In a simulation system and method thereof, the simulation includes, when a function value for a nominal point (NP) of an input is a first value, running a first simulation on the input; and when the function value for the NP of the input is a second value different from the first value, running a second simulation on the input. Here, the running of the second simulation may include (a) setting a boundary of an input distribution for the second value as a first distribution value, (b) generating input samples within the set boundary of the input distribution, (c) obtaining a worst case point (WCP) for the input by performing machine learning on the generated input samples, and (d) repeatedly performing the steps (a) to (c) while shifting the boundary of the input distribution until the boundary of the input distribution reaches a minimum critical value.

Systems and methods for support structures for additive manufacturing of solid models. A method includes receiving a solid model, for a physical object to be manufactured, that includes a plurality of boundary representation surfaces. The method includes analyzing the b-rep surfaces to generate point samples for potential support locations. The method includes clustering points on the solid model, corresponding to at least some of the point samples, to create support locations. The method includes generating column supports in the solid model that connect to the original solid model at the support locations. The method includes storing the solid model, including the column supports.

In one embodiment, a writing data verification method is for verifying a conversion error due to data conversion from first writing data in a vector format based on design data to second writing data in a pixel format. The method includes converting the second writing data to third writing data in a vector format, performing an exclusive OR operation on the first writing data and the third writing data, enlarging a graphic of the first writing data to obtain an enlarged graphic and generating a tolerance region graphic from a difference between the enlarged graphic and the graphic of the first writing data, and detecting a defect by performing a mask process on a graphic generated by the exclusive OR operation with the tolerance region graphic.

In an example, a system includes a Monte Carlo simulation module to calculate a collision force on a first vehicle based at least in part on first information, calculate a crush depth for a second vehicle (having unknown damage) based at least in part on the calculated collision force on the first vehicle and second information, calculate first total energy absorbed by the first vehicle based on the first information, calculate second total energy absorbed by the second vehicle based on the calculated crush depth and the second information; and calculate a first estimated impact severity for the first vehicle using the first total energy and a second estimated impact severity for the second vehicle using the second total energy.

Systems and methods for modeling an electrical power system are disclosed. A computer and an analytics server are in network connection. The computer comprises a processor coupled with a memory. The memory is configured to maintain at least one engine element and a component database. The analytics server comprises a virtual system modeling engine and an analytics engine. The component database is operable to store power system components. The at least one engine element is operable to generate a virtual system model of the electrical power system and generate predicted output based on the virtual system model. The analytics engine is operable to monitor the predicted output and real-time output from at least one sensor of the electrical power system, and calibrate the virtual system model based on a difference between the predicted output and the real-time output.

According to an embodiment, a method for cell placement in a semiconductor layout is provided. The method includes: providing a first cell having two sides, each side configured as at least one of a source side and a drain side; providing a place-and-route boundary (prBoundary) of the first cell based on the configuration of the two sides of the first cell; providing a second cell having two sides, each side configured as at least one of a source side and a drain side; providing a prBoundary of the second cell based on the configuration of the two sides of the second cell; and placing the first cell and the second cell based on the prBoundary of the first cell and the prBoundary of the second cell.

In an example, an IC package includes a package substrate including a plurality of bumps configured for coupling to a printed circuit board, the package substrate including a core disposed between a plurality of top-side conductive layers and a plurality of bottom-side conductive layers. The IC package further includes an IC die coupled to the package substrate and disposed on top of the plurality of top-side conductive layers. The IC die further includes a voltage regulator IC die disposed on the package substrate adjacent to the IC die, the voltage regulator IC die being coupled to the IC die using two of four top-most layers of the plurality of top-side conductive layers nearest the IC die.

A method to improve a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method including: obtaining a target feature; generating a perturbed target feature from the target feature by applying a perturbation thereto; generating a set of training examples includes the perturbed target feature and an indication as whether the perturbed target feature is deemed the same as the target feature; training a learning model with the set of training examples; classifying features in the portion of the design layout into at least two classes: being deemed the same as the target feature, and being deemed different from the target feature.

Systems and methods are provided for statistically equivalent level of safety modeling. One method includes identifying sub-fleets within a fleet based upon usage profiles, determining a sub-fleet reliability value for each sub-fleet, determining a baseline fleet reliability for the fleet by combining the sub-fleet reliability values on a weighted basis, applying at least one credit to at least one sub-fleet, determining a post-credit sub-fleet reliability value for each sub-fleet based upon the at least one credit, determining a post-credit fleet reliability for the fleet by combining the post-credit sub-fleet reliability values on a weighted basis, comparing the baseline fleet reliability with the post-credit fleet reliability to identify a change in fleet reliability and determining whether the change in fleet reliability is within a predetermined threshold to validate the at least one credit.

The present invention relates to the technical area of lens, particularly discloses a lens for focusing or collimating light emitted from an extended light source, which comprises a front surface facing towards the extended light source and a back surface facing away from the extended light source, wherein at least one of the surfaces comprises a central section and a plurality of annular sections concentrically surrounding the central section; and wherein each of the annular section corresponds to a small portion of the extended light source. A method of designing the above lens is also disclosed. Additionally, the present invention provides a cost-effective lens design with high precision and more particularly, a lens design which meets the transmittance requirement for extended light source.