Controlled Sequential Monte Carlo

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; e.g. for inference in non-linear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their performance. We introduce here a class of controlled sequential Monte Carlo algorithms, where the proposal distributions are determined by approximating the solution to an associated optimal control problem using an iterative scheme. This method builds upon a number of existing algorithms in econometrics, physics, and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models. We provide a theoretical analysis concerning the fluctuation and stability of this methodology that also provides insight into the properties of related algorithms. We demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications

How bees distinguish colors

Behind each facet of the compound eye, bees have photoreceptors for ultraviolet, green, and blue wavelengths that are excited by sunlight reflected from the surrounding panorama. In experiments that excluded ultraviolet, bees learned to distinguish between black, gray, white, and various colors. To distinguish two targets of differing color, bees detected, learned, and later recognized the strongest preferred inputs, irrespective of which target displayed them. First preference was the position and measure of blue reflected from white or colored areas. They also learned the positions and a measure of the green receptor modulation at vertical edges that displayed the strongest green contrast. Modulation is the receptor response to contrast and was summed over the length of a contrasting vertical edge. This also gave them a measure of angular width between outer vertical edges. Third preference was position and a measure of blue modulation. When they returned for more reward, bees recognized the familiar coincidence of these inputs at that place. They cared nothing for colors, layout of patterns, or direction of contrast, even at black/white edges. The mechanism is a new kind of color vision in which a large-field tonic blue input must coincide in time with small-field phasic modulations caused by scanning vertical edges displaying green or blue contrast. This is the kind of system to expect in medium-lowly vision, as found in insects; the next steps are fresh looks at old observations and quantitative models

How bees discriminate a pattern of two colours from its mirror image

A century ago, in his study of colour vision in the honeybee (Apis mellifera), Karl von Frisch showed that bees distinguish between a disc that is half yellow, half blue, and a mirror image of the same. Although his inference of colour vision in this example has been accepted, some discrepancies have prompted a new investigation of the detection of polarity in coloured patterns. In new experiments, bees restricted to their blue and green receptors by exclusion of ultraviolet could learn patterns of this type if they displayed a difference in green contrast between the two colours. Patterns with no green contrast required an additional vertical black line as a landmark. Tests of the trained bees revealed that they had learned two inputs; a measure and the retinotopic position of blue with large field tonic detectors, and the measure and position of a vertical edge or line with small-field phasic green detectors. The angle between these two was measured. This simple combination was detected wherever it occurred in many patterns, fitting the definition of an algorithm, which is defined as a method of processing data. As long as they excited blue receptors, colours could be any colour to human eyes, even white. The blue area cue could be separated from the green receptor modulation by as much as 50°. When some blue content was not available, the bees learned two measures of the modulation of the green receptors at widely separated vertical edges, and the angle between them. There was no evidence that the bees reconstructed the lay-out of the pattern or detected a tonic input to the green receptors

How bees distinguish black from white

Bee eyes have photoreceptors for ultraviolet, green, and blue wavelengths that are excited by reflected white but not by black. With ultraviolet reflections excluded by the apparatus, bees can learn to distinguish between black, gray, and white, but theories of color vision are clearly of no help in explaining how they succeed. Human vision sidesteps the issue by constructing black and white in the brain. Bees have quite different and accessible mechanisms. As revealed by extensive tests of trained bees, bees learned two strong signals displayed on either target. The first input was the position and a measure of the green receptor modulation at the vertical edges of a black area, which included a measure of the angular width between the edges of black. They also learned the average position and total amount of blue reflected from white areas. These two inputs were sufficient to help decide which of two targets held the reward of sugar solution, but the bees cared nothing for the black or white as colors, or the direction of contrast at black/white edges. These findings provide a small step toward understanding, modeling, and implementing in silicon the anti-intuitive visual system of the honeybee, in feeding behavior

Direct response of the crab Carcinus to the movement of the sun

1. The eyes of the crab follow the movement of the sun if stationary landmarks, which would arrest the eye movement, are obscured. 2. Therefore, even if the eyes do not move when the crab is in a normal environment, the sun's movement is certainly seen by the crab. 3. The eye movements in response to tilting the whole animal only partially compensate for the body tilt. Therefore an obvious contrasting object such as the sun is not absolutely stabilized on the retina in tilting. 4. This sensory ability of the crab could form the basis of a compass response with a minimum latency of 10 sec

Commentary: What does an insect see?

