Lipschitz bijections between boolean functions

We answer four questions from a recent paper of Rao and Shinkar on Lipschitz bijections between functions from $\{0,1\}^n$ to $\{0,1\}$. (1) We show that there is no $O(1)$-bi-Lipschitz bijection from $\mathrm{Dictator}$ to $\mathrm{XOR}$ such that each output bit depends on $O(1)$ input bits. (2) We give a construction for a mapping from $\mathrm{XOR}$ to $\mathrm{Majority}$ which has average stretch $O(\sqrt{n})$, matching a previously known lower bound. (3) We give a 3-Lipschitz embedding $\phi : \{0,1\}^n \to \{0,1\}^{2n+1}$ such that $\mathrm{XOR}(x) = \mathrm{Majority}(\phi(x))$ for all $x \in \{0,1\}^n$. (4) We show that with high probability there is a $O(1)$-bi-Lipschitz mapping from $\mathrm{Dictator}$ to a uniformly random balanced function

Concurrent Image Processing Executive (CIPE)

The design and implementation of a Concurrent Image Processing Executive (CIPE), which is intended to become the support system software for a prototype high performance science analysis workstation are discussed. The target machine for this software is a JPL/Caltech Mark IIIfp Hypercube hosted by either a MASSCOMP 5600 or a Sun-3, Sun-4 workstation; however, the design will accommodate other concurrent machines of similar architecture, i.e., local memory, multiple-instruction-multiple-data (MIMD) machines. The CIPE system provides both a multimode user interface and an applications programmer interface, and has been designed around four loosely coupled modules; (1) user interface, (2) host-resident executive, (3) hypercube-resident executive, and (4) application functions. The loose coupling between modules allows modification of a particular module without significantly affecting the other modules in the system. In order to enhance hypercube memory utilization and to allow expansion of image processing capabilities, a specialized program management method, incremental loading, was devised. To minimize data transfer between host and hypercube a data management method which distributes, redistributes, and tracks data set information was implemented

Spatial search by continuous-time quantum walks on complex networks

Spatial search by continuous-time quantum walks on complex networks is focused on using a quantum walk in continuous time in order to find a single or multiple marked vertices within the complex network. The specific formalism used here is to consider a coupling constant that shifts the state of the quantum walker from the initial state to the target state, which is the marked vertex. The thesis begins with establishing the mathematical framework of network theory, quantum walks and numerical methods that will be used in the remainder of the thesis. Then spatial search by continuous-time quantum walk is studied on regular and semi-regular graphs, where most analytical results can be found. This will get us acquainted with spatial search by quantum walk. The complex networks studied are Barabasi-Albert graphs and the Internet network on the level of autonomous systems. Different renormalized and pruned versions of the Internet network are studied. The parameters of the quantum walk that are focused on are the optimal values for the coupling constant, success probability, time and search time.Kvanttikulkujen spatiaalinen etsintä jatkuvassa ajassa kompleksisissa verkoissa keskittyy yhden tai useamman merkityn solmukohdan löytämiseen kompleksisesta verkosta käyttämällä kvanttikulkua jatkuvassa ajassa. Tässä työssä käytetty formalismi käsittelee kytkentävakiota, mikä siirtää kvanttikulkijan tilan alkutilasta tavoitetilaan, eli merkittyyn solmukohtaan. Tämä Pro Gradu alkaa matemaattisen viitekehyksen käsittelemisellä, jota tarvitaan lopputyössä. Tämä viitekehys sisältää verkkoteorian, kvanttikulut ja käytetyt numeeriset menetelmät. Tämän jälkeen kvanttikulun spatiaalista etsintää jatkuvassa ajassa tutkitaan säännöllisissä ja miltei säännöllisissä verkoissa, missä analyyttiset ratkaisut on löydettävissä. Tämän tarkoituksena on tutustua spatiaaliseen etsintään kvanttikululla. Barabasi-Albert -graafit ja Internet-verkko autonomisten järjestelmien tasolla ovat tässä työssä tutkittavat kompleksiset verkot. Tässä tutkitaan eri renormalisoituja ja karsittuja versioita Internet-verkosta. Kvanttikulun parametrit, joihin keskitytään, ovat optimaaliset arvot kytkentävakiolle, onnistumistodennäköisyydelle, ajalle ja etsintäajalle

