Abstract: It is provided a method for generating a supercontinuum, the method comprising the following steps: a) radiating a carrier laser pulse having a first temporal width onto a first non-linear material; b) at the same time, radiating a second shorter laser pulse having a second temporal width onto the first non-linear material, thereby changing the non-linear properties of the first non-linear material and imprinting a ghost pulse having a third temporal width into the carrier pulse; the second temporal width being at least two times shorter than the first temporal width, and c) radiating the carrier pulse with imprinted ghost pulse onto the first non-linear material or a second non-linear material and generating, by self-phase modulating, a supercontinuum around the center frequency of the carrier pulse.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing. An exemplary method comprises: inputting a plurality of to-be-optimized routing solution candidates to a Siamese neural network comprising a plurality of value prediction networks, each of the value prediction networks being trained to predict a cost associated with a to-be-optimized routing solution candidate; identifying one or more to-be-optimized routing solution candidates from the plurality of to-be-optimized routing solution candidates based on outputs of the Siamese neural network; inputting the one or more identified to-be-optimized routing solution candidates to a routing optimizer to obtain one or more optimized routing solution candidates; and determining an optimized routing solution with a lowest cost from the one or more optimized routing solution candidates.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for grouping a plurality of resources into a plurality of cohorts, wherein each of the plurality of resources is associated with a risk level and a benefit level, and resources in each cohort share the same risk level and the same benefit level; obtaining a plurality of provider-level adjustments; constructing an optimization model for determining a resource flow solution; and according to the plurality of cohort-provider-level adjustments, identifying one or more resources in each of the plurality of cohorts that are provided by a first provider to be transferred to a second provider; and automatically sending one or more requests to the first provider and the second provider to transfer the determined one or more first resources from the first provider to the second provider.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system that includes a number of individual solvers. The method includes: receiving data representing K global constraints and L local constraints of the KP; decomposing the KP into N sub-problems using K dual multipliers, each of the N sub-problems corresponding to a respective one of the N users and subject to the L local constraints w.r.t. the corresponding user, wherein N is in an order of billions or larger; determining the number of individual solvers for solving the N sub-problems; distributing the N sub-problems among the number of individual solvers; and solving the KP by the distributed computing system by performing two or more iterations.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing. An exemplary method comprises: inputting a plurality of to-be-optimized routing solution candidates to a Siamese neural network comprising a plurality of value prediction networks, each of the value prediction networks being trained to predict a cost associated with a to-be-optimized routing solution candidate; identifying one or more to-be-optimized routing solution candidates from the plurality of to-be-optimized routing solution candidates based on outputs of the Siamese neural network; inputting the one or more identified to-be-optimized routing solution candidates to a routing optimizer to obtain one or more optimized routing solution candidates; and determining an optimized routing solution with a lowest cost from the one or more optimized routing solution candidates.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system that includes a number of individual solvers. The method includes: receiving data representing K global constraints and L local constraints of the KP; decomposing the KP into N sub-problems using K dual multipliers, each of the N sub-problems corresponding to a respective one of the N users and subject to the L local constraints w.r.t. the corresponding user, wherein N is in an order of billions or larger; determining the number of individual solvers for solving the N sub-problems; distributing the N sub-problems among the number of individual solvers; and solving the KP by the distributed computing system by performing two or more iterations.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing. An exemplary method comprises: inputting a plurality of to-be-optimized routing solution candidates to a Siamese neural network comprising a plurality of value prediction networks, each of the value prediction networks being trained to predict a cost associated with a to-be-optimized routing solution candidate; identifying one or more to-be-optimized routing solution candidates from the plurality of to-be-optimized routing solution candidates based on outputs of the Siamese neural network; inputting the one or more identified to-be-optimized routing solution candidates to a routing optimizer to obtain one or more optimized routing solution candidates; and determining an optimized routing solution with a lowest cost from the one or more optimized routing solution candidates.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing. An exemplary method comprises: inputting a plurality of to-be-optimized routing solution candidates to a Siamese neural network comprising a plurality of value prediction networks, each of the value prediction networks being trained to predict a cost associated with a to-be-optimized routing solution candidate; identifying one or more to-be-optimized routing solution candidates from the plurality of to-be-optimized routing solution candidates based on outputs of the Siamese neural network; inputting the one or more identified to-be-optimized routing solution candidates to a routing optimizer to obtain one or more optimized routing solution candidates; and determining an optimized routing solution with a lowest cost from the one or more optimized routing solution candidates.

