10 results about "Orthonormal basis" patented technology

A computer-implemented method includes receiving at a processor an input set of multiway data. The method determines a set of persistent homology barcodes based on the multiway data and identifies at least a first significant persistent homology barcode in the set of persistent homology barcodes. A representative cycle of the first significant persistent homology is returned and an orthonormal basis for a boundary of the multiway data is computed. The method obtains a harmonic representative by computing a projection of the representative cycle to an orthogonal complement and generates a set of feature vectors using the harmonic representative. Each feature vector has a magnitude corresponding to an impact that feature has on a given condition. The method then ranks the feature vectors by feature vector magnitude.

This invention discloses a method for recognizing orbital angular momentum superposition states based on conditional generative adversarial networks (GANs). The improved GAN effectively recovers and identifies severely distorted vortex beams. A skip connection mechanism is introduced into the generator's network structure to preserve low-level detail features and improve image generation quality. Furthermore, a peak signal-to-noise ratio (PSNR) loss function is introduced into the generator's loss function, forcing the generated image to maintain a higher pixel-level similarity to the real image. Convolutional attention modules are introduced into both the generator and discriminator based on the improved GAN, enhancing the network's ability to extract key information. This method effectively recovers severely distorted vortex beams affected by strong turbulence and long-distance propagation conditions, ultimately achieving high recognition accuracy.

Methods, systems and apparatus for simulating a physical system described by an electronic structure Hamiltonian expressed in an orthonormal basis. In one aspect, a method includes decomposing the electronic structure Hamiltonian into a sum of sub-Hamiltonians, wherein each sub-Hamiltonian in the sum of sub-Hamiltonians is expressed in one of multiple bases; simulating evolution of the physical system using the decomposed electronic structure Hamiltonian; and using the simulated evolution of the physical system using the decomposed electronic structure Hamiltonian to determine properties of the physical system.

A method and network node for interference-aware dimension reduction via orthonormal basis selection are disclosed. According to one aspect, a method includes determining a beamformer for each wireless device (WD), each beamformer being based at least in part on an interference covariance matrix; determining a power in each dimension reduction basis vector based at least in part on the determined beamformers; and selecting a subset of the dimension reduction basis vectors based on the determined power. A number of selected dimension reduction basis vectors is less than a number of antenna elements of the network node. The method also includes multiplying a received signal vector by a dimension reduction matrix having as rows the selected subset of the dimension reduction basis vectors. The multiplying results in a reduced signal vector having a dimension equal to the number of selected rows of the dimension reduction matrix.

The invention provides a turbomachine design optimization method and system based on a dimension similarity principle. The method comprises the steps that a dimension matrix is established based on turbomachine flow field physical quantity parameters, a constraint equation is solved, a standard orthogonal basis of scaling parameters is obtained, and the scaling parameters are generated; generating enhanced data samples based on the scaling parameters and training a neural network; and training geometric parameters, working condition parameters and space coordinates of the target turbomachinery based on the trained neural network to complete optimization. According to the method, through combination of the deep learning model and the dimension similar data enhancement method, high-accuracy physical field prediction can be obtained under the condition of few samples, so that the iterative design period of engineering fields such as turbomachinery can be remarkably shortened. The method has obvious advantages in generalization ability of cross-working-condition and cross-design-variable combination, the dependence on massive numerical simulation data is effectively reduced, and the overall efficiency of optimization design is greatly improved.

A method for determining at least one characteristic of an electromagnetic signal using a quantum probe, the method including determining a resonant frequency of at least one qubit of at least one quantum probe, applying at least one pulse sequence to the at least one qubit, wherein the at least pulse sequence has a carrier frequency of the resonant frequency and is associated with a filter function that comprises an orthonormal basis, capturing a plurality of images associated with electromagnetic radiation emitted by the at least one qubit after applying the at least one pulse sequence to the at least one qubit, and determining at least one characteristic of the electromagnetic signal based on the plurality of images.

A computer-implemented method includes receiving at a processor an input set of multiway data. The method determines a set of persistent homology barcodes based on the multiway data and identifies at least a first significant persistent homology barcode in the set of persistent homology barcodes. A representative cycle of the first significant persistent homology is returned and an orthonormal basis for a boundary of the multiway data is computed. The method obtains a harmonic representative by computing a projection of the representative cycle to an orthogonal complement and generates a set of feature vectors using the harmonic representative. Each feature vector has a magnitude corresponding to an impact that feature has on a given condition. The method then ranks the feature vectors by feature vector magnitude.

The invention belongs to the technical field of optical communication, and particularly relates to an orbital angular momentum pattern recognition method based on deep learning. According to the OAM pattern recognition method, the efficiency and precision of model training are remarkably improved by introducing the adaptive learning rate scheduling and gradient cutting technology. In the experiment, the Two Phase Scheduler and Dynamic Range SGD optimizers provided by the invention can ensure the steady convergence of the model in different initial learning rate ranges, so that the training process is obviously accelerated, and the common convergence oscillation problem is effectively avoided. According to the method, a high-precision recognition result can be provided in an OAM speckle classification task, good generalization ability is shown in the face of various different scattering environments, and an efficient and robust solution is provided for the OAM mode recognition problem.

Methods, systems and apparatus for measuring the energy of a quantum chemical system. In one aspect, a method includes obtaining a Hamiltonian describing the chemical system, where the Hamiltonian is expressed in an orthonormal basis; decomposing the Hamiltonian into a sum of terms where each term comprises a respective operator that effects a respective single particle basis rotation, and one or more particle density operators; repeatedly, for each group comprising terms with a same operator that effects a respective single particle basis rotation, measuring expectation values of the terms included in the group, comprising: performing the respective single particle basis rotation on a qubit system encoding a state of the chemical system; and measuring Jordan-Wigner transformations of the one or more particle density operators in the group to obtain a respective measurement result for the group; and determining the energy of the chemical system using the obtained measurement results.

The invention discloses an orbital angular momentum superposition state identification method based on a conditional generative adversarial network. Vortex beams which are seriously distorted are effectively recovered and identified through the improved conditional generative adversarial network. A jump connection mechanism is introduced into a network structure of the generator, so that bottom detail features can be reserved, and the generation quality of the image is improved. In addition, a peak signal-to-noise ratio loss function is introduced into the loss function of the generator, and the generated image and the real image are forced to keep higher similarity at the pixel level. On the basis of the improved conditional generative adversarial network, convolution attention modules are introduced into a generator and a discriminator, so that the key information extraction capability of the network is improved. According to the method provided by the invention, the vortex beam which is seriously distorted due to the influence of strong turbulence and long-distance propagation conditions is effectively recovered, and finally relatively high identification accuracy is obtained.