More on complexity of operators in quantum field theory

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the ket vector and bra vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant

Principles and symmetries of complexity in quantum field theory

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems. Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry. Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems. We clarify why the bi-invariance is relevant in quantum field theoretic systems. After comparing our results with discrete qubit systems we show most results in $k$-local right-invariant metric can also appear in our framework. Based on the bi-invariance of our formalism, we propose a new interpretation for the Schr\"{o}dinger's equation in isolated systems - the quantum state evolves by the process of minimizing "computational cost."Comment: Published version; added a short introduction on Finsler geometr

Heterogeneous data fusion for three-dimensional gait analysis using wearable MARG sensors

Gait analysis has become a research highlight. In this paper, we propose a computing method using wearable magnetic angular rate and gravity (MARG) sensor arrays with wireless network, which calculates absolute and relative orientation and position information of human foot motion during level walking and stair climbing process. Three-dimensional foot orientation and position were estimated by a Kalman-based sensor fusion algorithm and validated by ground truth provided by Vicon system. The repeatability of the alignment procedure and the measurement errors were evaluated on healthy subjects. Experimental results demonstrate that the proposed method has a good performance at both motion patterns. No significant drifts exist in the overall results presented in the paper. The measured and estimated information can be transmitted to remote server through internet. Moreover, this method could be applied to other cyclical activity monitoring

Using Distributed Wearable Sensors to Measure and Evaluate Human Lower Limb Motions

This paper presents a wearable sensor approach to motion measurements of human lower limbs, in which subjects perform specified walking trials at self-administered speeds so that their level walking and stair ascent capacity can be effectively evaluated. After an initial sensor alignment with the reduced error, quaternion is used to represent 3-D orientation and an optimized gradient descent algorithm is deployed to calculate the quaternion derivative. Sensors on the shank offer additional information to accurately determine the instances of both swing and stance phases. The Denavit-Hartenberg convention is used to set up the kinematic chains when the foot stays stationary on the ground, producing state constraints to minimize the estimation error of knee position. The reliability of this system, from the measurement point of view, has been validated by means of the results obtained from a commercial motion tracking system, namely, Vicon, on healthy subjects. The step size error and the position estimation accuracy change are studied. The experimental results demonstrated that the extensively existed sensor misplacement and sensor drift problems can be well solved. The proposed self-contained and environment-independent system is capable of providing consistent tracking of human lower limbs without significant drift

Novel cloning machine with supplementary information

Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying superposition of multiple clones simultaneously. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI). For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived. Our investigation generalizes and completes the results in the literature.Comment: 22 pages; the presentation is revised, and some typos are correcte

Applications of MEMS Gyroscope for Human Gait Analysis

After decades of development, quantitative instruments for human gait analysis have become an important tool for revealing underlying pathologies manifested by gait abnormalities. However, the gold standard instruments (e.g., optical motion capture systems) are commonly expensive and complex while needing expert operation and maintenance and thereby be limited to a small number of specialized gait laboratories. Therefore, in current clinical settings, gait analysis still mainly relies on visual observation and assessment. Due to recent developments in microelectromechanical systems (MEMS) technology, the cost and size of gyroscopes are decreasing, while the accuracy is being improved, which provides an effective way for qualifying gait features. This chapter aims to give a close examination of human gait patterns (normal and abnormal) using gyroscope-based wearable technology. Both healthy subjects and hemiparesis patients participated in the experiment, and experimental results show that foot-mounted gyroscopes could assess gait abnormalities in both temporal and spatial domains. Gait analysis systems constructed of wearable gyroscopes can be more easily used in both clinical and home environments than their gold standard counterparts, which have few requirements for operation, maintenance, and working environment, thereby suggesting a promising future for gait analysis

A String-Inspired Quintom Model Of Dark Energy

We propose in this paper a quintom model of dark energy with a single scalar field $\phi$ given by the lagrangian ${\cal L}=-V(\phi)\sqrt{1-\alpha^\prime\nabla_{\mu}\phi\nabla^{\mu}\phi +\beta^\prime \phi\Box\phi}$. In the limit of $\beta^\prime\to$0 our model reduces to the effective low energy lagrangian of tachyon considered in the literature. We study the cosmological evolution of this model, and show explicitly the behaviors of the equation of state crossing the cosmological constant boundary.Comment: 6 pages, 4 figures, accepted by PL

Hydrate-based CO2 (carbon dioxide) capture from IGCC (integrated gasification combined cycle) synthesis gas using bubble method with a set of visual equipment

The hydrate-based carbon dioxide (CO2) capture from the integrated gasification combined cycle (IGCC) synthesis gas using the bubble method is investigated with a set of visual equipment in this work. The gas bubble is created with a bubble plate on the bottom of the equipment. By the visual equipment, the hydrate formation and the hydrate shape are visually captured. With the move of the gas bubble from the bottom to the top of the reactor, gas hydrate forms firstly from the gas-liquid boundary around the bubble, then the hydrate gradually grows up and piles up in the bottom side of the bubble to form a hydrate particle. The gas hydrate shape is affected by the gas flow rate. The hydrate is acicular crystal at the low gas flow rate while the hydrate is fine sand-like crystal at the high gas flow rate. The bubble size and the gas flow rate have an obvious impact on the hydrate-based CO2 separation process. The experimental results show the gas bubble of 50 mu m and the gas flow rate of 6.75 mL/min/L are ideal for CO2 capture from IGCC synthesis gas under the condition of 3.0 MPa and 274.15 K. (C) 2012 Elsevier Ltd. All rights reserved.</p