A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Investigating the potential value of individual parameters of histological grading systems in a sheep model of cartilage damage : the modified Mankin method

A total histological grade does not necessarily distinguish between different manifestations of cartilage damage or degeneration. An accurate and reliable histological assessment method is required to separate normal and pathological tissue within a joint during treatment of degenerative joint conditions and to sub-classify the latter in meaningful ways. The Modified Mankin method may be adaptable for this purpose. We investigated how much detail may be lost by assigning one composite score/grade to represent different degenerative components of the osteoarthritic condition. We used four ovine injury models (sham surgery, anterior cruciate ligament/medial collateral ligament instability, simulated anatomic anterior cruciate ligament reconstruction and meniscal removal) to induce different degrees and potentially 'types' (mechanisms) of osteoarthritis. Articular cartilage was systematically harvested, prepared for histological examination and graded in a blinded fashion using a Modified Mankin grading method. Results showed that the possible permutations of cartilage damage were significant and far more varied than the current intended use that histological grading systems allow. Of 1352 cartilage specimens graded, 234 different manifestations of potential histological damage were observed across 23 potential individual grades of the Modified Mankin grading method. The results presented here show that current composite histological grading may contain additional information that could potentially discern different stages or mechanisms of cartilage damage and degeneration in a sheep model. This approach may be applicable to other grading systems.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Practical client puzzles in the standard model

Client puzzles are cryptographic problems that are neither easy nor hard to solve. Most puzzles are based on either number theoretic or hash inversions problems. Hash-based puzzles are very efficient but so far have been shown secure only in the random oracle model; number theoretic puzzles, while secure in the standard model, tend to be inefficient. In this paper, we solve the problem of constucting cryptographic puzzles that are secure int he standard model and are very efficient. We present an efficient number theoretic puzzle that satisfies the puzzle security definition of Chen et al. (ASIACRYPT 2009). To prove the security of our puzzle, we introduce a new variant of the interval discrete logarithm assumption which may be of independent interest, and show this new problem to be hard under reasonable assumptions. Our experimental results show that, for 512-bit modulus, the solution verification time of our proposed puzzle can be up to 50x and 89x faster than the Karame-Capkum puzzle and the Rivest et al.'s time-lock puzzle respectively. In particular, the solution verification tiem of our puzzle is only 1.4x slower than that of Chen et al.'s efficient hash based puzzle.

Relative entropy rate based model selection for linear hybrid system filters of uncertain nonlinear systems

Hybrid system representations have been exploited in a number of challenging modelling situations, including situations where the original nonlinear dynamics are too complex (or too imprecisely known) to be directly filtered. Unfortunately, the question of how to best design suitable hybrid system models has not yet been fully addressed, particularly in the situations involving model uncertainty. This paper proposes a novel joint state-measurement relative entropy rate based approach for design of hybrid system filters in the presence of (parameterised) model uncertainty. We also present a design approach suitable for suboptimal hybrid system filters. The benefits of our proposed approaches are illustrated through design examples and simulation studies.

A holistic blended design studio model : a basis for exploring and expanding learning opportunities

While the studio environment has been promoted as an ideal educational setting for project-based disciplines, few qualitative studies have been undertaken in a comprehensive way (Bose, 2007). This study responds to this need by adopting Grounded Theory methodology in a qualitative comparative approach. The research aims to explore the limitations and benefits of a face-to-face (f2f) design studio as well as a virtual design studio (VDS) as experienced by architecture students and educators at an Australian university in order to find the optimal combination for a blended environment to maximize learning. The main outcome is a holistic multidimensional blended model being sufficiently flexible to adapt to various setting, in the process, facilitating constructivist learning through self-determination, self-management, and personalization of the learning environment.

An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

Stigmergy in Web 2.0 : a model for site dynamics

Building Web 2.0 sites does not necessarily ensure the success of the site. We aim to better understand what improves the success of a site by drawing insight from biologically inspired design patterns. Web 2.0 sites provide a mechanism for human interaction enabling powerful intercommunication between massive volumes of users. Early Web 2.0 site providers that were previously dominant are being succeeded by newer sites providing innovative social interaction mechanisms. Understanding what site traits contribute to this success drives research into Web sites mechanics using models to describe the associated social networking behaviour. Some of these models attempt to show how the volume of users provides a self-organising and self-contextualisation of content. One model describing coordinated environments is called stigmergy, a term originally describing coordinated insect behavior. This paper explores how exploiting stigmergy can provide a valuable mechanism for identifying and analysing online user behavior specifically when considering that user freedom of choice is restricted by the provided web site functionality. This will aid our building better collaborative Web sites improving the collaborative processes.

An Economic Exclusion/Male Peer Support Model Looks at 'Wedfare' and Woman Abuse

In recent years ‘‘welfare reform’’ has become a vehicle for many neo-conservative social commentators to invoke marriage vows as a cure for poverty and the abuse of poor women. Their basic claim is that cohabiting relationships are not only more violent than marriages, but that married couples are happier, healthier, and wealthier than cohabiting ones. A policy then of encouraging cohabitants to marry, they claim, would lead to increased family wealth and decreased family violence. We examine these claims in this article, along with the alternative argument that marriage per se is not a solution to these problems. Alternatively we propose an economic exclusion/male peer support model that explains why many cohabiting men abuse women in intimate relationships. If forcing these couples to marry is not a solution, then structural solutions are necessary, along with progressive policy suggestions that address the antecedents of poverty and abuse.

Thinking Critically About Rural Gender Relations: Toward a Rural Masculinity/Male Peer Support Model of Separation/Divorce Sexual Assault

After decades of neglect, a growing number of scholars have turned their attention to issues of crime and criminal justice in the rural context. Despite this improvement, rural crime research is underdeveloped theoretically, and is little informed by critical criminological perspectives. In this article, we introduce the broad tenets of a multi-level theory that links social and economic change to the reinforcement of rural patriarchy and male peer support, and in turn, how they are linked to separation/divorce sexual assault. We begin by addressing a series of misconceptions about what is rural, rural homogeneity and commonly held presumptions about the relationship of rurality, collective efficacy (and related concepts) and crime. We conclude by recommending more focused research, both qualitative and quantitative, to uncover specific link between the rural transformation and violence against women.

Towards a comprehensive and integrated knowledge-based urban development model : status quo and directions

Incorporating knowledge based urban development (KBUD) strategies in the urban planning and development process is a challenging and complex task due to the fragmented and incoherent nature of the existing KBUD models. This paper scrutinizes and compares these KBUD models with an aim of identifying key and common features that help in developing a new comprehensive and integrated KBUD model. The features and characteristics of the existing KBUD models are determined through a thorough literature review and the analysis reveals that while these models are invaluable and useful in some cases, lack of a comprehensive perspective and absence of full integration of all necessary development domains render them incomplete as a generic model. The proposed KBUD model considers all central elements of urban development and sets an effective platform for planners and developers to achieve more holistic development outcomes. The proposed model, when developed further, has a high potential to support researchers, practitioners and particularly city and state administrations that are aiming to a knowledge-based development.