Approximate Randomization of Quantum States With Fewer Bits of Key

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.Comment: 18 pages, Quantum Computing Back Action, IIT Kanpur, March 2006, volume 864 of AIP Conference Proceedings, pages 18--36. Springer, New Yor

Optimal Flood Control

A mathematical model for optimal control of the water levels in a chain of reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made

Visual stimulation of saccades in magnetically tethered Drosophila

Flying fruit flies, Drosophila melanogaster, perform `body saccades', in which they change heading by about 90° in roughly 70 ms. In free flight, visual expansion can evoke saccades, and saccade-like turns are triggered by similar stimuli in tethered flies. However, because the fictive turns in rigidly tethered flies follow a much longer time course, the extent to which these two behaviors share a common neural basis is unknown. A key difference between tethered and free flight conditions is the presence of additional sensory cues in the latter, which might serve to modify the time course of the saccade motor program. To study the role of sensory feedback in saccades, we have developed a new preparation in which a fly is tethered to a fine steel pin that is aligned within a vertically oriented magnetic field, allowing it to rotate freely around its yaw axis. In this experimental paradigm, flies perform rapid turns averaging 35° in 80 ms, similar to the kinematics of free flight saccades. Our results indicate that tethered and free flight saccades share a common neural basis, but that the lack of appropriate feedback signals distorts the behavior performed by rigidly fixed flies. Using our new paradigm, we also investigated the features of visual stimuli that elicit saccades. Our data suggest that saccades are triggered when expanding objects reach a critical threshold size, but that their timing depends little on the precise time course of expansion. These results are consistent with expansion detection circuits studied in other insects, but do not exclude other models based on the integration of local movement detectors

Free-flight responses of Drosophila melanogaster to attractive odors

Many motile organisms localize the source of attractive odorants by following plumes upwind. In the case of D. melanogaster, little is known of how individuals alter their flight trajectories after encountering and losing a plume of an attractive odorant. We have characterized the three-dimensional flight behavior of D. melanogaster in a wind tunnel under a variety of odor conditions. In the absence of olfactory cues, hungry flies initiate flight and display anemotactic orientation. Following contact with a narrow ribbon plume of an attractive odor, flies reduce their crosswind velocity while flying faster upwind, resulting in a surge directed toward the odor source. Following loss of odor contact due to plume truncation, flies frequently initiate a stereotyped crosswind casting response, a behavior rarely observed in a continuous odor plume. Similarly, within a homogeneous odor cloud, flies move fast while maintaining an upwind heading. These results indicate both similarities and differences between the behavior of D. melanogaster and the responses of male moths to pheromone plumes, suggesting possible differences in underlying neural mechanisms

Human behavioural analysis with self-organizing map for ambient assisted living

This paper presents a system for automatically classifying the resting location of a moving object in an indoor environment. The system uses an unsupervised neural network (Self Organising Feature Map) fully implemented on a low-cost, low-power automated home-based surveillance system, capable of monitoring activity level of elders living alone independently. The proposed system runs on an embedded platform with a specialised ceiling-mounted video sensor for intelligent activity monitoring. The system has the ability to learn resting locations, to measure overall activity levels and to detect specific events such as potential falls. First order motion information, including first order moving average smoothing, is generated from the 2D image coordinates (trajectories). A novel edge-based object detection algorithm capable of running at a reasonable speed on the embedded platform has been developed. The classification is dynamic and achieved in real-time. The dynamic classifier is achieved using a SOFM and a probabilistic model. Experimental results show less than 20% classification error, showing the robustness of our approach over others in literature with minimal power consumption. The head location of the subject is also estimated by a novel approach capable of running on any resource limited platform with power constraints