Finite closed coverings of compact quantum spaces

We show that a projective space P^\infty(Z/2) endowed with the Alexandrov topology is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this projective space. In technical terms, we prove that the category of finitely supported flabby sheaves of algebras is equivalent to the category of algebras with a finite set of ideals that intersect to zero and generate a distributive lattice. In particular, the Gelfand transform allows us to view finite closed coverings of compact Hausdorff spaces as flabby sheaves of commutative C*-algebras over P^\infty(Z/2).Comment: 26 pages, the Teoplitz quantum projective space removed to another paper. This is the third version which differs from the second one by fine tuning and removal of typo

Piecewise principal comodule algebras

A comodule algebra P over a Hopf algebra H with bijective antipode is called principal if the coaction of H is Galois and P is H-equivariantly projective (faithfully flat) over the coaction-invariant subalgebra PcoH. We prove that principality is a piecewise property: given N comodule-algebra surjections P → P_i whose kernels intersect to zero, P is principal if and only if all P_i’s are principal. Furthermore, assuming the principality of P, we show that the lattice these kernels generate is distributive if and only if so is the lattice obtained by intersection with PcoH. Finally, assuming the above distributivity property, we obtain a flabby sheaf of principal comodule algebras over a certain space that is universal for all such N-families of surjections P → P_i and such that the comodule algebra of global sections is P

A Closer Look at Hardware-Friendly Weight Quantization

Quantizing a Deep Neural Network (DNN) model to be used on a custom accelerator with efficient fixed-point hardware implementations, requires satisfying many stringent hardware-friendly quantization constraints to train the model. We evaluate the two main classes of hardware-friendly quantization methods in the context of weight quantization: the traditional Mean Squared Quantization Error (MSQE)-based methods and the more recent gradient-based methods. We study the two methods on MobileNetV1 and MobileNetV2 using multiple empirical metrics to identify the sources of performance differences between the two classes, namely, sensitivity to outliers and convergence instability of the quantizer scaling factor. Using those insights, we propose various techniques to improve the performance of both quantization methods - they fix the optimization instability issues present in the MSQE-based methods during quantization of MobileNet models and allow us to improve validation performance of the gradient-based methods by 4.0% and 3.3% for MobileNetV1 and MobileNetV2 on ImageNet respectively

On the use of economic price theory to determine the optimum levels of privacy and information utility in microdata anonymisation

Statistical data, such as in the form of microdata, is used by different organisations as a basis for creating knowledge to assist in their planning and decision-making activities. However, before microdata can be made available for analysis, it needs to be anonymised in order to protect the privacy of the individuals whose data is released. The protection of privacy requires us to hide or obscure the released data. On the other hand, making data useful for its users implies that we should provide data that is accurate, complete and precise. Ideally, we should maximise both the level of privacy and the level of information utility of a released microdata set. However, as we increase the level of privacy, the level of information utility decreases. Without guidelines to guide the selection of the optimum levels of privacy and information utility, it is difficult to determine the optimum balance between the two goals. The objective and constraints of this optimisation problem can be captured naturally with concepts from Economic Price Theory. In this thesis, we present an approach based on Economic Price Theory for guiding the process of microdata anonymisation such that optimum levels of privacy and information utility are achieved.Thesis (PhD)--University of Pretoria, 2010.Computer Scienceunrestricte