An introduction to Multitrace Formulations and Associated Domain Decomposition Solvers

Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We introduce in this paper MTFs on a simple model problem using concepts familiar to researchers in domain decomposition. This allows us to get a new understanding of MTFs and a natural block Jacobi iteration, for which we determine optimal relaxation parameters. We then show how iterative multitrace formulation solvers are related to a well known domain decomposition method called optimal Schwarz method: a method which used Dirichlet to Neumann maps in the transmission condition. We finally show that the insight gained from the simple model problem leads to remarkable identities for Calderon projectors and related operators, and the convergence results and optimal choice of the relaxation parameter we obtained is independent of the geometry, the space dimension of the problem{\color{black}, and the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We illustrate our analysis with numerical experiments

Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

Two-axis bend measurement with Bragg gratings in multicore optical fiber

We describe what is to our knowledge the first use of fiber Bragg gratings written into three separate cores of a multicore fiber for two-axis curvature measurement. The gratings act as independent, but isothermal, fiber strain gauges for which local curvature determines the difference in strain between cores, permitting temperature-independent bend measurement. (C) 2003 Optical Society of America

Gentamicin-loaded microspheres for treatment of experimental Brucella abortus infection in mice

Objectives: To evaluate the efficacy of gentamicin-loaded poly (lactide-co-glycolide) 50:50H (PLGA 50:50H) microspheres for the treatment of mice experimentally infected with Brucella abortus 2308. Methods: The microspheres were dispersed in either 2% (w/v) poloxamer 188 saline solution, or deionized water with the help of a cell homogenizer to break up particle aggregates, and were administered intravenously or intraperitoneally to B. abortus-infected mice 7 days post-infection. Results: Neither a single intravenous or intraperitoneal dose of 67 μg of gentamicin per mouse, nor three intraperitoneal doses of 100 μg of gentamicin per mouse, reduced the Brucella infection in the spleen compared with untreated mice 1 and 3 weeks post-treatment. Histological examination revealed granulation and tissue reaction in the periphery of spleen and liver of animals given three doses of the gentamicin-loaded microspheres. Conclusions: The lack of therapeutic activity of the gentamicin-loaded microspheres might be related to inappropriate microsphere size and aggregation, resulting also in a poor distribution of the microspheres in the spleen. The results might provide an example of practical problems related to particle size and aggregation for in vivo therapy with PLGA microsphere

Semantic Knowledge for Famous Names in Mild Cognitive Impairment

Person identification represents a unique category of semantic knowledge that is commonly impaired in Alzheimer\u27s disease (AD), but has received relatively little investigation in patients with mild cognitive impairment (MCI). The current study examined the retrieval of semantic knowledge for famous names from three time epochs (recent, remote, and enduring) in two participant groups: 23 amnestic MCI (aMCI) patients and 23 healthy elderly controls. The aMCI group was less accurate and produced less semantic knowledge than controls for famous names. Names from the enduring period were recognized faster than both recent and remote names in both groups, and remote names were recognized more quickly than recent names. Episodic memory performance was correlated with greater semantic knowledge particularly for recent names. We suggest that the anterograde memory deficits in the aMCI group interferes with learning of recent famous names and as a result produces difficulties with updating and integrating new semantic information with previously stored information. The implications of these findings for characterizing semantic memory deficits in MCI are discussed. (JINS, 2009, 15, 9-18.

Common Neural Systems Associated with the Recognition of Famous Faces and Names: An Event-Related fMRI Study

Person recognition can be accomplished through several modalities (face, name, voice). Lesion, neurophysiology and neuroimaging studies have been conducted in an attempt to determine the similarities and differences in the neural networks associated with person identity via different modality inputs. The current study used event-related functional-MRI in 17 healthy participants to directly compare activation in response to randomly presented famous and non-famous names and faces (25 stimuli in each of the four categories). Findings indicated distinct areas of activation that differed for faces and names in regions typically associated with pre-semantic perceptual processes. In contrast, overlapping brain regions were activated in areas associated with the retrieval of biographical knowledge and associated social affective features. Specifically, activation for famous faces was primarily right lateralized and famous names were left-lateralized. However, for both stimuli, similar areas of bilateral activity were observed in the early phases of perceptual processing. Activation for fame, irrespective of stimulus modality, activated an extensive left hemisphere network, with bilateral activity observed in the hippocampi, posterior cingulate, and middle temporal gyri. Findings are discussed within the framework of recent proposals concerning the neural network of person identification

Randomized clinical trial on epidural versus patient-controlled analgesia for laparoscopic colorectal surgery within an enhanced recovery pathway.

