Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

Chebyshev-type quadrature formulas for new weight classes

We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for applications. One of our motivations to consider these type of problems is the Faraday cage phenomenon for discrete charges as discussed by J. Korevaar and his colleagues.

A CHEBYSHEV-TYPE QUADRATURE RULE WITH SOME INTERESTING PROPERTIES

We give here an n-point Chebyshev-type rule of algebraic degree of precision n - 1, but having nodes that can be given explicitly. This quadrature rule also turns out to be one with an ''almost'' highest algebraic degree of precision.

Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

Paracoccidioides brasilinsis-Induced Migration of Dendritic Cells and Subsequent T-Cell Activation in the Lung-Draining Lymph Nodes

Paracoccidioidomycosis is a mycotic disease caused by a dimorphic fungus, Paracoccidioides brasiliensis (Pb), that starts with inhalation of the fungus; thus, lung cells such as DC are part of the first line of defense against this microorganism. Migration of DC to the lymph nodes is the first step in initiating T cell responses. The mechanisms involved in resistance to Pb infection are poorly understood, but it is likely that DC play a pivotal role in the induction of effector T cells that control Pb infection. In this study, we showed that after Pb Infection, an important modification of lung DC receptor expression occurred. We observed an increased expression of CCR7 and CD103 on lung DC after infection, as well as MHC-II. After Pb infection, bone marrow-derived DC as well lung DC, migrate to lymph nodes. Migration of lung DC could represent an important mechanism of pathogenesis during PCM infection. In resume our data showed that Pb induced DC migration. Furthermore, we demonstrated that bone marrow-derived DC stimulated by Pb migrate to the lymph nodes and activate a T helper (Th) response. To the best of our knowledge, this is the first reported data showing that Pb induces migration of DC and activate a T helper (Th) response.

Generalized connectivity between any two nodes in a complex network

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Direct Detection of Mycobacterium bovis in Bovine Lymph Nodes by PCR

P>Thirty-five lymph node samples were taken from animals with macroscopic lesions consistent with Mycobacterium bovis infection. The animals were identified by postmortem examination in an abattoir in the northwestern region of state of Parana, Brazil. Twenty-two of the animals had previously been found to be tuberculin skin test positive. Tissue samples were decontaminated by Petroff`s method and processed for acid-fast bacilli staining, culture in Stonebrink and Lowenstein-Jensen media and DNA extraction. Lymph node DNA samples were amplified by PCR in the absence and presence (inhibitor controls) of DNA extracted from M. bovis culture. Mycobacterium bovis was identified in 14 (42.4%) lymph node samples by both PCR and by culture. The frequency of PCR-positive results (54.5%) was similar to that of culture-positive results (51.5%, P > 0.05). The percentage of PCR-positive lymph nodes increased from 39.4% (13/33) to 54.5% (18/33) when samples that were initially PCR-negative were reanalysed using 2.5 mu l DNA (two samples) and 1 : 2 diluted DNA (three samples). PCR sensitivity was affected by inhibitors and by the amount of DNA in the clinical samples. Our results indicate that direct detection of M. bovis in lymph nodes by PCR may be a fast and useful tool for bovine tuberculosis epidemic management in the region.

Identifying rate-limiting nodes in large-scale cortical networks for visuospatial processing: an illustration using fMRI

With the advent of functional neuroimaging techniques, in particular functional magnetic resonance imaging (fMRI), we have gained greater insight into the neural correlates of visuospatial function. However, it may not always be easy to identify the cerebral regions most specifically associated with performance on a given task. One approach is to examine the quantitative relationships between regional activation and behavioral performance measures. In the present study, we investigated the functional neuroanatomy of two different visuospatial processing tasks, judgement of line orientation and mental rotation. Twenty-four normal participants were scanned with fMRI using blocked periodic designs for experimental task presentation. Accuracy and reaction time (RT) to each trial of both activation and baseline conditions in each experiment was recorded. Both experiments activated dorsal and ventral visual cortical areas as well as dorsolateral prefrontal cortex. More regionally specific associations with task performance were identified by estimating the association between (sinusoidal) power of functional response and mean RT to the activation condition; a permutation test based on spatial statistics was used for inference. There was significant behavioral-physiological association in right ventral extrastriate cortex for the line orientation task and in bilateral (predominantly right) superior parietal lobule for the mental rotation task. Comparable associations were not found between power of response and RT to the baseline conditions of the tasks. These data suggest that one region in a neurocognitive network may be most strongly associated with behavioral performance and this may be regarded as the computationally least efficient or rate-limiting node of the network.

Selective Vagal Denervation of the Sinus and Atrioventricular Nodes, Guided by Vagal Reflexes Induced by High Frequency Stimulation, to Treat Refractory Neurally Mediated Syncope

Vagal Denervation and Neurally Mediated Syncope. A 15-year-old female patient presented with frequent episodes of vasovagal syncope refractory to non-pharmacological and pharmacological measures. Two tilt-table tests performed before and after conventional therapy were positive and reproduced the patient`s clinical symptoms. Selective vagal denervation, guided by HFS, was performed. Six radiofrequency pulses were applied on the left and right sides of the interatrial septum, abolishing vagal responses at these locations. Basal sinus node and Wenckebach cycle lengths changed significantly following ablation. A tilt test performed after denervation was negative and revealed autonomic tone modification. The patient reported significant improvement in quality of life and remained asymptomatic for 9 months after denervation. After this period, three episodes of NMS occurred during a 4-month interval and a tilt test performed 11 months after the procedure demonstrated vagal activity recovery. (J Cardiovasc Electrophysiol, Vol. 20, pp. 558-563, May 2009).

