Classification of 2-node excitatory-inhibitory networks.

We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different types of excitatory-inhibitory networks: restricted, partially restricted, unrestricted and completely unrestricted. For each type we give two different classifications. Using results on ODE-equivalence and minimality, we classify the ODE-classes and present a minimal representative for each ODE-class. We also classify all the networks with valence ≤2. These classifications are up to renumbering of nodes and the interchange of 'excitatory' and 'inhibitory' on nodes and arrows. These classifications constitute a first step towards analysing dynamics and bifurcations of excitatory-inhibitory networks. The results have potential applications to biological network models, especially neuronal networks, gene regulatory networks, and synthetic gene networks.

Ablação de via anômala em região de cúspide coronariana esquerda / Ablation of an anomalous pathway in the region of the left coronary leaflet

INTRODUÇÃO: Vias acessórias são comumente encontradas ao longo do ânulo tricuspídeo e mitral. A região de continuidade mitroaórtica é uma rara localização, com dados significativos limitados. DESCRIÇÃO: Homem de 52 anos com palpitações taquicárdicas frequentes e ECG com pré-excitação ventricular e onda delta positiva de V1 a V6, em DII, DIII e aVF, negativa em aVR e aVL, foi encaminhado para estudo eletrofisiológico e ablação. Medidas iniciais mostraram HV 0 ms e QRS 130 ms. Estudo confirmou presença de via acessória com condução bidirecional e maior fusão atrioventricular no pólo distal do cateter decapolar inserido no seio coronariano. Realizada punção transeptal e mapeamento com cateter terapêutico de 4 mm, sendo encontrada maior fusão atrioventricular (AV) em ritmo sinusal em região anterior do anel mitral. Entretanto, pulsos de radiofrequência (30W, 60°C) aplicados neste local foram ineficazes, atingindo baixa potência. Novas aplicações com cateter terapêutico de 8 mm introduzido em veia cardíaca magna apresentaram a mesma limitação. Optado por acesso retroaórtico e mapeamento de região subvalvar de cúspide coronariana esquerda, condizente com região de continuidade mitroaórtica, que evidenciou fusão AV e precocidade de 30 ms do eletrograma ventricular em relação ao início da onda delta. Pulsos de radiofrequência (50W, 60°C) eliminaram rapidamente a condução pela via acessória nesta localização. CONCLUSÃO: Na região da continuidade mitroaórtica é rara a presença de via acessória devido à sua composição por tecido fibroso. Em situações sugestivas de via acessória anterior esquerda em que não há sucesso com aplicações de radiofrequência em ânulo mitral, é válido o mapeamento de regiões pouco usuais para o correto diagnóstico e ablação eficaz.

Viability assessment as a strategy to reduce long term events in left anterior descendent artery with chronic total occlusion

INTRODUCTION: Late intervention of a chronic total occlusion (CTO) in stable patients is not routinely recommended by randomized trials. Previous studies have confirmed the negative effect of CTOs on prognosis. Purpose: To evaluate if a strategy of viability assessment (VA) to guide revascularization in the left anterior descendent artery (LAD) CTO can reduce 5-year clinical outcomes. METHODS: Retrospective cohort with at 5-year follow-up of 223 patients with LAD with CTO without any other significant lesion. Patients with previous myocardial infarction, cardiomyopathy or clinical instability were excluded. The primary outcome was the composite end point of myocardial infarction (MI), death, new LAD revascularization, heart failure hospitalization (HFH) and severe arrhythmias. RESULTS: We identified 223 patients with LAD CTO as a single lesion. Only 53 (23.7%) had VA to guide therapy compared to 170 (76.2%) with no VA (NVA). The mean ejection fraction was higher in the group with NVA (54.5+/-13.1 vs 41.5+/-11.8 with p<0.001). The occurrence of angina was more common in the NVA group (64.7% vs 30.2% with p<0.001), mainly due to Canadian Cardiology Society II (71.8%). The VA group was more frequently maintained in optimal medical therapy (OMT) (54.7%) compared to the NVA group (23.5%). NVA group underwent revascularization more often than the VA group, PCI was performed in 59.4% vs 41.5% and CABG in 17.1% vs 3.8% respectively. The primary outcome occurred in 5.7% in the VA group compared to 22.4% in the NVA (p=0.056). CONCLUSION: VA is a feasible strategy to reduce the need of unnecessary interventions. There was a marginal reduction of the total number of events in the VA group in the 5-year follow-up, mainly with respect to reducing the need for new LAD revascularization.

Gradient and Hamiltonian coupled systems on undirected networks.

Many real world applications are modelled by coupled systems on undirected networks. Two striking classes of such systems are the gradient and the Hamiltonian systems. In fact, within these two classes, coupled systems are admissible only by the undirected networks. For the coupled systems associated with a network, there can be flow-invariant spaces (synchrony subspaces where some subsystems evolve synchronously), whose existence is independent of the systems equations and depends only on the network topology. Moreover, any coupled system on the network, when restricted to such a synchrony subspace, determines a new coupled system associated with a smaller network (quotient). The original network is said to be a lift of the quotient network. In this paper, we characterize the conditions for the coupled systems property of being gradient or Hamiltonian to be preserved by the lift and quotient coupled systems. This characterization is based on determining necessary and sufficient conditions for a quotient (lift) network of an undirected network to be also undirected. We show that the extra gradient or Hamiltonian structure of a coupled system admissible by an undirected network can be lost by the systems admissible by a (directed) quotient network. Conversely, gradient (Hamiltonian) dynamics can appear for an undirected quotient network of a directed network or of an undirected network whose associated dynamics is not gradient (Hamiltonian). We illustrate with a neural network given by two groups of neurons that are mutually coupled through either excitatory or inhibitory synapses, which is modelled by a coupled system exhibiting both gradient and Hamiltonian structures.

