Given a computable probability measure$P$over natural numbers or infinite binary sequences, there is no computable, randomized method that can produce an arbitrarily large sample such that none of its members are outliers of$P$. In addition, given a binary predicate$\gamma $, the length of the smallest program that computes a complete extension of$\gamma $is less than the size of the domain of$\gamma $plus the amount of information that$\gamma $has with the halting sequence.

We introduce notions of algorithmic mutual information and deficiency of randomness of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have minute self-algorithmic information. We provide an algorithmic variant to the no-cloning theorem, by showing that only a small minority of quantum pure states can clone a nonnegligible amount of algorithmic information. We also provide a chain rule inequality for quantum algorithmic entropy. We show that deficiency of randomness does not increase under POVM measurements.

Some people cannot use their hands to control a computer mouse due to conditions such as cerebral palsy or multiple sclerosis. For these individuals, there are various mouse-replacement solutions. One approach is to enable them to control the mouse pointer using head motions captured with a web camera. One such system, the Camera Mouse, uses an optical flow approach to track a manually-selected small patch of the subject’s face, such as the nostril or the edge of the eyebrow. The optical flow tracker may lose the facial feature when the tracked image patch drifts away from the initially-selected feature or when a user makes a rapid head movement. To address the problem of feature loss, we developed and incorporated the Kernel-Subset-Tracker into the Camera Mouse. The Kernel-Subset-Tracker is an exemplar-based method that uses a training set of representative images to produce online templates for positional tracking. We designed the augmented Camera Mouse so that it can compute these templates in real time, employing kernel techniques traditionally used for classification. We propose three versions of the Kernel-Subset-Tracker , each using a different kernel, and compared their performance to the optical-flow tracker under five different experimental conditions. Our experiments with test subjects show that augmenting the Camera Mouse with the Kernel-Subset-Tracker improves communication bandwidth statistically significantly. Tracking of facial features was accurate, without feature drift, even during rapid head movements and extreme head orientations. We conclude by describing how the Camera Mouse augmented with the Kernel-Subset-Tracker enabled a stroke-victim with severe motion impairments to communicate via an on-screen keyboard.

We extend the semi-least squares problem defined by Rao and Mitra ( 1971 ) to the kernel semi-least squares problem. We introduce subset projection, a technique that produces a solution to this problem. We show how the results of subset projection can be used to approximate a computationally expensive distance metric.

Users of mouse-replacement interfaces may have difficulty conforming to the motion requirements of their interface system. We have observed users with severe motor disabilities who controlled the mouse pointer with a head tracking interface. Our analysis shows that some users may be able to move in some directions easier than other directions. We propose several mouse pointer mappings that adapt to the user's movement abilities. These mappings will take into account the user's motions in two-or three-dimensions to move the mouse pointer in the intended direction.

Customizable Keyboard is an on-screen keyboard designed to be flexible and expandable. Instead of giving the user a keyboard layout Customizable Keyboard allows the user to create a layout that is accommodating to the user's needs. Customizable Keyboard also allows the user to select from a variety of ways to interact with the keyboard including but not limited to using the mouse pointer to select keys and different types of scan based systems. Customizable Keyboard provides more functionality than a typical onscreen keyboard including the ability to control infrared devices such as TVs and send Twitter® Tweets.

We introduce the Dynamic Policy Routing (DPR) model that captures the propagation of route updates under arbitrary changes in topology or path preferences. DPR introduces the notion of causation chains where the route flap at one node causes a flap at the next node along the chain.