Automatic generation of finite-element code by simultaneous optimization of expressions

AbstractThe paper presents a MATHEMATICA package SMS (Symbolic Mechanics System) for the automatic derivation of formulas needed in nonlinear finite element analysis. Symbolic generation of the characteristic arrays of nonlinear finite elements (e.g. nodal force vectors, stiffness matrices, sensitivity vectors) leads to exponential behavior, both in time and space. A new approach, implemented in SMS, avoids this problem by combining several techniques: symbolic capabilities of Mathematica, automatic differentiation technique, simultaneous optimization of expressions and a stochastic evaluation of the formulas instead of a conventional pattern matching technique. SMS translates the derived symbolic formulas into an efficient compiled language (FORTRAN or C). The generated code is then incorporated into an existing finite element analysis environment. SMS was already used to developed several new, geometrically and materially nonlinear finite elements with up to 72 degrees of freedom. The design and implementation of SMS are presented. Efficiency of the new approach is compared with the efficiency of the manually written code on an example

Techniques for improving efficiency and scalability for the integration of information retrieval and databases

PhDThis thesis is on the topic of integration of Information Retrieval (IR) and Databases (DB), with particular focuses on improving efficiency and scalability of integrated IR and DB technology (IR+DB). The main purpose of this study is to develop efficient and scalable techniques for supporting integrated IR and DB technology, which is a popular approach today for handling complex queries over text and structured data. Our specific interest in this thesis is how to efficiently handle queries over large-scale text and structured data. The work is based on a technology that integrates probability theory and relational algebra, where retrievals for text and data are to be expressed in probabilistic logical programs such as probabilistic relational algebra or probabilistic Datalog. To support efficient processing of probabilistic logical programs, we proposed three optimization techniques that focus on aspects covered logical and physical layers, which include: scoring-driven query optimization using scoring expression, query processing with top-k incorporated pipeline, and indexing with relational inverted index. Specifically, scoring expressions are proposed for expressing the scoring or probabilistic semantics of implied scoring functions of PRA expressions, so that efficient query execution plan can be generated by rule-based scoring-driven optimizer. Secondly, to balance efficiency and effectiveness so that to improve query response time, we studied methods for incorporating topk algorithms into pipelined query execution engine for IR+DB systems. Thirdly, the proposed relational inverted index integrates IR-style inverted index and DB-style tuple-based index, which can be used to support efficient probability estimation and aggregation as well as conventional relational operations. Experiments were carried out to investigate the performances of proposed techniques. Experimental results showed that the efficiency and scalability of an IR+DB prototype have been improved, while the system can handle queries efficiently on considerable large data sets for a number of IR tasks

Automated Code Generation for Industrial-Strength Systems

Model-driven engineering proposes to develop software systems by first creating an executable model of the system design and then transforming this model into an implementation. This paper discusses the design of an automatic code generation system that transforms such models into product implementations for highly reliable, industrial-strength systems. It provides insights, practical considerations, and lessons learned when developing code generators for applications that must conform to the constraints imposed by real-world, high-performance systems. Automatic code generation has played a large part in dramatically increasing both the quality and the reliability of software for these systems

Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.Comment: 21 pages, 2 figures, to be presented at CANS 201

Assessing the algebraic attainment of South African grade 9 learners: designing a test using Rasch analysis

A research report submitted to the school of Education, Faculty of Science, University of the Witwatersrand in partial fulfilment for the degree of Master of Science Johannesburg 2017South African learners perform poorly in national and international mathematics assessments (Howie, 2004). A contributing factor to this poor performance is low mathematics knowledge of mathematics teachers in South Africa (Howie, 2003). One means of addressing this is professional development programs. The Wits Maths Connect Secondary Project runs such a program. A test is required by the project in order to assess whether learners are making learning gains after being taught by teachers who participated in this program. The focus of this study is the design of a test used to assess learners’ algebraic attainment. The aim is to design an informative and fair test using Rasch analysis. A sample of 235 learners’ responses to 47 questions was analysed using the Rasch model. In this study, the mean person measure was 2,87 (SD=1,38) logits, while the mean item measure was 0,41 (SD=2,25) logits, suggesting that overall, the test was too difficult. For the learners who wrote this test the person separation index is 1,78 and the person reliability 0,76. This implies that the test may not be not sensitive enough to distinguish between learners of high attainment from learners with low attainment. Various ways of improving the test are discussed.MT 201

Program Improvement by Automatic Redistribution of Intermediate Results

This paper was originally a Ph.D. thesis proposal.The problem of automatically improving the performance of computer programs has many facets. A common source of program inefficiency is the use of abstraction techniques in program design: general tools used in a specific context often do unnecessary or redundant work. Examples include needless copy operations, redundant subexpressions, multiple traversals of the same datastructure and maintenance of overly complex data invariants. I propose to focus on one broadly applicable way of improving a program's performance: redistributing intermediate results so that computation can be avoided. I hope to demonstrate that this is a basic principle of optimization from which many of the current approaches to optimization may be derived. I propose to implement a system that automatically finds and exploits opportunities for redistribution in a given program. In addition to the program source, the system will accept an explanation of correctness and purpose of the code. Beyond the specific task of program improvement, I anticipate that the research will contribute to our understanding of the design and explanatory structure of programs. Major results will include (1) definition and manipulation of representation of correctness and purpose of a program's implementation, and (2) definition, construction, and use of a representation of a program's dynamic behavior.MIT Artificial Intelligence Laborator