Group Learning and Opinion Diffusion in a Broadcast Network

We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly generated rewards, whose statistics depend on the options chosen as well as the user itself, and are unknown to the users. Each user aims to maximize their expected total rewards over a certain time horizon through an online learning process, i.e., a sequence of exploration (sampling the return of each option) and exploitation (selecting empirically good options) steps. Within this context we consider two group learning scenarios, (1) users with uniform preferences and (2) users with diverse preferences, and examine how a user should construct its learning process to best extract information from other's decisions and experiences so as to maximize its own reward. Performance is measured in {\em weak regret}, the difference between the user's total reward and the reward from a user-specific best single-action policy (i.e., always selecting the set of options generating the highest mean rewards for this user). Within each scenario we also consider two cases: (i) when users exchange full information, meaning they share the actual rewards they obtained from their choices, and (ii) when users exchange limited information, e.g., only their choices but not rewards obtained from these choices

To Stay Or To Switch: Multiuser Dynamic Channel Access

In this paper we study opportunistic spectrum access (OSA) policies in a multiuser multichannel random access cognitive radio network, where users perform channel probing and switching in order to obtain better channel condition or higher instantaneous transmission quality. However, unlikely many prior works in this area, including those on channel probing and switching policies for a single user to exploit spectral diversity, and on probing and access policies for multiple users over a single channel to exploit temporal and multiuser diversity, in this study we consider the collective switching of multiple users over multiple channels. In addition, we consider finite arrivals, i.e., users are not assumed to always have data to send and demand for channel follow a certain arrival process. Under such a scenario, the users' ability to opportunistically exploit temporal diversity (the temporal variation in channel quality over a single channel) and spectral diversity (quality variation across multiple channels at a given time) is greatly affected by the level of congestion in the system. We investigate the optimal decision process in this case, and evaluate the extent to which congestion affects potential gains from opportunistic dynamic channel switching

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifolds

We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative two tori, the quantum part of the curvature consists of actions of the modular derivation through two local curvature functions. Explicit expressions for those functions are obtained for all even dimensions (greater than two). In dimension four, the one variable function shows striking similarity to the analytic functions of the characteristic classes appeared in the Atiyah-Singer local index formula, namely, it is roughly a product of the $j$-function (which defines the $\hat A$-class of a manifold) and an exponential function (which defines the Chern character of a bundle). By performing two different computations for the variation of the Einstein-Hilbert action, we obtain a deep internal relations between two local curvature functions. Straightforward verification for those relations gives a strong conceptual confirmation for the whole computational machinery we have developed so far, especially the Mathematica code hidden behind the paper.Comment: 44 pages, 11 figures, some minor updates from the previous versio

Earnings target and the competing use of abnormal R&D and abnormal accruals of R&D intensive firms : a thesis presented in partial fulfilment of the requirements for the degree of Master of Management in Accountancy at Massey University

The purpose of this study is to examine the competing use of real earnings management and accruals management in certain specific circumstances of firms where both real earnings management and accruals management are costly and where firms can either use both or any of the two methods of earnings management to meet earnings targets. A recent study, Zang (2005), examines the competing use of real earnings management and accruals management. She finds that in a broad sample firms tend to use real earnings management before accruals management. This study overlooks the issue that in such a sample firms that are not R&D intensive would find R&D reductions less costly than accruals management. She also overlooks the point that the tendency to use different methods of earnings management depends on how far the earnings are from the earnings targets. I conduct an examination of the competing use of real earnings management and accruals management in a sample of R&D intensive firms. I use R&D intensive firms because R&D reduction can be costly for them as costs of future earnings generation capacities. I also consider the distance of a firm from meeting its earnings target using the two methods of earnings management. My results indicate that when real earnings management and accruals management are both costly, firms tend to use both methods. However, as R&D activities are important for R&D intensive firms, they tend to use abnormal accruals more than abnormal R&D to manage their earnings. Based on such findings, I construe that the nature of the firm's activities and the distance of the earnings from the earnings target influence a firm's use of real earnings management and accruals management to meet its earnings target