Many-Body Localization in a Quasiperiodic System

Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in extended quantum systems far from the zero-temperature limit. It separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present numerical evidence that many-body localization also occurs in models without disorder but rather a quasiperiodic potential. In one dimension, these systems already have a single-particle localization transition, and we show that this transition becomes a many-body localization transition upon the introduction of interactions. We also comment on possible relevance of our results to experimental studies of many-body dynamics of cold atoms and non-linear light in quasiperiodic potentials.Comment: (12 pages + 3 page appendix, 11 figures) This version has been accepted to PRB. We have clarified certain points and slightly modified the organization of the paper in response to comments by two referee

Development of an innovative procedure to assess the crashworthiness of composite materials

L'abstract è presente nell'allegato / the abstract is in the attachmen

SPST-Index : a self pruning splay tree index for database cracking

Orientador : Prof. Dr. Eduardo Cunha de AlmeidaDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 24/02/2017Inclui referências : f. 41-43Área de concentração: Ciência da computaçãoResumo: Em Database Cracking, uma coluna de banco de dados se organiza fisicamente, de maneira autônoma, em partições, um índice é então criado para otimizar o acesso a essas partições. A árvore AVL é a estrutura de dados utilizada para implementar esse índice. Contudo, em termos de cache, ela é particularmente ineficiente para consultas de intervalos, já que seus nós acessados apenas algumas vezes e os nós frequentemente acessados estão espalhados por toda a árvore. Esse trabalho apresenta a Self-Pruning Splay Tree (SPST) que é uma estrutura de dados capaz de reorganizar os dados mais e menos acessados, melhorando o tempo de acesso para as partições mais acessadas. Para cada consulta de intervalo, a SPST rotaciona para a raiz os nós que apontam para os valores do predicado da consulta e o valor médio do intervalo. Eventualmente, os nós mais acessados da árvore irão permanecer próximos a raíz, melhorando a utilização da CPU e a atividade de cache. Os nós menos acessados permanecerão próximos às folhas e serão removidos para limparmos dados que não são utilizados, diminuindo o tamanho do índice e obtendo custos de leitura e atualização menores. Palavras-chave: Database Cracking, Índice para Cracking , Árvore Splay.Abstract: In database cracking, a database is physically self-organized into cracked partitions with cracker indices boosting the access to these partitions. The AVL Tree is the current data structure of choice to implement cracker indices. However, it is particularly cache-inefficient for range queries, because the nodes accessed only for a few times (i.e, "Cold Data") and the most accessed ones (i.e, "Hot Data") are spread all over the index. This work presents the Self-Pruning Splay Tree (SPST) data structure to index database cracking and reorganize "Hot Data" and "Cold Data" to boost the access to the cracked partitions. To every range query, the SPST rotates to the root the nodes pointing to the edges and to the middle value of the predicate interval. Eventually, the most accessed tree nodes remain close to the root improving CPU and cache activity. On the other hand, the least accessed tree nodes remain close to the leaves and are pruned to clean up unused data in order to diminish the storage footprint with significant improvements: smaller lookup/update costs. Keywords: Database Cracking, Cracker Index, Splay Tree

New Paths from Splay to Dynamic Optimality

Consider the task of performing a sequence of searches in a binary search tree. After each search, an algorithm is allowed to arbitrarily restructure the tree, at a cost proportional to the amount of restructuring performed. The cost of an execution is the sum of the time spent searching and the time spent optimizing those searches with restructuring operations. This notion was introduced by Sleator and Tarjan in (JACM, 1985), along with an algorithm and a conjecture. The algorithm, Splay, is an elegant procedure for performing adjustments while moving searched items to the top of the tree. The conjecture, called "dynamic optimality," is that the cost of splaying is always within a constant factor of the optimal algorithm for performing searches. The conjecture stands to this day. In this work, we attempt to lay the foundations for a proof of the dynamic optimality conjecture.Comment: An earlier version of this work appeared in the Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms. arXiv admin note: text overlap with arXiv:1907.0630

