Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

The application of Prony’s method to time-domain waveform data modeling in the presence of noise

In this paper,the Prony's method is applied to the time-domain waveform data modelling in the presence of noise.The following three problems encountered in this work are studied:(1)determination of the order of waveform;(2)de-termination of numbers of multiple roots;(3)determination of the residues.The methods of solving these problems are given and simulated on the computer.Finally,an output pulse of model PG-10N signal generator and the distorted waveform obtained by transmitting the pulse above mentioned through a piece of coaxial cable are modelled,and satisfactory results are obtained.So the effectiveness of Prony's method in waveform data modelling in the presence of noise is confirmed.

Fracture resistance of weakened roots restored with composite resin and glass fiber post

This study evaluated the fracture resistance of weakened roots restored with glass fiber posts, composite resin cores and complete metal crowns. Thirty maxillary canines were randomly divided into 3 groups of 10 teeth each: teeth without weakened roots (control); teeth with partially weakened roots (PWR) and teeth with and largely weakened roots (LWR). The control group was restored with glass fiber posts and a composite resin core. Teeth in the PWR and LWR groups were flared internally to standardized dimensions in order to simulate root weakness. Thereafter, the roots were partially filled with composite resin and restored in the same way as in the control group. The specimens were exposed to 250,000 cycles in a controlled chewing simulator. All intact specimens were subjected to a static load (N) in a universal testing machine at 45 degrees to the long axis of the tooth until failure. Data were analyzed by one-way ANOVA and Dunnett's test for multiple comparisons (p=0.05). There were statistically significant difference differences (p<0.01) among the groups (control group = 566.73 N; PWR = 409.64 N; and LWR = 410.91 N), with significantly higher fracture strength for the control group. There was no statistically significant difference (p>0.05) between the weakened groups. The results of this study showed that thicker root dentin walls significantly increase the fracture resistance of endodontically treated teeth.

TRANSFER OF A FASCICLE FROM THE POSTERIOR CORD TO THE SUPRASCAPULAR NERVE AFTER INJURY OF THE UPPER ROOTS OF THE BRACHIAL PLEXUS: TECHNICAL CASE REPORT

OBJECTIVE: A new nerve transfer technique using a healthy fascicle of the posterior cord for suprascapular nerve reconstruction is presented. This technique was used in a patient with posttraumatic brachial plexopathy resulting in upper trunk injury with proximal root stumps that were unavailable for grafting associated with multiple nerve dysfunction. CLINICAL PRESENTATION: A 45-year-old man sustained a right brachial plexus injury after a bicycle accident. Clinical evaluation and electromyography indicated upper trunk involvement. Trapezius muscle function and triceps strength were normal on physical examination. INTERVENTION: The patient underwent a combined supra- and infraclavicular approach to the brachial plexus. A neuroma-in-continuity of the upper trunk and fibrotic C5 and C6 roots were identified. Electrical stimulation of the phrenic and spinal accessory nerves produced no response. The suprascapular nerve was dissected from the upper trunk, transected, and rerouted to the infraclavicular fossa. A healthy fascicle of the posterior cord to the triceps muscle was transferred to the suprascapular nerve. At the time of the 1-year follow-up evaluation, arm abduction against gravity and external rotation reached 40 and 34 degrees, respectively. CONCLUSION: The posterior cord can be used as a source of donor fascicle to the suprascapular nerve after its infraclavicular relocation. This new intraplexal nerve transfer could be applied in patients with isolated injury of the upper trunk and concomitant lesion of the extraplexal nerve donors usually used for reinnervation of the suprascapular nerve.

