A composition theorem for parity kill number

In this work, we study the parity complexity measures ${\mathsf{C}^{\oplus}_{\min}}[f]$ and ${\mathsf{DT^{\oplus}}}[f]$. ${\mathsf{C}^{\oplus}_{\min}}[f]$ is the \emph{parity kill number} of $f$, the fewest number of parities on the input variables one has to fix in order to "kill" $f$, i.e. to make it constant. ${\mathsf{DT^{\oplus}}}[f]$ is the depth of the shortest \emph{parity decision tree} which computes $f$. These complexity measures have in recent years become increasingly important in the fields of communication complexity \cite{ZS09, MO09, ZS10, TWXZ13} and pseudorandomness \cite{BK12, Sha11, CT13}. Our main result is a composition theorem for ${\mathsf{C}^{\oplus}_{\min}}$. The $k$-th power of $f$, denoted $f^{\circ k}$, is the function which results from composing $f$ with itself $k$ times. We prove that if $f$ is not a parity function, then ${\mathsf{C}^{\oplus}_{\min}}[f^{\circ k}] \geq \Omega({\mathsf{C}_{\min}}[f]^{k}).$ In other words, the parity kill number of $f$ is essentially supermultiplicative in the \emph{normal} kill number of $f$ (also known as the minimum certificate complexity). As an application of our composition theorem, we show lower bounds on the parity complexity measures of $\mathsf{Sort}^{\circ k}$ and $\mathsf{HI}^{\circ k}$. Here $\mathsf{Sort}$ is the sort function due to Ambainis \cite{Amb06}, and $\mathsf{HI}$ is Kushilevitz's hemi-icosahedron function \cite{NW95}. In doing so, we disprove a conjecture of Montanaro and Osborne \cite{MO09} which had applications to communication complexity and computational learning theory. In addition, we give new lower bounds for conjectures of \cite{MO09,ZS10} and \cite{TWXZ13}

Style-Label-Free: Cross-Speaker Style Transfer by Quantized VAE and Speaker-wise Normalization in Speech Synthesis

Cross-speaker style transfer in speech synthesis aims at transferring a style from source speaker to synthesised speech of a target speaker's timbre. Most previous approaches rely on data with style labels, but manually-annotated labels are expensive and not always reliable. In response to this problem, we propose Style-Label-Free, a cross-speaker style transfer method, which can realize the style transfer from source speaker to target speaker without style labels. Firstly, a reference encoder structure based on quantized variational autoencoder (Q-VAE) and style bottleneck is designed to extract discrete style representations. Secondly, a speaker-wise batch normalization layer is proposed to reduce the source speaker leakage. In order to improve the style extraction ability of the reference encoder, a style invariant and contrastive data augmentation method is proposed. Experimental results show that the method outperforms the baseline. We provide a website with audio samples.Comment: Published to ISCSLP 202

Improving Prosody for Cross-Speaker Style Transfer by Semi-Supervised Style Extractor and Hierarchical Modeling in Speech Synthesis

Cross-speaker style transfer in speech synthesis aims at transferring a style from source speaker to synthesized speech of a target speaker's timbre. In most previous methods, the synthesized fine-grained prosody features often represent the source speaker's average style, similar to the one-to-many problem(i.e., multiple prosody variations correspond to the same text). In response to this problem, a strength-controlled semi-supervised style extractor is proposed to disentangle the style from content and timbre, improving the representation and interpretability of the global style embedding, which can alleviate the one-to-many mapping and data imbalance problems in prosody prediction. A hierarchical prosody predictor is proposed to improve prosody modeling. We find that better style transfer can be achieved by using the source speaker's prosody features that are easily predicted. Additionally, a speaker-transfer-wise cycle consistency loss is proposed to assist the model in learning unseen style-timbre combinations during the training phase. Experimental results show that the method outperforms the baseline. We provide a website with audio samples.Comment: Accepted by ICASSP202

Observation of a red-blue detuning asymmetry in matter-wave superradiance

We report the first experimental observations of strong suppression of matter-wave superradiance using blue-detuned pump light and demonstrate a pump-laser detuning asymmetry in the collective atomic recoil motion. In contrast to all previous theoretical frameworks, which predict that the process should be symmetric with respect to the sign of the pump-laser detuning, we find that for condensates the symmetry is broken. With high condensate densities and red-detuned light, the familiar distinctive multi-order, matter-wave scattering pattern is clearly visible, whereas with blue-detuned light superradiance is strongly suppressed. In the limit of a dilute atomic gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let

Network during light-induced cotyledons opening and greening in Astragalus membranaceus

Opening and greening are main characteristics of morphogenesis of cotyledons. For revealing interrelationship between metabolism and morphogenesis, metabolic shifts were analyzed in cotyledon of A. membranaceus seedlings with different stages in light and in darkness. Light induced 69 metabolites (MA), related to cotyledon greening; additional 89 metabolites (MB), related to cotyledon opening, were identified by WGCNA. The screening of metabolites shared in both MA and MB obtained 37 specific metabolites (MC) related to both opening and greening. In this context, main changes in MC occurred during A3, the stage in which cotyledons fully opened and greened. Within MC, few sugars, including L-(-)-sorbose, mannose, glucose and its derivatives, markedly decreased, while other sugars, amino acids, and unsaturated fatty acids increased. Most isoflavones and flavonols including ononin, caycosin-7-glucosides, quercetin, genistein, and catechin increased 5.3, 5.5, 13.4, 6.4 and 1.8 times, respectively. Thus, accumulated flavonoids play an important role during this developmental stage. © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group

Hybrid multi-strategy chaos somersault foraging chimp optimization algorithm research

To address the problems of slow convergence speed and low accuracy of the chimp optimization algorithm (ChOA), and to prevent falling into the local optimum, a chaos somersault foraging ChOA (CSFChOA) is proposed. First, the cat chaotic sequence is introduced to generate the initial solutions, and then opposition-based learning is used to select better solutions to form the initial population, which can ensure the diversity of the algorithm at the beginning and improve the convergence speed and optimum searching accuracy. Considering that the algorithm is likely to fall into local optimum in the final stage, by taking the optimal solution as the pivot, chimps with better adaptation at the mirror image position replace chimps from the original population using the somersault foraging strategy, which can increase the population diversity and expand the search scope. The optimization search tests were performed on 23 standard test functions and CEC2019 test functions, and the Wilcoxon rank sum test was used for statistical analysis. The CSFChOA was compared with the ChOA and other improved intelligent optimization algorithms. The experimental results show that the CSFChOA outperforms most of the other algorithms in terms of mean and standard deviation, which indicates that the CSFChOA performs well in terms of the convergence accuracy, convergence speed and robustness of global optimization in both low-dimensional and high-dimensional experiments. Finally, through the test and analysis comparison of two complex engineering design problems, the CSFChOA was shown to outperform other algorithms in terms of optimal cost. For the design of the speed reducer, the performance of the CSFChOA is 100% better than other algorithms in terms of optimal cost; and, for the design of a three-bar truss, the performance of the CSFChOA is 6.77% better than other algorithms in terms of optimal cost, which verifies the feasibility, applicability and superiority of the CSFChOA in practical engineering problems