Role of environmental correlations in the non-Markovian dynamics of a spin system

We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.

Propagation of nonclassical correlations across a quantum spin chain

We study the transport of quantum correlations across a chain of interacting spin-1/2 particles. As a quantitative figure of merit, we choose a symmetric version of quantum discord and compare it with the transported entanglement, addressing various operating regimes of the spin medium. Discord turns out to be better transported for a wide range of working points and initial conditions of the system. We relate this behavior to the efficiency of propagation of a single excitation across the spin chain. Moreover, we point out the role played by a magnetic field in the dynamics of discord in the effective channel embodied by the chain. Our analysis can be interestingly extended to transport processes in more complex networks and the study of nonclassical correlations under general quantum channels.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

Discrete Conditional Phase-type model (DC_Ph) for patient waiting time with a logistic regression component to predict patient admission to hospital

Discrete Conditional Phase-type (DC-Ph) models are a family of models which represent skewed survival data conditioned on specific inter-related discrete variables. The survival data is modeled using a Coxian phase-type distribution which is associated with the inter-related variables using a range of possible data mining approaches such as Bayesian networks (BNs), the Naïve Bayes Classification method and classification regression trees. This paper utilizes the Discrete Conditional Phase-type model (DC-Ph) to explore the modeling of patient waiting times in an Accident and Emergency Department of a UK hospital. The resulting DC-Ph model takes on the form of the Coxian phase-type distribution conditioned on the outcome of a logistic regression model.

Angular correlations in radiative cascades following resonant electron capture by highly charged ions

We investigate the angular correlations between the photons emitted in the dielectronic recombination (DR) of initially hydrogenlike heavy ions. The theoretical analysis is performed based on a density-matrix approach and Dirac's relativistic theory. Special emphasis has been placed upon the effects of the higher-order, nondipole terms in the expansion of the electron-photon interaction. To illustrate these effects, we present and discuss detailed calculations for K-LL DR of initially hydrogenlike xenon, gold, and uranium. These computations show that the angular correlations are significantly affected by interference between the leading electric-dipole (E1) and the magnetic-quadrupole (M2) transitions.

Dynamical role of system-environment correlations in non-Markovian dynamics

We analyze the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009)], we unveil a fundamental connection between non-Markovian behavior and dynamics of system-environment correlations. We derive an upper bound to the rate of change of the distinguishability between different states of the system that explicitly depends on the establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight into the mechanisms triggering non-Markovian evolution. © 2012 American Physical Society.

The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

Computational techniques for a simple theory of conditional preferences

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences.

Structure-Phenotype Correlations of Human CYP21A2 Mutations in Congenital Adrenal Hyperplasia

Congenital Adrenal Hyperplasia (CAH) is a family of autosomal recessive disorders involving impaired synthesis of cortisol from cholesterol by adrenal cortex. The predominant causes of the disorder are mutations in the CYP21A2 gene that encodes a Cytochrome P450 21-hydroxylase enzyme, which is central to steroidogenesis. The severity of the disease depends upon the extent of impaired enzymatic activity and can be classified under severe Classical form or the mild Non-Classical form, Molecular characterisation of CYP21A2 mutations can be used to predict clinical phenotype and disease severity based upon changes it brings in 21-hydroxylase enzyme structure. A humanized model of CYP21A2 has been used to map and investigate the structural role of all known disease-causing mutations. A structural explanation of clinical manifestation allows us to put forward criteria that might allow the prediction of clinical severity of the disease.

A Longitudinal Study of Stargardt Disease: Clinical and Electrophysiologic Assessment, Progression, and Genotype Correlations

Purpose: To investigate the clinical and electrophysiologic natural history of Stargardt disease and correlate with the genotype. Design: Cohort study of 59 patients. Methods: Clinical history, examination, and electrophysiologic assessment were undertaken in a longitudinal survey. Patients were classified into 3 groups based on electrophysiologic findings, as previously published: Group 1 had dysfunction confined to the macula; Group 2 had macular and generalized cone system dysfunction; and Group 3 had macular and both generalized cone and rod system dysfunction. At baseline, there were 27 patients in Group 1, 17 in Group 2, and 15 in Group 3. Amplitude reduction of >50% in the relevant electroretinogram (ERG) component or a peak time shift of >3 ms for the 30 Hz flicker ERG or bright flash a-wave was considered clinically significant ERG deterioration. Molecular screening of ABCA4 was undertaken. Results: The mean age at baseline was 31.7 years, with the mean follow-up interval being 10.5 years. A total of 22% of patients from Group 1 showed ERG group transition during follow-up, with 11% progressing to Group 2 and 11% to Group 3. Forty-seven percent of patients in Group 2 progressed to Group 3. There was clinically significant ERG deterioration in 54% of all subjects: 22% of Group 1, 65% of Group 2, and 100% of Group 3. At least 1 disease-causing ABCA4 variant was identified in 47 patients. Conclusions: All patients with initial rod ERG involvement demonstrated clinically significant electrophysiologic deterioration; only 20% of patients with normal full-field ERGs at baseline showed clinically significant progression. Such data assist counseling by providing more accurate prognostic information and are also highly relevant in the design, patient selection, and monitoring of potential therapeutic interventions. © 2013 Elsevier Inc. All rights reserved.