Influence of Filling Materials on the Bonding Interface of Thin-walled Roots Reinforced with Resin and Quartz Fiber Posts

Introduction: A common complication during the restoration of severely destroyed teeth is the loss of coronal root dentine. The aim of this study was to evaluate the influence of different sealers on the bonding interface of weakened roots reinforced with resin and fiber posts. Methods: Sixty extracted maxillary canines were used. The crowns were removed, and the thickness of root dentine was reduced in the experimental (n = 40) and positive control (n = 10) groups. The specimens of experimental group were assigned to four subgroups (n = 10) according to the filling material: gutta-percha + Grossmann`s sealer, gutta-percha + AH Plus (Dentsply De Trey Gmbh, Konstanz, Germany), gutta-percha + Epiphany (Pentron Clinical Technologies, Wallingford, CT), and Resilon (Resilon Research LLC, Madison, CT) + Epiphany. In the negative control group (n = 10), canals were not filled. After post space preparation, the roots were restored with composite resin light-activated through a translucent fiber post. After 24 hours, specimens were transversally sectioned into 1-mm-thick slices. Push-out test and scanning electron microscopic (SEM) analyses of different regions were performed. Data from push-out test were analyzed by using Tukey post hoc multiple comparison tests. The percentage of failure type was calculated. Data from SEM analysis were compared by Friedman and Kruskal-Wallis tests (alpha = 0.05). Results: The mean bond strength was significantly higher in the negative control group as compared with the other groups (P < .05). In all groups, the most frequent type of failure was adhesive. Overall, apical and middle regions presented a lower density of resin tags than the coronal region (P < .05). Conclusions: The push-out bond strength was not affected by sealer or region. The canal region affected significantly the resin tag morphology and density at the bonding interface. (J Endod 2011;37:531-537)

The Roots of Neurofibromas in Neurofibromatosis 1 — A Question of Multipotency, Differentiation and Hiding

Neurofibromatosis type 1 (NF1) is an autosomal dominant cancer predisposition syndrome that affects about 1 in 3500 individuals worldwide. NF1 is caused by mutations in the NF1 gene that encodes the tumor suppressor protein neurofibromin, an inactivator of the Ras oncogene. The hallmarks of NF1 include pigmentary lesions of the skin, Lisch nodules of the iris and cutaneous neurofibromas. Cutaneous neurofibromas are benign tumors composed of all the cell types of normal peripheral nerve. The traditional view of neurofibroma development has been that cutaneous neurofibromas arise from the disruption of the small nerve tributaries of the skin and subsequent proliferation of the resident cells. The second hit mutation in the NF1 gene has been considered as a prerequisite for neurofibroma development. The second hit is detectable in a subpopulation of primary Schwann cells cultured from neurofibromas. This thesis challenges the traditional concept of neurofibroma development. The results show that cutaneous neurofibromas are intimately associated with hair follicular structures and contain multipotent precursor cells (NFPs), suggesting that neurofibromas may arise from the multipotent cells which reside in hair follicles. Furthermore, this study presents that neurofibroma-derived Schwann cells that harbor bi-allelic inactivation in the NF1 gene express HLA class II genes and may act as nonprofessional antigen presenting cells. The CD4- and FoxP3-positive cells detected in cutaneous neurofibromas suggest that these cells may represent regulatory T cells (Tregs) which interact with HLA II –positive cells and aid the tumor cells in hiding from the immune system and are thus mediators of immune tolerance. This thesis also investigated neurofibroma development in the oral cavity and the use of different biomarkers to characterize cellular differentiation in neurofibromas. The results revealed that oral neurofibromas are not rare, but they usually appear as solitary lesions contrary to multiple cutaneous neurofibromas and present high heterogeneity within and between tumors. The use of class III beta-tubulin as a marker for neuronal differentiation led to an unexpected finding showing that multiple cell types express class III beta-tubulin during mitosis. The increased understanding of the multipotency of tumor cells, cellular differentiation and ability to hide from immune system will aid in the development of future treatments. Specifically, targeting Tregs in NF1 patients could provide a novel therapeutic approach to interfere with the development of neurofibromas.

