Geometric transformations in octrees using shears

Existent algorithms to perform geometric transformations on octrees can be classified in two families: inverse transformation and address computation ones. Those in the inverse transformation family essentially resample the target octree from the source one, and are able to cope with all the affine transformations. Those in the address computation family only deal with translations, but are commonly accepted as faster than the former ones for they do no intersection tests, but directly calculate the transformed address of each black node in the source tree. This work introduces a new translation algorithm that shows to perform better than previous one when very small displacements are involved. This property is particularly useful in applications such as simulation, robotics or computer animation.Postprint (published version

Algorithms For Phylogeny Reconstruction In a New Mathematical Model

The evolutionary history of a set of species is represented by a tree called phylogenetic tree or phylogeny. Its structure depends on precise biological assumptions about the evolution of species. Problems related to phylogeny reconstruction (i.e., finding a tree representation of information regarding a set of items) are widely studied in computer science. Most of these problems have found to be NP-hard. Sometimes they can solved polynomially if appropriate restrictions on the structure of the tree are fixed. This paper summarizes the most recent problems and results in phylogeny reconstruction, and introduces an innovative tree model, called Phylogenetic Parsimonious Tree, which is justified by significant biological hypothesis. Using PPT two problems are studied: the existence and the reconstruction of a tree both when sequences of characters and partial order on interspecies distances are given. We rove complexity results that confirm the hardness of this class of problems

Wavelengths switching and allocation algorithms in multicast technology using m-arity tree networks topology

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University London.In this thesis, the m-arity tree networks have been investigated to derive equations for their nodes, links and required wavelengths. The relationship among all parameters such as leaves nodes, destinations, paths and wavelengths has been found. Three situations have been explored, firstly when just one server and the leaves nodes are destinations, secondly when just one server and all other nodes are destinations, thirdly when all nodes are sources and destinations in the same time. The investigation has included binary, ternary, quaternary and finalized by general equations for all m-arity tree networks. Moreover, a multicast technology is analysed in this thesis to transmit data carried by specific wavelengths to several clients. Wavelengths multicast switching is well examined to propose split-convert-split-convert (S-C-S-C) multicast switch which consists of light splitters and wavelengths converters. It has reduced group delay by 13% and 29% compared with split-convert (S-C) and split-convert-split (S-C-S) multicast switches respectively. The proposed switch has also increased the received signal power by a significant value which reaches 28% and 26.92% compared with S-C-S and S-C respectively. In addition, wavelengths allocation algorithms in multicast technology are proposed in this thesis using tree networks topology. Distributed scheme is adopted by placing wavelength assignment controller in all parents’ nodes. Two distributed algorithms proposed shortest wavelength assignment (SWA) and highest number of destinations with shortest wavelength assignment (HND-SWA) algorithms to increase the received signal power, decrease group delay and reduce dispersion. The performance of the SWA algorithm was almost better or same as HND-SWA related to the power, dispersion and group delay but they are always better than other two algorithms. The required numbers of wavelengths and their utilised converters have been examined and calculated for the researched algorithms. The HND-SWA has recorded the superior performance compared with other algorithms. It has reduced number of utilised wavelengths up to about 19% and minimized number of the used wavelengths converters up to about 29%. Finally, the centralised scheme is discussed and researched and proposed a centralised highest number of destinations (CHND) algorithm with static and dynamic scenarios to reduce network capacity decreasing (Cd) after each wavelengths allocation. The CDHND has reduced (Cd) by about 16.7% compared with the other algorithms

Constructs and evaluation strategies for intelligent speculative parallelism - armageddon revisited

This report addresses speculative parallelism (the assignment of spare processing resources to tasks which are not known to be strictly required for the successful completion of a computation) at the user and application level. At this level, the execution of a program is seen as a (dynamic) tree —a graph, in general. A solution for a problem is a traversal of this graph from the initial state to a node known to be the answer. Speculative parallelism then represents the assignment of resources to múltiple branches of this graph even if they are not positively known to be on the path to a solution. In highly non-deterministic programs the branching factor can be very high and a naive assignment will very soon use up all the resources. This report presents work assignment strategies other than the usual depth-first and breadth-first. Instead, best-first strategies are used. Since their definition is application-dependent, the application language contains primitives that allow the user (or application programmer) to a) indícate when intelligent OR-parallelism should be used; b) provide the functions that define "best," and c) indícate when to use them. An abstract architecture enables those primitives to perform the search in a "speculative" way, using several processors, synchronizing them, killing the siblings of the path leading to the answer, etc. The user is freed from worrying about these interactions. Several search strategies are proposed and their implementation issues are addressed. "Armageddon," a global pruning method, is introduced, together with both a software and a hardware implementation for it. The concepts exposed are applicable to áreas of Artificial Intelligence such as extensive expert systems, planning, game playing, and in general to large search problems. The proposed strategies, although showing promise, have not been evaluated by simulation or experimentation

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

DECENTRALIZED NETWORK BANDWIDTH PREDICTION AND NODE SEARCH

As modern computing becomes increasingly data-intensive and distributed, it is becoming crucial to effectively manage and exploit end-to-end network bandwidth information from hosts on wide-area networks. Inspired by the finding that Internet bandwidth can be represented approximately in a tree metric space, we focus on three specific research problems. First, we have designed a decentralized algorithm for network bandwidth prediction. The algorithm embeds the bandwidth information as distance in an edge-weighted tree, without performing full n-to-n measurements. No central and fixed infrastructure is required. Each joining node performs a limited number of sampling measurements. Second, we designed a decentralized algorithm to search for a centroid node that has high-bandwidth connections with a given set of nodes. The algorithm can find a centroid accurately and efficiently using the bandwidth data produced by the prediction algorithm. Last, we have designed another type of decentralized search algorithm to find a cluster of nodes that have high-bandwidth interconnections. While the clustering problem is NP-complete in a general graph, our algorithm runs in polynomial time with the bandwidth data predicted in a tree metric space. We provide proofs that our algorithms for bandwidth prediction and node search have perfect accuracy and high scalability when a network is modeled as a tree metric space. Also, experimental results with real-world data sets validate the high accuracy and scalability of our approaches