'Eden Cinema' by Marguerite Duras

Duras’s theatre work has been profoundly neglected by UK theatre academics and practitioners, and Eden Cinema has almost no performance history in Britain. My project asked three interconnected research questions: how developing the performance contributes to understanding Duras’s theatre and specifically Eden Cinema’s problems of performability; how multimedia performance emphasising mediated sound and the live body reconfigures memory, autobiography, storytelling, gender and racial identity; how to locate a performance style appropriate for Durasian narratives of displacement and death which reflect the discontinuous and mutable form of Duras’s ‘texte/film/théâtre’. Drawing on my research interests in gender, post-colonial hybridity and performed deconstruction, I focused my staging decisions on the discontinuities and ambivalences of the text. I addressed performability by avoiding the temptation to resolve the strange ellipses in the text and instead evoked the text’s imperfect and fragmented memories, and its uncertain spatial and temporal locations, by means of a fluid theatrical form. The mise-en-scène represented imagined and remembered spaces simultaneously, and co-existing historical moments. The performance style counterpointed live and mediated action and audio-visual forms. A complex through-composed soundscape, comprising voice-over, sound and music, became a key means for evoking overlapping temporalities, interconnected narratives and fragmented memories that were dispersed across the performance. The disempowerment of the mother figure and the silent indigenous servant in the text was demonstrated through their spatial centrality but physical stillness. The servant’s colonial subaltern identity was paralleled and linked with the mother’s disenfranchisement through their proxemic relationships. I elicited a performance style which evoked ‘characters’, whose being was deferred across different regimes of reality and who ‘haunted’ the stage rather than inhabited it. I developed the project further in the additional written outcomes and presentations, and the subsequent performance of Savannah Bay where problems of performability intensify until embodiment is almost erased except via voice.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Ionospheric signatures of pulsed reconnection at the Earth's magnetopause

THE plasma precipitating into the Earth's dayside auroral atmosphere has characteristics which show that it originates from the shocked solar-wind plasma of the magnetosheath1'2. The particles of the magnetosheath plasma precipitate down a funnel-shaped region (cusp) of open field lines resulting from reconnection of the geomagnetic field with the interplanetary magnetic field3. Although the cusp has long been considered a well defined spatial structure maintained by continuous reconnection, it has recently been suggested4–6 that reconnection instead may take place in a series of discontinuous events; this is the ‘pulsating cusp model’. Here we present coordinated radar and satellite observations of a series of discrete, poleward-moving plasma structures that are consistent with the pulsating-cusp model.

Bond graph models of DC-DC converters operating in both CCM and DCM

In this paper, Bond Graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a Modulated Transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a Boost and Buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operation area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the Normalised Root Means Square Error and the Maximum Absolute Error remaining adequately low. The model is also experimentally tested on a Buck topology.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.

Do jumps matter for volatility forecasting? Evidence from energy markets

This paper characterizes the dynamics of jumps and analyzes their importance for volatility forecasting. Using high-frequency data on four prominent energy markets, we perform a model-free decomposition of realized variance into its continuous and discontinuous components. We find strong evidence of jumps in energy markets between 2007 and 2012. We then investigate the importance of jumps for volatility forecasting. To this end, we estimate and analyze the predictive ability of several Heterogenous Autoregressive (HAR) models that explicitly capture the dynamics of jumps. Conducting extensive in-sample and out-of-sample analyses, we establish that explicitly modeling jumps does not significantly improve forecast accuracy. Our results are broadly consistent across our four energy markets, forecasting horizons, and loss functions

Dystrophin analysis using a panel of anti-dystrophin antibodies in Duchenne and Becker muscular dystrophy.

Dystrophin, the protein product of the Duchenne muscular dystrophy (DMD) gene, was studied in 19 patients with Xp21 disorders and in 25 individuals with non-Xp21 muscular dystrophy. Antibodies raised to seven different regions spanning most of the protein were used for immunocytochemistry. In all patients specific dystrophin staining anomalies were detected and correlated with clinical severity and also gene deletion. In patients with Becker muscular dystrophy (BMD) the anomalies detected ranged from inter- and intra-fibre variation in labelling intensity with the same antibody or several antibodies to general reduction in staining and discontinuous staining. In vitro evidence of abnormal dystrophin breakdown was observed reanalysing the muscle of patients, with BMD and not that of non-Xp21 dystrophies, after it has been stored for several months. A number of patients with DMD showed some staining but this did not represent a diagnostic problem. Based on the data presented, it was concluded that immunocytochemistry is a powerful technique in the prognostic diagnosis of Xp21 muscular dystrophies.