Conflict, wages, and multiple equilibria

Firms’ compensation practices affect the protection of investors’ interests and the degree of economic inequality by changing the stakes of engaging in appropriation activities versus respecting the status quo. We use a general equilibrium model where workers can either work peacefully or join a guerrilla movement that expropriates entrepreneurs. If workers are peaceful, they receive a competitive wage. If they join a guerrilla movement, they receive a share of the appropriated wealth, which depends positively on the number of guerrilla members. In this framework, we find one low-income, low-wage equilibrium with guerrilla activity and one peaceful, high-income, high-wage equilibrium. The peaceful equilibrium can be reached through redistribution policies, which can be implemented at the firm level. In essence, through their compensation policies entrepreneurs, not the state might be able to protect their assets against expropriation and simultaneously control the internal principal-agent problem.

Concurrent recordings of bladder afferents from multiple nerves using a microfabricated PDMS microchannel electrode array

In this paper we present a compliant neural interface designed to record bladder afferent activity. We developed the implant's microfabrication process using multiple layers of silicone rubber and thin metal so that a gold microelectrode array is embedded within four parallel polydimethylsiloxane (PDMS) microchannels (5 mm long, 100 μm wide, 100 μm deep). Electrode impedance at 1 kHz was optimized using a reactive ion etching (RIE) step, which increased the porosity of the electrode surface. The electrodes did not deteriorate after a 3 month immersion in phosphate buffered saline (PBS) at 37 °C. Due to the unique microscopic topography of the metal film on PDMS, the electrodes are extremely compliant and can withstand handling during implantation (twisting and bending) without electrical failure. The device was transplanted acutely to anaesthetized rats, and strands of the dorsal branch of roots L6 and S1 were surgically teased and inserted in three microchannels under saline immersion to allow for simultaneous in vivo recordings in an acute setting. We utilized a tripole electrode configuration to maintain background noise low and improve the signal to noise ratio. The device could distinguish two types of afferent nerve activity related to increasing bladder filling and contraction. To our knowledge, this is the first report of multichannel recordings of bladder afferent activity.

The role of multiple partners in a digestive mutualism with a protocarnivorous plant

Background and aimsThe protocarnivorous plant Paepalanthus bromelioides (Eriocaulaceae) is similar to bromeliads in that this plant has a rosette-like structure that allows rainwater to accumulate in leaf axils (i.e. phytotelmata). Although the rosettes of P. bromelioides are commonly inhabited by predators (e.g. spiders), their roots are wrapped by a cylindrical termite mound that grows beneath the rosette. In this study it is predicted that these plants can derive nutrients from recycling processes carried out by termites and from predation events that take place inside the rosette. It is also predicted that bacteria living in phytotelmata can accelerate nutrient cycling derived from predators.MethodsThe predictions were tested by surveying plants and animals, and also by performing field experiments in rocky fields from Serra do Cipó, Brazil, using natural abundance and enriched isotopes of 15N. Laboratory bioassays were also conducted to test proteolytic activities of bacteria from P. bromelioides rosettes.Key ResultsAnalyses of 15N in natural nitrogen abundances showed that the isotopic signature of P. bromelioides is similar to that of carnivorous plants and higher than that of non-carnivorous plants in the study area. Linear mixing models showed that predatory activities on the rosettes (i.e. spider faeces and prey carcass) resulted in overall nitrogen contributions of 26·5 % (a top-down flux). Although nitrogen flux was not detected from termites to plants via decomposition of labelled cardboard, the data on 15N in natural nitrogen abundance indicated that 67 % of nitrogen from P. bromelioides is derived from termites (a bottom-up flux). Bacteria did not affect nutrient cycling or nitrogen uptake from prey carcasses and spider faeces.ConclusionsThe results suggest that P. bromelioides derive nitrogen from associated predators and termites, despite differences in nitrogen cycling velocities, which seem to have been higher in nitrogen derived from predators (leaves) than from termites (roots). This is the first study that demonstrates partitioning effects from multiple partners in a digestion-based mutualism. Despite most of the nitrogen being absorbed through their roots (via termites), P. bromelioides has all the attributes necessary to be considered as a carnivorous plant in the context of digestive mutualism. © 2012 The Author. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved.