REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Two-matrix string model as constrained (2+1)-dimensional integrable system

We show that the 2-matrix string model corresponds to a coupled system of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific symmetry constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Backhand transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.

Search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks using a matrix element method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

Reference model for implementing an MRP system in a highly diverse component and seasonal lean production environment

Companies are currently choosing to integrate logics and systems to achieve better solutions. These combinations also include companies striving to join the logic of material requirement planning (MRP) system with the systems of lean production. The purpose of this article was to design an MRP as part of the implementation of an enterprise resource planning (ERP) in a company that produces agricultural implements, which has used the lean production system since 1998. This proposal is based on the innovation theory, theory networks, lean production systems, ERP systems and the hybrid production systems, which use both components and MRP systems, as concepts of lean production systems. The analytical approach of innovation networks enables verification of the links and relationships among the companies and departments of the same corporation. The analysis begins with the MRP implementation project carried out in a Brazilian metallurgical company and follows through the operationalisation of the MRP project, until its production stabilisation. The main point is that the MRP system should help the company's operations with regard to its effective agility to respond in time to demand fluctuations, facilitating the creation process and controlling the branch offices in other countries that use components produced in the matrix, hence ensuring more accurate estimates of stockpiles. Consequently, it presents the enterprise knowledge development organisational modelling methodology in order to represent further models (goals, actors and resources, business rules, business process and concepts) that should be included in this MRP implementation process for the new configuration of the production system.

The r-matrix of the Alday-Arutyunov-Frolov model

We investigate the classical integrability of the Alday-Arutyunov-Frolov model, and show that the Lax connection can be reduced to a simpler 2 x 2 representation. Based on this result, we calculate the algebra between the L-operators and find that it has a highly non-ultralocal form. We then employ and make a suitable generalization of the regularization technique proposed by Mail let for a simpler class of non-ultralocal models, and find the corresponding r- and s-matrices. We also make a connection between the operator-regularization method proposed earlier for the quantum case, and the Mail let's symmetric limit regularization prescription used for non-ultralocal algebras in the classical theory.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Influence of diurnal hyperosmotic loading on the metabolism and matrix gene expression of a whole-organ intervertebral disc model

It is generally agreed that the mechanical environment of intervertebral disc cells plays an important role in maintaining a balanced matrix metabolism. The precise mechanism by which the signals are transduced into the cells is poorly understood. Osmotic changes in the extracellular matrix (ECM) are thought to be involved. Current in-vitro studies on this topic are mostly short-term and show conflicting data on the reaction of disc cells subjected to osmotic changes which is partially due to the heterogenous and often substantially-reduced culture systems. The aim of the study was therefore to investigate the effects of cyclic osmotic loading for 4 weeks on metabolism and matrix gene expression in a full-organ intervertebral disc culture system. Intervertebral disc/endplate units were isolated from New Zealand White Rabbits and cultured either in iso-osmotic media (335 mosmol/kg) or were diurnally exposed for 8 hours to hyper-osmotic conditions (485 mosmol/kg). Cell viability, metabolic activity, matrix composition and matrix gene expression profile (collagen types I/II and aggrecan) were monitored using Live/Dead cell viability assay, tetrazolium reduction test (WST 8), proteoglycan and DNA quantification assays and quantitative PCR. The results show that diurnal osmotic stimulation did not have significant effects on proteoglycan content, cellularity and disc cell viability after 28 days in culture. However, hyperosmolarity caused increased cell death in the early culture phase and counteracted up-regulation of type I collagen gene expression in nucleus and annulus cells. Moreover, the initially decreased cellular dehydrogenase activity recovered with osmotic stimulation after 4 weeks and aggrecan gene down-regulation was delayed, although the latter was not significant according to our statistical criteria. In contrast, collagen type II did not respond to the osmotic changes and was down-regulated in both groups. In conclusion, diurnal hyper-osmotic stimulation of a whole-organ disc/endplate culture partially inhibits a matrix gene expression profile as encountered in degenerative disc disease and counteracts cellular metabolic hypo-activity.

