The matrix metalloproteinase inhibitor RS-130830 attenuates brain injury in experimental pneumococcal meningitis.

BACKGROUND Pneumococcal meningitis (PM) is characterized by high mortality and morbidity including long-term neurofunctional deficits. Neuropathological correlates of these sequelae are apoptosis in the hippocampal dentate gyrus and necrosis in the cortex. Matrix metalloproteinases (MMPs) play a critical role in the pathophysiology of PM. RS-130830 (Ro-1130830, CTS-1027) is a potent partially selective inhibitor of MMPs of a second generation and has been evaluated in clinical trials as an anti-arthritis drug. It inhibits MMPs involved in acute inflammation but has low activity against MMP-1 (interstitial collagenase), MMP-7 (matrilysin) and tumour necrosis factor α converting enzyme (TACE). METHODS A well-established infant rat model of PM was used where live Streptococcus pneumoniae were injected intracisternally and antibiotic treatment with ceftriaxone was initiated 18 h post infection (hpi). Treatment with RS-130830 (75 mg/kg bis in die (bid) i.p., n = 40) was started at 3 hpi while control littermates received the vehicle (succinylated gelatine, n = 42). RESULTS Cortical necrosis was significantly attenuated in animals treated with RS-130830, while the extent of hippocampal apoptosis was not influenced. At 18 hpi, concentrations of interleukin (IL)-1β and IL-10 were significantly lower in the cerebrospinal fluid of treated animals compared to controls. RS-130830 significantly reduced weight loss and leukocyte counts in the cerebrospinal fluid of survivors of PM. CONCLUSION This study identifies MMP inhibition, specifically with RS-130830, as an efficient strategy to attenuate disease severity and cortical brain injury in PM.

Comparison of the capacity of enamel matrix derivative gel and enamel matrix derivative in liquid formulation to adsorb to bone grafting materials.

BACKGROUND The use of an enamel matrix derivative (EMD) has been shown to enhance periodontal regeneration (e.g., formation of root cementum, periodontal ligament, and alveolar bone). However, in certain clinical situations, the use of EMD alone may not be sufficient to prevent flap collapse or provide sufficient stability of the blood clot. Data from clinical and preclinical studies have demonstrated controversial results after application of EMD combined with different types of bone grafting materials in periodontal regenerative procedures. The aim of the present study is to investigate the adsorption properties of enamel matrix proteins to bone grafts after surface coating with either EMD (as a liquid formulation) or EMD (as a gel formulation). METHODS Three different types of grafting materials, including a natural bone mineral (NBM), demineralized freeze-dried bone allograft (DFDBA), or a calcium phosphate (CaP), were coated with either EMD liquid or EMD gel. Samples were analyzed by scanning electron microscopy or transmission electron microscopy (TEM) using an immunostaining assay with gold-conjugated anti-EMD antibody. Total protein adsorption to bone grafting material was quantified using an enzyme-linked immunosorbent assay (ELISA) kit for amelogenin. RESULTS The adsorption of amelogenin to the surface of grafting material varied substantially based on the carrier system used. EMD gel adsorbed less protein to the surface of grafting particles, which easily dissociated from the graft surface after phosphate-buffered saline rinsing. Analyses by TEM revealed that adsorption of amelogenin proteins were significantly farther from the grafting material surface, likely a result of the thick polyglycolic acid gel carrier. ELISA protein quantification assay demonstrated that the combination of EMD liquid + NBM and EMD liquid + DFDBA adsorbed higher amounts of amelogenin than all other treatment modalities. Furthermore, amelogenin proteins delivered by EMD liquid were able to penetrate the porous surface structure of NBM and DFDBA and adsorb to the interior of bone grafting particles. Grafting materials coated with EMD gel adsorbed more frequently to the exterior of grafting particles with little interior penetration. CONCLUSIONS The present study demonstrates a large variability of adsorbed amelogenin to the surface of bone grafting materials when enamel matrix proteins were delivered in either a liquid formulation or gel carrier. Furthermore, differences in amelogenin adsorption were observed among NBM, DFDBA, and biphasic CaP particles. Thus, the potential for a liquid carrier system for EMD, used to coat EMD, may be advantageous for better surface coating.

Healing of localized gingival recessions treated with coronally advanced flap alone or combined with either a resorbable collagen matrix or subepithelial connective tissue graft: A preclinical study.

