A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

A meta-analytic clarification of the relationship between posttraumatic growth and symptoms of posttraumatic distress disorder

Traumatic experiences can have a powerful impact on individuals and communities but the relationship between perceptions of beneficial and pathological outcomes are not known. Therefore, this meta-analysis examined both the strength and the linearity of the relationship between symptoms of posttraumatic stress disorder (PTSD) and perceptions of posttraumatic growth (PTG) as well as identifying the potential moderating roles of trauma type and age. Literature searches of all languages were conducted using the ProQuest, Wiley Interscience, ScienceDirect, Informaworld and Web of Science databases. Linear and quadratic (curvilinear) rs as well as βs were analysed. Forty-two studies (N=11, 469) that examined both PTG and symptoms of PTSD were included in meta-analytic calculations. The combined studies yielded a significant linear relationship between PTG and PTSD symptoms (r=.315, CI = 0.299, 0.331), but also a significantly stronger (as tested by Fisher’s transformation) curvilinear relationship (r=.372, CI = 0.353, 0.391). The strength and linearity of these relationships differed according to trauma type and age. The results remind those working with traumatised people that positive and negative post-trauma outcomes can co-occur. A focus only on PTSD symptoms only may limit or slow recovery and mask the potential for growth.

Block models for improved earthwork allocation planning in linear infrastructure construction

Earthwork planning has been considered in this article and a generic block partitioning and modelling approach has been devised to provide strategic plans of various levels of detail. Conceptually this approach is more accurate and comprehensive than others, for instance those that are section based. In response to environmental concerns the metric for decision making was fuel consumption and emissions. Haulage distance and gradient are also included as they are important components of these metrics. Advantageously the fuel consumption metric is generic and captures the physical difficulties of travelling over inclines of different gradients, that is consistent across all hauling vehicles. For validation, the proposed models and techniques have been applied to a real world road project. The numerical investigations have demonstrated that the models can be solved with relatively little CPU time. The proposed block models also result in solutions of superior quality, i.e. they have reduced fuel consumption and cost. Furthermore the plans differ considerably from those based solely upon a distance based metric thus demonstrating a need for industry to reflect upon their current practices.

A coordinated voltage control approach for coordination of OLTC, voltage regulator and DG to regulate voltage in a distribution feeder

Integration of small-scale electricity generators, known as Distributed Generation (DG), into the distribution networks has become increasingly popular at the present. This tendency together with the falling price of synchronous-type generator has potential to give the DG a better chance in participating in the voltage regulation process together with other devices already available in the system. The voltage control issue turns out to be a very challenging problem for the distribution engineers since existing control coordination schemes would need to be reconsidered to take into account the DG operation. In this paper, we propose a control coordination technique, which is able to utilize the ability of the DG as a voltage regulator, and at the same time minimizes interaction with other active devices, such as On-load Tap Changing Transformer (OLTC) and voltage regulator. The technique has been developed based on the concept of control zone, Line Drop Compensation (LDC), as well as the choice of controller's parameters. Simulations carried out on an Australian system show that the technique is suitable and flexible for any system with multiple regulating devices including DG.

Higher-order non-linear analysis of steel structures. Part I : elastic second-order formulation

This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.

Higher-order non-linear analysis of steel structures. Part II : refined plastic hinge formulation

In the companion paper, a fourth-order element formulation in an updated Lagrangian formulation was presented to handle geometric non-linearities. The formulation of the present paper extends this to include material non-linearity by proposing a refined plastic hinge approach to analyse large steel framed structures with many members, for which contemporary algorithms based on the plastic zone approach can be problematic computationally. This concept is an advancement of conventional plastic hinge approaches, as the refined plastic hinge technique allows for gradual yielding, being recognized as distributed plasticity across the element section, a condition of full plasticity, as well as including strain hardening. It is founded on interaction yield surfaces specified analytically in terms of force resultants, and achieves accurate and rapid convergence for large frames for which geometric and material non-linearity are significant. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. In addition to the numerical efficiency, the present versatile approach is able to capture different kinds of material and geometric non-linearities on general applications of steel structures, and thereby it offers an efficacious and accurate means of assessing non-linear behaviour of the structures for engineering practice.

