STORRE Community: This community contains the ePrints and eTheses produced by Computing Science and Mathematics staff and students.
http://hdl.handle.net/1893/35
This community contains the ePrints and eTheses produced by Computing Science and Mathematics staff and students.2023-05-28T10:11:45ZProgram Transformation Landscapes for Automated Program Modification Using Gin
http://hdl.handle.net/1893/35130
Title: Program Transformation Landscapes for Automated Program Modification Using Gin
Author(s): Petke, Justyna; Alexander, Brad; Barr, Earl T; Brownlee, Alexander; Wagner, Markus; White, David
Abstract: Automated program modification underlies two successful research areas-genetic improvement and program repair. Under the generate-and-validate strategy, automated program modification transforms a program, then validates the result against a test suite. Much work has focused on the search space of application of single fine-grained operators-copy, delete, replace , and swap at both line and statement granularity. This work explores the limits of this strategy. We scale up existing findings an order of magnitude from small corpora to 10 real-world Java programs comprising up to 500k LoC. We decisively show that the grammar-specificity of statement granular edits pays off: its pass rate triples that of line edits and uses 10% less computational resources. We confirm previous findings that delete is the most effective operator for creating test-suite equivalent program variants. We go farther than prior work by exploring the limits of delete's effectiveness by exhaustively applying it. We show this strategy is too costly in practice to be used to search for improved software variants. We further find that pass rates drop from 12-34% for single statement edits to 2-6% for 5-edit sequences, which implies that further progress will need human-inspired operators that target specific faults or improvements. A program is amenable to automated modification to the extent to which automatically editing it is likely to produce test-suite passing variants. We are the first to systematically search for a code measure that correlates with a program's amenability to automated modification. We found no strong correlations , leaving the question open.Some classes of topological vector spaces associated with the Closed graph theorem
http://hdl.handle.net/1893/35115
Title: Some classes of topological vector spaces associated with the Closed graph theorem
Author(s): Popoola, Joseph Oyeniyi
Abstract: Introduction: Given two topological vector spaces E and F and a linear mapping t : E → F with a closed graph, t may or may not be continuous. When such a linear mapping t is necessarily continuous, the closed graph theorem is said to hold for E and F . For example, if E and F are Banach spaces, then every linear mapping with a closed graph of E into F is necessarily continuous.
The main aim of this thesis is to give precise descriptions of certain topological vector spaces that can serve as domain spaces, and also those that can serve as range spaces for a closed graph theorem. This is motivated by the works of M. Mahowald [35], N. Adasch [1], V. Eberhardt [12, 14, 11] and N.J. Kalton [25],
Chapter 2 of the thesis is concerned with the concept of essential separability which turns out to be a useful variation of separability. We look at various characterizations of essential separability and link it up with the well-known concepts of weak compactness and weak relative compactness (Section 2.2).
In Chapter 3, we introduce the class of 6-barrelled spaces which serve as domain spaces for some closed graph theorems (Theorems 3.1.2 and 4,1.3). We show that in the separated case, 6-barrelled spaces can be characterized in terms of essential separability (Theorem 3.1.1). We establish also some of the basic permanence properties of 6-barrelled spaces including the countable codimensional subspace property (Theorem 3.1.6). It is seen that the class of separated δ-barrelled spaces is a proper subclass of Kalton's domain spaces and strictly contains the class of separated barrelled spaces (Example 3.1.1(a), (d)). Also in this Chapter, conditions under which a δ-barrelled space is barrelled are considered.
In Chapter 4, those locally convex spaces which can serve as range spaces in our closed graph theorem in which the domain space is an arbitrary δ-barrelled space with its Mackey topology are considered. These are the infra- δ-spaces. We also look at the domain spaces (δ-spaces) for the corresponding open mapping theorem (Theorem 4.1.4).
Finally, Chapter 5 deals with some topics that are closely related to the concept of δ-barrelledness. In particular, we look at the closed graph theorem when the range space is not assumed to be complete. Then we generalize δ-barrelledness to δ-ultrabarrelledness in general topological vector spaces. In a way similar to the characterization of δ-barrelledness, we obtain a characterization of δ-ultrabarrelledness by means of a closed graph theorem (Theorem 5.2.2). We end the Chapter with a generalization of some of our concepts to arbitrary infinite cardinals.1976-01-01T00:00:00ZTopics in the isomorphism of group rings
http://hdl.handle.net/1893/35106
Title: Topics in the isomorphism of group rings
Author(s): Mehrvarz, Ali Akbar
Abstract: Introduction: Let R be a ring and let G be a group. The group ring R(G) of G over R is the free left R-module over the set of elements of G as a basis in which the multiplication induced by G is extended linearly to R(G) , [12].