CLINICAL AND HISTOPATHOLOGICAL AXILLARY ASSESSMENT / Avaliação clínica e histopatológica axilar após esvaziamento por câncer de mama

Introduction: The proper selection of patients for sentinel lymph node biopsy is essential and depends on the evaluation of the patient's prediction for lymph node involvement and an evaluation of the accuracy of the clinical examination. Objective: This study aimed to evaluate the axillary contents of 102 breast cancer patients with tumors between 3 and 5 centimeters who underwent axillary dissection between January 2010 and December 2013. Methods: The data were categorized according to positive or negative axillary clinical evaluation and positive or negative anatomopathological evaluation. Results: The value for positive predictive values for physical examination was 83.5% and the negative predictive value was 34.88%. In addition, axillary physical examination showed 63.6% sensitivity and 60% specificity. Most patients with axillary involvement in the anatomopathological evaluation correlated with tumor grade, size, location and angiolymphatic invasion. Conclusion: It is believed that a better evaluation of the prediction of lymph node involvement, considering some clinicopathological risk factors in patients with suspicious lymph nodes, should be performed to aid the preoperative study of the axilla and the axillary approach screening

Introdução: Atualmente, precisamos selecionar adequadamente as pacientes a serem submetidas à biópsia de linfonodo sentinela. Para isso, são imprescindíveis a avaliação da predição daquele paciente acerca do comprometimento linfonodal e a avaliação da acurácia do exame clínico. Objetivo: O presente estudo teve como objetivo avaliar o conteúdo axilar de pacientes portadoras de câncer de mama com tumores entre três e cinco centímetros submetidas ao esvaziamento axilar entre 2010 e 2013, por meio da análise de 102 prontuários. Métodos: Os dados foram categorizados segundo a avaliação clínica axilar positiva ou negativa e a avaliação anatomopatológica positiva ou negativa. Resultados: Observaram-se valor preditivo positivo do exame físico de 83,5% e preditivo negativo de 34,88%. O exame físico axilar mostrou sensibilidade de 63,6% e especificidade de 60%. A maioria das pacientes com comprometimento axilar no anatomopatológico mostrou correlação com o grau tumoral, tamanho, localização e invasão angiolinfática. Conclusão: Acredita-se que uma melhor avaliação quanto à predição do comprometimento linfonodal, levando em consideração alguns fatores clinicopatológicos de risco nas pacientes com linfonodos suspeitos, deve ser feita como auxílio no estudo pré-operatório da axila e triagem no tocante à abordagem axilar

Synchronization and equitable partitions in weighted networks.

The work presented in this paper has two purposes. One is to expose that the coupled cell network formalism of Golubitsky, Stewart, and collaborators accommodates in a natural way the weighted networks, that is, graphs where the connections have associated weights that can be any real number. Recall that, in the former setup, the network connections have associated nonnegative integer values. Here, some of the central concepts and results in the former formalism are present and applied to the weighted setup. These results are strongly associated with the existence of synchrony subspaces and balanced relations. This work also makes the correspondence between the concepts of synchrony subspace and balanced relation with those of cluster of synchrony and equitable partition, respectively, which are used in the other strand of literature. This correspondence implies that the results of these two strands of literature are linked. In particular, we remark that the results stated here for weighted coupled cell networks apply in that other strand of literature, and examples are given to illustrate that.

Patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks.

We consider feed-forward and auto-regulation feed-forward neural (weighted) coupled cell networks. In feed-forward neural networks, cells are arranged in layers such that the cells of the first layer have empty input set and cells of each other layer receive only inputs from cells of the previous layer. An auto-regulation feed-forward neural coupled cell network is a feed-forward neural network where additionally some cells of the first layer have auto-regulation, that is, they have a self-loop. Given a network structure, a robust pattern of synchrony is a space defined in terms of equalities of cell coordinates that is flow-invariant for any coupled cell system (with additive input structure) associated with the network. In this paper, we describe the robust patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks. Regarding feed-forward neural networks, we show that only cells in the same layer can synchronize. On the other hand, in the presence of auto-regulation, we prove that cells in different layers can synchronize in a robust way and we give a characterization of the possible patterns of synchrony that can occur for auto-regulation feed-forward neural networks.

Regular synchrony lattices for product coupled cell networks.

There are several ways for constructing (bigger) networks from smaller networks. We consider here the cartesian and the Kronecker (tensor) product networks. Our main aim is to determine a relation between the lattices of synchrony subspaces for a product network and the component networks of the product. In this sense, we show how to obtain the lattice of regular synchrony subspaces for a product network from the lattices of synchrony subspaces for the component networks. Specifically, we prove that a tensor of subspaces is of synchrony for the product network if and only if the subspaces involved in the tensor are synchrony subspaces for the component networks of the product. We also show that, in general, there are (irregular) synchrony subspaces for the product network that are not described by the synchrony subspaces for the component networks, concluding that, in general, it is not possible to obtain the all synchrony lattice for the product network from the corresponding lattices for the component networks. We also make the following remark concerning the fact that the cartesian and Kronecker products, as graph operations, are quite different, implying that the associated coupled cell systems have distinct structures. Although, the kinds of dynamics expected to occur are difficult to compare, we establish an inclusion relation between the lattices of synchrony subspaces for the cartesian and Kronecker products.