Abstract: A cross reality system that provides an immersive user experience by storing persistent spatial information about the physical world that one or multiple user devices can access to determine position within the physical world and that applications can access to specify the position of virtual objects within the physical world. Persistent spatial information enables users to have a shared virtual, as well as physical, experience when interacting with the cross reality system. Further, persistent spatial information may be used in maps of the physical world, enabling one or multiple devices to access and localize into previously stored maps, reducing the need to map a physical space before using the cross reality system in it. Persistent spatial information may be stored as persistent coordinate frames, which may include a transformation relative to a reference orientation and information derived from images in a location corresponding to the persistent coordinate frame.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: A computer implemented method of reducing data elements in a data file includes: receiving a data file including one or more primary data elements; storing the data file in a memory coupled to the processor; generating, from at least one of the one or more primary data elements, a plurality of supplemental data elements; determining whether any of the plurality of supplemental data elements and any of the primary data elements offset each other; and upon determining that at least one of the plurality of supplemental data elements and at least one of the primary data elements offset each other, deleting, from the data file, at least one of the offset supplemental data elements or primary data elements.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: A computer implemented method of reducing data elements in a data file includes: receiving a data file including one or more primary data elements; storing the data file in a memory coupled to the processor; generating, from at least one of the one or more primary data elements, a plurality of supplemental data elements; determining whether any of the plurality of supplemental data elements and any of the primary data elements offset each other; and upon determining that at least one of the plurality of supplemental data elements and at least one of the primary data elements offset each other, deleting, from the data file, at least one of the offset supplemental data elements or primary data elements.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: Systems are provided for compressing portfolios of open option positions. Market participants may provide constraints, such as net delta and gamma values within a specific tolerance. A compression engine uses a linear, integer and/or linear-quadratic programming solver to analyze portfolios of multiple market participants and identify multilateral option spread trades that result in portfolios that are compressed subject to the constraints.

Abstract: A computer implemented method of reducing data elements in a data file includes: receiving a data file including one or more primary data elements; storing the data file in a memory coupled to the processor; generating, from at least one of the one or more primary data elements, a plurality of supplemental data elements; determining whether any of the plurality of supplemental data elements and any of the primary data elements offset each other; and upon determining that at least one of the plurality of supplemental data elements and at least one of the primary data elements offset each other, deleting, from the data file, at least one of the offset supplemental data elements or primary data elements.

Abstract: A computer implemented method of reducing data elements in a data file includes: receiving a data file including one or more primary data elements; storing the data file in a memory coupled to the processor; generating, from at least one of the one or more primary data elements, a plurality of supplemental data elements; determining whether any of the plurality of supplemental data elements and any of the primary data elements offset each other; and upon determining that at least one of the plurality of supplemental data elements and at least one of the primary data elements offset each other, deleting, from the data file, at least one of the offset supplemental data elements or primary data elements.

Abstract: A computer implemented method of reducing data elements in a data file includes: receiving a data file including one or more primary data elements; storing the data file in a memory coupled to the processor; generating, from at least one of the one or more primary data elements, a plurality of supplemental data elements; determining whether any of the plurality of supplemental data elements and any of the primary data elements offset each other; and upon determining that at least one of the plurality of supplemental data elements and at least one of the primary data elements offset each other, deleting, from the data file, at least one of the offset supplemental data elements or primary data elements.

Abstract: A stackable electrical socket has an insulating body with a longitudinally extending bore for receiving an electrical plug member. Electrical contact elements extend partially into the bore for contact with the plug member when inserted, such contact elements having a leg part accommodated in one of a pair of first and second slots so as to extend from that one slot outwardly of the body for electrical connection. In this manner two similar insulating bodies of stackable electrical sockets can be stacked one on another so that the first and second slots of the overlying socket each overlie one of a first and second slot of the underlying connector and the leg part of the overlying connector which is presented for electrical connection is received through one of the first or second slots which is vacant of a leg part of the underlying socket for the leg part of the overlying socket to be presented for electrical connection from the underlying socket.

Abstract: A circuit board assembly and a method of manufacturing such an assembly has a circuit board 1 with spaced holes 6 which receive projections 15 of a rigid metal chassis 11 which is part of a sub-assembly 10. The projections 15 are soldered in the holes 6 to rigidly secure the sub-assembly to the circuit board. The sub-assembly 10 has a pair of terminal posts 18 from which extend electrical connections 25, 26 having ends formed as fingers 30, 31. The fingers 30 and 31 are received in sets of corresponding holes 8 and 7 respectively in the circuit board and soldered in their respective holes to provide an electrical connection between the strips 25 and 26 and circuit lines 5 and 4 respectively on the circuit board. The soldered joints between the projections 15 and the circuit board permits torque applied to the terminal posts 18 to be accommodated by the circuit board assembly.