Hierarchically Clustered Adaptive Quantization CMAC and Its Learning Convergence

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Cold Dark Matter I: The Formation of Dark Halos

We use numerical simulations of critically-closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to $256^3$ particles using the particle-mesh (PM) method and with up to $144^3$ particles using the adaptive particle-particle --particle-mesh (P$^3$M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all $\Omega=1$ CDM models for linear amplitude \sigma_8\gsim 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low mass halos. The distribution of halos characterized by their circular velocities for the P$^3$M simulations is in reasonable agreement with the observations for 150\kms\lsim V_{\rm circ} \lsim 350\kms.}}Comment: 41 pages, plain tex, ApJ, 236, in press; postscript figures available in ftp://arcturus.mit.edu/Preprints/CDM1_figs.tar.

Distributed Algorithms for Spectrum Allocation, Power Control, Routing, and Congestion Control in Wireless Networks

We develop distributed algorithms to allocate resources in multi-hop wireless networks with the aim of minimizing total cost. In order to observe the fundamental duplexing constraint that co-located transmitters and receivers cannot operate simultaneously on the same frequency band, we first devise a spectrum allocation scheme that divides the whole spectrum into multiple sub-bands and activates conflict-free links on each sub-band. We show that the minimum number of required sub-bands grows asymptotically at a logarithmic rate with the chromatic number of network connectivity graph. A simple distributed and asynchronous algorithm is developed to feasibly activate links on the available sub-bands. Given a feasible spectrum allocation, we then design node-based distributed algorithms for optimally controlling the transmission powers on active links for each sub-band, jointly with traffic routes and user input rates in response to channel states and traffic demands. We show that under specified conditions, the algorithms asymptotically converge to the optimal operating point.Comment: 14 pages, 5 figures, submitted to IEEE/ACM Transactions on Networkin

Asymptotically Optimal Multiple-access Communication via Distributed Rate Splitting

We consider the multiple-access communication problem in a distributed setting for both the additive white Gaussian noise channel and the discrete memoryless channel. We propose a scheme called Distributed Rate Splitting to achieve the optimal rates allowed by information theory in a distributed manner. In this scheme, each real user creates a number of virtual users via a power/rate splitting mechanism in the M-user Gaussian channel or via a random switching mechanism in the M-user discrete memoryless channel. At the receiver, all virtual users are successively decoded. Compared with other multiple-access techniques, Distributed Rate Splitting can be implemented with lower complexity and less coordination. Furthermore, in a symmetric setting, we show that the rate tuple achieved by this scheme converges to the maximum equal rate point allowed by the information-theoretic bound as the number of virtual users per real user tends to infinity. When the capacity regions are asymmetric, we show that a point on the dominant face can be achieved asymptotically. Finally, when there is an unequal number of virtual users per real user, we show that differential user rate requirements can be accommodated in a distributed fashion.Comment: Submitted to the IEEE Transactions on Information Theory. 15 Page

Predicting the expected behavior of agents that learn about agents: the CLRI framework

We describe a framework and equations used to model and predict the behavior of multi-agent systems (MASs) with learning agents. A difference equation is used for calculating the progression of an agent's error in its decision function, thereby telling us how the agent is expected to fare in the MAS. The equation relies on parameters which capture the agent's learning abilities, such as its change rate, learning rate and retention rate, as well as relevant aspects of the MAS such as the impact that agents have on each other. We validate the framework with experimental results using reinforcement learning agents in a market system, as well as with other experimental results gathered from the AI literature. Finally, we use PAC-theory to show how to calculate bounds on the values of the learning parameters