Generalizability and Applicability of Model-Based Business Process Compliance-Checking Approaches – A State-of-the-Art Analysis and Research Roadmap

With a steady increase of regulatory requirements for business processes, automation support of compliance management is a field garnering increasing attention in Information Systems research. Several approaches have been developed to support compliance checking of process models. One major challenge for such approaches is their ability to handle different modeling techniques and compliance rules in order to enable widespread adoption and application. Applying a structured literature search strategy, we reflect and discuss compliance-checking approaches in order to provide an insight into their generalizability and evaluation. The results imply that current approaches mainly focus on special modeling techniques and/or a restricted set of types of compliance rules. Most approaches abstain from real-world evaluation which raises the question of their practical applicability. Referring to the search results, we propose a roadmap for further research in model-based business process compliance checking.

Assessment of the Matrix Degenerative Effects of MMP-3, ADAMTS-4 and HTRA1 injected into a bovine Intervertebral Disc Organ Culture Model

Study Design. In vitro study to develop an intervertebral disc degeneration (IDD) organ culture model, using coccygeal bovine intervertebral discs (IVDs) and injection of proteolytic enzymes MMP-3, ADAMTS-4 and HTRA1.Objective. This study aimed to develop an in-vitro model of enzyme-mediated IDD to mimic the clinical outcome in humans for investigation of therapeutic treatment options.Summary of Background Data. Bovine IVDs are comparable to human IVDs in terms of cell composition and biomechanical behavior. Researchers injected papain and trypsin into them to create an IDD model with a degenerated nucleus pulposus (NP) area. They achieved macroscopic cavities as well as a loss of glycosaminoglycans (GAGs). However, none of these enzymes are clinically relevant.Methods. Bovine IVDs were harvested maintaining the endplates. Active forms of MMP-3, ADAMTS-4 and HTRA1 were injected at a dose of 10μg/ml each. Phosphate buffered saline (PBS) was injected as a control. Discs were cultured for 8 days and loaded diurnally (day 1 to day 4 with 0.4 MPa for 16 h) and left under free swelling condition from day 4 to day 8 to avoid expected artifacts due to dehydration of the NP. Outcome parameters included disc height, metabolic cell activity, DNA content, glycosaminoglycan (GAG) content, total collagen content, relative gene expression and histological investigation.Results. The mean metabolic cell activity was significantly lower in the NP area of discs injected with ADAMTS-4 compared to the day 0 control discs. Disc height was decreased following injection with HTRA1, and was significantly correlated with changes in GAG/DNA of the NP tissue. Total collagen content tended to be lower in groups injected with ADAMTS4 and MMP-3.Conclusion. MMP-3, ADAMTS-4 and HTRA1 neither provoked visible matrix degradation nor major shifts in gene expression. However, cell activity was significantly reduced and HTRA1 induced loss of disc height which positively correlated with changes in GAG/DNA content. The use of higher doses of these enzymes or a combination thereof may therefore be necessary to induce disc degeneration

Levels of matrix metalloproteinase-9 within cerebrospinal fluid in a rabbit model of coccidioidal meningitis and vasculitis.

Matrix metalloproteinase (MMP)-9 is produced by the central nervous system and inflammatory cells in a variety of inflammatory conditions in both animals and humans. MMP-9 promotes inflammation, breakdown of the blood-brain barrier, and vasculitis. Because vasculitis is seen frequently in patients with coccidioidal meningitis (CM), this study evaluated the presence of MMP-9 within the cerebrospinal fluid (CSF) of rabbits infected intracisternally with Coccidioides immitis arthroconidia. Infected rabbits demonstrated systemic and neurological sequelae to infection, including CSF pleocytosis. Levels of MMP-9 within CSF were assayed by use of zymography and compared with MMP-2 levels, which served as an internal control. Elevated levels of MMP-9 were detectable by day 3, continued to increase through day 10, and declined by day 15 after infection. MMP-9 may contribute to inflammation and vasculitis in this animal model. Future work can focus on evaluation of MMP inhibitors, to gain a better perspective of the role of this MMP in CM.

