Multi-wise and constrained fully weighted Davenport constants and interactions with coding theory

We consider two families of weighted zero-sum constants for finite abelian groups. For a finite abelian group $( G , + )$, a set of weights $W \subset \mathbb{Z}$, and an integral parameter $m$, the $m$-wise Davenport constant with weights $W$ is the smallest integer $n$ such that each sequence over $G$ of length $n$ has at least $m$ disjoint zero-subsums with weights $W$. And, for an integral parameter $d$, the $d$-constrained Davenport constant with weights $W$ is the smallest $n$ such that each sequence over $G$ of length $n$ has a zero-subsum with weights $W$ of size at most $d$. First, we establish a link between these two types of constants and several basic and general results on them. Then, for elementary $p$-groups, establishing a link between our constants and the parameters of linear codes as well as the cardinality of cap sets in certain projective spaces, we obtain various explicit results on the values of these constants

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

An Unsupervised Approach to Modelling Visual Data

For very large visual datasets, producing expert ground-truth data for training supervised algorithms can represent a substantial human effort. In these situations there is scope for the use of unsupervised approaches that can model collections of images and automatically summarise their content. The primary motivation for this thesis comes from the problem of labelling large visual datasets of the seafloor obtained by an Autonomous Underwater Vehicle (AUV) for ecological analysis. It is expensive to label this data, as taxonomical experts for the specific region are required, whereas automatically generated summaries can be used to focus the efforts of experts, and inform decisions on additional sampling. The contributions in this thesis arise from modelling this visual data in entirely unsupervised ways to obtain comprehensive visual summaries. Firstly, popular unsupervised image feature learning approaches are adapted to work with large datasets and unsupervised clustering algorithms. Next, using Bayesian models the performance of rudimentary scene clustering is boosted by sharing clusters between multiple related datasets, such as regular photo albums or AUV surveys. These Bayesian scene clustering models are extended to simultaneously cluster sub-image segments to form unsupervised notions of “objects” within scenes. The frequency distribution of these objects within scenes is used as the scene descriptor for simultaneous scene clustering. Finally, this simultaneous clustering model is extended to make use of whole image descriptors, which encode rudimentary spatial information, as well as object frequency distributions to describe scenes. This is achieved by unifying the previously presented Bayesian clustering models, and in so doing rectifies some of their weaknesses and limitations. Hence, the final contribution of this thesis is a practical unsupervised algorithm for modelling images from the super-pixel to album levels, and is applicable to large datasets

DYNAMIC LOW-RANK MATRIX RECOVERY: THEORY AND APPLICATIONS

The purpose of this work is to provide both theoretical understanding of and practical algorithms for dynamic low-rank matrix recovery. Although the benefits of exploiting dynamics in low-rank matrix recovery have been observed in many applications, the theoretical understanding of and justification for these methods is limited. This dissertation concerns two widely-used dynamics models in the context of low-rank matrix recovery: random walk dynamics and measurement induced dynamics. For random walk dynamics, we propose a locally weighted matrix smoothing (LOWEMS) framework, establish its recovery guarantee and algorithmic convergence, and discuss two practical extensions for it. For measurement induced dynamics, we propose a general DynEmb framework and demonstrate its effectiveness for the knowledge tracing application. In the end, we conduct some initial theoretical analysis on a simplified measurement induced dynamic model.Ph.D

The Plus-Minus Davenport Constant of Finite Abelian Groups

Let G be a finite abelian group, written additively. The Davenport constant, D(G), is the smallest positive number s such that any subset of the group G, with cardinality at least s, contains a non-trivial zero-subsum. We focus on a variation of the Davenport constant where we allow addition and subtraction in the non-trivial zero-subsum. This constant is called the plus-minus Davenport constant, D±(G). In the early 2000’s, Marchan, Ordaz, and Schmid proved that if the cardinality of G is less than or equal to 100, then the D±(G) is the floor of log2 n + 1, the basic upper bound, with few exceptions. The value of D±(G) is primarily known when the rank of G at most two and the cardinality of G is less than or equal to 100. In most cases, when D±(G) is known, D±(G)= floor(log2 |G|) + 1, with the exceptions of when G is a 3-group or a 5-group. We have studied a class of groups where the cardinality of G is a product of two prime powers. We look more closely to when the primes are 2 and 3, since the plus-minus Davenport constant of a 2-group attains the basic upper bound and while the plus-minus Davenport constant of a 3-group does not. To help us compute D±(G), we define the even plus-minus Davenport constant, De±(G), that guarantees a pm zero-subsum of even length. Let Cn be a cyclic group of order n. Then D(Cn) = n and D±(Cn) =floor( log2 n)+1. We have shown that De±(Cn) depends on whether n is even or odd. When n is even and not a power of 2, then De±(Cn) = floor(log2 n) + 2. When n = 2k , then De±(Cn) = floor(log2 n) + 1. The case when n is odd, De±(Cn) varies depending on how close n is to a power of 2. We have also shown that a subset containing the Jacobsthal numbers provides a subset of Cn that does not contain an even pm zero-subsum for certain values of n. When G is a finite abelian group, we provide bounds for De±(G). If D±(G) is known, then we given an improvement to the lower bound of De±(G). Additional improvements are shown when G is a direct sum an elementary abelian p-groups where p is prime. Then we compute the values of De±(Cr3 ) when 2 ≤ r ≤ 9 and provide an optimal lower bound for larger r. For the group C2 ⊕ Cr3 , D±(C2 ⊕ Cr3 ) = De±(Cr3 ). When r \u3c 10, D±(C2 ⊕ Cr3 ) does not attain the basic upper bound. We conjecture that as r increases, D±(C2 ⊕ Cr3 ) will not attain the basic upper bound. Now, let G = Cq2 ⊕ Cr3 . We compute the values of D±(G) for general q and small r. In this case, we show that if D±(G) attains the basic upper bound then so does De±(G). We then look at the case when the cardinality of G is a product of two prime powers and show improvements on the lower bound by using the fractional part of log2 p of each prime. Furthermore, we compute the values of D±(G) when 100 \u3c |G| ≤ 200, with some exceptions

The role of tacit knowledge in knowledge intensive project management

The traditional doctrine of project management, having evolved from operations management, has been dominated by a rationalist approach in terms of planning and control. There is increasing criticism that this prescriptive approach is deficient for the management of dynamically complex projects which is a common characteristic for modern-day projects. In response to this and the relative lack of scholarly literature, this study uses an emergent grounded theory design to discover and understand the softer, intangible aspects of project management. With primary data collected from twenty semi-structured personal interviews, this study explores the lived experiences of project practitioners and how they ‘muddle through’ the complex social setting of a knowledge intensive financial services organisation. The model which evolved from the research portrays the project practitioner as being exposed to multiple cues, with multiple meanings around five causal themes: environmental, organisational, nature of the task, role and knowledge capability. In response to these cues, the practitioner reflects upon their emotions and past experiences in order to make sense of the uncertain situation to determine their necessary course of action. As a coping strategy the project practitioner takes on the role of bricoleur, by making do by applying combinations of the resources at hand, in order to facilitate the successful delivery of their projects