A general model for MAC generation using direct injection

This paper presents a model for generating a MAC tag by injecting the input message directly into the internal state of a nonlinear filter generator. This model generalises a similar model for unkeyed hash functions proposed by Nakano et al. We develop a matrix representation for the accumulation phase of our model and use it to analyse the security of the model against man-in-the-middle forgery attacks based on collisions in the final register contents. The results of this analysis show that some conclusions of Nakano et al regarding the security of their model are incorrect. We also use our results to comment on several recent MAC proposals which can be considered as instances of our model and specify choices of options within the model which should prevent the type of forgery discussed here. In particular, suitable initialisation of the register and active use of a secure nonlinear filter will prevent an attacker from finding a collision in the final register contents which could result in a forged MAC.

Complications related to therapeutic anticoagulation in total hip arthroplasty

Bleeding related wound complications cause significant morbidity in lower limb arthroplasty surgery. Patients who require therapeutic anticoagulation in the peri operative period are potentially at higher risk of these complications. This is a retrospective case control study reviewing all primary total hip replacements performed in a single center over a five year period and comparing outcomes of the patients on warfarin with a double-matched control group of patients not on warfarin. The warfarin group had significantly higher risk of deep joint infection (9% vs 2.2%), haematoma/ wound ooze (28% vs 4%) and superficial infection (13.5% vs 2.2%). Managing the total hip arthroplasty patient with therapeutic anticoagulation is a balance between the risk of thromboembolic disease and bleeding related complications. Improved understanding of this risk will better allow the patient to make an informed decision regarding their elective arthroplasty surgery.

Gene transfer vectors targeted to human prostate cancer : do we need better preclinical testing systems?

Destruction of cancer cells by genetically modified viral and nonviral vectors has been the aim of many research programs. The ability to target cytotoxic gene therapies to the cells of interest is an essential prerequisite, and the treatment has always had the potential to provide better and more long-lasting therapy than existing chemotherapies. However, the potency of these infectious agents requires effective testing systems, in which hypotheses can be explored both in vitro and in vivo before the establishment of clinical trials in humans. The real prospect of off-target effects should be eliminated in the preclinical stage, if current prejudices against such therapies are to be overcome. In this review we have set out, using adenoviral vectors as a commonly used example, to discuss some of the key parameters required to develop more effective testing, and to critically assess the current cellular models for the development and testing of prostate cancer biotherapy. Only by developing models that more closely mirror human tissues will we be able to translate literature publications into clinical trials and hence into acceptable alternative treatments for the most commonly diagnosed cancer in humans.

An analytical method for assessing stage-specific drug activity in Plasmodium vivax malaria : implications for ex vivo drug susceptibility testing

The emergence of highly chloroquine (CQ) resistant P. vivax in Southeast Asia has created an urgent need for an improved understanding of the mechanisms of drug resistance in these parasites, the development of robust tools for defining the spread of resistance, and the discovery of new antimalarial agents. The ex vivo Schizont Maturation Test (SMT), originally developed for the study of P. falciparum, has been modified for P. vivax. We retrospectively analysed the results from 760 parasite isolates assessed by the modified SMT to investigate the relationship between parasite growth dynamics and parasite susceptibility to antimalarial drugs. Previous observations of the stage-specific activity of CQ against P. vivax were confirmed, and shown to have profound consequences for interpretation of the assay. Using a nonlinear model we show increased duration of the assay and a higher proportion of ring stages in the initial blood sample were associated with decreased effective concentration (EC50) values of CQ, and identify a threshold where these associations no longer hold. Thus, starting composition of parasites in the SMT and duration of the assay can have a profound effect on the calculated EC50 for CQ. Our findings indicate that EC50 values from assays with a duration less than 34 hours do not truly reflect the sensitivity of the parasite to CQ, nor an assay where the proportion of ring stage parasites at the start of the assay does not exceed 66%. Application of this threshold modelling approach suggests that similar issues may occur for susceptibility testing of amodiaquine and mefloquine. The statistical methodology which has been developed also provides a novel means of detecting stage-specific drug activity for new antimalarials.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Slide attacks on the Sfinks stream cipher

Sfinks is a shift register based stream cipher designed for hardware implementation and submitted to the eSTREAM project. In this paper, we analyse the initialisation process of Sfinks. We demonstrate a slid property of the loaded state of the Sfinks cipher, where multiple key-IV pairs may produce phase shifted keystream sequences. The state update functions of both the initialisation process and keystream generation and also the pattern of the padding affect generation of the slid pairs.

Quantifying the roles of cell motility and cell proliferation in a circular barrier assay

Moving fronts of cells are essential features of embryonic development, wound repair and cancer metastasis. This paper describes a set of experiments to investigate the roles of random motility and proliferation in driving the spread of an initially confined cell population. The experiments include an analysis of cell spreading when proliferation was inhibited. Our data have been analysed using two mathematical models: a lattice-based discrete model and a related continuum partial differential equation model. We obtain independent estimates of the random motility parameter, D, and the intrinsic proliferation rate, λ, and we confirm that these estimates lead to accurate modelling predictions of the position of the leading edge of the moving front as well as the evolution of the cell density profiles. Previous work suggests that systems with a high λ/D ratio will be characterized by steep fronts, whereas systems with a low λ/D ratio will lead to shallow diffuse fronts and this is confirmed in the present study. Our results provide evidence that continuum models, based on the Fisher–Kolmogorov equation, are a reliable platform upon which we can interpret and predict such experimental observations.

