Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Nutrient partitioning during treatment of tuberculosis: gain in body fat mass but not in protein mass

Background: Tuberculosis is an important cause of wasting. The functional consequences of wasting and recovery may depend on the distribution of lost and gained nutrient stores between protein and fat masses. Objective: The goal was to study nutrient partitioning, ie, the proportion of weight change attributable to changes in fat mass (FM) versus protein mass (PM), during anti mycobacterial treatment. Design: Body-composition measures were made of 21 men and 9 women with pulmonary tuberculosis at baseline and after 1 and 6 mo of treatment. All subjects underwent dual-energy X-ray absorptiometry and deuterium bromide dilution tests, and a four-compartment model of FM, total body water (TBW), bone minerals (BM), and PM was derived. The ratio of PM to FM at any time was expressed as the energy content (p-ratio). Changes in the p-ratio were related to disease severity as measured by radiologic criteria. Results: Patients gained 10% in body weight (P < 0.001) from baseline to month 6. This was mainly due to a 44% gain in FM (P < 0.001); PM, BM, and TBW did not change significantly. Results were similar in men and women. The p-ratio decreased from baseline to month 1 and then fell further by month 6. Radiologic disease severity was not correlated with changes in the p-ratio. Conclusions: Microbiological cure of tuberculosis does not restore PM within 6 mo, despite a strong anabolic response. Change in the p-ratio is a suitable parameter for use in studying the effect of disease on body composition because it allows transformation of such effects into a normal distribution across a wide range of baseline proportion between fat and protein mass.

Equivalence between two-mode spin squeezed states and pure entangled states with equal spin

We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and provide a counterexample to the generalization of this result to two subsystems of unequal spin.

Using continuous measurement to protect a universal set of quantum gates within a perturbed decoherence-free subspace

We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits. Using second-order perturbation theory and a measuring device modelled by an infinite set of harmonic oscillators, simply coupled to the system, we show that continuous observation of the coupling agent induces inhibition of the decoherence due to spurious perturbations. We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information.

Communicating continuous quantum variables between different Lorentz frames

We show how to communicate Heisenberg-limited continuous (quantum) variables between Alice and Bob in the case where they occupy two inertial reference frames that differ by an unknown Lorentz boost. There are two effects that need to be overcome: the Doppler shift and the absence of synchronized clocks. Furthermore, we show how Alice and Bob can share Doppler-invariant entanglement, and we demonstrate that the protocol is robust under photon loss.

Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?

In cell lifespan studies the exponential nature of cell survival curves is often interpreted as showing the rate of death is independent of the age of the cells within the population. Here we present an alternative model where cells that die are replaced and the age and lifespan of the population pool is monitored until a, steady state is reached. In our model newly generated individual cells are given a determined lifespan drawn from a number of known distributions including the lognormal, which is frequently found in nature. For lognormal lifespans the analytic steady-state survival curve obtained can be well-fit by a single or double exponential, depending on the mean and standard deviation. Thus, experimental evidence for exponential lifespans of one and/or two populations cannot be taken as definitive evidence for time and age independence of cell survival. A related model for a dividing population in steady state is also developed. We propose that the common adoption of age-independent, constant rates of change in biological modelling may be responsible for significant errors, both of interpretation and of mathematical deduction. We suggest that additional mathematical and experimental methods must be used to resolve the relationship between time and behavioural changes by cells that are predominantly unsynchronized.

A Comparison of Methodologies from Two Longitudinal Community-Based Randomized Controlled Trials of Similar Interventions in Palliative Care: What Worked and What Did Not

Background: Methodological challenges such as recruitment problems and participant burden make clinical trials in palliative care difficult. In 2001-2004, two community-based randomized controlled trials (RCTs) of case conferences in palliative care settings were independently conducted in Australia-the Queensland Case Conferences trial (QCC) and the Palliative Care Trial (PCT). Design: A structured comparative study of the QCC and PCT was conducted, organized by known practical and organizational barriers to clinical trials in palliative care. Results: Differences in funding dictated study designs and recruitment success; PCT had 6 times the budget of QCC. Sample size attainment. Only PCT achieved the sample size goal. QCC focused on reducing attrition through gatekeeping while PCT maximized participation through detailed recruitment strategies and planned for significant attrition. Testing sustainable interventions. QCC achieved a higher percentage of planned case conferences; the QCC strategy required minimal extra work for clinicians while PCT superimposed conferences on normal work schedules. Minimizing participant burden. Differing strategies of data collection were implemented to reduce participant burden. QCC had short survey instruments. PCT incorporated all data collection into normal clinical nursing encounters. Other. Both studies had acceptable withdrawal rates. Intention-to-treat analyses are planned. Both studies included substudies to validate new outcome measures. Conclusions: Health service interventions in palliative care can be studied using RCTs. Detailed comparative information of strategies, successes and challenges can inform the design of future trials. Key lessons include adequate funding, recruitment focus, sustainable interventions, and mechanisms to minimize participant burden.

A simple proof of the strong subadditivity inequality

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Teleportation via Multi-Qubit Channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of 2L qubits. In this procedure a protocol is employed whereby L Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the 2(2L)-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects 2L qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.