OBJECTIVES To histologically evaluate the effectiveness of a porcine derived collagen matrix (CM) and a subepithelial connective tissue graft (CTG) for coverage of localized gingival recessions. MATERIALS AND METHODS Chronic single Miller Class I-like recessions were created at the buccal at the canines and at the third and fourth premolars in the upper and lower jaws of six beagle dogs. The defects were randomly treated with (1) coronally advanced flap surgery (CAF) + CM, (2) CAF + CTG, or (3) CAF alone. At 12 weeks, histometric measurements were made, e.g., between a reference point (N) - and the gingival margin (GM) - and the outer contour of the adjacent soft tissue (gingival thickness [GT]). RESULTS The postoperative healing was uneventful in all animals. No complications such as allergic reactions, abscesses or infections were noted throughout the entire study period. All three treatments resulted in coverage of localized gingival recessions. The histological analysis failed to identify any residues of CM or CTG. The histometric measurements revealed comparable outcomes for N-GM and GT values for all three groups (CAF + CM: 1.04 ± 0.69 mm/0.68 ± 0.33 mm; CAF + CTG: 1.15 ± 1.12 mm/0.76 ± 0.37 mm; CAF: 1.43 ± 0.45 mm/0.79 ± 0.24 mm). CONCLUSIONS In the used defect model, the application of CTG or CM in conjunction with CAF did not have an advantage over the use of CAF alone. CLINICAL RELEVANCE The use of CAF alone is a valuable option for the treatment localized Miller Class I recessions.

Effect of bone graft density on in vitro cell behavior with enamel matrix derivative

OBJECTIVES Bone replacement grafting materials play an important role in regenerative dentistry. Despite a large array of tested bone-grafting materials, little information is available comparing the effects of bone graft density on in vitro cell behavior. Therefore, the aim of the present study is to compare the effects of cells seeded on bone grafts at low and high density in vitro for osteoblast adhesion, proliferation, and differentiation. MATERIALS AND METHODS The response of osteoblasts to the presence of a growth factor (enamel matrix derivative, (EMD)) in combination with low (8 mg per well) or high (100 mg per well) bone grafts (BG; natural bone mineral, Bio-Oss®) density, was studied and compared for osteoblast cell adhesion, proliferation, and differentiation as assessed by real-time PCR. Standard tissue culture plastic was used as a control with and without EMD. RESULTS The present study demonstrates that in vitro testing of bone-grafting materials is largely influenced by bone graft seeding density. Osteoblast adhesion was up to 50 % lower when cells were seeded on high-density BG when compared to low-density BG and control tissue culture plastic. Furthermore, proliferation was affected in a similar manner whereby cell proliferation on high-density BG (100 mg/well) was significantly increased when compared to that on low-density BG (8 mg/well). In contrast, cell differentiation was significantly increased on high-density BG as assessed by real-time PCR for markers collagen 1 (Col 1), alkaline phosphatase (ALP), and osteocalcin (OC) as well as alizarin red staining. The effects of EMD on osteoblast adhesion, proliferation, and differentiation further demonstrated that the bone graft seeding density largely controls in vitro results. EMD significantly increased cell attachment only on high-density BG, whereas EMD was able to further stimulate cell proliferation and differentiation of osteoblasts on control culture plastic and low-density BG when compared to high-density BG. CONCLUSION The results from the present study demonstrate that the in vitro conditions largely influence cell behavior of osteoblasts seeded on bone grafts and in vitro testing. CLINICAL RELEVANCE These results also illustrate the necessity for careful selection of bone graft seeding density to optimize in vitro testing and provide the clinician with a more accurate description of the osteopromotive potential of bone grafts.

Enamel matrix derivative and bone grafts for periodontal regeneration of intrabony defects. A systematic review and meta-analysis