State convergence in bit-based stream ciphers

Well-designed initialisation and keystream generation processes for stream ciphers should ensure that each key-IV pair generates a distinct keystream. In this paper, we analyse some ciphers where this does not happen due to state convergence occurring either during initialisation, keystream generation or both. We show how state convergence occurs in each case and identify two mechanisms which can cause state convergence.

Slid pairs in the initialisation of the A5/1 stream cipher

A5/1 is a shift register based stream cipher which uses a majority clocking rule to update its registers. It is designed to provide privacy for the GSM system. In this paper, we analyse the initialisation process of A5/1. We demonstrate a sliding property of the A5/1 cipher, where every valid internal state is also a legitimate loaded state and multiple key-IV pairs produce phase shifted keystream sequences. We describe a possible ciphertext only attack based on this property.

The deep trauma of secondary victimisation : parents of sex offenders

The publication of the fourth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV; American Psychiatric Association, 1994) introduced the notion that a life-threatening illness can be a stressor and catalyst for Posttraumatic Stress Disorder (PTSD). Since then a solid body of research has been established investigating the post-diagnosis experience of cancer. These studies have identified a number of short and long-term life changes resulting from a diagnosis of cancer and associated treatments. In this chapter, we discuss the psychosocial response to the cancer experience and the potential for cancer-related distress. Cancer can represent a life-threatening diagnosis that may be associated with aggressive treatments and result in physical and psychological changes. The potential for future trauma through the lasting effects of the disease and treatment, and the possibility of recurrence, can be a source of continued psychological distress. In addition to the documented adverse repercussions of cancer, we also outline the recent shift that has occurred in the psycho-oncology literature regarding positive life change or posttraumatic growth that is commonly reported after a diagnosis of cancer. Adopting a salutogenic framework acknowledges that the cancer experience is a dynamic psychosocial process with both negative and positive repercussions. Next, we describe the situational and individual factors that are associated with posttraumatic growth and the types of positive life change that are prevalent in this context. Finally, we discuss the implications of this research in a therapeutic context and the directions of future posttraumatic growth research with cancer survivors. This chapter will present both quantitative and qualitative research that indicates the potential for personal growth from adversity rather than just mere survival and return to pre-diagnosis functioning. It is important to emphasise however, that the presence of growth and prevalence of resilience does not negate the extremely distressing nature of a cancer diagnosis for the patient and their families and the suffering that can accompany treatment regimes. Indeed, it will be explained that for growth to occur, the experience must be one that quite literally shatters previously held schemas in order to act as a catalyst for change.

Experimental and modelling investigation of monolayer development with clustering

Standard differential equation–based models of collective cell behaviour, such as the logistic growth model, invoke a mean–field assumption which is equivalent to assuming that individuals within the population interact with each other in proportion to the average population density. Implementing such assumptions implies that the dynamics of the system are unaffected by spatial structure, such as the formation of patches or clusters within the population. Recent theoretical developments have introduced a class of models, known as moment dynamics models, which aim to account for the dynamics of individuals, pairs of individuals, triplets of individuals and so on. Such models enable us to describe the dynamics of populations with clustering, however, little progress has been made with regard to applying moment dynamics models to experimental data. Here, we report new experimental results describing the formation of a monolayer of cells using two different cell types: 3T3 fibroblast cells and MDA MB 231 breast cancer cells. Our analysis indicates that the 3T3 fibroblast cells are relatively motile and we observe that the 3T3 fibroblast monolayer forms without clustering. Alternatively, the MDA MB 231 cells are less motile and we observe that the MDA MB 231 monolayer formation is associated with significant clustering. We calibrate a moment dynamics model and a standard mean–field model to both data sets. Our results indicate that the mean–field and moment dynamics models provide similar descriptions of the 3T3 fibroblast monolayer formation whereas these two models give very different predictions for the MDA MD 231 monolayer formation. These outcomes indicate that standard mean–field models of collective cell behaviour are not always appropriate and that care ought to be exercised when implementing such a model.

Editorial : infectious disease modelling

The aim of this Special Issue is to collect together a group of outstanding applied mathematics research articles that provide new insight into our understanding of infectious diseases and infectious disease modelling. The scope of the articles is broad, encompassing both specific applications of modelling to particular examples of infectious diseases, as well as articles that are devoted to the development of more general theoretical insight.

Language, Literacy and Literature

"Language, Literacy and Literature combines concepts of language, literature and literacy within a pedagogical framework that leads readers through a series of learning processes. In other words, it is as much a book about teaching English as it is a book about learning how to learn about teaching. The book provides models for pre-service teachers to help identify the kinds of dispositions towards learning that a teacher needs to develop, such as curiosity, collaboration and willingness to ‘give things a go’. It further challenges the pre-service teacher to question what they think they know, as well as discover what they need to know. A range of practical and relevant exercises and activities assist in building habits of reflexive practice."-- publisher website

Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.