The compound eye of the bee is an array of photoreceptors, each at an angle to the next, and therefore it catches an image of the outside world just as does the human eye, except that the image is not inverted. Eye structure, however, tells us little about what the bee actually abstracts from the panorama. Moreover, it is not sufficient to observe that bees recognise patterns, because they may be responding to only small parts of them. The only way we can tell what the bee actually detects is to train bees to come to simple patterns or distinguish between two patterns and then present the trained bees with test patterns to see what they have learned. After much training and numerous tests, it was possible to identify the parameters in the patterns that the bees detected and remembered, to study the responses of the trained bees to unfamiliar patterns and to infer the steps in the visual processing mechanism. We now have a simple mechanistic explanation for many observations that for almost a century have been explained by analogy with cognitive behaviour of higher animals. A re-assessment of the capabilities of the bee is required. Below the photoreceptors, the next components of the model mechanism are small feature detectors that are one, two or three ommatidia wide that respond to light intensity, direction of passing edges or orientation of edges displayed by parameters in the pattern. At the next stage, responses of the feature detectors for area and edges are summed in various ways in each local region of the eye to form several types of local internal feature totals, here called cues. The cues are the units of visual memory in the bee. At the next stage, summation implies that there is one of each type in each local eye region and that local details of the pattern are lost. Each type of cue has its own identity, a scalar quantity and a position. The coincidence of the cues in each local region of the eye is remembered as a retinotopic label for a landmark. Bees learn landmark labels at large angles to each other and use them to identify a place and find the reward. The receptors, feature detectors, cues and coincidences of labels for landmarks at different angles, correspond to a few letters, words and sentences and a summary description for a place. Shapes, objects and cognitive appraisal of the image have no place in bee vision. Several factors prevented the advance in understanding until recently. Firstly, until the mid-century, so little was known that no mechanisms were proposed. At that time it was thought that the mechanism of the visual processing could be inferred intuitively from a successful training alone or from quantitative observations of the percentage of correct choices after manipulation of the patterns displayed. The components were unknown and there were too many unidentified channels of causation in parallel (too many cues learned at the same time) for this method to succeed. Secondly, for 100 years, the criterion of success of the bees was their landing at or near the reward hole in the centre of the pattern. At the moment of choice, therefore, the angle subtended by the pattern at the eye of the bees was very large, 100-130deg., with the result that a large part of the eye learned a number of cues and several labels on the target. As a result, in critical tests the bees would not respond but just went away, so that the components of the system could not be identified. Much effort was therefore wasted. These problems were resolved when the size of the target was reduced to about the size of one or two fields of the cues and landmark labels, 40-45 deg., and the trained bees were tested to see whether they could or could not recognise the test targets

Multiphase flow in pipelines: An analysis of the influence of empirical correlations on mechanistic models

Empirical correlations in mechanistic models make them data-sensitive. This study proposes a systematic method for replacing alternative empirical correlations in a mechanistic model with the view of optimising or simplifying the model, and suggests that current industry practice needs to be changed to first test the data fit of the empirical correlations, before selecting the appropriate mechanistic model. The method is demonstrated on a widely-used model for two-phase slug flow, relevant to petroleum production

HORNET: High-speed Onion Routing at the Network Layer

We present HORNET, a system that enables high-speed end-to-end anonymous channels by leveraging next generation network architectures. HORNET is designed as a low-latency onion routing system that operates at the network layer thus enabling a wide range of applications. Our system uses only symmetric cryptography for data forwarding yet requires no per-flow state on intermediate nodes. This design enables HORNET nodes to process anonymous traffic at over 93 Gb/s. HORNET can also scale as required, adding minimal processing overhead per additional anonymous channel. We discuss design and implementation details, as well as a performance and security evaluation.Comment: 14 pages, 5 figure