Dominance of chemokine ligand 2 and matrix metalloproteinase-2 and -9 and suppression of pro-inflammatory cytokines in the epidural compartment after intervertebral disc extrusion in a canine model

BACKGROUND CONTEXT In canine intervertebral disc (IVD) disease, a useful animal model, only little is known about the inflammatory response in the epidural space. PURPOSE To determine messenger RNA (mRNA) expressions of selected cytokines, chemokines, and matrix metalloproteinases (MMPs) qualitatively and semiquantitatively over the course of the disease and to correlate results to neurologic status and outcome. STUDY DESIGN/SETTING Prospective study using extruded IVD material of dogs with thoracolumbar IVD extrusion. PATIENT SAMPLE Seventy affected and 13 control (24 samples) dogs. OUTCOME MEASURES Duration of neurologic signs, pretreatment, neurologic grade, severity of pain, and outcome were recorded. After diagnostic imaging, decompressive surgery was performed. METHODS Messenger RNA expressions of interleukin (IL)-1β, IL-2, IL-4, IL-6, IL-8, IL-10, tumor necrosis factor (TNF), interferon (IFN)γ, MMP-2, MMP-9, chemokine ligand (CCL)2, CCL3, and three housekeeping genes was determined in the collected epidural material by Panomics 2.0 QuantiGene Plex technology. Relative mRNA expression and fold changes were calculated. Relative mRNA expression was correlated statistically to clinical parameters. RESULTS Fold changes of TNF, IL-1β, IL-2, IL-4, IL-6, IL-10, IFNγ, and CCL3 were clearly downregulated in all stages of the disease. MMP-9 was downregulated in the acute stage and upregulated in the subacute and chronic phase. Interleukin-8 was upregulated in acute cases. MMP-2 showed mild and CCL2 strong upregulation over the whole course of the disease. In dogs with severe pain, CCL3 and IFNγ were significantly higher compared with dogs without pain (p=.017/.020). Dogs pretreated with nonsteroidal anti-inflammatory drugs revealed significantly lower mRNA expression of IL-8 (p=.017). CONCLUSIONS The high CCL2 levels and upregulated MMPs combined with downregulated T-cell cytokines and suppressed pro-inflammatory genes in extruded canine disc material indicate that the epidural reaction is dominated by infiltrating monocytes differentiating into macrophages with tissue remodeling functions. These results will help to understand the pathogenic processes representing the basis for novel therapeutic approaches. The canine IVD disease model will be rewarding in this process.

Effect of enamel matrix derivative on periodontal wound healing and regeneration in an osteoporotic model.

BACKGROUND Despite the worldwide increased prevalence of osteoporosis, no data are available evaluating the effect of an enamel matrix derivative (EMD) on the healing of periodontal defects in patients with osteoporosis. This study aims to evaluate whether the regenerative potential of EMD may be suitable for osteoporosis-related periodontal defects. METHODS Forty female Wistar rats (mean body weight: 200 g) were used for this study. An osteoporosis animal model was carried out by bilateral ovariectomy (OVX) in 20 animals. Ten weeks after OVX, bilateral fenestration defects were created at the buccal aspect of the first mandibular molar. Animals were randomly assigned to four groups of 10 animals per group: 1) control animals with unfilled periodontal defects; 2) control animals with EMD-treated defects; 3) OVX animals with unfilled defects; and 4) OVX animals with EMD-treated defects. The animals were euthanized 28 days later, and the percentage of defect fill and thickness of newly formed bone and cementum were assessed by histomorphometry and microcomputed tomography (micro-CT) analysis. The number of osteoclasts was determined by tartrate-resistant acid phosphatase (TRAP), and angiogenesis was assessed by analyzing formation of blood vessels. RESULTS OVX animals demonstrated significantly reduced bone volume in unfilled defects compared with control defects (18.9% for OVX animals versus 27.2% for control animals) as assessed by micro-CT. The addition of EMD in both OVX and control animals resulted in significantly higher bone density (52.4% and 69.2%, respectively) and bone width (134 versus 165μm) compared with untreated defects; however, the healing in OVX animals treated with EMD was significantly lower than that in control animals treated with EMD. Animals treated with EMD also demonstrated significantly higher cementum formation in both control and OVX animals. The number of TRAP-positive osteoclasts did not vary between untreated and EMD-treated animals; however, a significant increase was observed in all OVX animals. The number of blood vessels and percentage of new vessel formation was significantly higher in EMD-treated samples. CONCLUSIONS The results from the present study suggest that: 1) an osteoporotic phenotype may decrease periodontal regeneration; and 2) EMD may support greater periodontal regeneration in patients suffering from the disease. Additional clinical studies are necessary to fully elucidate the possible beneficial effect of EMD for periodontal regeneration in patients suffering from osteoporosis.