On the Capacity of the Finite Field Counterparts of Wireless Interference Networks

This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over $\mathbb{F}_{p^n}$ are analogous to n x n vector (MIMO) channels in the wireless setting, but with an important distinction -- there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity optimal solutions for their finite field counterparts. This is shown through the study of the 2-user X channel and the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over $\mathbb{F}_{p^n}$ also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.Comment: Full version of paper accepted for presentation at ISIT 201

An Improved Distributed Algorithm for Maximal Independent Set

The Maximal Independent Set (MIS) problem is one of the basics in the study of locality in distributed graph algorithms. This paper presents an extremely simple randomized algorithm providing a near-optimal local complexity for this problem, which incidentally, when combined with some recent techniques, also leads to a near-optimal global complexity. Classical algorithms of Luby [STOC'85] and Alon, Babai and Itai [JALG'86] provide the global complexity guarantee that, with high probability, all nodes terminate after $O(\log n)$ rounds. In contrast, our initial focus is on the local complexity, and our main contribution is to provide a very simple algorithm guaranteeing that each particular node $v$ terminates after $O(\log \mathsf{deg}(v)+\log 1/\epsilon)$ rounds, with probability at least $1-\epsilon$. The guarantee holds even if the randomness outside $2$-hops neighborhood of $v$ is determined adversarially. This degree-dependency is optimal, due to a lower bound of Kuhn, Moscibroda, and Wattenhofer [PODC'04]. Interestingly, this local complexity smoothly transitions to a global complexity: by adding techniques of Barenboim, Elkin, Pettie, and Schneider [FOCS'12, arXiv: 1202.1983v3], we get a randomized MIS algorithm with a high probability global complexity of $O(\log \Delta) + 2^{O(\sqrt{\log \log n})}$, where $\Delta$ denotes the maximum degree. This improves over the $O(\log^2 \Delta) + 2^{O(\sqrt{\log \log n})}$ result of Barenboim et al., and gets close to the $\Omega(\min\{\log \Delta, \sqrt{\log n}\})$ lower bound of Kuhn et al. Corollaries include improved algorithms for MIS in graphs of upper-bounded arboricity, or lower-bounded girth, for Ruling Sets, for MIS in the Local Computation Algorithms (LCA) model, and a faster distributed algorithm for the Lov\'asz Local Lemma

On stochastic control and optimal measurement strategies

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered

Competitive Targeted Advertising with Price Discrimination

This paper investigates the effects of price discrimination by means of targeted advertising in a duopolistic market where the distribution of consumers' preferences is discrete and where advertising plays two major roles. It is used by firms as a way to transmit relevant information to otherwise uninformed consumers, and it is used as a price discrimination device. We compare the firms' optimal marketing mix (advertising and pricing) when they adopt mass advertising/non-discrimination strategies and targeted advertising/price discrimination strategies. If firms are able to adopt targeted advertising strategies, we find that the symmetric price equilibrium is in mixed strategies, while the advertising is chosen deterministically. Our results also unveil that as long as we allow for imperfect substitutability between the goods, ?rms do not necessarily target more ads to their own market. In particular, firms' optimal marketing mix leads to higher advertising reach in the rival's market than in the firms' own market, provided that advertising costs are sufficiently low in relation to the consumer's reservation value. The comparison of the optimal marketing-mix under mass advertising strategies and targeted advertising strategies reveals that targeted advertising might constitute a tool to dampen price competition. In particular, if advertising costs are sufficiently low in relation to the value of the goods, we obtain that average prices with non-discrimination (mass advertising) are below those with price discrimination and targeted advertising (regardless of the market segment). Accordingly, when (i) goods are imperfect substitutes, (ii) advertising is not too expensive, and (iii) targeted advertising constitutes an effective price discrimination tool, price discrimination through targeted advertising may be detrimental to social welfare since it boosts industry profits at the expense of consumer surplus.

Optimal-constraint lexicons for requirements specifications

Constrained Natural Languages (CNLs) are becoming an increasingly popular way of writing technical documents such as requirements specifications. This is because CNLs aim to reduce the ambiguity inherent within natural languages, whilst maintaining their readability and expressiveness. The design of existing CNLs appears to be unfocused towards achieving specific quality outcomes, in that the majority of lexical selections have been based upon lexicographer preferences rather than an optimum trade-off between quality factors such as ambiguity, readability, expressiveness, and lexical magnitude. In this paper we introduce the concept of 'replaceability' as a way of identifying the lexical redundancy inherent within a sample of requirements. Our novel and practical approach uses Natural Language Processing (NLP) techniques to enable us to make dynamic trade-offs between quality factors to optimise the resultant CNL. We also challenge the concept of a CNL being a one-dimensional static language, and demonstrate that our optimal-constraint process results in a CNL that can adapt to a changing domain while maintaining its expressiveness. © Springer-Verlag Berlin Heidelberg 2007