconstriction focusing on the distinct clinical implications and highlights the role of calcium and mitochondria in acute versus the role of reactive oxygen species and Rho GTPases in chronic HPV. Furthermore it identifies gaps of knowledge and need for further research in humans to clearly define this phenomenon and the underlying mechanism

Impact of neurocognitive deficits on patient-proxy agreement regarding health-related quality of life in low-grade glioma patients

Purpose Clinical trials in glioma patients with neurocognitive deficits face challenges due to lacking or unreliable patient self-reports on their health-related quality of life (HRQOL). Patient–proxy data could help solve this issue. We determined whether patient–proxy concordance levels were affected by patients’ neurocognitive functioning. Methods Patient and patient-by-proxy HRQOL ratings were assessed via SF-36 and EORTC QLQ-BN20, respectively, in 246 patients. Data on neurocognitive functioning were collected on a subgroup of 195 patients. Patient–proxy agreement was measured using the Bland–Altman limit of agreement, the mean difference, the concordance correlation coefficient (CCC), and the percentage difference (PD, ±0, 5, or 10 points). We defined patients to be cognitively impaired (n = 66) or cognitively intact (n = 129) based on their neurocognitive performance. Results Patients rated their physical function and general health to be better than their proxies did, while at the same time, patients reported more visual disorders, communication deficits, itchy skin, and problems with bladder control. The cognitively impaired subgroup reported poorer physical functioning, more visual disorders, headaches, itchy skin, and issues with bladder control. In the cognitively intact group, no statistical significant differences were observed between patients and proxies. Not surprisingly, Bland–Altman plots revealed a high agreement between the patient and patient-by-proxy rating in all HRQOL domains ranging from 95 to 99 %. The CCC was fairly high in all HRQOL domains (0.37–0.80), and the percentage of perfect agreement (PD ± 0) ranged from 8.5 to 76.8 %. In the cognitively impaired patients, the mean difference between patients and proxies was overall larger, and accordingly, agreement based on Bland–Altman plots was lower. Conclusions The level of agreement between patient and patient-by-proxy ratings of low-grade glioma patients’ HRQOL is generally high. However, patient–proxy agreement is lower in patients with neurocognitive deficits than in patients without neurocognitive deficits