An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems

In this paper we present a new residual-based reliable a posteriori error estimator for the local discontinuous Galerkin approximations of linear and nonlinear diffusion problems in polygonal regions of R ². Our analysis, which applies to convex and nonconvex domains, is based on Helmholtz decompositions of the error and a suitable auxiliary polynomial function interpolating the Dirichlet datum. Several examples confirming the reliability of the estimator and providing numerical evidences for its efficiency are given. Furthermore, the associated adaptive method, which considers meshes with and without hanging nodes, is shown to be much more efficient than a uniform refinement to compute the discrete solutions. In particular, the experiments illustrate the ability of the adaptive algorithm to localize the singularities of each problem.Mathematics Subject Classifications (1991). 65N30This revised version was published online in July 2005 with corrected volume and issue numbers.     

Element-by-Element Post-Processing of Discontinuous Galerkin Methods for Timoshenko Beams

In this paper, we consider discontinuous Galerkin approximations to the solution of Timoshenko beam problems and show how to post-process them in an element-by-element fashion to obtain a far better approximation. Indeed, we show numerically that, if polynomials of degree p≥1 are used, the post-processed approximation converges with order 2p+1 in the L ^∞-norm throughout the domain. This has to be contrasted with the fact that before post-processing, the approximation converges with order p+1 only. Moreover, we show that this superconvergence property does not deteriorate as the the thickness of the beam becomes extremely small.Supported in part by NSF Grant DMS-0411254 and by the University of Minnesota Supercomputing Institute.     

Development of a system for categorizing client reactions to therapist interventions.

We developed a measure of client reactions to therapist interventions. The 21 categories of the measure were divided into 14 positive and 7 negative reactions, which differed significantly from each other on client helpfulness ratings. Preliminary validity data indicated that therapist intentions were related to client reactions more for successful cases than unsuccessful cases, pretreatment symptomatology was highly predictive of which reactions the clients reported, there were some predictable changes in reactions across time in treatment, and within-case correlations of reactions with client-rated session depth and smoothness indicated some similarities across cases. We discuss the case-specific nature of client reactions, methodological issues, and the need for greater therapist awareness of client reactions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Occurrence of copper resistant mutants in the toxic cyanobacteria Microcystis aeruginosa: characterisation and future implications in the use of copper sulphate as algaecide

Freshwater toxic cyanobacteria are an increasing problem to human and animal health. Control of cyanobacteria in water supply reservoirs involves the use of algaecides, such as copper sulphate, usually in a repetitive way. Repercussions of recurrent algaecide treatments on cyanobacteria population dynamics remain still unknown. We studied the adaptation of cyanobacteria to lethal doses of copper sulphate by using Microcystis aeruginosa as an experimental model. A fluctuation analysis demonstrated that copper-resistant cells arise by spontaneous mutations that occur randomly prior to exposition to copper sulphate. The rate of spontaneous mutation from copper sensitivity to resistance was 1.76×10⁻⁶ mutants per cell division. Resistant mutants exhibited a diminished fitness in the absence of copper sulphate, but only these variants were able to grow at Cu²⁺ concentrations higher than 5.8 μM. In addition, copper-resistant cells were significantly smaller than wild-type ones. Warnings on the long-term consequences of repetitive algaecide treatments in water supplies are suggested.     

Direct electron transfer of cytochrome P450 2B4 at electrodes modified with nonionic detergent and colloidal clay nanoparticles

A method for construction of biosensors with membranous cytochrome P450 isoenzymes was developed based on clay/detergent/protein mixed films. Thin films of sodium montmorillonite colloid with incorporated cytochrome P450 2B4 (CYP2B4) with nonionic detergent were prepared on glassy carbon electrodes. The modified electrodes were electrochemically characterized, and bioelectrocatalytic reactions were followed. CYP2B4 can be reduced fast on clay-modified glassy carbon electrodes in the presence of the nonionic detergent Tween 80. In anaerobic solutions, reversible oxidation and reduction is obtained with a formal potential between -0.292 and -0.305 V vs Ag/AgCl 1 M KCl depending on the preparation of the biosensor. In air-saturated solution, bioelectrocatalytic reduction currents can be obtained with the CYP2B4-modified electrode on addition of typical substrates such as aminopyrine and benzphetamine. This reaction was suppressed when methyrapone, an inhibitor of P450 reactions, was present. Measurement of product formation also indicates the bioelectrocatalysis by CYP2B4.     