Fundamental Computational Geometry on the GPU

Ph.DDOCTOR OF PHILOSOPH

Exploiting Wireless Broadcast by Opportunistic Packet Splaying

The IEEE 802.11 random access MAC suffers from expensive channel acquisition costs which are exacerbated by the use of TCP. This floor acquisition mechanism is primarily a way to fashion unicast "links" out of what is fundamentally a broadcast medium. The main thesis of this paper is that such unicast usage of the wireless channel is unnecessary, and that once the floor has been acquired, we can instead "splay" packets to as many potential receivers as possible using the fact that wireless is a broadcast medium. Splay is placed between the IP and MAC layers and reduces the expensive cost of channel acquisition by opportunistically combining packets intended for different receivers. Splay allows for the use of sophisticated coding approaches to augment the IEEE 802.11 stop-and-go ARQ. This also helps prevent IEEE 802.11 from incorrectly backing off exponentially in response to fading losses on intermediate quality links, which are quite common in practice. We are currently implementing Splay as a Linux kernel module.DARPA / N66001-06-C-2021 and N00014-0-1-1-0576AFOSR / F49620-02-1-0217NSF / NSF CNS 05-19535, ANI 02-21357, and CCR-0325716USARO / DAAD19-01010-465DARPA/AFOSR / F49620-02-1-0325Vodafone Graduate FellowshipOpe

To assess the value of satellite photographs in resource evaluation on a national scale

The author has identified the following significant results. The limit of resolution on ERTS imagery is normally acknowledged to be about 60 miles although very long features such as roads and railways which are often less than 10 miles long are easily detectable. An example is the north-south road and railway from Lobatse to Francistown. Vegetation growth from winter to summer is readily monitored on false color imagery. The limits of government ranches and special farming areas can be quite accurately ascertained from ERTS imagery. Another aspect to which ERTS imagery lends itself is the location and demarcation of bush fires, many of which were seen on the first imagery which was acquired at the end of the cold, dry season. As a whole, MSS 7 offers maximum reflectance contrast among black and white imagery and is the wavelength used most for interpretation

Praktické datové struktury

V této práci implementujeme datové struktury pro uspořádané a neuspořádané slovníky a měříme jejich výkon v hlavní paměti pomocí syntetických i praktických experimentů. Náš průzkum zahrnuje jak obvyklé datové struktury (B-stromy, červeno-černé stromy, splay stromy a hashování), tak exotičtější přístupy (k-splay stromy a k-lesy). Powered by TCPDF (www.tcpdf.org)In this thesis, we implement several data structures for ordered and unordered dictionaries and we benchmark their performance in main memory on synthetic and practical workloads. Our survey includes both well-known data structures (B-trees, red-black trees, splay trees and hashing) and more exotic approaches (k-splay trees and k-forests). Powered by TCPDF (www.tcpdf.org)Department of Applied MathematicsKatedra aplikované matematikyMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Sketchmate: A digital drawing tool for the splay tree data structure

When discussing complex concepts, people often draw pictures to provide concrete representations of these ideas. Instructors use images to reinforce information when teaching abstract concepts. Computer programs can be used to help present these ideas and provide added benefits. This dissertation explores the creation of such a computer program and the lessons learned during the development process. We chose to focus on the splay tree data structure and report the many details we learned during development. Our findings are useful for others creating teaching tools in other domains. Currently there are a variety of existing programs for splay tree instruction, however, these tools lack functionality. We designed Sketchmate to add more functionality and present it as two different programs: an instructor version and a student version.The instructor\u27s version gives users the ability to create specific tree configurations and provides a history mechanism to revert the tree to a previous state. The student version presents two different types of splay-tree exercises. One type allows students to manipulate individual nodes through drag and drop operations. The second exercise type allows students to click buttons to demonstrate higher level operations. Both versions employ a novel algorithm to lay out tree nodes to maximize screen space. Additionally, both make use of smooth animation between the algorithm steps, providing context for the user. We conducted a series of experiments with each version to measure the usefulness and ease of use for Sketchmate. Results from tests with the instructor\u27s tool suggest users can prepare and demonstrate more examples using Sketchmate and those examples are more accurate than with pencil and paper.Experiments with the student\u27s tool suggest students working example problems enjoy using Sketchmate more than pencil and paper. Also, students using Sketchmate with feedback complete their exercises quicker and still perform just as well on follow up quizzes, suggesting that they learned just as much, with less time spent with the material. These results form the basis for concluding that Sketchmate should prove useful as a possible learning tool for teaching splay trees, both for instructors during algorithm presentation and for students working exercises