Symmetry-extended counting rules for periodic frameworks.

A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Full counting statistics of transport through two-channel Coulomb blockade systems

A mesoscopic Coulomb blockade system with two transport channels is studied in terms of full counting statistics. It is found that the shot noise and skewness are crucially affected by the quantum mechanical interference. In particular, the super-Poisson behavior can be induced as a consequence of constructive interference, and can be understood by the formation of effective fast-and-slow transport channels. Dephasing and finite temperature effects are carried out together with physical interpretations.

Real-time counting of single electron tunneling through a T-shaped double quantum dot system

Real-time detection of single electron tunneling through a T-shaped double quantum dot is simulated, based on a Monte Carlo scheme. The double dot is embedded in a dissipative environment and the presence of electrons on the double dot is detected with a nearby quantum point contact. We demonstrate directly the bunching behavior in electron transport, which leads eventually to a super-Poissonian noise. Particularly, in the context of full counting statistics, we investigate the essential difference between the dephasing mechanisms induced by the quantum point contact detection and the coupling to the external phonon bath. A number of intriguing noise features associated with various transport mechanisms are revealed.

a computational proof of complexity of some restricted counting problems

South Central University

The Role of Attention in Binocular Rivalry as Revealed Through Optokinetic Nystagmus

When stimuli presented to the two eyes differ considerably, stable binocular fusion fails, and the subjective percept alternates between the two monocular images, a phenomenon known as binocular rivalry. The influence of attention over this perceptual switching has long been studied, and although there is evidence that attention can affect the alternation rate, its role in the overall dynamics of the rivalry process remains unclear. The present study investigated the relationship between the attention paid to the rivalry stimulus, and the dynamics of the perceptual alternations. Specifically, the temporal course of binocular rivalry was studied as the subjects performed difficult nonvisual and visual concurrent tasks, directing their attention away from the rivalry stimulus. Periods of complete perceptual dominance were compared for the attended condition, where the subjects reported perceptual changes, and the unattended condition, where one of the simultaneous tasks was performed. During both the attended and unattended conditions, phases of rivalry dominance were obtained by analyzing the subject"s optokinetic nystagmus recorded by an electrooculogram, where the polarity of the nystagmus served as an objective indicator of the perceived direction of motion. In all cases, the presence of a difficult concurrent task had little or no effect on the statistics of the alternations, as judged by two classic tests of rivalry, although the overall alternation rate showed a small but significant increase with the concurrent task. It is concluded that the statistical patterns of rivalry alternations are not governed by attentional shifts or decision-making on the part of the subject.

A Binocular, Foveated Active Vision System

This report documents the design and implementation of a binocular, foveated active vision system as part of the Cog project at the MIT Artificial Intelligence Laboratory. The active vision system features a three degree of freedom mechanical platform that supports four color cameras, a motion control system, and a parallel network of digital signal processors for image processing. To demonstrate the capabilities of the system, we present results from four sample visual-motor tasks.

On Learning Counting Functions With Queries

We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p, the class of disjunctions of integer-weighted counting functions with modulus p over the domain Znq (or Zn) for any given integer q ≥ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Zp. The result is obtained through learning linear systems over an arbitrary field. In general a counting function may have a composite modulus. We prove that, for any given integer q ≥ 2, over the domain Zn2, the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial time learnable with only one equivalence query, and the class of disjunctions of log log n Boolean-weighted counting functions with modulus q is polynomial time learnable. Finally, we present an algorithm for learning graph-based counting functions.

Multi-scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation approaches. This paper describes an alternative formulation for dense scene flow estimation that provides convincing results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. To handle the aperture problems inherent in the estimation task, a multi-scale method along with a novel adaptive smoothing technique is used to gain a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization-two problems commonly associated with basic multi-scale approaches. Internally, the framework generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than standard stereo and optical flow methods allow. Experiments with synthetic and real test data demonstrate the effectiveness of the approach.

Multi-Scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.