Functional analysis of the cysteine residues and the repetitive sequence of Saccharomyces cerevisiae Pir4/Cis3: the repetitive sequence is needed for binding to the cell wall beta-1,3-glucan

Identification of PIR/CIS3 gene was carried out by amino-terminal sequencing of a protein band released by beta-mercaptoethanol (beta-ME) from S. cerevisiae mnn9 cell walls. The protein was released also by digestion with beta-1,3-glucanases (laminarinase or zymolyase) or by mild alkaline solutions. Deletion of the two carboxyterminal Cys residues (Cys(214)-12aa-Cys(227)-COOH), reduced but did not eliminate incorporation of Pir4 (protein with internal repeats) by disulphide bridges. Similarly, site-directed mutation of two other cysteine amino acids (Cys(130)Ser or Cys(197)Ser) failed to block incorporation of Pir4; the second mutation produced the appearance of Kex2-unprocessed Pir4. Therefore, it seems that deletion or mutation of individual cysteine molecules does not seem enough to inhibit incorporation of Pir4 by disulphide bridges. In fks1Delta and gsc2/fks2Delta cells, defective in beta-1,3-glucan synthesis, modification of the protein pattern found in the supernatant of the growth medium, as well as the material released by beta-ME or laminarinase, was evident. However, incorporation of Pir4 by both disulphide bridges and to the beta-1,3-glucan of the cell wall continued. Deletion of the repetitive sequence (QIGDGQVQA) resulted in the secretion and incorporation by disulphide bridges of Pir4 in reduced amounts together with substantial quantities of the Kex2-unprocessed Pir4 form. Pir4 failed to be incorporated in alkali-sensitive linkages involving beta-1,3-glucan when the first repetitive sequence was deleted. Therefore, this suggests that this sequence is needed in binding Pir4 to the beta-1,3-glucan.     

A hybrid VNS approach for the short-term production planning and scheduling: A case study in the pulp and paper industry

Mathematical formulations for production planning are increasing complexity, in order to improve their realism. In short-term planning, the desirable level of detail is particularly high. Exact solvers fail to generate good quality solutions for those complex models on medium- and large-sized instances within feasible time. Motivated by a real-world case study in the pulp and paper industry, this paper provides an efficient solution method to tackle the short-term production planning and scheduling in an integrated mill. Decisions on the paper machine setup pattern and on the production rate of the pulp digester (which is constrained to a maximum variation) complicate the problem. The approach is built on top of a mixed integer programming (MIP) formulation derived from the multi-stage general lotsizing and scheduling problem. It combines a Variable Neighbourhood Search procedure which manages the setup-related variables, a specific heuristic to determine the digester's production speeds and an exact method to optimize the production and flow movement decisions. Different strategies are explored to speed-up the solution procedure and alternative variants of the algorithm are tested on instances based on real data from the case study. The algorithm is benchmarked against exact procedures.     

Adaptive value function approximation for continuous-state stochastic dynamic programming

Approximate dynamic programming (ADP) commonly employs value function approximation to numerically solve complex dynamic programming problems. A statistical perspective of value function approximation employs a design and analysis of computer experiments (DACE) approach, where the “computer experiment” yields points on the value function curve. The DACE approach has been used to numerically solve high-dimensional, continuous-state stochastic dynamic programming, and performs two tasks primarily: (1) design of experiments and (2) statistical modeling. The use of design of experiments enables more efficient discretization. However, identifying the appropriate sample size is not straightforward. Furthermore, identifying the appropriate model structure is a well-known problem in the field of statistics. In this paper, we present a sequential method that can adaptively determine both sample size and model structure. Number-theoretic methods (NTM) are used to sequentially grow the experimental design because of their ability to fill the design space. Feed-forward neural networks (NNs) are used for statistical modeling because of their adjustability in structure-complexity . This adaptive value function approximation (AVFA) method must be automated to enable efficient implementation within ADP. An AVFA algorithm is introduced, that increments the size of the state space training data in each sequential step, and for each sample size a successive model search process is performed to find an optimal NN model. The new algorithm is tested on a nine-dimensional inventory forecasting problem.