Insertion Of New Nodes Research Articles

Optimized smoothing of discrete models of the implicitly defined geometrical objects' surfaces

When using many modern methods of automatic generation of surface meshes of implicitly defined geometric objects, the accuracy of approximation in the vicinity of surface singularities (holes, breaks, etc.) is lost. To improve surface meshes of geometric objects, various methods of smoothing are used. The existing smoothing methods are focused on triangular elements, but optimization of surface meshes of geometric objects on the basis of elements of another shape (for example, quadrangles) is less studied. The paper proposes the mathematical apparatus based on the use of the energy functional for each model node. The proposed functional considers the distance from the current node to the adjacent nodes and the distance from the geometric centers of the incident elements to the surface. The algorithm for minimizing the energy functional for smoothing surface meshes of implicitly defined geometric objects is developed. The developed algorithm is a modification of the Gaussian method for the case of search for a minimum in the local coordinates of a polygon formed by neighboring elements. The algorithm is local: minimization is performed consistently for each model node, so its repeated application provides models with more accurate approximation of the boundary. The developed algorithm for minimizing the functional does not require the insertion of new nodes. As a consequence, it is possible, using a single procedure, to optimize meshes based on triangles, quadrangles or mixed type (containing triangles and quadrangles simultaneously). As a result, the accuracy of the approximation of surfaces in the vicinity of their singularities increases, as demonstrated by the examples of smoothing models of complex objects.

Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

A node‐pair finite element/volume mesh adaptation technique for compressible flows based on a hierarchical approach

SUMMARYA grid adaptation technique for two‐dimensional unstructured grids of triangles and quadrilaterals is presented. The error estimation procedure is formulated in terms of a node pair‐based data structure that allows for a unified description of the finite element and finite volume schemes. The adaptation algorithm is based on a strategy of hierarchical corrections, where a suitable number of intermediate adapted grids are generated and successively corrected by employing a simple node insertion technique at the midpoint of the element edges. Coarsening of the grid is obtained in an implicit fashion by avoiding the insertion of new nodes during the correction phase. The adaptation history, from the initial to the current grid, including all intermediate grids, is stored and updated through the whole process. No intermediate grid is therefore required to be stored explicitly. The adapted grid is anisotropic, thanks to the adoption of both regular triangular and quadrilateral elements with high aspect ratio that are gathered in, for example, boundary layer or wake regions. Numerical experiments of steady compressible flows, including both inviscid and viscous flows, are presented to support the suitability of the adaptation technique. Copyright © 2012 John Wiley & Sons, Ltd.

Simulation of Neuronal Death and Network Recovery in a Computational Model of Distributed Cortical Activity

The authors utilize a model of activity-dependent neuronal plasticity to study the interplay between synaptogenesis, neuronal death, and neurogenesis on the resulting pattern of neuronal connectivity. A mathematical model of neuronal network activity was employed, with plasticity instantiated by an activity-dependent rewiring rule. In particular, the authors modeled a neural system as a collection of "nodes" (neural subsystems) connected by "links" (anatomical connectivity). Neuronal damage was simulated by deletion of nodes in this evolving network through either random or targeted attack. Neurogenesis was likewise simulated by insertion of new nodes with random connections. Local and global structural network properties were characterized using the metrics of local and global "efficiency," and network "reachability." Activity-dependent plasticity yields a network that is robust to random node deletion, with preservation of a "small-world" architecture, characterized by high local and global efficiency. In contrast, targeted deletion of central nodes leads to a drop in reachability and global efficiency, with a consequent loss of small-world properties. Simulated neurogenesis is able to compensate for this targeted cell loss even when rates of new cell formation are considerably slower than that of simulated cell death. The rapid growth of computational neuroscience enables to study the interplay between neuronal plasticity and cell death in computational models of brain network activity. Although the current simulations lack much of the rich physiology of real neuronal systems, they nevertheless allow us to make tentative hypotheses of the effects of neuronal lesions on the resulting neuroanatomical connectivity networks.

GEMS: Gossip-Enabled Monitoring Service for Scalable Heterogeneous Distributed Systems

Gossip protocols have proven to be effective means by which failures can be detected in large, distributed systems in an asynchronous manner without the limitations associated with reliable multicasting for group communications. In this paper, we discuss the development and features of a Gossip-Enabled Monitoring Service (GEMS), a highly responsive and scalable resource monitoring service, to monitor health and performance information in heterogeneous distributed systems. GEMS has many novel and essential features such as detection of network partitions and dynamic insertion of new nodes into the service. Easily extensible, GEMS also incorporates facilities for distributing arbitrary system and application-specific data. We present experiments and analytical projections demonstrating scalability, fast response times and low resource utilization requirements, making GEMS a potent solution for resource monitoring in distributed computing.

The Complexity of Constructing Evolutionary Trees Using Experiments

<p>We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(n d logd n) using at most n |d/2| (log2|d/2|−1 n + O(1)) experiments for d > 2, and<br />at most n(log n + O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor Theta(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an <br />Omega(nd logd n) lower bound, matching our upper bounds and improving the previous best lower bound<br />by a factor Theta(logd n). Central to our algorithm is the construction and maintenance of separator trees of small height. We present how to maintain separator trees with height log n + O(1) under the insertion of new nodes in amortized time O(log n). Part of our dynamic algorithm is an algorithm for computing a centroid tree in optimal time O(n).</p><p>Keywords: Evolutionary trees, Experiment model, Separator trees, Centroid tree, Lower bounds</p>