On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Largest connected component of a star graph with faulty vertices

In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n >= 3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.

Next-generation sequencing reveals large connected networks of intra-host HCV variants

Background: Next-generation sequencing (NGS) allows for sampling numerous viral variants from infected patients. This provides a novel opportunity to represent and study the mutational landscape of Hepatitis C Virus (HCV) within a single host.Results: Intra-host variants of the HCV E1/E2 region were extensively sampled from 58 chronically infected patients. After NGS error correction, the average number of reads and variants obtained from each sample were 3202 and 464, respectively. The distance between each pair of variants was calculated and networks were created for each patient, where each node is a variant and two nodes are connected by a link if the nucleotide distance between them is 1. The work focused on large components having > 5% of all reads, which in average account for 93.7% of all reads found in a patient. The distance between any two variants calculated over the component correlated strongly with nucleotide distances (r = 0.9499; p = 0.0001), a better correlation than the one obtained with Neighbour-Joining trees (r = 0.7624; p = 0.0001). In each patient, components were well separated, with the average distance between (6.53%) being 10 times greater than within each component (0.68%). The ratio of nonsynonymous to synonymous changes was calculated and some patients (6.9%) showed a mixture of networks under strong negative and positive selection. All components were robust to in silico stochastic sampling; even after randomly removing 85% of all reads, the largest connected component in the new subsample still involved 82.4% of remaining nodes. In vitro sampling showed that 93.02% of components present in the original sample were also found in experimental replicas, with 81.6% of reads found in both. When syringe-sharing transmission events were simulated, 91.2% of all simulated transmission events seeded all components present in the source.Conclusions: Most intra-host variants are organized into distinct single-mutation components that are: well separated from each other, represent genetic distances between viral variants, robust to sampling, reproducible and likely seeded during transmission events. Facilitated by NGS, large components offer a novel evolutionary framework for genetic analysis of intra-host viral populations and understanding transmission, immune escape and drug resistance.

Connectivity and dynamics of neuronal networks as defined by the shape of individual neurons

Biological neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the two-dimensional (2D) plane and establishing connections whenever a piece of dendrite falls inside an axon. Several topological and dynamical properties of the resulting graph are measured, including the degree distribution, clustering coefficients, symmetry of connections, size of the largest connected component, as well as three hierarchical measurements of the local topology. By varying the number of processes of the individual basic patterns, we can quantify relationships between the individual neuronal shape and the topological and dynamical features of the networks. Integrate-and-fire dynamics on these networks is also investigated with respect to transient activation from a source node, indicating that long-range connections play an important role in the propagation of avalanches.

Utilização de GPGPUs para a identificação de objectos em imagens tomográficas

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Percolation and epidemic thresholds in clustered networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks, thus extending this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.

Project for Active and Robot Vision Course

Tässä työssä raportoidaan harjoitustyön kehittäminen ja toteuttaminen Aktiivisen- ja robottinäön kurssille. Harjoitustyössä suunnitellaan ja toteutetaan järjestelmä joka liikuttaa kappaleita robottikäsivarrella kolmiuloitteisessa avaruudessa. Kappaleidenpaikkojen määrittämiseen järjestelmä käyttää digitaalisia kuvia. Tässä työssä esiteltävässä harjoitustyötoteutuksessa käytettiin raja-arvoistusta HSV-väriavaruudessa kappaleiden segmentointiin kuvasta niiden värien perusteella. Segmentoinnin tuloksena saatavaa binäärikuvaa suodatettiin mediaanisuotimella kuvan häiriöiden poistamiseksi. Kappaleen paikkabinäärikuvassa määritettiin nimeämällä yhtenäisiä pikseliryhmiä yhtenäisen alueen nimeämismenetelmällä. Kappaleen paikaksi määritettiin suurimman nimetyn pikseliryhmän paikka. Kappaleiden paikat kuvassa yhdistettiin kolmiuloitteisiin koordinaatteihin kalibroidun kameran avulla. Järjestelmä liikutti kappaleita niiden arvioitujen kolmiuloitteisten paikkojen perusteella.

A camera based digit location and recognition system for garment tracking

Garment information tracking is required for clean room garment management. In this paper, we present a camera-based robust system with implementation of Optical Character Reconition (OCR) techniques to fulfill garment label recognition. In the system, a camera is used for image capturing; an adaptive thresholding algorithm is employed to generate binary images; Connected Component Labelling (CCL) is then adopted for object detection in the binary image as a part of finding the ROI (Region of Interest); Artificial Neural Networks (ANNs) with the BP (Back Propagation) learning algorithm are used for digit recognition; and finally the system is verified by a system database. The system has been tested. The results show that it is capable of coping with variance of lighting, digit twisting, background complexity, and font orientations. The system performance with association to the digit recognition rate has met the design requirement. It has achieved real-time and error-free garment information tracking during the testing.

Building a tropical-extratropical cloud band metbot

An automated cloud band identification procedure is developed that captures the meteorology of such events over southern Africa. This “metbot” is built upon a connected component labelling method that enables blob detection in various atmospheric fields. Outgoing longwave radiation is used to flag candidate cloud band days by thresholding the data and requiring detected blobs to have sufficient latitudinal extent and exhibit positive tilt. The Laplacian operator is used on gridded reanalysis variables to highlight other features of meteorological interest. The ability of this methodology to capture the significant meteorology and rainfall of these synoptic systems is tested in a case study. Usefulness of the metbot in understanding event to event similarities of meteorological features is demonstrated, highlighting features previous studies have noted as key ingredients to cloud band development in the region. Moreover, this allows the presentation of a composite cloud band life cycle for southern Africa events. The potential of metbot to study multiscale interactions is discussed, emphasising its key strength: the ability to retain details of extreme and infrequent events. It automatically builds a database that is ideal for research questions focused on the influence of intraseasonal to interannual variability processes on synoptic events. Application of the method to convergence zone studies and atmospheric river descriptions is suggested. In conclusion, a relation-building metbot can retain details that are often lost with object-based methods but are crucial in case studies. Capturing and summarising these details may be necessary to develop deeper process-level understanding of multiscale interactions.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Unsupervised segmentation method for cuboidal cell nuclei in histological prostate images based on minimum cross entropy

This paper presents a novel segmentation method for cuboidal cell nuclei in images of prostate tissue stained with hematoxylin and eosin. The proposed method allows segmenting normal, hyperplastic and cancerous prostate images in three steps: pre-processing, segmentation of cuboidal cell nuclei and post-processing. The pre-processing step consists of applying contrast stretching to the red (R) channel to highlight the contrast of cuboidal cell nuclei. The aim of the second step is to apply global thresholding based on minimum cross entropy to generate a binary image with candidate regions for cuboidal cell nuclei. In the post-processing step, false positives are removed using the connected component method. The proposed segmentation method was applied to an image bank with 105 samples and measures of sensitivity, specificity and accuracy were compared with those provided by other segmentation approaches available in the specialized literature. The results are promising and demonstrate that the proposed method allows the segmentation of cuboidal cell nuclei with a mean accuracy of 97%. © 2013 Elsevier Ltd. All rights reserved.