Abstract: A durable and water-resistant or water-proof communication accessory with a built-in battery for a mobile communication device capable of enclosing, powering, and protecting a mobile device and protecting it from dirt, water, weather, bumps, and scratches. The built-in battery can extend the life of mobile communication device while protecting the sensitive electronics, glass screen, and data.

Abstract: A method performs an image processing application by expressing the image processing application as a non-negative quadratic program (NNQP) with a quadratic objective, and nonnegativity constraints. A Karush-Kuhn-Tucker condition of the NNQP is expressed as a fixpoint ratio. Then, the fixpoint ratio is determined iteratively until a solution to the image processing application is reached with a desired precision.

Abstract: A method determines trajectories of redundant actuators of a machine including a first actuator and a second actuator. The method determines a first trajectory of the first actuator tracking a reference trajectory with an error tolerance, wherein the error tolerance is a function of a constraint of the second actuator, and determines a second trajectory of the second actuator based on a difference between the reference trajectory and the first trajectory.

Abstract: A path of a cutter head of a laser cutting machine is modified to cut features according to a pattern from a material. A no-travel zone that the laser cutter avoids while performing lateral movements between cuts is specified. Locations of the path that cross the no-travel zones are also specified. The path is then modified such that all locations that violate the no-travel zone are removed so that the laser cutter detours around the no-travel zone when performing the lateral movements.

Abstract: Locations in a pattern of a part are evaluated to determine if the locations are interior or exterior to a feature of the pattern. The pattern is used to cut the feature from a material by a laser cutting machine. A location in the feature is rendered into an array stored in a memory so that a value stored at an address in the array corresponding to coordinates of the location is either odd or even as determined by a counting process of the rendering. Then, the location is identified as being interior if the value is odd, and as being exterior if the value is even. The rendering can use modified forms of either rasterization or ray casting.

Abstract: A set of costs representing operations of a machine along a set of trajectories connecting a set of exit and entry points on contours of a pattern is determined. Each trajectory represents an operation of the machine proceeding from an exit point with an exit velocity to an entry point with an entry velocity according to dynamics of the machine. The set of trajectories includes at least one trajectory representing the operation along a contour with non-zero velocities at corresponding exit and entry points, and at least one trajectory representing the operation between different contours with non-zero velocities at the corresponding exit and entry points. A sequence of the trajectories optimizing a total cost of operation of the machine tracking the pattern is determined based on the costs, and a set of instructions for controlling the machine is determined according to the sequence.

Abstract: A method solves a quadratic programming (QP) problem in real-time implementations of model predictive control for automation applications. The method can be implemented for fine-grained parallel solutions. Due to the extreme simplicity of the method, even serial implementations offer considerable speed advantages. The method solves the problem by formulating, over a predetermined time interval, an optimization problem with a quadratic cost function, and linear state and control constraints as a quadratic program for the application. Then, the quadratic program is solved by applying a parallel quadratic programming update law starting from a positive initial estimate to obtain control actions for the application.

Abstract: Radiation doses are optimized by providing a model of the set of beams and a target dose in normalized forms. A Gram matrix is determined from the model. The target dose is subsampled to determine initial intensity values for the set of beams. Then, the following steps are iterated until convergence. A very small positive value, 0<?<<1, is added to each intensity value to ensure the intensity value is greater than zero. Each intensity value is multiplied by the Gram matrix to determine a product, which is divided element-wise into the normalized target dose to determine corresponding ratios. If the ratios are all close to 1, within a numerical error tolerance, the intensity values of the set of beam are output. Otherwise, the intensity values are multiplied by the ratios before a next iteration.

Abstract: A method for controlling a motion of a first car and a second car in a multi-car elevator system, wherein the first car and the second car move independently in an elevator shaft, determines alternately motion plans for the first the second cars wherein each part of a motion plan for the first car is determined for a planning period of the first car, wherein a beginning of the planning period of the first car is determined by an end of the planning period of the second car, and an end of the planning period of the first car is determined by a home position of the first car on the motion plan, wherein the part of the motion plan is determined based on motion constraints, a set of requests, and the motion plan of the second car determined by the beginning of the planning period of the first car.

