A general quantum algorithm for numerical integration

Quantum algorithms have shown their superiority in many application fields. However, a general quantum algorithm for numerical integration, an indispensable tool for processing sophisticated science and engineering issues, is still missing. Here, we first proposed a quantum integration algorithm suitable for any continuous functions that can be approximated by polynomials. More impressively, the algorithm achieves quantum encoding of any integrable functions through polynomial approximation, then constructs a quantum oracle to mark the number of points in the integration area and finally converts the statistical results into the phase angle in the amplitude of the superposition state. The quantum algorithm introduced in this work exhibits quadratic acceleration over the classical integration algorithms by reducing computational complexity from O(N) to O(√N). Our work addresses the crucial impediments for improving the generality of quantum integration algorithm, which provides a meaningful guidance for expanding the superiority of quantum computing.

Spatiotemporal reconstruction method of carotid artery ultrasound from freehand sonography

PURPOSE

4D reconstruction based on radiation-free ultrasound can provide valuable information about the anatomy. Current 4D US technologies are either faced with limited field-of-view (FoV), technical complications, or cumbersome setups. This paper proposes a spatiotemporal US reconstruction framework to enhance its ability to provide dynamic structure information.

METHODS

We propose a spatiotemporal US reconstruction framework based on freehand sonography. First, a collecting strategy is presented to acquire 2D US images in multiple spatial and temporal positions. A morphology-based phase extraction method after pose correction is presented to decouple the compounding image variations. For temporal alignment and reconstruction, a robust kernel regression model is established to reconstruct images in arbitrary phases. Finally, the spatiotemporal reconstruction is demonstrated in the form of 4D movies by integrating the US images according to the tracked poses and estimated phases.

RESULTS

Quantitative and qualitative experiments were conducted on the carotid US to validate the feasibility of the proposed pipeline. The mean phase localization and heart rate estimation errors were 0.07 ± 0.04 s and 0.83 ± 3.35 bpm, respectively, compared with cardiac gating signals. The assessment of reconstruction quality showed a low RMSE (<0.06) between consecutive images. Quantitative comparisons of anatomy reconstruction from the generated US volumes and MRI showed an average surface distance of 0.39 ± 0.09 mm on the common carotid artery and 0.53 ± 0.05 mm with a landmark localization error of 0.60 ± 0.18 mm on carotid bifurcation.

CONCLUSION

A novel spatiotemporal US reconstruction framework based on freehand sonography is proposed that preserves the utility nature of conventional freehand US. Evaluations on in vivo datasets indicated that our framework could achieve acceptable reconstruction performance and show potential application value in the US examination of dynamic anatomy.

Phase portraits as movement primitives for fast humanoid robot control

Currently, usual approaches for fast robot control are largely reliant on solving online optimal control problems. Such methods are known to be computationally intensive and sensitive to model accuracy. On the other hand, animals plan complex motor actions not only fast but seemingly with little effort even on unseen tasks. This natural sense to infer temporal dynamics and coordination motivates us to approach robot control from a motor skill learning perspective to design fast and computationally light controllers that can be learned autonomously by the robot under mild modeling assumptions. This article introduces Phase Portrait Movement Primitives (PPMP), a primitive that predicts dynamics on a low dimensional phase space which in turn is used to govern the high dimensional kinematics of the task. The stark difference with other primitive formulations is a built-in mechanism for phase prediction in the form of coupled oscillators that replaces model-based state estimators such as Kalman filters. The policy is trained by optimizing the parameters of the oscillators whose output is connected to a kinematic distribution in the form of a phase portrait. The drastic reduction in dimensionality allows us to efficiently train and execute PPMPs on a real human-sized, dual-arm humanoid upper body on a task involving 20 degrees-of-freedom. We demonstrate PPMPs in interactions requiring fast reactions times while generating anticipative pose adaptation in both discrete and cyclic tasks.