OBJECTIVE The aim of the present systematic review and meta-analysis was to assess the clinical efficacy of regenerative periodontal surgery of intrabony defects using a combination of enamel matrix derivative (EMD) and bone graft compared with that of EMD alone. MATERIALS AND METHODS The Cochrane Oral Health Group specialist trials, MEDLINE, and EMBASE databases were searched for entries up to February 2014. The primary outcome was gain of clinical attachment (CAL). Weighted means and forest plots were calculated for CAL gain, probing depth (PD), and gingival recession (REC). RESULTS Twelve studies reporting on 434 patients and 548 intrabony defects were selected for the analysis. Mean CAL gain amounted to 3.76 ± 1.07 mm (median 3.63 95 % CI 3.51-3.75) following treatment with a combination of EMD and bone graft and to 3.32 ± 1.04 mm (median 3.40; 95 % CI 3.28-3.52) following treatment with EMD alone. Mean PD reduction measured 4.22 ± 1.20 mm (median 4.10; 95 % CI 3.96-4.24) at sites treated with EMD and bone graft and yielded 4.12 ± 1.07 mm (median 4.00; 95 % CI 3.88-4.12) at sites treated with EMD alone. Mean REC increase amounted to 0.76 ± 0.42 mm (median 0.63; 95 % CI 0.58-0.68) at sites treated with EMD and bone graft and to 0.91 ± 0.26 mm (median 0.90; 95 % CI 0.87-0.93) at sites treated with EMD alone. CONCLUSIONS Within their limits, the present results indicate that the combination of EMD and bone grafts may result in additional clinical improvements in terms of CAL gain and PD reduction compared with those obtained with EMD alone. The potential influence of the chosen graft material or of the surgical procedure (i.e., flap design) on the clinical outcomes is unclear. CLINICAL RELEVANCE The present findings support the use of EMD and bone grafts for the treatment of intrabony periodontal defects.

Effect of nonsurgical periodontal treatment in conjunction with either systemic administration of amoxicillin and metronidazole or additional photodynamic therapy on the concentration of matrix metalloproteinases 8 and 9 in gingival crevicular fluid in patients with aggressive periodontitis.

BACKGROUND To evaluate in patients with aggressive periodontitis (AgP) the effect of nonsurgical periodontal treatment in conjunction with either additional administration of systemic antibiotics (AB) or application of photodynamic therapy (PDT) on the gingival crevicular fluid (GCF) concentration of matrix metalloproteinases 8 and 9 (MMP-8 and -9). METHODS Thirty-six patients with AgP were included in the study. Patients were randomly assigned to treatment with either scaling and root planing (SRP) followed by systemic administration of AB (e.g. Amoxicillin + Metronidazole) or SRP + PDT. The analysis of MMP-8 and -9 GCF concentrations was performed at baseline and at 3 and 6 months after treatment. Nonparametric U-Mann-Whitney test was used for comparison between groups. Changes from baseline to 3 and 6 months were analyzed with the Friedman's ANOVA test with Kendall's index of consistency. RESULTS In the AB group, patients showed a statistically significant (p = 0.01) decrease of MMP-8 GCF level at both 3 and 6 months post treatment. In the PDT group, the change of MMP-8 GCF level was not statistically significant. Both groups showed at 3 and 6 months a decrease in MMP-9 levels. However, this change did not reach statistical significance. CONCLUSIONS Within the limits of the present study, it may be suggested that in patients with AgP, nonsurgical periodontal therapy in conjunction with adjunctive systemic administration of amoxicilin and metronidazole is more effective in reducing GCF MMP-8 levels compared to the adjunctive use of PDT.

Activating enhancer binding protein 2 epsilon (AP-2ε)-deficient mice exhibit increased matrix metalloproteinase 13 expression and progressive osteoarthritis development.

INTRODUCTION The transcription factor activating enhancer binding protein 2 epsilon (AP-2ε) was recently shown to be expressed during chondrogenesis as well as in articular chondrocytes of humans and mice. Furthermore, expression of AP-2ε was found to be upregulated in affected cartilage of patients with osteoarthritis (OA). Despite these findings, adult mice deficient for AP-2ε (Tfap2e(-/-)) do not exhibit an obviously abnormal cartilaginous phenotype. We therefore analyzed embryogenesis of Tfap2e(-/-) mice to elucidate potential transient abnormalities that provide information on the influence of AP-2ε on skeletal development. In a second part, we aimed to define potential influences of AP-2ε on articular cartilage function and gene expression, as well as on OA progression, in adult mice. METHODS Murine embryonic development was accessed via in situ hybridization, measurement of skeletal parameters and micromass differentiation of mesenchymal cells. To reveal discrepancies in articular cartilage of adult wild-type (WT) and Tfap2e(-/-) mice, light and electron microscopy, in vitro culture of cartilage explants, and quantification of gene expression via real-time PCR were performed. OA was induced via surgical destabilization of the medial meniscus in both genotypes, and disease progression was monitored on histological and molecular levels. RESULTS Only minor differences between WT and embryos deficient for AP-2ε were observed, suggesting that redundancy mechanisms effectively compensate for the loss of AP-2ε during skeletal development. Surprisingly, though, we found matrix metalloproteinase 13 (Mmp13), a major mediator of cartilage destruction, to be significantly upregulated in articular cartilage of adult Tfap2e(-/-) mice. This finding was further confirmed by increased Mmp13 activity and extracellular matrix degradation in Tfap2e(-/-) cartilage explants. OA progression was significantly enhanced in the Tfap2e(-/-) mice, which provided evidence for in vivo relevance. This finding is most likely attributable to the increased basal Mmp13 expression level in Tfap2e(-/-) articular chondrocytes that results in a significantly higher total Mmp13 expression rate during OA as compared with the WT. CONCLUSIONS We reveal a novel role of AP-2ε in the regulation of gene expression in articular chondrocytes, as well as in OA development, through modulation of Mmp13 expression and activity.