Capturing complex, non-linear team behaviours during competitive football performance

This study investigated changes in the complexity (magnitude and structure of variability) of the collective behaviours of association football teams during competitive performance. Raw positional data from an entire competitive match between two professional teams were obtained with the ProZone® tracking system. Five compound positional variables were used to investigate the collective patterns of performance of each team including: surface area, stretch index, team length, team width, and geometrical centre. Analyses involve the coefficient of variation (%CV) and approximate entropy (ApEn), as well as the linear association between both parameters. Collective measures successfully captured the idiosyncratic behaviours of each team and their variations across the six time periods of the match. Key events such as goals scored and game breaks (such as half time and full time) seemed to influence the collective patterns of performance. While ApEn values significantly decreased during each half, the %CV increased. Teams seem to become more regular and predictable, but with increased magnitudes of variation in their organisational shape over the natural course of a match.

Comparison of high level FPGA hardware design for solving tri-diagonal linear systems

Reconfigurable computing devices can increase the performance of compute intensive algorithms by implementing application specific co-processor architectures. The power cost for this performance gain is often an order of magnitude less than that of modern CPUs and GPUs. Exploiting the potential of reconfigurable devices such as Field-Programmable Gate Arrays (FPGAs) is typically a complex and tedious hardware engineering task. Re- cently the major FPGA vendors (Altera, and Xilinx) have released their own high-level design tools, which have great potential for rapid development of FPGA based custom accelerators. In this paper, we will evaluate Altera’s OpenCL Software Development Kit, and Xilinx’s Vivado High Level Sythesis tool. These tools will be compared for their per- formance, logic utilisation, and ease of development for the test case of a Tri-diagonal linear system solver.

Detecting and Analyzing Linear Structures in Biomedical Images : A Case Study Using Corneal Nerve Fibers

Diabetic peripheral neuropathy (DPN) is one of the most common long-term complications of diabetes. The accurate detection and quantification of DPN are important for defining at-risk patients, anticipating deterioration, and assessing new therapies. Current methods of detecting and quantifying DPN, such as neurophysiology, lack sensitivity, require expert assessment and focus primarily on large nerve fibers. However, the earliest damage to nerve fibers in diabetic neuropathy is to the small nerve fibers. At present, small nerve fiber damage is currently assessed using skin/nerve biopsy; both are invasive technique and are not suitable for repeated investigations.

Transforming morning to afternoon using linear regression techniques

Visual localization in outdoor environments is often hampered by the natural variation in appearance caused by such things as weather phenomena, diurnal fluctuations in lighting, and seasonal changes. Such changes are global across an environment and, in the case of global light changes and seasonal variation, the change in appearance occurs in a regular, cyclic manner. Visual localization could be greatly improved if it were possible to predict the appearance of a particular location at a particular time, based on the appearance of the location in the past and knowledge of the nature of appearance change over time. In this paper, we investigate whether global appearance changes in an environment can be learned sufficiently to improve visual localization performance. We use time of day as a test case, and generate transformations between morning and afternoon using sample images from a training set. We demonstrate the learned transformation can be generalized from training data and show the resulting visual localization on a test set is improved relative to raw image comparison. The improvement in localization remains when the area is revisited several weeks later.

UV Photodissociation Action Spectroscopy of Haloanilinium Ions in a Linear Quadrupole Ion Trap Mass Spectrometer

UV-vis photodissociation action spectroscopy is becoming increasingly prevalent because of advances in, and commercial availability of, ion trapping technologies and tunable laser sources. This study outlines in detail an instrumental arrangement, combining a commercial ion-trap mass spectrometer and tunable nanosecond pulsed laser source, for performing fully automated photodissociation action spectroscopy on gas-phase ions. The components of the instrumentation are outlined, including the optical and electronic interfacing, in addition to the control software for automating the experiment and performing online analysis of the spectra. To demonstrate the utility of this ensemble, the photodissociation action spectra of 4-chloroanilinium, 4-bromoanilinium, and 4-iodoanilinium cations are presented and discussed. Multiple photoproducts are detected in each case and the photoproduct yields are followed as a function of laser wavelength. It is shown that the wavelength-dependent partitioning of the halide loss, H loss, and NH3 loss channels can be broadly rationalized in terms of the relative carbon-halide bond dissociation energies and processes of energy redistribution. The photodissociation action spectrum of (phenyl)Ag-2 (+) is compared with a literature spectrum as a further benchmark.

Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.