Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Risk sensitivity in a motor task with speed-accuracy trade-off.

When a racing driver steers a car around a sharp bend, there is a trade-off between speed and accuracy, in that high speed can lead to a skid whereas a low speed increases lap time, both of which can adversely affect the driver's payoff function. While speed-accuracy trade-offs have been studied extensively, their susceptibility to risk sensitivity is much less understood, since most theories of motor control are risk neutral with respect to payoff, i.e., they only consider mean payoffs and ignore payoff variability. Here we investigate how individual risk attitudes impact a motor task that involves such a speed-accuracy trade-off. We designed an experiment where a target had to be hit and the reward (given in points) increased as a function of both subjects' endpoint accuracy and endpoint velocity. As faster movements lead to poorer endpoint accuracy, the variance of the reward increased for higher velocities. We tested subjects on two reward conditions that had the same mean reward but differed in the variance of the reward. A risk-neutral account predicts that subjects should only maximize the mean reward and hence perform identically in the two conditions. In contrast, we found that some (risk-averse) subjects chose to move with lower velocities and other (risk-seeking) subjects with higher velocities in the condition with higher reward variance (risk). This behavior is suboptimal with regard to maximizing the mean number of points but is in accordance with a risk-sensitive account of movement selection. Our study suggests that individual risk sensitivity is an important factor in motor tasks with speed-accuracy trade-offs.

Efficient minimum manoeuvre time optimisation of an oversteering vehicle at constant forward speed

A receding horizon steering controller is presented, capable of pushing an oversteering nonlinear vehicle model to its handling limit while travelling at constant forward speed. The controller is able to optimise the vehicle path, using a computationally efficient and robust technique, so that the vehicle progression along a track is maximised as a function of time. The resultant method forms part of the solution to the motor racing objective of minimising lap time. © 2011 AACC American Automatic Control Council.

Neural representations of courtship song in the Drosophila brain.

Acoustic communication in drosophilid flies is based on the production and perception of courtship songs, which facilitate mating. Despite decades of research on courtship songs and behavior in Drosophila, central auditory responses have remained uncharacterized. In this study, we report on intracellular recordings from central neurons that innervate the Drosophila antennal mechanosensory and motor center (AMMC), the first relay for auditory information in the fly brain. These neurons produce graded-potential (nonspiking) responses to sound; we compare recordings from AMMC neurons to extracellular recordings of the receptor neuron population [Johnston's organ neurons (JONs)]. We discover that, while steady-state response profiles for tonal and broadband stimuli are significantly transformed between the JON population in the antenna and AMMC neurons in the brain, transient responses to pulses present in natural stimuli (courtship song) are not. For pulse stimuli in particular, AMMC neurons simply low-pass filter the receptor population response, thus preserving low-frequency temporal features (such as the spacing of song pulses) for analysis by postsynaptic neurons. We also compare responses in two closely related Drosophila species, Drosophila melanogaster and Drosophila simulans, and find that pulse song responses are largely similar, despite differences in the spectral content of their songs. Our recordings inform how downstream circuits may read out behaviorally relevant information from central neurons in the AMMC.

Stability control of a railway vehicle using absolute stiffness and inerters

Work presented in this paper studies the potential of employing inerters -a novel mechanical device used successfully in racing cars- in active suspension configurations with the aim to enhance railway vehicle system performance. The particular element of research in this paper concerns railway wheelset lateral stability control. Controlled torques are applied to the wheelsets using the concept of absolute stiffness. The effects of a reduced set of arbitrary passive structures using springs, dampers and inerters integrated to the active solution are discussed. A multi-objective optimisation problem is defined for tuning the parameters of the proposed configurations. Finally, time domain simulations are assessed for the railway vehicle while negotiating a curved track. A simplification of the design problem for stability is attained with the integration of inerters to the active solutions. © 2012 IEEE.

