Using topological sweep to extract the boundaries of regions in maps represented by region quadtrees

A variant of the plane sweep paradigm known as topological sweep is adapted to solve geometric problems involving two-dimensional regions when the underlying representation is a region quadtree. The utility of this technique is illustrated by showing how it can be used to extract the boundaries of a map in O(M) space and O(Ma(M)) time, where M is the number of quad tree blocks in the map, and a(·) is the (extremely slowly growing) inverse of Ackerman's function. The algorithm works for maps that contain multiple regions as well as holes. The algorithm makes use of active objects (in the form of regions) and an active border. It keeps track of the current position in the active border so that at each step no search is necessary. The algorithm represents a considerable improvement over a previous approach whose worst-case execution time is proportional to the product of the number of blocks in the map and the resolution of the quad tree (i.e., the maximum level of decomposition). The algorithm works for many different quadtree representations including those where the quadtree is stored in external storage

Model Checking with the Sweep-Line Method

Explicit-state model checking is a formal software verification technique that differs from peer review and unit testing, in that model checking does an exhaustive state space search. With model checking one takes a system model, traverse all reachable states, and check theses according to formal stated properties over the variables in the model. The properties can be expressed with linear temporal logic or computation tree logic, and can for example be that the value of some variable x should always be positive. When conducting an explicit state space exploration one is guaranteed that the complete state space is checked according to the given property. This is not the case in for instance unit testing, where only fragments of a system are tested. In the case that a property is violated, the model checking algorithm should present an error trace. The error trace represents an execution path of the model, demonstrating why it does not satisfy the property. The main disadvantage of model checking, is that the number of reachable states may grow exponentially in the number of variables. This is known as the state explosion problem. This thesis focuses on explicit-state model checking using the sweep-line method. To combat the state explosion problem, the sweep-line method exploits the notion of progress that a system makes, and is able to delete states from memory on-the-fly during the verification process. The notion of progress is captured by progress measures. Since the standard model checking algorithms rely upon having the whole state space in memory, they are not directly compatible with the sweep-line method. We survey differences of standard model checking algorithms and the sweep-line method, and present previous research on verifying properties and providing error traces with the sweep-line method. The new contributions of this thesis are as follows: (1) We develop a new general technique for providing an error trace for linear temporal logic properties, verified using the sweep-line method; (2) A new algorithm for verifying two key computation tree logic properties, on models limited to monotonic progress measures; (3) A unified library for the sweep-line method is implemented with the algorithms developed in this thesis, and the previous developed algorithms for verifying safety properties and linear temporal logic property checking. All algorithms implemented, are validated by checking properties on a model of a stop-and-wait communication protocol.Masteroppgave i informatikkINF39

A Method of Rendering CSG-Type Solids Using a Hybrid of Conventional Rendering Methods and Ray Tracing Techniques

This thesis describes a fast, efficient and innovative algorithm for producing shaded, still images of complex objects, built using constructive solid geometry ( CSG ) techniques. The algorithm uses a hybrid of conventional rendering methods and ray tracing techniques. A description of existing modelling and rendering methods is given in chapters 1, 2 and 3, with emphasis on the data structures and rendering techniques selected for incorporation in the hybrid method. Chapter 4 gives a general description of the hybrid method. This method processes data in the screen coordinate system and generates images in scan-line order. Scan lines are divided into spans (or segments) using the bounding rectangles of primitives calculated in screen coordinates. Conventional rendering methods and ray tracing techniques are used interchangeably along each scan-line. The method used is detennined by the number of primitives associated with a particular span. Conventional rendering methods are used when only one primitive is associated with a span, ray tracing techniques are used for hidden surface removal when two or more primitives are involved. In the latter case each pixel in the span is evaluated by accessing the polygon that is visible within each primitive associated with the span. The depth values (i. e. z-coordinates derived from the 3-dimensional definition) of the polygons involved are deduced for the pixel's position using linear interpolation. These values are used to determine the visible polygon. The CSG tree is accessed from the bottom upwards via an ordered index that enables the 'visible' primitives on any particular scan-line to be efficiently located. Within each primitive an ordered path through the data structure provides the polygons potentially visible on a particular scan-line. Lists of the active primitives and paths to potentially visible polygons are maintained throughout the rendering step and enable span coherence and scan-line coherence to be fully utilised. The results of tests with a range of typical objects and scenes are provided in chapter 5. These results show that the hybrid algorithm is significantly faster than full ray tracing algorithms

CTL Model Checking with the Sweep-line State Space Exploration Method

Model checking is a powerful approach to verification of distributed systems. The sweep-line method alleviates the inherent state explosion problem in model checking by exploiting progress in the system being verified. Verification with the sweep-line method has until now been restricted to verification of safety and linear-time properties. The contribution of this paper is a new model checking algorithm that enables verification of two common branching time properties. The basic idea is to combine the sweep-line method with on-the-fly computation and inspection of strongly connected components. We experimentally evaluate our algorithm on a communication protocol

Matrix Product State applications for the ALPS project

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix-product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism.Comment: 11+5 pages, 8 figures, 2 example

Self-sustainable protonic ceramic electrochemical cells using a triple conducting electrode for hydrogen and power production.

The protonic ceramic electrochemical cell (PCEC) is an emerging and attractive technology that converts energy between power and hydrogen using solid oxide proton conductors at intermediate temperatures. To achieve efficient electrochemical hydrogen and power production with stable operation, highly robust and durable electrodes are urgently desired to facilitate water oxidation and oxygen reduction reactions, which are the critical steps for both electrolysis and fuel cell operation, especially at reduced temperatures. In this study, a triple conducting oxide of PrNi0.5Co0.5O3-δ perovskite is developed as an oxygen electrode, presenting superior electrochemical performance at 400~600 °C. More importantly, the self-sustainable and reversible operation is successfully demonstrated by converting the generated hydrogen in electrolysis mode to electricity without any hydrogen addition. The excellent electrocatalytic activity is attributed to the considerable proton conduction, as confirmed by hydrogen permeation experiment, remarkable hydration behavior and computations

Feasibility of using the Massively Parallel Processor for large eddy simulations and other Computational Fluid Dynamics applications

The results of an investigation into the feasibility of using the MPP for direct and large eddy simulations of the Navier-Stokes equations is presented. A major part of this study was devoted to the implementation of two of the standard numerical algorithms for CFD. These implementations were not run on the Massively Parallel Processor (MPP) since the machine delivered to NASA Goddard does not have sufficient capacity. Instead, a detailed implementation plan was designed and from these were derived estimates of the time and space requirements of the algorithms on a suitably configured MPP. In addition, other issues related to the practical implementation of these algorithms on an MPP-like architecture were considered; namely, adaptive grid generation, zonal boundary conditions, the table lookup problem, and the software interface. Performance estimates show that the architectural components of the MPP, the Staging Memory and the Array Unit, appear to be well suited to the numerical algorithms of CFD. This combined with the prospect of building a faster and larger MMP-like machine holds the promise of achieving sustained gigaflop rates that are required for the numerical simulations in CFD