CHP toolkit: case study of LAIe sensitivity to discontinuity of canopy cover in fruit plantations

This paper presents an open-source canopy height profile (CHP) toolkit designed for processing small-footprint full-waveform LiDAR data to obtain the estimates of effective leaf area index (LAIe) and CHPs. The use of the toolkit is presented with a case study of LAIe estimation in discontinuous-canopy fruit plantations. The experiments are carried out in two study areas, namely, orange and almond plantations, with different percentages of canopy cover (48% and 40%, respectively). For comparison, two commonly used discrete-point LAIe estimation methods are also tested. The LiDAR LAIe values are first computed for each of the sites and each method as a whole, providing “apparent” site-level LAIe, which disregards the discontinuity of the plantations’ canopies. Since the toolkit allows for the calculation of the study area LAIe at different spatial scales, between-tree-level clumpingcan be easily accounted for and is then used to illustrate the impact of the discontinuity of canopy cover on LAIe retrieval. The LiDAR LAIe estimates are therefore computed at smaller scales as a mean of LAIe in various grid-cell sizes, providing estimates of “actual” site-level LAIe. Subsequently, the LiDAR LAIe results are compared with theoretical models of “apparent” LAIe versus “actual” LAIe, based on known percent canopy cover in each site. The comparison of those models to LiDAR LAIe derived from the smallest grid-cell sizes against the estimates of LAIe for the whole site has shown that the LAIe estimates obtained from the CHP toolkit provided values that are closest to those of theoretical models.

Alternative mating tactics in dimorphic males of the harvestman Longiperna concolor (Arachnida: Opiliones)

Intense male-male competition for females may drive the evolution of male morphological dimorphism, which is frequently associated with alternative mating tactics. Using modern techniques for the detection of discontinuous allometries, we describe male dimorphism in the Neotropical harvestman Longiperna concolor, the males of which use their elongated, sexually dimorphic legs IV in fights for the possession of territories where females lay eggs. We also tested three predictions related to the existence of alternative mating tactics: (1) if individuals with relatively longer legs IV (majors) are more likely to monopolize access to reproductive resources, they are expected to remain close to stable groups of females more than individuals with relatively shorter legs IV (minors) do; (2) if minors achieve fertilization by moving between territories, they are expected to be less faithful to specific sites; and (3) majors should be observed in aggressive interactions more often. We individually marked all the individuals from a population of Longiperna during the reproductive season and recorded the location of each sighting for males and females as well as the identity of males involved in fights. Majors were more likely to have harems, and large majors were even more likely to do so. Majors were more philopatric and all males involved in fights belonged to this morph. These results strongly suggest that the mating tactic of the majors is based on resource defense whereas that of the minors probably relies on sneaking into the territories of the majors and furtively copulating with females.

Separation and viability of gill and hepatopancreatic cells of a mangrove crab Ucides cordatus

The gills contain essential cells for respiration and osmoregulation, whereas the hepatopancreas is the site of digestion, absorption, and nutrients storage. The aim of this work was to separate and characterize gill and hepatopancreatic cells of the mangrove crab, Ucides cordatus. For gills, the methodology consisted of an enzymatic cellular dissociation using Trypsin at 0.5%, observation of cellular viability with Tripan Blue, and separation of cells using discontinuous sucrose gradient at concentrations of 10%, 20%, 30%, and 40%. The hepatopancreatic cells were dissociated by magnetic stirring, with posterior separation by sucrose gradient at the same concentrations above. For gills, a high cellular viability was observed (92.5 +/- 2.1%), with hemocyte cells in 10% sucrose layer (57.99 +/- 0.17%, *P < 0.05), principal cells in the 20% sucrose layer (57.33 +/- 0.18, *P < 0.05), and thick cells and pillar cells in the 30% and 40% sucrose layers, respectively (39.54 +/- 0.05%, *P < 0.05; and 41.81 +/- 0.04%, *P < 0.05). The hepatopancreatic cells also showed good viability (79.22 +/- 0.02%), with the observation of embryonic (E) cells in the 10% sucrose layer (67.87 +/- 0.06%, **P < 0.001), resorptive (R) and fibrillar (F) cells in the 20% and 30% sucrose layers (44.71 +/- 0.06%, **P < 0.001, and 43.25 +/- 0.01%, *P < 0.05; respectively), and blister (B) cells in the 40% sucrose layer (63.09 +/- 0.03%, **P < 0.001). The results are a starting point for in vitro studies of heavy metal transport in isolated cells of the mangrove crab U. cordatus, subjected to contamination by metals in the mangrove habitat where they are found.