Abstract: Techniques are discussed for modifying map elements associated with map data. Map data can include three-dimensional data (e.g., LIDAR data) representing an environment, while map elements can be associated with the map data to identify locations and semantic information associated with an environment, such as regions that correspond to driving lanes or crosswalks. A trajectory associated with the map data can be updated, such as when aligning one or more trajectories in response to a loop closure, updated calibration, etc. The transformation between a trajectory and an updated trajectory can be applied to map elements to warp the map elements so that they correspond to the updated map data, thereby providing automatic and accurate techniques for updating map elements associated with map data.

Abstract: This self-compensating spiral spring for a mechanical balance-spiral spring oscillator for a watch or clock movement or other precision instrument, made of an Nb—Hf paramagnetic alloy possessing a thermal coefficient of Young's modulus (TCE), such that it enables the following expression to be substantially equal to zero: 1 E ⁢ ⅆ E ⅆ T + 3 ⁢ α s - 2 ⁢ α b where: E: Young's modulus of the spiral spring of the oscillator; 1 E ⁢ ⅆ E ⅆ T = T ⁢   ⁢ C ⁢   ⁢ E

Abstract: This self-compensating spiral for a mechanical spiral balance-wheel oscillator in watchwork or other precision instrument, made of a paramagnetic alloy, contains at least one of the elements Nb, V, Ta, Ti, Zr, Hf and is covered with a substantially uniform oxide layer having a thickness greater than or equal to 20 nm, formed by subjecting the said spiral to an anodizing treatment.

Abstract: This self-compensating spiral spring for a mechanical balance-spiral spring oscillator for a watch or clock movement or other precision instrument, made of an Nb-Hf paramagnetic alloy possessing a thermal coefficient of Young's modulus (TCE), such that it enables the following expression to be substantially equal to zero: 1 1 E ⁢ ⅆ E ⅆ T + 3 ⁢ α s - 2 ⁢ α b

Abstract: This self-compensating spiral for a mechanical spiral balance-wheel oscillator in watchwork or other precision instrument, made of a paramagnetic alloy, contains at least one of the elements Nb, V, Ta, Ti, zr, Hf and is covered with a substantially uniform oxide layer having a thickness greater than or equal to 20 nm, formed by subjecting the said spiral to an anodizing treatment.

Abstract: This self-compensating spiral for a mechanical spiral balance-wheel oscillator in watchwork or other precision instrument, made of a paramagnetic alloy, contains at least one of the elements Nb, V, Ta, Ti, Zr, Hf and is covered with a substantially uniform oxide layer having a thickness greater than or equal to 20 nm, formed by subjecting the said spiral to an anodizing treatment.

Abstract: A self-compensating spring for a balance-spring for a balance-spring/balance assembly of a mechanical oscillator of a horological movement or of any other precision instrument, made of a paramagnetic Nb--Zr alloy containing between 5% and 25% by weight of Zr, obtained by cold rolling or cold drawing, and having a Young's modulus whose temperature coefficient (TCY) is adjustable by precipitation of Zr-rich phases in the Nb--Zr solid-solution. It contains at least 500 ppm by weight of an interstitial doping agent at least partly formed of oxygen.