Coalition Formation Game for Cooperative Cognitive Radio Using Gibbs Sampling

This paper considers a cognitive radio network in which each secondary user selects a primary user to assist in order to get a chance of accessing the primary user channel. Thus, each group of secondary users assisting the same primary user forms a coaltion. Within each coalition, sequential relaying is employed, and a relay ordering algorithm is used to make use of the relays in an efficient manner. It is required then to find the optimal sets of secondary users assisting each primary user such that the sum of their rates is maximized. The problem is formulated as a coalition formation game, and a Gibbs Sampling based algorithm is used to find the optimal coalition structure.Comment: 7 pages, 2 figure

The Dot-com Meltdown and the Web

Presents findings from a survey conducted between August and September 2001. Looks at how the collapse of the dot-com economy has had tangible effects on personal lives, and how online Americans have made quick adjustments to the changing Web environment

The Social Medium Selection Game

We consider in this paper competition of content creators in routing their content through various media. The routing decisions may correspond to the selection of a social network (e.g. twitter versus facebook or linkedin) or of a group within a given social network. The utility for a player to send its content to some medium is given as the difference between the dissemination utility at this medium and some transmission cost. We model this game as a congestion game and compute the pure potential of the game. In contrast to the continuous case, we show that there may be various equilibria. We show that the potential is M-concave which allows us to characterize the equilibria and to propose an algorithm for computing it. We then give a learning mechanism which allow us to give an efficient algorithm to determine an equilibrium. We finally determine the asymptotic form of the equilibrium and discuss the implications on the social medium selection problem

On the movements of deep mesoscale eddies in the North Atlantic

A simplified three layer model is considered in order to examine the movements of deep mesoscale eddies such as the isolated Mediterranean eddies observed off the Bahamas. These anticyclonic eddies are found in the permanent thermocline more than 6000 km away from their parent water mass and are characterized by a lens-like cross section...

Reply to comments on ‘On the steadiness of separating meandering currents’

The authors thank Nof et al. for their comments on the authors’ paper ‘‘On the steadiness of separating meandering currents.’’ The authors’ paper was motivated by a series of papers by Nof et al. Under a certain set of conditions (reduced gravity, steady state, no meridional velocity at outflow, and parallel outflow), Nof et al. showed that a separating and retroflecting frictionless current cannot be steady because of a momentum imbalance. The main conclusion of the authors’ paper was that they agree with the Nof et al. result that a momentum imbalance exists and extended the proof to all possible configurations of retroflecting currents, even including friction. The authors’ results point to a new mechanism for the generation of variability in the ocean that is not related to dynamical instability of the flow. The main claim in the comments is that the authors incorrectly argued in the appendix that the steadystate solutions presented by Nof et al. in several papers fulfill the extra constraint u2 5g9h. In the original paper, the authors showed that it follows from the geostrophic assumption stated implicitly in all these Nof et al. papers, because the flow is assumed to be parallel. Nof et al. now argue that the flow is only approximately geostrophic in all Nof et al. papers. The authors show in this reply that for steady weakly meandering outflows approximate geostrophy does lead to a momentum imbalance paradox as Nof et al. claim. However, for a steady strongly meandering outflow, approximate geostrophy is not enough and one has to use the method explored by van Leeuwen and De Ruijter to derive a momentum imbalance paradox

On the migration of isolated eddies with application to Gulf Stream rings

An analytical model describing the β-induced drift of isolated nonlinear eddies such as the cold- and warm-core rings observed in the Atlantic Ocean is proposed. The ocean is approximated by two layers and attention is focused on frictionless upper ocean eddies whose surface area is finite. These isolated eddies are nonlinear in the sense that (a) the corresponding Rossby number is relatively large and (b) the interface vertical displacements ( amplitudes ) are comparable to the upper layer undisturbed depth. Solutions for steadily translating eddies which carry their entire mass as they move are sought. Examination of the problem in a moving coordinate system enables one to construct such solutions analytically by using the equations of motion in an integrated form and a power series expansion.Significant differences between the behavior of cyclonic and anticyclonic eddies are found. Although both cyclonic and anticyclonic eddies drift to the west due to β, their speeds and dynamical behavior are very different. For some range of parameters the β-induced drift of an anticyclonic eddy differs by as much as 400% from the drift of a cyclonic eddy with similar characteristics. Furthermore, the β-induced translation of cyclonic eddies increases with size and decreases with amplitude whereas the speed of anticyclonic eddies decreases with size and increases with increasing amplitude. In addition, the translation of anticyclonic eddies is larger than the long wave speed (based on the undisturbed depth) whereas the translation of cyclonic eddies is smaller than the long wave speed. Since such a dynamical behavior is not revealed by quasi-geostrophic theory (which does not distinguish between cyclonic and anticyclonic eddies) it is suggested that nonlinearity plays an important role in the dynamics of some isolated rings.Application of the theory to the Gulf Stream rings suggests that the self-propelled movement due to β is ≈2 cm sec−1 for cold-core rings and ≈1 cm sec−1 for warm-core rings. Each ring may carry as much as 8–10,000 km3 of upper ocean water as it moves

Choked flows and wind-driven interbasin exchange

The classical question of how much water flows from one ocean to the other via connecting passages is addressed with a nonlinear analytical model. The focus is on gaps that are too broad to be influenced by the so-called “hydraulic control” and yet too narrow to allow free (“unchoked”) flow through them. We consider two rectangular oceanic basins, one containing a light upper layer overlying a slightly heavier deep layer and the other containing only one layer of fluid (whose density is identical to that of the lower fluid in the first basin). The basins are separated by a thin wall containing a gap which is initially blocked by a gate. All fluids are initially at rest and the pressure exerted on the gate corresponds to a sea-level difference (between the two basins) that is set up by the wind field. The conceptual gate is then removed and the resulting nonlinear flow from the inner basin to the outer basin is computed. The final steady state is taken to be analogous to the actual oceanic situation. The analytical calculations are based on an integrated momentum constraint which allows computation of the mass flow through the gap without solving for the rather complicated nonlinear flow within the gap itself and in its immediate vicinity. It is found that the sea-level difference between the oceans drives a nonlinear flow (i.e., high amplitude and large Rossby number flow) parallel to the separating wall. Surprisingly, only about 40% of the generated upstream flow enters the gap. The remaining transport stays in the inner basin. A simple “gap formula” which enables one to compute the nonlinear transport via the gap is derived. In terms of the sea-level difference, the transport is [g′H2/2f0](1 − 1/e)2, where H is the undisturbed upper layer depth in the inner basin and the remaining notation is conventional. For the special case of no wind stress curl above the inner basin and no significant western boundary current, it is possible to relate the transport directly to the wind field. One finds that, for this particular case, the transport is independent of the stratification and is given by 0.3996 ∫0L τs(x) dx/f0ρ, where L is the width of the inner basin, τ(x) s the zonal wind stress and ρ is the density of the water. Qualitative “kitchen-type” laboratory experiments on a rotating table demonstrate that, as the theory predicts, only a fraction of the generated flow enters the gap. Quantitative numerical experiments using the Bleck and Boudra reduced gravity isopycnic model provide an even stronger support for the theory. They show that the analytically calculated transports are within 10–15% of the numerical calculations. Possible application of this theory to a number of passages such as the Windward Passage and the Indonesian throughflow is discussed