OBJECTIVE: To compare epidural analgesia (EDA) to patient-controlled opioid-based analgesia (PCA) in patients undergoing laparoscopic colorectal surgery. BACKGROUND: EDA is mainstay of multimodal pain management within enhanced recovery pathways [enhanced recovery after surgery (ERAS)]. For laparoscopic colorectal resections, the benefit of epidurals remains debated. Some consider EDA as useful, whereas others perceive epidurals as unnecessary or even deleterious. METHODS: A total of 128 patients undergoing elective laparoscopic colorectal resections were enrolled in a randomized clinical trial comparing EDA versus PCA. Primary end point was medical recovery. Overall complications, hospital stay, perioperative vasopressor requirements, and postoperative pain scores were secondary outcome measures. Analysis was performed according to the intention-to-treat principle. RESULTS: Final analysis included 65 EDA patients and 57 PCA patients. Both groups were similar regarding baseline characteristics. Medical recovery required a median of 5 days (interquartile range [IQR], 3-7.5 days) in EDA patients and 4 days (IQR, 3-6 days) in the PCA group (P = 0.082). PCA patients had significantly less overall complications [19 (33%) vs 35 (54%); P = 0.029] but a similar hospital stay [5 days (IQR, 4-8 days) vs 7 days (IQR, 4.5-12 days); P = 0.434]. Significantly more EDA patients needed vasopressor treatment perioperatively (90% vs 74%, P = 0.018), the day of surgery (27% vs 4%, P < 0.001), and on postoperative day 1 (29% vs 4%, P < 0.001), whereas no difference in postoperative pain scores was noted. CONCLUSIONS: Epidurals seem to slow down recovery after laparoscopic colorectal resections without adding obvious benefits. EDA can therefore not be recommended as part of ERAS pathways in laparoscopic colorectal surgery

Gentamicin-loaded microspheres for reducing the intracellular Brucella abortus load in infected monocytes

Objectives: The intracellular antibiotic efficiency of gentamicin-loaded microspheres in the context of Brucella-infected murine monocytes was examined in vitro with a view to developing improved therapies for the treatment of brucellosis. Methods: Biodegradable microspheres made of end-group capped and uncapped poly(lactide-co-glycolide) 50:50 (PLGA 50:50 and PLGA 50:50H) and containing gentamicin sulphate were used to target Brucella abortus-infected J774 monocyte-macrophages. The infected cells were treated with 15 µg of free or microencapsulated gentamicin and the efficacy of the treatments was measured after 24 h. Results: The particle sizes were below 8 µm and in vitro release of gentamicin from the microspheres followed a continuous (PLGA 50:50H) or a multiphasic (PLGA 50:50) pattern over 50 days. Treatment with gentamicin microencapsulated into the end-group uncapped PLGA 50:50H microspheres, decreased significantly the number of intracellular bacteria (typically by 2 log10) in comparison with untreated infected cells. Addition of 2% poloxamer 188 to the microsphere dispersion medium further reduced the infection (3.5 log10). Opsonization of the particles with non-immune mouse serum had no effect on the antibacterial efficacy of the microspheres. End-group capped PLGA 50:50 type microspheres containing the antibiotic were less effective at reducing intracellular bacteria (∼1 log10 reduction), although addition of poloxamer 188 to the dispersion medium again enhanced their intracellular antibacterial activity. Placebo PLGA 50:50 and PLGA 50:50H microspheres had no bactericidal activity. Conclusions: The results indicate that PLGA 50:50-microencapsulated gentamicin sulphate may be suitable for efficient drug targeting and delivery to reduce intracellular Brucella infection

Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator

We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly. We propose solving the related constant coefficient Helmholtz equation with Fast Fourier Transform (FFT) based on carefully designed extensions and restrictions of the equation. The proposed Fourier method, combined with proper eigensolver, results in an efficient and clear approach for computing the Stekloff eigenvalues.Comment: 12 pages, 4 figure

In vitro cell compatibility and antibacterial activity of microencapsulated doxycycline designed for improved localized therapy of septic arthritis

OBJECTIVES: For the treatment of septic arthritis in large animals, the local application of antibiotics as a slow release system may be an appropriate means to reach high local bioactivity and low systemic side effects and drug residues. In this study, doxycycline microspheres were developed and tested in vitro for their drug-release properties, suitability for intra-articular application and antimicrobial activity. METHODS: The development of a slow release system was achieved by microencapsulation of the drug into poly(lactide-co-glycolide) microspheres by a novel ultrasonic atomization method. Drug elution was evaluated from microspheres dispersed in elution medium at pre-defined time points by HPLC. Joint-tissue compatibility was tested on cultured bovine synoviocytes by evaluating the expression of pro-inflammatory cytokine mRNA and the production of nitric oxide (NO). Finally, the antimicrobial activity of the released antibiotic was assessed with gram-negative and gram-positive bacteria exposed to release medium sampled at days 1, 7 and 12 after microsphere suspension. RESULTS: An adequate size of the microspheres, sufficient stabilization of doxycycline in aqueous environment and drug release (25 mg microspheres in 4 mL medium) above MIC for bacteria usually isolated in bovine and equine joints were obtained over 15 days. Although the cytokine mRNA expression reflected the excellent tissue compatibility, the results with NO yielded contradictory results. Antimicrobial tests of the release medium proved to match perfectly the activity of non-encapsulated, free doxycycline as reported in the literature. CONCLUSIONS: The newly developed doxycycline delivery system achieved the target specifications and is ready for in vivo testin