A twisted group ring Ry (G) of G over R is an R-algebra with basis {ḡ |g ε G} and with an associative multiplication ḡ ħ = Y(g, h) ḡħ for all g, h ε G , where y(g, h) is a unit in the centre of R , [13].
In [5] Higman proved that the only units of finite order in the group ring R(G), where R is the ring of rational integers and G is a finite abelian group, are ± g, g ε G . In [16] Sehgal proved that the only units of finite order in the group ring R(G), where R is the ring of rational integers and G is an arbitrary abelian group, are ± t where t is a torsion element of G. Moreover in [16] he proved that the units of R(G), where R is an integral domain and G is a torsion-free abelian group, are of the form r g where r is a unit in R and g ε G. Also in [15] he proved that the units of R(<x>), where R is a commutative ring with no non-zero nilpotents and no non-trivial idempotents and <x> is an infinite cyclic group, are of the form r g where r is a unit in R and g ε <x>.
In [17] Zariski and Samuel studied R-automorphisms of the polynomial rings R[x], (that is, automorphisms of R[x] which restrict to the identity mapping on R) where R is an integral domain. In [3] Gilmer determined R-automorphisms of the polynomial rings R[x] where R is a commutative ring. In [2] Coleman and Enochs studied the corresponding results in general. In [9] Parmenter studied R-automorphisms of the group ring R(<x>) where <x> is an infinite cyclic group and he determined necessary and sufficient conditions that x → Σ aixi induces an R-automorphism of R(<x>). He also studied the units of R(G) where R is a commutative ring and G is a right-ordered group.
This thesis consists of five chapters. Chapter 1 contains some well known results and definitions that are needed in this thesis. In Chapter 2 we extend some ideas of [9] to a twisted group ring RY (<x>) where <x> is an infinite cyclic group and we determine a necessary and sufficient condition that x̄ → Σ l aixi induces an R-automorphism of RY (<x>) . Chapter 3 studies R-automorphism of R(G) where R is either a field or a ring with a unique proper ideal and G is a finitely generated torsion-free abelian group. In Chapter 4 we determine the units and study the K-automorphisms of K(<x> x <y>) where K is a field and <x> is an infinite 2 cyclic group, y2 = 1. In [10] Passman proved that the group algebras of all non-isomorphic p-groups of order at most p4 over the prime field of p elements are non-isomorphic. In Chapter 5 we attempt to find the corresponding results for the p-groups of order p 5, but the problem is still open.1979-01-01T00:00:00ZInvestigating Causal links from Observed Features in the first COVID-19 Waves in California
http://hdl.handle.net/1893/35101
Title: Investigating Causal links from Observed Features in the first COVID-19 Waves in California
Author(s): Good, Sarah; O'Hare, Anthony
Abstract: Determining who is at risk from a disease is important in order to protect vulnerable subpopula- tions during an outbreak. We are currently in a SARS-COV-2 (commonly referred to as COVID-19) pandemic which has had a massive impact across the world, with some communities and individuals seen to have a higher risk of severe outcomes and death from the disease compared to others. These risks are compounded for people of lower socioeconomic status, those who have limited access to health care, higher rates of chronic diseases, such as hypertension, diabetes (type-2), obesity, likely due to the chronic stress of these types of living conditions. Essential workers are also at a higher risk of COVID-19 due to having higher rates of exposure due to the nature of their work. In this study we determine the important features of the pandemic in California in terms of cumulative cases and deaths per 100,000 of population up to the date of 5 July, 2021 (the date of analysis) using Pearson correlation coefficients between population demographic features and cumulative cases and deaths. The most highly correlated features, based on the absolute value of their Pearson Correlation Coefficients in relation to cases or deaths per 100,000, were used to create regression models in two ways: using the top 5 features and using the top 20 features filtered out to limit interactions between features. These models were used to determine a) the most significant features out of these subsets and b) features that approximate different potential forces on COVID- 19 cases and deaths (especially in the case of the latter set). Additionally, co-correlations, defined as demographic features not within a given input feature set for the regression models but which are strongly correlated with the features included within, were calculated for all features. The five features which had the highest correlations to cumulative cases per 100,000 were found to be the following: Overcrowding (% of households), Average Household Size, Hispanic ethnicity (% of population), Ages 0-19 (% population), education level of 9th to 12th with no high school diploma (% of population older than 25 years), and incidence rates of Long-term Diabetes Compli- cations (per 100,000 population). For cumulative deaths per 100,000, the feature set was similar except Overcrowding (% of households) replaced Long-term Diabetes Complications. The feature set for uncorrelated features was the same for both cases and deaths. This set was comprised of Overcrowding (% of households), Wholesale trade (% of workforce employed in), ‘Transportation, warehousing, and utilities’ (% of workforce employed in), and ‘Graduate or professional degree’ (% of population older than 25 years).2023-03-25T00:00:00Z