Matrix-Monotonic Optimization for MIMO Systems

For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables e.g., precoders, equalizers, training sequences, etc. are usually matrices. It is well known that matrix operations are usually more complicated compared to their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.Comment: 37 Pages, 5 figures, IEEE Transactions on Signal Processing, Final Versio

Application of Nonlinear Dynamical Methods for Arc Welding Quality Monitoring

Owing to its diverse, the stability of arc signals in high-powered submerged arc welding is not very salient, and weld defects are difficult to detect automatically. Aimed at this problem, this paper proposes a noise robustness algorithm for calibrating the singularity points and denoting the kinetics and stability of arc. Firstly, reconstruct a vector, which is the calculation of the approximate entropy in phase space, denotes the distortion of arc. Then, a algorithm for calculation is given based on reconstruction of chaotic time series in phase space. Finally, we apply the calculation of approximate entropy algorithm in phase space to flaw detection for arc signals, which is efficient proved by experimental results

What limits the simulation of quantum computers?

It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. Real quantum computing devices, however, are characterized by an exponentially decaying fidelity $\mathcal{F} \sim (1-\epsilon)^{ND}$ with an error rate $\epsilon$ per operation as small as $\approx 1\%$ for current devices. In this work, we demonstrate that real quantum computers can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wavefunctions using matrix product states (MPS), which capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $\epsilon$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$. We illustrate our algorithms with simulations of random circuits for qubits connected in both one and two dimensional lattices. We find that $\epsilon$ can be decreased at a polynomial cost in computing power down to a minimum error $\epsilon_\infty$. Getting below $\epsilon_\infty$ requires computing resources that increase exponentially with $\epsilon_\infty/\epsilon$. For a two dimensional array of $N=54$ qubits and a circuit with Control-Z gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor three for similar computing time.Comment: New data added, 14 figure

Periodontal health and quality of life in patients with chronic obstructive pulmonary disease

SummaryObjectiveTo evaluate the association of periodontal health and parameters of quality of life assessed in 306 Chinese patients with chronic obstructive pulmonary disease (COPD).MethodsPeriodontal status and respiratory function in 306 COPD patients were clinically evaluated and their quality of life was assessed using the standardized St George’s Respiratory Questionnaire (SGRQ).ResultsThe SGRQ scores were all significantly correlated with major lung function parameters (r2 = −0.37 to −0.28; all p < 0.0001) and Medical Research Council dyspnoea scale (r2 = 0.23 to 0.30; all p < 0.0001). The SGRQ scores also correlated with the 6-min walk test (r2 = −0.15 to −0.13; all p < 0.05). Of periodontal health parameters, missing tooth number and plaque index appeared to be related to the scores of quality of life. The age- and gender-adjusted Pearson’s correlation coefficients between missing teeth and total score, symptoms score, and activity score were 0.09, 0.12, and 0.12, respectively (all p < 0.05). The Pearson’s correlation coefficients between plaque index and symptoms score and activity score were 0.09 and 0.09 (p < 0.05). After adjusting for age, gender, body mass index, and smoking status, missing teeth remained significantly associated with symptom score (p = 0.030) and activity score (p = 0.033) while plaque index was significantly associated with symptom score (p = 0.007).ConclusionsPoor periodontal health as reflected by missing teeth and plaque index was significantly associated with lower quality of life in COPD patients. Our findings indicate the importance of promoting dental care in current public health strategies to improve the quality of life in COPD patients

Efficacy of Er:YAG laser on periodontitis as an adjunctive non‐surgical treatment: A split‐mouth randomized controlled study

Aim To evaluate the adjunctive efficacy of Er:YAG laser use with mechanical scaling and root planing (SRP ) for non‐surgical treatment of periodontitis. Materials and Methods In a randomized, single‐blinded, controlled trial, 27 patients were recruited. Using a split‐mouth design, two quadrants were randomly allocated into either a test group or a control group. The test quadrants received Er:YAG laser (ERL ; 100 mJ /pulse; 15 Hz to hard tissue and 50 mJ /pulse; 30 Hz to soft tissue) plus SRP treatment, while the control quadrants received SRP only. We evaluated periodontal indexes, including probing depth (PD ), clinical attachment level (CAL ), bleeding index (BI ), and plaque index (PLI ) at baseline, 3 months, and 6 months. Results The PD and CAL means in the ERL + SRP group were significantly lower than those in the SRP group at 3‐month follow‐up (PD : 2.98 ± 0.38 mm vs. 3.09 ± 0.35 mm; CAL : 4.51 ± 0.69 mm vs. 4.72 ± 0.67 mm) and 6‐month follow‐up (PD : 2.91 ± 0.31 mm vs. 3.02 ± 0.30 mm; CAL : 4.52 ± 0.65 mm vs. 4.72 ± 0.66 mm; p = 0.03 for both PD and CAL ). There were no significant differences in BI and PLI between two groups. Conclusions The Er:YAG laser treatment combined with conventional SRP significantly improved PD and CAL compared to SRP therapy alone; however, these differences were very small and, as a result, the adjunctive effect of Er:YAG laser is likely to be minimal clinically important