Absence of lymph nodes in the resected specimen after radical surgery for distal rectal cancer and neoadjuvant chemoradiation therapy: What does it mean?

Purpose: The number of retrieved lymph nodes during radical surgery has been considered of great importance to ensure adequate staging and radical resection. However, this finding may not be applicable after neoadjuvant therapy in which, not only is there a decrease in lymph nodes recovered, but also a subgroup of patients with absence of lymph nodes in the resected specimen. Methods: Patients with absence of lymph nodes were compared with patients with ypN0 disease and patients with ypN+ disease. Results: Thirty-two patients (11 percent) had absence of lymph nodes, 171 patients (61 percent) had ypN0 disease, and 78 patients (28 percent) had ypN+ disease. Patients with absence of lymph nodes had significantly lower ypT status (ypT0-1, 40 vs. 13 percent; P < 0.001) and decreased risk of perineural invasion (6 vs. 21 percent; P = 0.04) compared with ypN0 patients. Five-year disease-free survival (74 percent) was similar to patients with ypN0 (59 percent; P = 0.2), and both were significantly better than patients with ypN+ disease (30 percent; P < 0.001). Conclusions: Absence of lymph nodes retrieved from the resected specimen is associated with favorable pathologic features (ypT and perineural invasion status) and good disease-free survival rates. In this setting, absence of retrieved lymph nodes may reflect improved response to neoadjuvant chemoradiation therapy rather than inappropriate or suboptimal oncologic radicality.

Distribution of lymph nodes in the mesorectum: how deep is TME necessary?

Background Standardization of total mesorectal excision (TME) had a great impact on decreasing local recurrence rates for the treatment of rectal cancer. However, exact numbers and distribution of lymph nodes (LN) along the mesorectum remains controversial with some studies suggesting that few LNs are present in the distal third of the mesorectum. Methods Eighteen fresh cadavers without a history of rectal cancer were studied. The rectum was removed by TME and then was divided into right lateral, posterior and left lateral sides, which were further subdivided into 3 levels (upper, middle and lower). A pathologist determined the number and sizes of the LNs in each of the nine areas, b linded to their anatomical origin. Results Overall, the mesorectum had a mean of 5.7 LNs (SD=3.7) and on average each LN had a maximum diameter of 3.0 mm (SD=2.7). There was no association between the mean number or size of LNs with gender, BMI, or age. There was a significantly higher prevalence of LNs in the posterior location (2.8 per mesorectum) than in the two lateral locations (0.8 and 1.2 per mesorectum; p=0.02). The distribution of LNs in the three levels of the rectum was not significant. Conclusions The distribution of LNs reinforces the fact that TME should always include the distal third of the mesorectum. Care must be taken to not violate the posterior aspect of the mesorectum.

Lymphadenectomy in Colorectal Cancer Liver Metastases Resection: Incidence of Hilar Limph Nodes Micrometastasis

Background: Liver resection is considered the best treatment for metastatic colorectal cancer. Several prognostic factors have been investigated, and many studies have shown that hepatic hilum lymph nodes involvement has a negative impact on prognosis. The present study evaluated the frequency of microscopic involvement of hilar lymph nodes, through systematic lymphadenectomy and analysis of micrometastases in patients undergoing hepatectomy due to colorectal metastasis. Methods: A total of 28 patients underwent hepatic resection with hilar lymphadenectomy. Lymph nodes considered negative by conventional hematoxylin and eosin (H&E) staining were analyzed by serial sectioning with 100-mu m intervals and immunohistochemistry (IHC) with antihuman pancytokeratin antibody AE1/AE3. Results: In average, 6.18 lymph nodes were dissected per patient. No morbidity or mortality was associated to lymphadenectomy. In two patients, conventional H&E analysis showed presence of microscopic lymph node metastasis. H&E analysis allowed the identification of three other patients with lymph node micrometastases. The overall frequency of microscopic metastases, including micrometastasis, was 18%. Conclusions: Systematic lymphadenectomy allowed the detection of microscopic lymph node metastases, resulting in more accurate staging of extrahepatic disease. The inclusion of IHC increased the detection of lymph node micrometastasis. J. Surg. Oncol. 2009;100:534-537. (C) 2009 Wiley-Liss, Inc.

Antigen-presenting cells in draining lymph nodes of goats repeatedly infested by the Cayenne tick Amblyomma cajennense nymphs

Resistance to tick feeding has been previously shown to be an acquired, immunologically mediated phenomenon in goats, associated with cutaneous basophilia to nymphs of Amblyomma cajennense, the Cayenne tick, after repeated infestations. On the other hand, it is well known that antigen-presenting cells (APCs) play an important role in the host immune reaction to tick infestations. The most able APCs for Th cells are the well defined dendritic cells, mononuclear phagocytes and B-lymphocytes. Immunohistochemical analysis of draining lymph nodes of goats repeatedly infested with nymphs of the ixodid tick A. cajennense to search for APCs was done. Pre-scapular lymph nodes draining the tick attachment sites were collected 15 days after both the first and third infestations. Tick infestations resulted in increased number of CD21(+) B lymphocytes in lymph nodes after the tertiary infestation. However, the number of CD11b(+) and CD11c(+) cells were not altered after the successive infestations. Lower numbers of CD11c(+) cells had infiltrated lymph nodes responsible for draining the tick infested skin. These findings suggest that acquired immunity of goats against nymphs of A. cajennense is possibly established by B lymphocytes during the first infestation and that APCs may play a key role in this mechanism.