Detecting non-multiplicative genotype relative risks from transmissions of parental alleles to affected children

The differential transmission of alleles from parents to affected children indicates that the locus under investigation is either directly involved in the occurrence of the disease or that there are allelic associations with other loci that are directly involved. Conditional logistic regression applied to a diallelic locus leads to a test with two degrees of freedom. The power of a single degree of freedom test to detect non-multiplicative allelic effects is discussed here.

Design and development of a dextrous manipulator

This paper develops a novel method of actuation for robotic hands. The solution employs Bowden cable routed to each joint as the means by which the finger is actuated. The use of Bowden cable is shown to be feasible for this purpose, even with the changing frictional forces associated with it's use. This method greatly simplifies the control of the hand by removing the coupling between joints, and allows for direct and accurate translation between the joints and the motors driving the Bowden wires. The design also allows for two degrees of freedom (with the same centre of rotation) to be realised in the largest knuckle of each finger, meaning biological finger kinematics are more accurately emulated.

Design and development of a dextrous manipulator

This paper describes a novel method of actuation for robotic hands. The solution employs a Bowden cable routed to each joint. The use of a Bowden cable is shown to be feasible for this purpose, ever, with the changing frictional forces associated with it. This method greatly simplifies the control of the hand by removing the coupling between joints, and provides for direct and accurate translation between the joints and the servo motors driving the cables. The design also allows for two degrees of freedom with the same centre of rotation to be realized in the largest knuckle of each finger; thus biological finger kinematics are more closely emulated.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Mechatronic design of a high frequency probe for haptic interaction

Current force feedback, haptic interface devices are generally limited to the display of low frequency, high amplitude spatial data. A typical device consists of a low impedance framework of one or more degrees-of-freedom (dof), allowing a user to explore a pre-defined workspace via an end effector such as a handle, thimble, probe or stylus. The movement of the device is then constrained using high gain positional feedback, thus reducing the apparent dof of the device and conveying the illusion of hard contact to the user. Such devices are, however, limited to a narrow bandwidth of frequencies, typically below 30Hz, and are not well suited to the display of surface properties, such as object texture. This paper details a device to augment an existing force feedback haptic display with a vibrotactile display, thus providing a means of conveying low amplitude, high frequency spatial information of object surface properties. 1. Haptics and Haptic Interfaces Haptics is the study of human touch and interaction with the external environment via touch. Information from the human sense of touch can be classified in to two categories, cutaneous and kinesthetic. Cutaneous information is provided via the mechanoreceptive nerve endings in the glabrous skin of the human hand. It is primarily a means of relaying information regarding small-scale details in the form of skin stretch, compression and vibration.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

The lottery-panel task for bi-dimensional parameter-free elicitation of risk attitudes

We propose first, a simple task for the eliciting attitudes toward risky choice, the SGG lottery-panel task, which consists in a series of lotteries constructed to compensate riskier options with higher risk-return trade-offs. Using Principal Component Analysis technique, we show that the SGG lottery-panel task is capable of capturing two dimensions of individual risky decision making i.e. subjects’ average risk taking and their sensitivity towards variations in risk-return. From the results of a large experimental dataset, we confirm that the task systematically captures a number of regularities such as: A tendency to risk averse behavior (only around 10% of choices are compatible with risk neutrality); An attraction to certain payoffs compared to low risk lotteries, compatible with over-(under-) weighting of small (large) probabilities predicted in PT and; Gender differences, i.e. males being consistently less risk averse than females but both genders being similarly responsive to the increases in risk-premium. Another interesting result is that in hypothetical choices most individuals increase their risk taking responding to the increase in return to risk, as predicted by PT, while across panels with real rewards we see even more changes, but opposite to the expected pattern of riskier choices for higher risk-returns. Therefore, we conclude from our data that an “economic anomaly” emerges in the real reward choices opposite to the hypothetical choices. These findings are in line with Camerer's (1995) view that although in many domains, paid subjects probably do exert extra mental effort which improves their performance, choice over money gambles is not likely to be a domain in which effort will improve adherence to rational axioms (p. 635). Finally, we demonstrate that both dimensions of risk attitudes, average risk taking and sensitivity towards variations in the return to risk, are desirable not only to describe behavior under risk but also to explain behavior in other contexts, as illustrated by an example. In the second study, we propose three additional treatments intended to elicit risk attitudes under high stakes and mixed outcome (gains and losses) lotteries. Using a dataset obtained from a hypothetical implementation of the tasks we show that the new treatments are able to capture both dimensions of risk attitudes. This new dataset allows us to describe several regularities, both at the aggregate and within-subjects level. We find that in every treatment over 70% of choices show some degree of risk aversion and only between 0.6% and 15.3% of individuals are consistently risk neutral within the same treatment. We also confirm the existence of gender differences in the degree of risk taking, that is, in all treatments females prefer safer lotteries compared to males. Regarding our second dimension of risk attitudes we observe, in all treatments, an increase in risk taking in response to risk premium increases. Treatment comparisons reveal other regularities, such as a lower degree of risk taking in large stake treatments compared to low stake treatments and a lower degree of risk taking when losses are incorporated into the large stake lotteries. Results that are compatible with previous findings in the literature, for stake size effects (e.g., Binswanger, 1980; Antoni Bosch-Domènech & Silvestre, 1999; Hogarth & Einhorn, 1990; Holt & Laury, 2002; Kachelmeier & Shehata, 1992; Kühberger et al., 1999; B. J. Weber & Chapman, 2005; Wik et al., 2007) and domain effect (e.g., Brooks and Zank, 2005, Schoemaker, 1990, Wik et al., 2007). Whereas for small stake treatments, we find that the effect of incorporating losses into the outcomes is not so clear. At the aggregate level an increase in risk taking is observed, but also more dispersion in the choices, whilst at the within-subjects level the effect weakens. Finally, regarding responses to risk premium, we find that compared to only gains treatments sensitivity is lower in the mixed lotteries treatments (SL and LL). In general sensitivity to risk-return is more affected by the domain than the stake size. After having described the properties of risk attitudes as captured by the SGG risk elicitation task and its three new versions, it is important to recall that the danger of using unidimensional descriptions of risk attitudes goes beyond the incompatibility with modern economic theories like PT, CPT etc., all of which call for tests with multiple degrees of freedom. Being faithful to this recommendation, the contribution of this essay is an empirically and endogenously determined bi-dimensional specification of risk attitudes, useful to describe behavior under uncertainty and to explain behavior in other contexts. Hopefully, this will contribute to create large datasets containing a multidimensional description of individual risk attitudes, while at the same time allowing for a robust context, compatible with present and even future more complex descriptions of human attitudes towards risk.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Protein precipitation behaviour of condensed tannins from Lotus pedunculatus and Trifolium repens with different mean degrees of polymerization

The precipitation of bovine serum albumin (BSA), lysozyme (LYS) and alfalfa leaf protein (ALF) by two large- and two medium-sized condensed tannin (CT) fractions of similar flavan-3-ol subunit composition is described. CT fractions isolated from white clover flowers and big trefoil leaves exhibited high purity profiles by 1D/2D NMR and purities >90% (determined by thiolysis). At pH 6.5, large CTs with a mean degree of polymerization (mDP) of ~18 exhibited similar protein precipitation behaviors and were significantly more effective than medium CTs (mDP ~9). Medium CTs exhibited similar capacities to precipitate ALF or BSA, but showed small but significant differences in their capacity to precipitate LYS. All CTs precipitated ALF more effectively than BSA or LYS. Aggregation of CT-protein complexes likely aided precipitation of ALF and BSA, but not LYS. This study, one of the first to use CTs of confirmed high purity, demonstrates that mDP of CTs influences protein precipitation efficacy.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Water management in Minoan Crete, Greece: the two cisterns of one Middle Bronze Age settlement

The two earliest structures of Minoan Crete that may be considered as large cisterns were both built in the first half of the second millennium BC (the time of the first Minoan palaces) at Myrtos-Pyrgos (lerapetra). A considerable feat of engineering and social management, they remain a most unusual attribute of a Minoan settlement, all the more so since the Myrtos river is/was available to supply water at the foot of the hill of Pyrgos. This paper presents these cisterns, briefly, in terms of geology and technology, the history of their use and re-use, and their relevance to understanding the culture and society (at local and regional levels) of Crete in the time of the Old Palaces, as well as their possible contribution to the political and military history of the period. I then review possible precursors of, and architectural parallels to, the Pyrgos cisterns at Knossos, Malia and Phaistos (none of which has been proved to be a cistern), and the later history of cisterns in Bronze Age Crete. Since only three others are known (at Archanes, Zakro and Tylissos, of Late Bronze Age date), the two cisterns of Myrtos-Pyrgos are an important addition to our still rudimentary knowledge of how the Bronze Age Cretans managed their water supplies.

Inherited resistance to arsenate toxicity in two populations of Lumbricus rubellus

No unequivocal evidence exists of genetically inherited resistance to metals/metalloids in field populations of earthworms. We studied cocoon production in adult Lumbricus rubellus Hoffmeister collected from an abandoned arsenic and copper mine (Devon Great Consols, Devon, UK), and abandoned tungsten mine (Carrock Fell, Cumbria, UK) and an uncontaminated cultured population. The earthworms were kept in uncontaminated soil for nine weeks. From a total of 42 L. rubellus from each site, Devon Great Consols adults produced 301 cocoons, of which 42 were viable; Carrock Fell 60 cocoons, of which 11 were viable; and the reference population 101 cocoons, of which 62 were viable. The hatchlings were collected and stored at 4degreesC at weekly intervals. After 12 weeks, all hatchlings were transferred to clean soil and maintained at 15degreesC for 20 weeks until they showed evidence of a clitellum. In toxicity trials, F1 generation L. rubellus were exposed to 2,000 mg As/kg as sodium arsenate or 300 mg Cu/kg as copper chloride for 28 d. The F1 generation L. rubellus from Devon Great Consols mine demonstrated resistance to arsenate but not copper. All L. rubellus from Devon Great Consols kept in soil treated with sodium arsenate remained in good condition over the 28-d period but lost condition rapidly and suffered high mortality in soil treated with copper chloride. The control population suffered high mortality in soil treated with sodium arsenate and copper chloride. Previous work has shown that field-collected adults demonstrate resistance to both arsenate and Cu toxicity under these conditions. Thus, while arsenate resistance may be demonstrated in F1 generation L. rubellus from one of the contaminated sites, Cu resistance is not. The F1 adults and F2 cocoons did not have significantly higher levels of As than the control population, with no residual As tissue burden, suggesting that resistance to As in these populations may be inherited.

Questions of Friendship and Degrees of Transnationality among Second-Generation Return Migrants to Barbados

While the academic literature has demonstrated the importance of social networks in relation to the process of migration, investigations have rarely examined in detail the personal-social adjustment issues that migrants and return migrants face. This study examines the context and types of friendship pattern that young return migrants from Britain cultivate in Barbados. The research centres on a wholly under-researched demographic groupyoung return migrants or second-generation Barbadians who have decided to return to the birthplace of their parents. The investigation is based on 51 in-depth interviews carried out with these young returnees to Barbados. Presenting a taxonomy of friendship types, it is argued that, for the 'Bajan-Brits' under study, the cultivation of new friendships is highly problematic. The research identifies what we refer to as the 'insular transnational', the 'we are different' and the 'all-inclusive transnational' friendship types among the young returnees. Our analysis also shows that problems of friendship are highly gendered, with females reporting the most problems due to what is perceived as sexual and workplace competition. It is stressed that these circumstances exemplify the essentially 'hybrid', 'liminal' and 'in-between' positionality of these second-generation migrants within contemporary Barbadian society.