Effect of Enamel Matrix Derivative Liquid on Osteoblast and Periodontal Ligament Cell Proliferation and Differentiation.

BACKGROUND Enamel matrix derivatives (EMDs) have been used clinically for more than a decade for the regeneration of periodontal tissues. The aim of the present study is to analyze the effect on cell growth of EMDs in a gel carrier in comparison to EMDs in a liquid carrier. EMDs in a liquid carrier have been shown to adsorb better to bone graft materials. METHODS Primary human osteoblasts and periodontal ligament (PDL) cells were exposed to EMDs in both gel and liquid carriers and compared for their ability to induce cell proliferation and differentiation. Alizarin red staining and real-time polymerase chain reaction for expression of genes encoding collagen 1, osteocalcin, and runt-related transcription factor 2, as well as bone morphogenetic protein 2 (BMP2), transforming growth factor (TGF)-β1, and interleukin (IL)-1β, were assessed. RESULTS EMDs in both carriers significantly increased cell proliferation of both osteoblasts and PDL cells in a similar manner. Both formulations also significantly upregulated the expression of genes encoding BMP2 and TGF-β1 as well as decreased the expression of IL-1β. EMDs in the liquid carrier further retained similar differentiation potential of both osteoblasts and PDL cells by demonstrating increased collagen and osteocalcin gene expression and significantly higher alizarin red staining. CONCLUSIONS The results from the present study indicate that the new formulation of EMDs in a liquid carrier is equally as potent as EMDs in a gel carrier in inducing osteoblast and PDL activity. Future study combining EMDs in a liquid carrier with bone grafting materials is required to further evaluate its potential for combination therapies.

Development of combined micro -preparation, separation, and mass spectrometry methods and application in the microdialysis study of neuropeptide metabolism

Two sets of mass spectrometry-based methods were developed specifically for the in vivo study of extracellular neuropeptide biochemistry. First, an integrated micro-concentration/desalting/matrix-addition device was constructed for matrix-assisted laser desorption ionization mass spectrometry (MALDI MS) to achieve attomole sensitivity for microdialysis samples. Second, capillary electrophoresis (CE) was incorporated into the above micro-liquid chromatography (LC) and MALDI MS system to provide two-dimensional separation and identification (i.e. electrophoretic mobility and molecular mass) for the analysis of complex mixtures. The latter technique includes two parts of instrumentation: (1) the coupling of a preconcentration LC column to the inlet of a CE capillary, and (2) the utilization of a matrix-precoated membrane target for continuous CE effluent deposition and for automatic MALDI MS analysis (imaging) of the CE track.^ Initial in vivo data reveals a carboxypeptidase A (CPA) activity in rat brain involved in extracellular neurotensin metabolism. Benzylsuccinic acid, a CPA inhibitor, inhibited neurotensin metabolite NT1-12 formation by 70%, while inhibitors of other major extracellular peptide metabolizing enzymes increased NT1-12 formation. CPA activity has not been observed in previous in vitro experiments. Next, the validity of the methodology was demonstrated in the detection and structural elucidation of an endogenous neuropeptide, (L)VV-hemorphin-7, in rat brain upon ATP stimulation. Finally, the combined micro-LC/CE/MALDI MS was used in the in vivo metabolic study of peptide E, a mu-selective opioid peptide with 25 amino acid residues. Profiles of 88 metabolites were obtained, their identity being determined by their mass-to-charge ratio and electrophoretic mobility. The results indicate that there are several primary cleavage sites in vivo for peptide E in the release of its enkephalin-containing fragments. ^

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Efficient numerical methods for global linear instability. Analysis and modeling of non-orthogonal swept attachment-line boundary layer flow

The aim of this thesis is to study the mechanisms of instability that occur in swept wings when the angle of attack increases. For this, a simplified model for the a simplified model for the non-orthogonal swept leading edge boundary layer has been used as well as different numerical techniques in order to solve the linear stability problem that describes the behavior of perturbations superposed upon this base flow. Two different approaches, matrix-free and matrix forming methods, have been validated using direct numerical simulations with spectral resolution. In this way, flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via the solution of the pertinent global (Bi-Global) PDE-based eigenvalue problem. Subsequently, a simple extension of the extended G¨ortler-H¨ammerlin ODEbased polynomial model proposed by Theofilis, Fedorov, Obrist & Dallmann (2003) for orthogonal flow, which includes previous models as particular cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the stability results and unravel the limits of validity of the basic flow model analyzed. The effect of the angle of attack, AoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from AoA = 0 (orthogonal flow) up to values close to _/2 which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at 0 _ AoA _ _/2 are shown to be recoverable from those of orthogonal flow, via a simple analytical transformation involving AoA. These results can help to understand the mechanisms of destabilization that occurs in the attachment line of wings at finite angles of attack. Studies taking into account variations of the pressure field in the basic flow or the extension to compressible flows are issues that remain open. El objetivo de esta tesis es estudiar los mecanismos de la inestabilidad que se producen en ciertos dispositivos aerodinámicos cuando se aumenta el ángulo de ataque. Para ello se ha utilizado un modelo simplificado del flujo de base, así como diferentes técnicas numéricas, con el fin de resolver el problema de estabilidad lineal asociado que describe el comportamiento de las perturbaciones. Estos métodos; sin y con formación de matriz, se han validado utilizando simulaciones numéricas directas con resolución espectral. De esta manera, la inestabilidad del flujo de capa límite laminar oblicuo entorno a la línea de estancamiento se aborda en un marco de análisis lineal por medio del método Bi-Global de resolución del problema de valores propios en derivadas parciales. Posteriormente se propone una extensión simple para el flujo no-ortogonal del modelo polinomial de ecuaciones diferenciales ordinarias, G¨ortler-H¨ammerlin extendido, propuesto por Theofilis et al. (2003) para el flujo ortogonal, que incluye los modelos previos como casos particulares y recupera los resultados del analisis global de estabilidad lineal. Se han realizado simulaciones directas con el fin de verificar los resultados del análisis de estabilidad así como para investigar los límites de validez del modelo de flujo base utilizado. En este trabajo se ha documentado el efecto del ángulo de ataque AoA en las condiciones críticas del problema no ortogonal obteniendo que el incremento del ángulo de ataque, de AoA = 0 (flujo ortogonal) hasta valores próximos a _/2, en el cual las hipótesis sobre las que se basa el flujo base dejan de ser válidas, tiende sistemáticamente a desestabilizar el flujo. Las condiciones críticas del caso no ortogonal 0 _ AoA _ _/2 pueden recuperarse a partir del caso ortogonal mediante el uso de una transformación analítica simple que implica el ángulo de ataque AoA. Estos resultados pueden ayudar a comprender los mecanismos de desestabilización que se producen en el borde de ataque de las alas de los aviones a ángulos de ataque finitos. Como tareas pendientes quedaría realizar estudios que tengan en cuenta variaciones del campo de presión en el flujo base así como la extensión de éste al caso de flujos compresibles.

Order 10 4 speedup in global linear instability analysis using matrix formation

A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.

Numerical methods for option pricing.

This thesis aims to introduce some fundamental concepts underlying option valuation theory including implementation of computational tools. In many cases analytical solution for option pricing does not exist, thus the following numerical methods are used: binomial trees, Monte Carlo simulations and finite difference methods. First, an algorithm based on Hull and Wilmott is written for every method. Then these algorithms are improved in different ways. For the binomial tree both speed and memory usage is significantly improved by using only one vector instead of a whole price storing matrix. Computational time in Monte Carlo simulations is reduced by implementing a parallel algorithm (in C) which is capable of improving speed by a factor which equals the number of processors used. Furthermore, MatLab code for Monte Carlo was made faster by vectorizing simulation process. Finally, obtained option values are compared to those obtained with popular finite difference methods, and it is discussed which of the algorithms is more appropriate for which purpose.