Abstract: A computer accesses an input element storage and an output element storage. The computer accesses a symbolic expression for output element storage as a function of the input element storage. The computer computes, using a symbolic computation engine of the computer, a symbolic expression for the tangent space Jacobian of the output element storage with respect to an input tangent space. The computer outputs the computed expression.

Abstract: A computer accesses a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory. The computer computes a first Jacobian of the input matrix with respect to an input tangent space. The computer computes a second Jacobian of the output matrix with respect to the input matrix. The computer computes a third Jacobian of an output tangent space with respect to the input matrix. The computer applies symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression, the second symbolic expression representing a computed tangent-space Jacobian.

Abstract: A backdrop stand may have a hub with an arm receiving portion with an arm opening. An arm may be selectively located in the arm opening and moved between a first position and a second position to permit backdrops of different sizes to be used with the stand.

Abstract: A backdrop stand may have a hub with an arm receiving portion with an arm opening. An arm may be selectively located in the arm opening and moved between a first position and a second position to permit backdrops of different sizes to be used with the stand.

Abstract: A computer accesses an input element storage and an output element storage. The computer accesses a symbolic expression for output element storage as a function of the input element storage. The computer computes, using a symbolic computation engine of the computer, a symbolic expression for the tangent space Jacobian of the output element storage with respect to an input tangent space. The computer outputs the computed expression.

Abstract: A computer accesses a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory. The computer computes a first Jacobian of the input matrix with respect to an input tangent space. The computer computes a second Jacobian of the output matrix with respect to the input matrix. The computer computes a third Jacobian of an output tangent space with respect to the input matrix. The computer applies symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression, the second symbolic expression representing a computed tangent-space Jacobian.

Abstract: A computer accesses a first symbolic expression for an output value as a function of an input value. The computer computes a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition. The computer computes a second symbolic Jacobian of the output value with respect to the input value. The computer computes a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition. The computer applies symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression.

Abstract: A computer of an unmanned aerial vehicle (UAV) accesses, from a memory unit, a problem definition comprising cost functions associated with travel of the UAV. The computer causes movement of the UAV based on the cost functions. The computer adjusts one or more of the cost functions during a flight of the UAV. The computer causes further movement of the UAV based on the adjusted one or more of the cost functions.

Abstract: Described herein is an illumination device for projecting light in a predetermined illumination pattern on a surface. The illumination device includes a light module having a light source and a light pipe configured to transmit light in any suitable manner. The illumination device also includes a housing having a cavity, an entrance opening for receiving the light emitted from the light source, and an aperture at a second housing end. Within the housing between the entrance opening and the aperture is a screen at least partially disposed in the cavity, the screen having at least one opening defining a base pattern configuration corresponding to the predetermined illumination pattern. The light pipe is configured to selectively transmit light from the light source to the cavity and may be linear or non-linear such that the light source and the surface to be illuminated do not need to face one another.

Abstract: Described herein is an illumination device for projecting light in a predetermined illumination pattern on a surface. The illumination device includes a light module having a light source and a light pipe configured to transmit light in any suitable manner. The illumination device also includes a housing having a cavity, an entrance opening for receiving the light emitted from the light source, and an aperture at a second housing end. Within the housing between the entrance opening and the aperture is a screen at least partially disposed in the cavity, the screen having at least one opening defining a base pattern configuration corresponding to the predetermined illumination pattern. The light pipe is configured to selectively transmit light from the light source to the cavity and may be linear or non-linear such that the light source and the surface to be illuminated do not need to face one another.

Abstract: A fluorescence detection system includes a light source for coupling with a mobile device and software, having machine readable instructions loadable into memory of the mobile device and executable by a processor of the mobile device, capable of: activating the light source in coordination with capturing one or more images using a camera of the mobile device; analyzing an image captured with the light source on with an image captured with the light source off, to detect a shift of intensity within a predetermined color range within the images; and identifying and authenticating objects by measuring the intensity shift within the images.

Abstract: A support in the form of a high directional having a configurable number of telescoping legs is disclosed. The support provides a head and a plurality of telescoping legs, the head having a plurality of head units and each head unit having at least one associated leg depending therefrom. Each head unit being adapted to be coupled to at least two other head units.

Abstract: Systems and methods authenticate an object using IR. IR is projected at a first wavelength onto the object and a first image of the object is captured during the projection of the IR. The object is authenticated by processing the first image to detect IR fluorescence from an IR fluorescing material incorporated into the object in response to the projected IR, where presence of the IR fluorescence within the first image indicates authentication of the object.

Abstract: A fluorescence detection system includes a light source for coupling with a mobile device and software, having machine readable instructions loadable into memory of the mobile device and executable by a processor of the mobile device, capable of: activating the light source in coordination with capturing one or more images using a camera of the mobile device; analyzing an image captured with the light source on with an image captured with the light source off, to detect a shift of intensity within a predetermined color range within the images; and identifying and authenticating objects by measuring the intensity shift within the images.

Abstract: A computer implemented method, apparatus, and computer usable program code for the distributed monitoring of a SOAP service is provided. A test configuration file specifying a test input is distributed from a central reporting location to at least one remote data processing system that has access to a SOAP service to be tested. The test configuration file is created without accessing the SOAP service to be tested. Furthermore, the user that created the test configuration file is not allowed access to the SOAP service to be tested.

Abstract: A support in the form of a high directional having a configurable number of telescoping legs is disclosed. The support provides a head and a plurality of telescoping legs, the head having a plurality of head units and each head unit having at least one associated leg depending therefrom. Each head unit being adapted to be coupled to at least two other head units.