三层交换机中DHCP中继代理的改进与实现

社区宽带综合业务网络系统使用交换式以太网技术。为社区用户提供Intemet接入、电视、IP电话等服务。根据系统的实际需求，提出了一种改进的DHCP中继代理机制，并将该机制在系统的核心三层交换机SW1200的驱动程序中实现。

汉字音匹配和半球加工

This study explores hemispheric processing and relations during the homophone matching. In the literature summary, we review the past studies employing Tachistoscopic Presentation of Divided View Field (DVF) to the two hemispheres cooperation, and point out the different and complex opinions about both homophone matching and hemispheric processing. to some focuses, we handle this study by six behavioral experiments. First, under the condition of stimulus presenting simultaneously and function of graphic/semantic dimension, we study the bilateral/unilateral processing efficiency, the function on the level of synonym/similar grapheme. Main result shows, during homophone matching, bilateral processing is better than unilateral one, i.e., bilateral processing advantage rises. For further study whether the effects of transferring information between hemispheres will change along the time, combining with the paradigm of Priming, we make the stimulus present in the certain order; and under the function of graphic/semantic dimension, we also study the bilateral/unilateral processing efficiency, the function on the level of synonym/similar grapheme. Results show, there is semantic/graphic information which brings effects on homophone matching transferring between two hemispheres. And semantic/graphic information can be affected with the time, for example, when SOA = 210ms, the effect of semantic/graphic information disappears. When homophone present in the sequence, bilateral processing advantage also disappears, there are no significant differences between bilateral processing and unilateral one. In addition, we also explore whether sex differences exist during bilateral homophone matching, and we get, there are no significant differences between different sex. Among all experimental results, we also find several special phenomenon as the following example: 1) when stimuli presenting simultaneously during homophone matching on the level of synonym/similar grapheme, the processing effect of LVF(Left View Field) is better than RVF (Right View Field). 2) when stimuli presenting simultaneously, during homophone matching on the level of synonym/similar grapheme, one hemisphere may inhibit the other (because of the interference). to wrap up, under certain condition bilateral processing advantage is obtained, and during the interhemispheric interaction when homophone matching, some kind of information will relay between two hemispheres. And when two hemispheres cooperate, mutual inhibition (or interference) also follows. Further, interhemispheric interaction is closely connected with time, the attribution of stimuli, and so on. At last, a model is put forward to describe the coordinated process and the possible relations between two hemispheres.

dPAM: A Distributed Prefetching Protocol for Scalable Asynchronous Multicast in P2P Systems

We leverage the buffering capabilities of end-systems to achieve scalable, asynchronous delivery of streams in a peer-to-peer environment. Unlike existing cache-and-relay schemes, we propose a distributed prefetching protocol where peers prefetch and store portions of the streaming media ahead of their playout time, thus not only turning themselves to possible sources for other peers but their prefetched data can allow them to overcome the departure of their source-peer. This stands in sharp contrast to existing cache-and-relay schemes where the departure of the source-peer forces its peer children to go the original server, thus disrupting their service and increasing server and network load. Through mathematical analysis and simulations, we show the effectiveness of maintaining such asynchronous multicasts from several source-peers to other children peers, and the efficacy of prefetching in the face of peer departures. We confirm the scalability of our dPAM protocol as it is shown to significantly reduce server load.

Planning the deployment of fault-tolerant wireless sensor networks

Since Wireless Sensor Networks (WSNs) are subject to failures, fault-tolerance becomes an important requirement for many WSN applications. Fault-tolerance can be enabled in different areas of WSN design and operation, including the Medium Access Control (MAC) layer and the initial topology design. To be robust to failures, a MAC protocol must be able to adapt to traffic fluctuations and topology dynamics. We design ER-MAC that can switch from energy-efficient operation in normal monitoring to reliable and fast delivery for emergency monitoring, and vice versa. It also can prioritise high priority packets and guarantee fair packet deliveries from all sensor nodes. Topology design supports fault-tolerance by ensuring that there are alternative acceptable routes to data sinks when failures occur. We provide solutions for four topology planning problems: Additional Relay Placement (ARP), Additional Backup Placement (ABP), Multiple Sink Placement (MSP), and Multiple Sink and Relay Placement (MSRP). Our solutions use a local search technique based on Greedy Randomized Adaptive Search Procedures (GRASP). GRASP-ARP deploys relays for (k,l)-sink-connectivity, where each sensor node must have k vertex-disjoint paths of length ≤ l. To count how many disjoint paths a node has, we propose Counting-Paths. GRASP-ABP deploys fewer relays than GRASP-ARP by focusing only on the most important nodes – those whose failure has the worst effect. To identify such nodes, we define Length-constrained Connectivity and Rerouting Centrality (l-CRC). Greedy-MSP and GRASP-MSP place minimal cost sinks to ensure that each sensor node in the network is double-covered, i.e. has two length-bounded paths to two sinks. Greedy-MSRP and GRASP-MSRP deploy sinks and relays with minimal cost to make the network double-covered and non-critical, i.e. all sensor nodes must have length-bounded alternative paths to sinks when an arbitrary sensor node fails. We then evaluate the fault-tolerance of each topology in data gathering simulations using ER-MAC.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Repairing wireless sensor network connectivity in damaged environments

