4,325 research outputs found
Generating similar images using bag context picture grammars
A Dissertation submitted to the Faculty of Science in partial fulfilment of the requirements for the degree of Master of Science University of the Witwatersrand, Johannesburg, February 2018Formal language theory was born in the middle of the 20th century as a tool for modeling and investigating syntax of natural languages. It was developed in connection with the handling of programming languages. Bag context grammars are a fairly new grammar class where bag context tree grammars have been defined. Bag context is used to regulate rewriting in tree grammars.
In this dissertation we use bag context to regulate rewriting in picture grammars and thus to generate similar pictures. This work is exploratory work since bag context picture grammars have not been defined. We use examples to show how bag context picture grammars can be used to generate pictures. In this work bag context picture grammars are defined and used to generate similar pictures. Pictures generated by random context picture grammars and three of their sub-classes are selected and bag context picture grammars are used to generate the same pictures to those selected. A lemma is defined that is used to convert the class of random context picture grammars and three of their sub-classes into equivalent bag context picture grammars. For each grammar selected, an equivalent bag context picture grammar is created and used to generate several pictures that are similar to each other. Similarity is defined by noting small differences that are seen in pictures that belong to the same gallery. In this work we generate similar pictures with bag context picture grammars and thus make the discovery that bag context gives a certain level of control in terms of rules applied in a grammar.XL201
Inverse Classification for Comparison-based Interpretability in Machine Learning
In the context of post-hoc interpretability, this paper addresses the task of
explaining the prediction of a classifier, considering the case where no
information is available, neither on the classifier itself, nor on the
processed data (neither the training nor the test data). It proposes an
instance-based approach whose principle consists in determining the minimal
changes needed to alter a prediction: given a data point whose classification
must be explained, the proposed method consists in identifying a close
neighbour classified differently, where the closeness definition integrates a
sparsity constraint. This principle is implemented using observation generation
in the Growing Spheres algorithm. Experimental results on two datasets
illustrate the relevance of the proposed approach that can be used to gain
knowledge about the classifier.Comment: preprin
Ogden's lemma for random permitting and forbidding context picture languages and table-driven context-free picture languages
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, February 16, 2015.Random context picture grammars are used to generate pictures through successive refinement.
There are three important subclasses of random context picture grammars, namely random permitting
context picture grammars, random forbidding context picture grammars and table-driven
context-free picture grammars. These grammars generate the random permitting context picture
languages, random forbidding context picture languages and table-driven context-free picture
languages, respectively. Theorems exist which provide necessary conditions that have to be
satisfied by a language before it can be classified under a particular subclass. Some of these
theorems include the pumping and shrinking lemmas, which have been developed for random
permitting context picture languages and random forbidding context picture languages respectively.
Two characterization theorems were developed for the table-driven context-free picture
languages.
This dissertation examines these existing theorems for picture languages, i.e., the pumping
and shrinking lemmas and the two characterisation theorems, and attempts to prove theorems,
which will provide an alternative to the existing theorems and thus provide new tools for identifying
languages that do not belong to the various classes. This will be done by adapting Ogden’s
idea of marking parts of a word which was done for the string case. Our theorems essentially involve
marking parts of a picture such that the pumping operation increases the number of marked
symbols and the shrinking operation reduces it
On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
The main part of this contribution to the special issue of EJM-B/Fluids
dedicated to Patrick Huerre outlines the problem of the subcritical transition
to turbulence in wall-bounded flows in its historical perspective with emphasis
on plane Couette flow, the flow generated between counter-translating parallel
planes. Subcritical here means discontinuous and direct, with strong
hysteresis. This is due to the existence of nontrivial flow regimes between the
global stability threshold Re_g, the upper bound for unconditional return to
the base flow, and the linear instability threshold Re_c characterized by
unconditional departure from the base flow. The transitional range around Re_g
is first discussed from an empirical viewpoint ({\S}1). The recent
determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane
Couette flow is next examined. In laboratory conditions, its transitional range
displays an oblique pattern made of alternately laminar and turbulent bands, up
to a third threshold Re_t beyond which turbulence is uniform. Our current
theoretical understanding of the problem is next reviewed ({\S}2): linear
theory and non-normal amplification of perturbations; nonlinear approaches and
dynamical systems, basin boundaries and chaotic transients in minimal flow
units; spatiotemporal chaos in extended systems and the use of concepts from
statistical physics, spatiotemporal intermittency and directed percolation,
large deviations and extreme values. Two appendices present some recent
personal results obtained in plane Couette flow about patterning from numerical
simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid
Regulated rewriting in formal language theory
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.Context-free grammars are well-studied and well-behaved in terms of decidability, but many
real-world problems cannot be described with context-free grammars. Grammars with regulated
rewriting are grammars with mechanisms to regulate the applications of rules, so that
certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms,
one can often generate languages that are not context-free.
In this thesis we study grammars with regulated rewriting mechanisms. We consider problems
in which context-free grammars are insufficient and in which more descriptive grammars
are required. We compare bag context grammars with other well-known classes of grammars
with regulated rewriting mechanisms. We also discuss the relation between bag context grammars
and recognizing devices such as counter automata and Petri net automata. We show
that regular bag context grammars can generate any recursively enumerable language. We
reformulate the pumping lemma for random permitting context languages with context-free
rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism.
We conclude the thesis with decidability and complexity properties of grammars with
regulated rewriting
Celebrating Diversity through Spirituality in the Workplace: Transforming Organizations Holistically
Managing diversity effectively is the key to attract and retain a productive workforce. Research demonstrates that celebrating diversity leads to greater productivity, increased creativity, and heightened morale and motivation. Organizations often benefit from the differing perspectives and rich experiences a diverse workforce provides. Similarly, organizations can enhance their creativity by encouraging diverse perspectives and opinions. Thus, issues of managing diversity, valuing diversity, and celebrating diversity have assumed added importance. This paper suggests that diversity is not a problem, but rather a solution to most of the challenges organizations face such as employee engagement and participation. Managing workforce diversity effectively transcends meeting a company’s legal requirements and complying with equal opportunity and non-discrimination regulation. Leaders need to understand and deal constructively with their own biases and prejudices that hinder diversity. Celebrating diversity is the extension of healthy spirituality that leads us to celebrate our differences and view diversity as different manifestations of the underlying Unity that permeates every phenomenon. This paper discusses key advantages of celebrating diversity, pinpoints barriers to organizational diversity, and offers some perspectives to overcome barriers to inclusiveness
Asymptotics of unitary and othogonal matrix integrals
In this paper, we prove that in small parameter regions, arbitrary unitary
matrix integrals converge in the large limit and match their formal
expansion. Secondly we give a combinatorial model for our matrix integral
asymptotics and investigate examples related to free probability and the HCIZ
integral. Our convergence result also leads us to new results of smoothness of
microstates. We finally generalize our approach to integrals over the othogonal
group.Comment: 41 pages, important modifications, new section about orthogonal
integral
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