81,310 research outputs found
Generalized prisoner's dilemma
Prisoner's dilemma has been heavily studied. In classical model, each player
chooses to either "Cooperate" or "Defect". In this paper, we generalize the
prisoner's dilemma with a new alternative which is neither defect or
cooperation. The classical model is the special case under the condition that
the third state is not taken into consideration.Comment: 7 pages, 2 figure
Revisiting Optimal Power Control: its Dual Effect on SNR and Contention
In this paper we study a transmission power tune problem with densely
deployed 802.11 Wireless Local Area Networks (WLANs). While previous papers
emphasize on tuning transmission power with either PHY or MAC layer separately,
optimally setting each Access Point's (AP's) transmission power of a densely
deployed 802.11 network considering its dual effects on both layers remains an
open problem. In this work, we design a measure by evaluating impacts of
transmission power on network performance on both PHY and MAC layers. We show
that such an optimization problem is intractable and then we investigate and
develop an analytical framework to allow simple yet efficient solutions.
Through simulations and numerical results, we observe clear benefits of the
dual-effect model compared to solutions optimizing solely on a single layer;
therefore, we conclude that tuning transmission power from a dual layer
(PHY-MAC) point of view is essential and necessary for dense WLANs. We further
form a game theoretical framework and investigate above power-tune problem in a
strategic network. We show that with decentralized and strategic users, the
Nash Equilibrium (N.E.) of the corresponding game is in-efficient and
thereafter we propose a punishment based mechanism to enforce users to adopt
the social optimal strategy profile under both perfect and imperfect sensing
environments
Recovery of an embedded obstacle and the surrounding medium for Maxwell's system
In this paper, we are concerned with the inverse electromagnetic scattering
problem of recovering a complex scatterer by the corresponding electric
far-field data. The complex scatterer consists of an inhomogeneous medium and a
possibly embedded perfectly electric conducting (PEC) obstacle. The far-field
data are collected corresponding to incident plane waves with a fixed incident
direction and a fixed polarisation, but frequencies from an open interval. It
is shown that the embedded obstacle can be uniquely recovered by the
aforementioned far-field data, independent of the surrounding medium.
Furthermore, if the surrounding medium is piecewise homogeneous, then the
medium can be recovered as well. Those unique recovery results are new to the
literature. Our argument is based on low-frequency expansions of the
electromagnetic fields and certain harmonic analysis techniques.Comment: 15 page
Hardy Spaces () over Lipschitz Domains
Let be a Lipschitz curve on the complex plane and
is the domain above , we define Hardy space
as the set of holomorphic functions satisfying . We mainly
focus on the case of in this paper, and prove that if , then has non-tangential boundary limit a.e.
on , and is the Cauchy integral of . We denote the
conformal mapping from onto as , and then prove
that, is isomorphic to , the classical
Hardy space on upper half plane, under the mapping , where .Comment: 25 page
Quantum games of opinion formation based on the Marinatto-Weber quantum game scheme
Quantization becomes a new way to study classical game theory since quantum
strategies and quantum games have been proposed. In previous studies, many
typical game models, such as prisoner's dilemma, battle of the sexes, Hawk-Dove
game, have been investigated by using quantization approaches. In this paper,
several game models of opinion formations have been quantized based on the
Marinatto-Weber quantum game scheme, a frequently used scheme to convert
classical games to quantum versions. Our results show that the quantization can
change fascinatingly the properties of some classical opinion formation game
models so as to generate win-win outcomes.Comment: 19 page
Learning-based Prediction, Rendering and Association Optimization for MEC-enabled Wireless Virtual Reality (VR) Network
Wireless-connected Virtual Reality (VR) provides immersive experience for VR
users from any-where at anytime. However, providing wireless VR users with
seamless connectivity and real-time VR video with high quality is challenging
due to its requirements in high Quality of Experience (QoE) and low VR
interaction latency under limited computation capability of VR device. To
address these issues,we propose a MEC-enabled wireless VR network, where the
field of view (FoV) of each VR user can be real-time predicted using Recurrent
Neural Network (RNN), and the rendering of VR content is moved from VR device
to MEC server with rendering model migration capability. Taking into account
the geographical and FoV request correlation, we propose centralized and
distributed decoupled Deep Reinforcement Learning (DRL) strategies to maximize
the long-term QoE of VR users under the VR interaction latency constraint.
Simulation results show that our proposed MEC rendering schemes and DRL
algorithms substantially improve the long-term QoE of VR users and reduce the
VR interaction latency compared to rendering at VR device
A quantum extension to inspection game
Quantum game theory is a new interdisciplinary field between game theory and
physical research. In this paper, we extend the classical inspection game into
a quantum game version by quantizing the strategy space and importing
entanglement between players. Our result shows that the quantum inspection game
has various Nash equilibrium depending on the initial quantum state of the
game. It is also shown that quantization can respectively help each player to
increase his own payoff, yet fails to bring Pareto improvement for the
collective payoff in the quantum inspection game.Comment: 6 page
Notes of Boundedness on Cauchy Integrals on Lipschitz Curves ()
We provide the details of the first proof in~\cite{CJS89}, which proved that
Cauchy transform of ~functions on Lipschitz curves is bounded. We then
prove that every ~function on Lipschitz curves is the sum of
non-tangential boundary limit of functions in , the Hardy
spaces on domains over and under the Lipschitz curve. We also obtain a more
accurate boundary of Cauchy transform under the condition that the Lipschitz
curve is the real axis.Comment: 22 page
First exit and Dirichlet problem for the nonisotropic tempered -stable processes
This paper discusses the first exit and Dirichlet problems of the
nonisotropic tempered -stable process . The upper bounds of all
moments of the first exit position and the first exit
time are firstly obtained. It is found that the probability density
function of or exponentially decays with the
increase of or , and
,\
. Since is the infinitesimal generator
of the anisotropic tempered stable process, we obtain the Feynman-Kac
representation of the Dirichlet problem with the operator
. Therefore, averaging the generated
trajectories of the stochastic process leads to the solution of the Dirichlet
problem, which is also verified by numerical experiments.Comment: 23 pages, 5 figure
Hardy Spaces over Half-strip Domains
We define Hardy spaces on half-strip domain~ and
, where , and
prove that functions in has non-tangential boundary limit
a.e. on , the common boundary of . We then prove that
Cauchy integral of functions in are in , where
, that is, Cauchy transform is bounded. Besides, if , then functions are the Cauchy integral of their
non-tangential boundary limits. We also establish an isomorphism between
and , the classical Hardy spaces over
upper and lower half complex planes.Comment: 38 page
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