A wireless sensor network can become partitioned due to node failure, requiring the deployment of additional relay nodes in order to restore network connectivity. This introduces an optimisation problem involving a tradeoff between the number of additional nodes that are required and the costs of moving through the sensor field for the purpose of node placement. This tradeoff is application-dependent, influenced for example by the relative urgency of network restoration. In addition, minimising the number of relay nodes might lead to long routing paths to the sink, which may cause problems of data latency. This data latency is extremely important in wireless sensor network applications such as battlefield surveillance, intrusion detection, disaster rescue, highway traffic coordination, etc. where they must not violate the real-time constraints. Therefore, we also consider the problem of deploying multiple sinks in order to improve the network performance. Previous research has only parts of this problem in isolation, and has not properly considered the problems of moving through a constrained environment or discovering changes to that environment during the repair or network quality after the restoration. In this thesis, we firstly consider a base problem in which we assume the exploration tasks have already been completed, and so our aim is to optimise our use of resources in the static fully observed problem. In the real world, we would not know the radio and physical environments after damage, and this creates a dynamic problem where damage must be discovered. Therefore, we extend to the dynamic problem in which the network repair problem considers both exploration and restoration. We then add a hop-count constraint for network quality in which the desired locations can talk to a sink within a hop count limit after the network is restored. For each new problem of the network repair, we have proposed different solutions (heuristics and/or complete algorithms) which prioritise different objectives. We evaluate our solutions based on simulation, assessing the quality of solutions (node cost, movement cost, computation time, and total restoration time) by varying the problem types and the capability of the agent that makes the repair. We show that the relative importance of the objectives influences the choice of algorithm, and different speeds of movement for the repairing agent have a significant impact on performance, and must be taken into account when selecting the algorithm. In particular, the node-based approaches are the best in the node cost, and the path-based approaches are the best in the mobility cost. For the total restoration time, the node-based approaches are the best with a fast moving agent while the path-based approaches are the best with a slow moving agent. For a medium speed moving agent, the total restoration time of the node-based approaches and that of the path-based approaches are almost balanced.

Intraoperative spectral domain optical coherence tomography for vitreoretinal surgery.

We demonstrate in vivo human retinal imaging using an intraoperative microscope-mounted optical coherence tomography system (MMOCT). Our optomechanical design adapts an Oculus Binocular Indirect Ophthalmo Microscope (BIOM3), suspended from a Leica ophthalmic surgical microscope, with spectral domain optical coherence tomography (SD-OCT) scanning and relay optics. The MMOCT enables wide-field noncontact real-time cross-sectional imaging of retinal structure, allowing for SD-OCT augmented intrasurgical microscopy for intraocular visualization. We experimentally quantify the axial and lateral resolution of the MMOCT and demonstrate fundus imaging at a 20Hz frame rate.

Enhancing imaging systems using transformation optics.

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Metamaterial-enhanced coupling between magnetic dipoles for efficient wireless power transfer

Nonradiative coupling between conductive coils is a candidate mechanism for wireless energy transfer applications. In this paper we propose a power relay system based on a near-field metamaterial superlens and present a thorough theoretical analysis of this system. We use time-harmonic circuit formalism to describe all interactions between two coils attached to external circuits and a slab of anisotropic medium with homogeneous permittivity and permeability. The fields of the coils are found in the point-dipole approximation using Sommerfeld integrals which are reduced to standard special functions in the long-wavelength limit. We show that, even with a realistic magnetic loss tangent of order 0.1, the power transfer efficiency with the slab can be an order of magnitude greater than free-space efficiency when the load resistance exceeds a certain threshold value. We also find that the volume occupied by the metamaterial between the coils can be greatly compressed by employing magnetic permeability with a large anisotropy ratio. © 2011 American Physical Society.