Abstract: Disclosed methods, systems, and apparatus, include computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system. The method includes: receiving data representing K global constraints and L local constraints of the KP; transforming the KP into a dual problem using K dual multipliers; decomposing the dual problem into N sub-problems; performing two or more iterations in solving the dual problem, wherein in one iteration, for each dual multiplier corresponding to a global constraint corresponding to a pool: determining an updated dual multiplier for the global constraint corresponding to the pool to be a non-negative threshold; and computing M decision variables of each of the N users corresponding to the updated dual multiplier in solving each of the N sub-problems corresponding to the each of the N users.

Abstract: Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing allocation of M resources among N users into K pools by solving a knapsack problem (KP) using a distributed computing system that includes a number of individual solvers. The method includes: receiving data representing K global constraints and L local constraints of the KP; decomposing the KP into N sub-problems using K dual multipliers, each of the N sub-problems corresponding to a respective one of the N users and subject to the L local constraints w.r.t. the corresponding user, wherein N is in an order of billions or larger; determining the number of individual solvers for solving the N sub-problems; distributing the N sub-problems among the number of individual solvers; and solving the KP by the distributed computing system by performing two or more iterations.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for optimizing resource allocation are provided. One of the methods includes: processing a plurality of first objective functions in parallel to determine a plurality of allocation plans, wherein each of the allocation plans corresponds to allocating zero or more of a plurality of resources associated with a platform to a user, and the plurality of first objective functions share one or more dual multipliers; determining a plurality of profits and costs for the platform in parallel based on the plurality of the allocation plans; aggregating the calculated profits and costs using parallel reduction; updating the one or more dual multipliers based on the aggregated costs to determine whether an exit condition is satisfied; if the exit condition is not satisfied, repeating the processing the plurality of the first objective functions based on the updated dual multipliers.

Abstract: Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing allocating M resources subject to L constraints. The method includes: receiving data representing L constraints, wherein each of the L constraints corresponds to a subset of M resources and restricts a respective maximum number C of resources to be selected among the subset of the M resources, wherein the L constraints has a hierarchal structure; determining a topological ordering of the L constraints; selecting all the M resources as an initial selection; removing resources from the initial selection by traversing each constraint in the topological ordering of the L constraints; and allocating the selected resources after traversing all the L constraints in the topological ordering of the L constraints.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing using reinforcement learning (RL) are provided. One of the methods includes: initializing a state of an RL model based on a routing solution, wherein the RL model comprises a plurality of improvement actions for applying to the state; applying one or more of the plurality of improvement actions to the state to obtain updated routing solutions until a predetermined condition is satisfied; applying a perturbation action to obtain a perturbed routing solution and feeding the perturbed routing solution back to the RL model for the RL model to perform the applying one or more of the plurality of improvement actions according to the policy; and determining a routing solution with a minimum cost from the updated routing solutions.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for optimizing resource allocation are provided. One of the methods includes: processing a plurality of first objective functions in parallel to determine a plurality of allocation plans, wherein each of the allocation plans corresponds to allocating zero or more of a plurality of resources associated with a platform to a user, and the plurality of first objective functions share one or more dual multipliers; determining a plurality of profits and costs for the platform in parallel based on the plurality of the allocation plans; aggregating the calculated profits and costs using parallel reduction; updating the one or more dual multipliers based on the aggregated costs to determine whether an exit condition is satisfied; if the exit condition is not satisfied, repeating the processing the plurality of the first objective functions based on the updated dual multipliers.

Abstract: Methods, systems, and apparatus, including computer programs encoded on computer storage media, for determining routing using reinforcement learning (RL) are provided. One of the methods includes: initializing a state of an RL model based on a routing solution, wherein the RL model comprises a plurality of improvement actions for applying to the state; applying one or more of the plurality of improvement actions to the state to obtain updated routing solutions until a predetermined condition is satisfied; applying a perturbation action to obtain a perturbed routing solution and feeding the perturbed routing solution back to the RL model for the RL model to perform the applying one or more of the plurality of improvement actions according to the policy; and determining a routing solution with a minimum cost from the updated routing solutions.