Automating Topology Aware Mapping for Supercomputers

Petascale machines with hundreds of thousands of cores are being built. These machines have varying interconnect topologies and large network diameters. Computation is cheap and communication on the network is becoming the bottleneck for scaling of parallel applications. Network contention, specifically, is becoming an increasingly important factor affecting overall performance. The broad goal of this dissertation is performance optimization of parallel applications through reduction of network contention. Most parallel applications have a certain communication topology. Mapping of tasks in a parallel application based on their communication graph, to the physical processors on a machine can potentially lead to performance improvements. Mapping of the communication graph for an application on to the interconnect topology of a machine while trying to localize communication is the research problem under consideration. The farther different messages travel on the network, greater is the chance of resource sharing between messages. This can create contention on the network for networks commonly used today. Evaluative studies in this dissertation show that on IBM Blue Gene and Cray XT machines, message latencies can be severely affected under contention. Realizing this fact, application developers have started paying attention to the mapping of tasks to physical processors to minimize contention. Placement of communicating tasks on nearby physical processors can minimize the distance traveled by messages and reduce the chances of contention. Performance improvements through topology aware placement for applications such as NAMD and OpenAtom are used to motivate this work. Building on these ideas, the dissertation proposes algorithms and techniques for automatic mapping of parallel applications to relieve the application developers of this burden. The effect of contention on message latencies is studied in depth to guide the design of mapping algorithms. The hop-bytes metric is proposed for the evaluation of mapping algorithms as a better metric than the previously used maximum dilation metric. The main focus of this dissertation is on developing topology aware mapping algorithms for parallel applications with regular and irregular communication patterns. The automatic mapping framework is a suite of such algorithms with capabilities to choose the best mapping for a problem with a given communication graph. The dissertation also briefly discusses completely distributed mapping techniques which will be imperative for machines of the future.published or submitted for publicationnot peer reviewe

Parallel algorithms for lattice QCD

SIGLEAvailable from British Library Document Supply Centre- DSC:D81971 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Parallelization of Ant Colony Optimization via Area of Expertise Learning

Ant colony optimization algorithms have long been touted as providing an effective and efficient means of generating high quality solutions to NP-hard optimization problems. Unfortunately, while the structure of the algorithm is easy to parallelize, the nature and amount of communication required for parallel execution has meant that parallel implementations developed suffer from decreased solution quality, slower runtime performance, or both. This thesis explores a new strategy for ant colony parallelization that involves Area of Expertise (AOE) learning. The AOE concept is based on the idea that individual agents tend to gain knowledge of different areas of the search space when left to their own devices. After developing a sense of their own expertness on a portion of the problem domain, agents share information and incorporate knowledge from other agents without having to experience it first-hand. This thesis shows that when incorporated within parallel ACO and applied to multi-objective environments such as a gridworld, the use of AOE learning can be an effective and efficient means of coordinating the efforts of multiple ant colony agents working in tandem, resulting in increased performance. Based on the success of the AOE/ACO combination in gridworld, a similar configuration is applied to the single objective traveling salesman problem. Yet while it was hoped that AOE learning would allow for a fast and beneficial sharing of knowledge between colonies, this goal was not achieved, despite the efforts detailed within. The reason for this lack of performance is due to the nature of the TSP, whose single objective landscape discourages colonies from learning unique portions of the search space. Without this specialization, AOE was found to make parallel ACO faster than the use of a single large colony but less efficient than multiple independent colonies

Chance and Necessity in Evolution: Lessons from RNA

The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are realized much more frequently than others), (2) the notion of shape space covering (that all typical shapes are realized in a small neighborhood of any random sequence), and (3) the notion of a neutral network (that sequences folding into the same typical shape form networks that percolate through sequence space). Neutral networks loosen the requirements on the mutation rate for selection to remain effective. The original (genotypic) error threshold has to be reformulated in terms of a phenotypic error threshold. With regard to adaptation, neutrality has two seemingly contradictory effects: It acts as a buffer against mutations ensuring that a phenotype is preserved. Yet it is deeply enabling, because it permits evolutionary change to occur by allowing the sequence context to vary silently until a single point mutation can become phenotypically consequential. Neutrality also influences predictability of adaptive trajectories in seemingly contradictory ways. On the one hand it increases the uncertainty of their genotypic trace. At the same time neutrality structures the access from one shape to another, thereby inducing a topology among RNA shapes which permits a distinction between continuous and discontinuous shape transformations. To the extent that adaptive trajectories must undergo such transformations, their phenotypic trace becomes more predictable.Comment: 37 pages, 14 figures; 1998 CNLS conference; high quality figures at http://www.santafe.edu/~walte