On Optimality of Myopic Sensing Policy with Imperfect Sensing in Multi-channel Opportunistic Access

We consider the channel access problem under imperfect sensing of channel state in a multi-channel opportunistic communication system, where the state of each channel evolves as an independent and identically distributed Markov process. The considered problem can be cast into a restless multi-armed bandit (RMAB) problem that is of fundamental importance in decision theory. It is well-known that solving the RMAB problem is PSPACE-hard, with the optimal policy usually intractable due to the exponential computation complexity. A natural alternative is to consider the easily implementable myopic policy that maximizes the immediate reward but ignores the impact of the current strategy on the future reward. In this paper, we perform an analytical study on the optimality of the myopic policy under imperfect sensing for the considered RMAB problem. Specifically, for a family of generic and practically important utility functions, we establish the closed-form conditions under which the myopic policy is guaranteed to be optimal even under imperfect sensing. Despite our focus on the opportunistic channel access, the obtained results are generic in nature and are widely applicable in a wide range of engineering domains.Comment: 21 pages regular pape

On Optimality of Myopic Policy for Restless Multi-armed Bandit Problem with Non i.i.d. Arms and Imperfect Detection

We consider the channel access problem in a multi-channel opportunistic communication system with imperfect channel sensing, where the state of each channel evolves as a non independent and identically distributed Markov process. This problem can be cast into a restless multi-armed bandit (RMAB) problem that is intractable for its exponential computation complexity. A natural alternative is to consider the easily implementable myopic policy that maximizes the immediate reward but ignores the impact of the current strategy on the future reward. In particular, we develop three axioms characterizing a family of generic and practically important functions termed as $g$-regular functions which includes a wide spectrum of utility functions in engineering. By pursuing a mathematical analysis based on the axioms, we establish a set of closed-form structural conditions for the optimality of myopic policy.Comment: Second version, 16 page

Gradient moduli lens models: how material properties and application of forces can affect deformation and distributions of stress

The human lens provides one-third of the ocular focussing power and is responsible for altering focus over a range of distances. This ability, termed accommodation, defines the process by which the lens alters shape to increase or decrease ocular refractive power; this is mediated by the ciliary muscle through the zonule. This ability decreases with age such that around the sixth decade of life it is lost rendering the eye unable to focus on near objects. There are two opponent theories that provide an explanation for the mechanism of accommodation; definitive support for either of these requires investigation. This work aims to elucidate how material properties can affect accommodation using Finite Element models based on interferometric measurements of refractive index. Gradients of moduli are created in three models from representative lenses, aged 16, 35 and 48 years. Different forms of zonular attachments are studied to determine which may most closely mimic the physiological form by comparing stress and displacement fields with simulated shape changes to accommodation in living lenses. The results indicate that for models to mimic accommodation in living eyes, the anterior and posterior parts of the zonule need independent force directions. Choice of material properties affects which theory of accommodation is supported

Finite element modelling of human eye lens

The human lens provides one-third of the ocular focussing power and is responsible for altering focus over a range of distances. This ability, termed accommodation, defines the process by which the lens changes its shape, in response to the movement of ciliary body, to adjust the refractive power. The accommodative ability gradually decreases with age such that around the fifth to sixth decades of life it is lost rendering the eye unable to focus on near objects. Current technologies are unable to effectively restore the requisite optical powers and accommodative ability of a presbyopic eye as the mechanism of accommodation is not fully understood. Plausible explanations, which are contradicted to each other, require definitive supports. Nevertheless, experimental evidences are difficult to obtain from living eye. Computational modelling serves as an alternative solution for the understanding of the physiological process of accommodation. An accurate and detailed model can closely simulate the in vivo behaviour of the eye lens. To date, the relevance of available models to the physiology needs to be further explored. The accuracy of any computational model highly depends on the input parameters. To build up a complete lens model one needs to seek resources from different studies and to assemble parameters of lenses from different subjects, which bring great challenges to this research field. The present work utilizes the Finite Element Analysis as the fundamental approach for investigating the mechanical and optical performances of lens models built at various ages based on input parameters from both in vivo and in vitro studies. The contributions of different ocular parameters to the accommodative loss are investigated i.e. the lens geometries, material properties, capsular thickness, capsular elasticity, zonular angles. Relations between two seemingly contradicting accommodative theories are demonstrated and possible explanations for the presbyopia are proposed