Abstract: A motion of a first car and a second car in a multi-car elevator system, wherein the first car and the second car move independently in an elevator shaft, is controlled by generating a command to move the first car according to a first deceleration curve, if a relationship between a position and a velocity of the first car corresponds to a value on the first deceleration curve; and by generating a command to move the second car according to a second deceleration curve, if a relationship between position and a velocity of the second car corresponds to a value on the second deceleration curve, wherein a distance between the first and the second deceleration curve is equals or greater than a minimum distance.

Abstract: A method performs an image processing application by expressing the image processing application as a non-negative quadratic program (NNQP) with a quadratic objective, and nonnegativity constraints. A Karush-Kuhn-Tucker condition of the NNQP is expressed as a fixpoint ratio. Then, the fixpoint ratio is determined iteratively until a solution to the image processing application is reached with a desired precision.

Abstract: A set of cars in an elevator system are scheduled by assigning passengers to the cars such that a current schedule for each car does not exceed a predetermined maximum number of stops per round trip, and the car is filled as near as possible to a maximum capacity at a predetermined bottleneck.

Abstract: A method edits editing an input image to produce an output image by first partitioning pixels of the input image into sets of adjacent pixels. Then, for each set, a trellis of nodes connected by directed links is defined. Each node corresponds to one of the pixels in the set of pixels, and an action and location of the pixel in the output image. Costs are assigned to the nodes and the links. A least cost path through the trellis is determined, and pixels corresponding to the nodes on the least cost path are edited according to the action and location to form the output image.

Abstract: A location and orientation in an environment is determined by first acquiring a real omni-directional image of an unknown skyline in the environment. A set of virtual omni-directional images of known skylines are synthesized from a 3D model of the environment, wherein each virtual omni-directional image is associated with a known location and orientation. The real omni-directional image with each virtual omni-directional images to determine a best matching virtual omni-directional image with the associated known location and orientation.

Abstract: An image for a virtual view of a scene is generated based on a set of texture images and a corresponding set of depth images acquired of the scene. A set of candidate depth values associated with each pixel of a selected image is determined. For each candidate depth value, a cost that estimates a synthesis quality of the virtual image is determined. The candidate depth value with a least cost is selected to produce an optimal depth value for the pixel. Then, the virtual image is synthesized based on the optimal depth value of each pixel and the texture images.

Abstract: A method solves a quadratic programming (QP) problem in real-time implementations of model predictive control for automation applications. The method can be implemented for fine-grained parallel solutions. Due to the extreme simplicity of the method, even serial implementations offer considerable speed advantages. The method solves the problem by formulating, over a predetermined time interval, an optimization problem with a quadratic cost function, and linear state and control constraints as a quadratic program for the application. Then, the quadratic program is solved by applying a parallel quadratic programming update law starting from a positive initial estimate to obtain control actions for the application.

Abstract: A motion of a first car and a second car in a multi-car elevator system, wherein the first car and the second car move independently in an elevator shaft, is controlled by generating a command to move the first car according to a first deceleration curve, if a relationship between a position and a velocity of the first car corresponds to a value on the first deceleration curve; and by generating a command to move the second car according to a second deceleration curve, if a relationship between position and a velocity of the second car corresponds to a value on the second deceleration curve, wherein a distance between the first and the second deceleration curve is equals or greater than a minimum distance.

Abstract: A method for controlling a motion of a first car and a second car in a multi-car elevator system, wherein the first car and the second car move independently in an elevator shaft, determines alternately motion plans for the first the second cars wherein each part of a motion plan for the first car is determined for a planning period of the first car, wherein a beginning of the planning period of the first car is determined by an end of the planning period of the second car, and an end of the planning period of the first car is determined by a home position of the first car on the motion plan, wherein the part of the motion plan is determined based on motion constraints, a set of requests, and the motion plan of the second car determined by the beginning of the planning period of the first car.