Scaling Laws of Cognitive Networks

We consider a cognitive network consisting of n random pairs of cognitive transmitters and receivers communicating simultaneously in the presence of multiple primary users. Of interest is how the maximum throughput achieved by the cognitive users scales with n. Furthermore, how far these users must be from a primary user to guarantee a given primary outage. Two scenarios are considered for the network scaling law: (i) when each cognitive transmitter uses constant power to communicate with a cognitive receiver at a bounded distance away, and (ii) when each cognitive transmitter scales its power according to the distance to a considered primary user, allowing the cognitive transmitter-receiver distances to grow. Using single-hop transmission, suitable for cognitive devices of opportunistic nature, we show that, in both scenarios, with path loss larger than 2, the cognitive network throughput scales linearly with the number of cognitive users. We then explore the radius of a primary exclusive region void of cognitive transmitters. We obtain bounds on this radius for a given primary outage constraint. These bounds can help in the design of a primary network with exclusive regions, outside of which cognitive users may transmit freely. Our results show that opportunistic secondary spectrum access using single-hop transmission is promising.Comment: significantly revised and extended, 30 pages, 13 figures, submitted to IEEE Journal of Special Topics in Signal Processin

Throughput and Delay Scaling in Supportive Two-Tier Networks

Consider a wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier consists of randomly distributed legacy nodes of density $n$, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed cognitive nodes of density $m=n^\beta$ with $\beta\geq 2$, which can only access the spectrum opportunistically to limit the interference to the primary tier. Based on the assumption that the secondary tier is allowed to route the packets for the primary tier, we investigate the throughput and delay scaling laws of the two tiers in the following two scenarios: i) the primary and secondary nodes are all static; ii) the primary nodes are static while the secondary nodes are mobile. With the proposed protocols for the two tiers, we show that the primary tier can achieve a per-node throughput scaling of $\lambda_p(n)=\Theta(1/\log n)$ in the above two scenarios. In the associated delay analysis for the first scenario, we show that the primary tier can achieve a delay scaling of $D_p(n)=\Theta(\sqrt{n^\beta\log n}\lambda_p(n))$ with $\lambda_p(n)=O(1/\log n)$. In the second scenario, with two mobility models considered for the secondary nodes: an i.i.d. mobility model and a random walk model, we show that the primary tier can achieve delay scaling laws of $\Theta(1)$ and $\Theta(1/S)$, respectively, where $S$ is the random walk step size. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC 201

Fractal analyses of networks of integrate-and-fire stochastic spiking neurons

Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series of simulated neuronal networks composed of integrate-and-fire stochastic spiking neurons, and the utility of fractal methods in assessing network criticality. Simulated time-series were derived from a network model of fully connected discrete-time stochastic excitable neurons. Monofractal and multifractal analyses were applied to neuronal gain time-series. Fractal scaling was greatest in networks with a mid-range of neuronal plasticity, versus extremely high or low levels of plasticity. Peak fractal scaling corresponded closely to additional indices of criticality, including average branching ratio. Networks exhibited multifractal structure, or multiple scaling relationships. Multifractal spectra around peak criticality exhibited elongated right tails, suggesting that the fractal structure is relatively insensitive to high-amplitude local fluctuations. Networks near critical states exhibited mid-range multifractal spectra width and tail length, which is consistent with literature suggesting that networks poised at quasi-critical states must be stable enough to maintain organization but unstable enough to be adaptable. Lastly, fractal analyses may offer additional information about critical state dynamics of networks by indicating scales of influence as networks approach critical states.Comment: 11 pages, 3 subfigures divided into 2 figure

Capacity scaling law by multiuser diversity in cognitive radio systems

This paper analyzes the multiuser diversity gain in a cognitive radio (CR) system where secondary transmitters opportunistically utilize the spectrum licensed to primary users only when it is not occupied by the primary users. To protect the primary users from the interference caused by the missed detection of primary transmissions in the secondary network, minimum average throughput of the primary network is guaranteed by transmit power control at the secondary transmitters. The traffic dynamics of a primary network are also considered in our analysis. We derive the average achievable capacity of the secondary network and analyze its asymptotic behaviors to characterize the multiuser diversity gains in the CR system.Comment: 5 pages, 2 figures, ISIT2010 conferenc

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Between social physics and phenomenology

In recent years, both phenomenology and social physics, which might be thought of asoccupying the humanistic and scientific poles of urban discourse, have taken an interestin space syntax as a means of furthering their academic aims. Here we suggest that thiscould presage a far deeper theoretical integration of the multi-disciplinary study of citiesthan either currently envisage