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.

Two Views of ‘Subordination’: the Personal Scope of Employment Discrimination Law in Jivraj v Hashwani

In Jivraj v Hashwani, the Supreme Court considered what requirements are necessary for a relationship to be considered as an employment relationship for the purposes of determining the scope of domestic employment discrimination law. The Court held that an element of subordination was necessary for the relationship to be considered employment under a contract personally to do work. This article discusses what the Court in Jivraj meant by this requirement, contrasting two differing views of subordination. It examines some implications of the decision for the relationship between employment law and anti-discrimination law, and for recent debates on the scope of employment law more generally.

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.

Shock avoidance by discrimination learning in the shore crab (Carcinus maenas) is consistent with a key criterion for pain

Nociception allows for immediate reflex withdrawal whereas pain allows for longer-term protection via rapid learning. We examine here whether shore crabs placed within a brightly lit chamber learn to avoid one of two dark shelters when that shelter consistently results in shock. Crabs were randomly selected to receive shock or not prior to making their first choice and were tested again over 10 trials. Those that received shock in trial 2, irrespective of shock in trial 1, were more likely to switch shelter choice in the next trial and thus showed rapid discrimination. During trial 1, many crabs emerged from the shock shelter and an increasing proportion emerged in later trials, thus avoiding shock by entering a normally avoided light area. In a final test we switched distinctive visual stimuli positioned above each shelter and/or changed the orientation of the crab when placed in the chamber for the test. The visual stimuli had no effect on choice, but crabs with altered orientation now selected the shock shelter, indicating that they had discriminated between the two shelters on the basis of movement direction. These data, and those of other recent experiments, are consistent with key criteria for pain experience and are broadly similar to those from vertebrate studies. © 2013. Published by The Company of Biologists Ltd.

Chiral thiouronium salts: synthesis, characterisation and application in NMR enantio-discrimination of chiral oxoanions

Chiral thioureas and functionalised chiral thiouronium salts were synthesised starting from the relatively cheap and easily available chiral amines: (S)-methylbenzylamine and rosin-derived (+)-dehydroabietylamine. The introduction of a delocalised positive charge to the thiourea functionality, by an alkylation reaction at the sulfur atom, enables dynamic rotameric processes: hindered rotations about the delocalised CN and CS bonds. Hence, four different rotamers/isomers may be recognised: syn-syn, syn-anti, anti-syn and anti-anti. Extensive H-1 and C-13 NMR studies have shown that in hydrogen-bond acceptor solvents, such as perdeuteriated dimethyl sulfoxide, the syn-syn conformation is preferable. On the other hand, when using non-polar solvents, such as CDCl3, the mixture of syn-syn and syn-anti isomers is detectable, with an excess of the latter. Apart from this, in the case of S-butyl-N,N'-bis(dehydroabietyl)thiouronium ethanoate in CDCl3, the H-1 NMR spectrum revealed that strong bifurcated hydrogen bonding between the anion and the cation causes global rigidity without signs of hindered rotamerism observable on the NMR time scale. This suggested that these new salts might be used as NMR discriminating agents for chiral oxoanions, and are indeed more effective than their archetypal guanidinium analogues or the neutral thioureas. The best results in recognition of a model substrate, mandelate, were obtained with S-butyl-N,N'-bis(dehydroabietyl) thiouronium bistriflamide. It was confirmed that the chiral recognition occurred not only for carboxylates but also for sulfonates and phosphonates. Further H-1 NMR studies confirmed a 1 : 1 recognition mode between the chiral agent (host) and the substrate (guest); binding constants were determined by H-1 NMR titrations in solutions of DMSO-d(6) in CDCl3. It was also found that the anion of the thiouronium salt had a significant influence on the recognition process: anions with poor hydrogen-bond acceptor abilities led to the best discrimination. The presence of host-guest hydrogen bonding was confirmed in the X-ray crystal structure of S-butyl-N,N'-bis(dehydroabietyl)thiouronium bromide and by computational studies (density functional theory).