Enhancing the spectral gap of networks by node removal

Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation time of a random walk. A large spectral gap is usually associated with high network performance, such as facilitated synchronization and rapid convergence. In this study, we seek to enhance the spectral gap of undirected and unweighted networks by removing nodes because, practically, the removal of nodes often costs less than the addition of nodes, addition of links, and rewiring of links. In particular, we develop a perturbative method to achieve this goal. The proposed method realizes better performance than other heuristic methods on various model and real networks. The spectral gap increases as we remove up to half the nodes in most of these networks.Comment: 5 figure

Clinical significance of perioperative Q-wave myocardial infarction: The Emory Angioplasty versus Surgery Trial

AbstractObjective: The primary end point of the Emory Angioplasty versus Surgery Trial was a composite of three events: death, Q-wave infarction, and a new large defect on 3-year postoperative thallium scan. This study examines the clinical significance of Q-wave infarction in the surgical cohort (194 patients) of the Emory trial. Methods: Twenty patients (10.3%) with Q-wave infarctions were identified: 13 patients had inferior Q-wave infarctions and seven patients had anterior, lateral, septal, or posterior Q-wave infarctions (termed anterior Q-wave infarctions). Results: In the inferior Q-wave infarction group, postoperative cardiac catheterization (at 1 year or 3 years) in 11 patients revealed normal ejection fraction (ejection fraction >55%) in 10 (91%), no wall motion abnormalities in 10 (91%), and all grafts patent in 10 (91%). In the anterior Q-wave infarction group, postoperative catheterizatiOn in six patients revealed normal ejection fractions in five (83%), no wall motion abnormalities in three (50%), and all grafts patent in three (50%). Average peak postoperative creatine kinase MB levels were as follows: no Q-wave infarction (n = 174) 37 ± 43 IU/L, inferior Q-wave infarction 40 ± 27 IU/L, and anterior Q-wave infarction 58 ± 38 IU/L. Mortality in the 20 patients with Q-wave infarctions was 5% (1/20) at 3 years; in patients without a Q-wave infarction it was 6.3% (11/174) (p = 0.64). Of 17 patients with a Q-wave infarction who underwent postoperative catheterization, 11 (65%) had a normal ejection fraction, normal wall motion, and all grafts patent with an uneventful 3-year postoperative course. Conclusions: The core laboratory screening of postoperative electrocardiograms, particularly in the case of inferior Q-wave infarctions, appears to identify a number of patients as having a Q-wave infarction with minimal clinical significance. Q-wave infarction identified in the postoperative period seems to be a weak end point with little prognostic significance and therefore not valuable for future randomized trials. (J Thorac Cardiovasc Surg 1996;112:1447-54

Peristaltic Transport of a Rheological Fluid: Model for Movement of Food Bolus Through Esophagus

Fluid mechanical peristaltic transport through esophagus has been of concern in the paper. A mathematical model has been developed with an aim to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed with the specific aim of exploring some important information concerning the movement of food bolus through the esophagus. The analysis has been carried out by using lubrication theory. The study is particularly suitable for cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes places by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocity, particle trajectory and reflux are investigated for a single wave as well as for a train of periodic peristaltic waves. Locally variable pressure is seen to be highly sensitive to the flow index `n'. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is much more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.Comment: Accepted for publication in Applied Mathematics and Mechanics (AMM), Springe

Biomechanical Comparison of Open versus Percutaneous Techniques for Primary Mid-Substance Achilles Tendon Repair: A Meta-Analysis

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Detrended Fluctuation Analysis of Systolic Blood Pressure Control Loop

We use detrended fluctuation analysis (DFA) to study the dynamics of blood pressure oscillations and its feedback control in rats by analyzing systolic pressure time series before and after a surgical procedure that interrupts its control loop. We found, for each situation, a crossover between two scaling regions characterized by exponents that reflect the nature of the feedback control and its range of operation. In addition, we found evidences of adaptation in the dynamics of blood pressure regulation a few days after surgical disruption of its main feedback circuit. Based on the paradigm of antagonistic, bipartite (vagal and sympathetic) action of the central nerve system, we propose a simple model for pressure homeostasis as the balance between two nonlinear opposing forces, successfully reproducing the crossover observed in the DFA of actual pressure signals

Network Physiology reveals relations between network topology and physiological function

The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here, we develop a framework to probe interactions among diverse systems, and we identify a physiologic network. We find that each physiologic state is characterized by a specific network structure, demonstrating a robust interplay between network topology and function. Across physiologic states the network undergoes topological transitions associated with fast reorganization of physiologic interactions on time scales of a few minutes, indicating high network flexibility in response to perturbations. The proposed system-wide integrative approach may facilitate the development of a new field, Network Physiology.Comment: 12 pages, 9 figure

Virtual Patients and Sensitivity Analysis of the Guyton Model of Blood Pressure Regulation: Towards Individualized Models of Whole-Body Physiology

Mathematical models that integrate multi-scale physiological data can offer insight into physiological and pathophysiological function, and may eventually assist in individualized predictive medicine. We present a methodology for performing systematic analyses of multi-parameter interactions in such complex, multi-scale models. Human physiology models are often based on or inspired by Arthur Guyton's whole-body circulatory regulation model. Despite the significance of this model, it has not been the subject of a systematic and comprehensive sensitivity study. Therefore, we use this model as a case study for our methodology. Our analysis of the Guyton model reveals how the multitude of model parameters combine to affect the model dynamics, and how interesting combinations of parameters may be identified. It also includes a “virtual population” from which “virtual individuals” can be chosen, on the basis of exhibiting conditions similar to those of a real-world patient. This lays the groundwork for using the Guyton model for in silico exploration of pathophysiological states and treatment strategies. The results presented here illustrate several potential uses for the entire dataset of sensitivity results and the “virtual individuals” that we have generated, which are included in the supplementary material. More generally, the presented methodology is applicable to modern, more complex multi-scale physiological models