STORRE Community: This community contains the ePrints and eTheses produced by Computing Science and Mathematics staff and students.This community contains the ePrints and eTheses produced by Computing Science and Mathematics staff and students.http://hdl.handle.net/1893/352023-06-08T14:16:08Z2023-06-08T14:16:08ZGMM-IL: Image Classification Using Incrementally Learnt, Independent Probabilistic Models for Small Sample SizesJohnston, PennyNogueira, KeillerSwingler, Kevinhttp://hdl.handle.net/1893/351842023-06-07T00:01:59Z2023-01-01T00:00:00ZTitle: GMM-IL: Image Classification Using Incrementally Learnt, Independent Probabilistic Models for Small Sample Sizes
Author(s): Johnston, Penny; Nogueira, Keiller; Swingler, Kevin
Abstract: When deep-learning classifiers try to learn new classes through supervised learning, they exhibit catastrophic forgetting issues. In this paper we propose the Gaussian Mixture Model - Incremental Learner (GMM-IL), a novel two-stage architecture that couples unsupervised visual feature learning with supervised probabilistic models to represent each class. The key novelty of GMM-IL is that each class is learnt independently of the other classes. New classes can be incrementally learnt using a small set of annotated images with no requirement to relearn data from existing classes. This enables the incremental addition of classes to a model, that can be indexed by visual features and reasoned over based on perception. Using Gaussian Mixture Models to represent the independent classes, we outperform a benchmark of an equivalent network with a Softmax head, obtaining increased accuracy for sample sizes smaller than 12 and increased weighted F1 score for 3 imbalanced class profiles in that sample range. This novel method enables new classes to be added to a system with only access to a few annotated images of the new class.2023-01-01T00:00:00ZProgram Transformation Landscapes for Automated Program Modification Using GinPetke, JustynaAlexander, BradBarr, Earl TBrownlee, AlexanderWagner, MarkusWhite, Davidhttp://hdl.handle.net/1893/351302023-05-27T00:00:40ZTitle: 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 theoremPopoola, Joseph Oyeniyihttp://hdl.handle.net/1893/351152023-05-26T13:09:48Z1976-01-01T00:00:00ZTitle: 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 ringsMehrvarz, Ali Akbarhttp://hdl.handle.net/1893/351062023-05-25T15:32:48Z1979-01-01T00:00:00ZTitle: 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.1979-01-01T00:00:00Z