Quantum neural networks model based on swap test and phase estimation

In this paper, a neural networks model for quantum computer is proposed. The core of this model is quantum neuron. Firstly, the inner product of the input qubits and the weight qubits is mapped to the phase of the control qubits in the neuron by the swap test technology, and then these phases are obtained by the phase estimation method, which are further used as the phase of the output qubit in the neuron. In this way, the mapping of input qubits to output qubit in quantum neuron is completed. The quantum neurons mentioned above can be used to construct quantum neural networks. In this paper, the quantum circuit for each operation step are given. The simulation results on the classic computer verify the effectiveness of the proposed model.

Adaptive phase correction of diffusion-weighted images

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

Two-dimensional affine model-based estimators for principal strain vascular ultrasound elastography with compound plane wave and transverse oscillation beamforming

Polar strain (radial and circumferential) estimations can suffer from artifacts because the center of a nonsymmetrical carotid atherosclerotic artery, defining the coordinate system in cross-sectional view, can be misregistered. Principal strains are able to remove coordinate dependency to visualize vascular strain components (i.e., axial and lateral strains and shears). This paper presents two affine model-based estimators, the affine phase-based estimator (APBE) developed in the framework of transverse oscillation (TO) beamforming, and the Lagrangian speckle model estimator (LSME). These estimators solve simultaneously the translation (axial and lateral displacements) and deformation (axial and lateral strains and shears) components that were then used to compute principal strains. To improve performance, the implemented APBE was also tested by introducing a time-ensemble estimation approach. Both APBE and LSME were tested with and without the plane strain incompressibility assumption. These algorithms were evaluated on coherent plane wave compounded (CPWC) images considering TO. LSME without TO but implemented with the time-ensemble and incompressibility constraint (Porée et al., 2015) served as benchmark comparisons. The APBE provided better principal strain estimations with the time-ensemble and incompressibility constraint, for both simulations and in vitro experiments. With a few exceptions, TO did not improve principal strain estimates for the LSME. With simulations, the smallest errors compared with ground true measures were obtained with the LSME considering time-ensemble and the incompressibility constraint. This latter estimator also provided the highest elastogram signal-to-noise ratios (SNRs) for in vitro experiments on a homogeneous vascular phantom without any inclusion, for applied strains varying from 0.07% to 4.5%. It also allowed the highest contrast-to-noise ratios (CNRs) for a heterogeneous vascular phantom with a soft inclusion, at applied strains from 0.07% to 3.6%. In summary, the LSME outperformed the implemented APBE, and the incompressibility constraint improved performances of both estimators.

Multi-SNP Haplotype Analysis Methods for Association Analysis

Haplotype analysis forms the basis of much of genetic association analysis using both related and unrelated individuals (we concentrate on unrelated). For example, haplotype analysis indirectly underlies the SNP imputation methods that are used for testing trait associations with known but unmeasured variants and for performing collaborative post-GWAS meta-analysis. This chapter is focused on the direct use of haplotypes in association testing. It reviews the rationale for haplotype-based association testing, discusses statistical issues related to haplotype uncertainty that affect the analysis, then gives practical guidance for testing haplotype-based associations with phenotype or outcome trait, first of candidate gene regions and then for the genome as a whole. Haplotypes are interesting for two reasons, first they may be in closer LD with a causal variant than any single measured SNP, and therefore may enhance the coverage value of the genotypes over single SNP analysis. Second, haplotypes may themselves be the causal variants of interest and some solid examples of this have appeared in the literature.This chapter discusses three possible approaches to incorporation of SNP haplotype analysis into generalized linear regression models: (1) a simple substitution method involving imputed haplotypes, (2) simultaneous maximum likelihood (ML) estimation of all parameters, including haplotype frequencies and regression parameters, and (3) a simplified approximation to full ML for case-control data.Examples of the various approaches for a haplotype analysis of a candidate gene are provided. We compare the behavior of the approximation-based methods and argue that in most instances the simpler methods hold up well in practice. We also describe the practical implementation of haplotype risk estimation genome-wide and discuss several shortcuts that can be used to speed up otherwise potentially very intensive computational requirements.