One-Pass Learning with Incremental and Decremental Features

In many real tasks the features are evolving, with some features being vanished and some other features augmented. For example, in environment monitoring some sensors expired whereas some new ones deployed; in mobile game recommendation some games dropped whereas some new ones added. Learning with such incremental and decremental features is crucial but rarely studied, particularly when the data coming like a stream and thus it is infeasible to keep the whole data for optimization. In this paper, we study this challenging problem and present the OPID approach. Our approach attempts to compress important information of vanished features into functions of survived features, and then expand to include the augmented features. It is the one-pass learning approach, which only needs to scan each instance once and does not need to store the whole data, and thus satisfy the evolving streaming data nature. The effectiveness of our approach is validated theoretically and empirically

B\to K_1\pi(K) decays in the perturbative QCD approach

Within the framework of the perturbative QCD approach, we study the two-body charmless decays $B\to K_1(1270)(K_1(1400))\pi(K)$. We find the following results: (i) The decays $\bar B^0\to K_1(1270)^+\pi^-, K_1(1400)^+\pi^-$ are incompatible with the present experimental data. There exists a similar situation for the decays $\bar B^0\to a_1(1260)^+K^-, b_1(1235)^+K^-$, which are usually considered that the nonperturbative contributions are needed to explain the data. But the difference is that the nonperturbative contributions seem to play opposite roles in these two groups of decays.(ii) The pure annihilation type decays $\bar B^0\to K_1^{\pm}(1270)K^{\mp}, K_1^{\pm}(1400)K^{\mp}$ are good channels to test whether an approach can be used to calculate correctly the strength of the penguin-annihilation amplitudes. Their branching ratios are predicted at $10^{-7}$ order, which are larger than the QCDF results. (iii) The dependence of the direct CP-violating asymmetries of these decays on the mixing angle $\theta_{K_1}$ are also considered.Comment: 18 pages, 4 figure

qq-Analogues of some series for powers of π\pi

We obtain $q$-analogues of several series for powers of $\pi$. For example, the identity $$\sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)^3}=\frac{\pi^3}{32}$$ has the following $q$-analogue: \begin{equation*} \sum_{k=0}^\infty(-1)^k\frac{q^{2k}(1+q^{2k+1})}{(1-q^{2k+1})^3}=\frac{(q^2;q^4)_{\infty}^2(q^4;q^4)_{\infty}^6} {(q;q^2)_{\infty}^4}, \end{equation*} where $q$ is any complex number with $|q|<1$. We also give $q$-analogues of four new series for powers of $\pi$ found by the second author.Comment: 10 pages. Add Theorem 1.

Hydrogen influence on generalized stacking fault of zirconium basal plane: a first-principles calculation study

The infuences of hydrogen on the generalized stacking fault (GSF) energies of the basal plane along the and directions in the hcp Zr were investigated using the first-principles calculation method. The modifications of the GSF energies were studied with respect to the different distances of H atoms away from the slip plane and hydrogen content there. The calculation results have shown that the GSF energies along the direction drastically reduce when H atoms locate nearby the slip plane. But H atoms slightly decrease the GSF barrier for the slipping case. Meanwhile, with the increase of hydrogen density around the slip plane, the GSF energies along both the two shift directions further reduced greatly. The physical origin of the reduction of GSF energies due to the existence of hydrogen atoms in Zr was analyzed based on the Bader charge method. It is interpreted by the Coulomb repulsion of the Zr atoms beside the slip plane due to the charge transfer from Zr to H

Learning with Interpretable Structure from Gated RNN

The interpretability of deep learning models has raised extended attention these years. It will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks~(RNNs) especially gated RNNs whose inner mechanism is still not clearly understood. We find that Finite State Automaton~(FSA) that processes sequential data has more interpretable inner mechanism according to the definition of interpretability and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. With the learned FSA and via experiments on artificial and real datasets, we find that FSA is more trustable than the RNN from which it learned, which gives FSA a chance to substitute RNNs in applications involving humans' lives or dangerous facilities. Besides, we analyze how the number of gates affects the performance of RNN. Our result suggests that gate in RNN is important but the less the better, which could be a guidance to design other RNNs. Finally, we observe that the FSA learned from RNN gives semantic aggregated states and its transition graph shows us a very interesting vision of how RNNs intrinsically handle text classification tasks

Structure, elastic and bonding properties of hcp ZrxTi1-x binary alloy from first-principles calculations

First principles calculations were performed to study the structural, elastic, and bonding properties of hcp ZrxTi1-x binary alloy. The special quasi- random structure (SQS) method is employed to mimic the random hcp ZrxTi1-x alloy. It is found that Bulk modulus, B, Young's modulus, E, and shear modulus, G, exhibit decreasing trends as increasing the amount of Zr. A ductile behavior ZrxTi1-x is predicted in the whole composition range. In terms of Mulliken charge analisis, we found that the element Ti behaves much more electronegative than Zr in hcp ZrxTi1-x alloy, and the charge transfer of an atom is approximately linear to the amount of other element atom surrounding it

On monotonicity of some combinatorial sequences

We confirm Sun's conjecture that (\root{n+1}\of{F_{n+1}}/\root{n}\of{F_n})_{n\ge 4} is strictly decreasing to the limit 1, where $(F_n)_{n\ge0}$ is the Fibonacci sequence. We also prove that the sequence (\root{n+1}\of{D_{n+1}}/\root{n}\of{D_n})_{n\ge3} is strictly decreasing with limit $1$, where $D_n$ is the $n$-th derangement number. For $m$-th order harmonic numbers $H_n^{(m)}=\sum_{k=1}^n 1/k^m\ (n=1,2,3,\ldots)$, we show that$(\root{n+1}\of{H^{(m)}_{n+1}}/\root{n}\of{H^{(m)}_n})_{n\ge3}$ is strictly increasing.Comment: 10 page

On qq-analogues of some series for π\pi and π2\pi^2

We obtain a new $q$-analogue of the classical Leibniz series $\sum_{k=0}^\infty(-1)^k/(2k+1)=\pi/4$, namely \begin{equation*} \sum_{k=0}^\infty\frac{(-1)^kq^{k(k+3)/2}}{1-q^{2k+1}}=\frac{(q^2;q^2)_{\infty}(q^8;q^8)_{\infty}}{(q;q^2)_{\infty}(q^4;q^8)_{\infty}}, \end{equation*} where $q$ is a complex number with $|q|<1$. We also show that the Zeilberger-type series $\sum_{k=1}^\infty(3k-1)16^k/(k\binom{2k}k)^3=\pi^2/2$ has two $q$-analogues with $|q|<1$, one of which is $$\sum_{n=0}^\infty q^{n(n+1)/2} \frac {1-q^{3n+2}} {1-q} \cdot\frac{(q;q)_n^3 (-q;q)_n}{(q^3;q^2)_{n}^3} = (1-q)^2 \frac{(q^2;q^2)^4_\infty}{(q;q^2)^4_\infty}.$$Comment: 11 page

Learning with Feature Evolvable Streams

Learning with streaming data has attracted much attention during the past few years. Though most studies consider data stream with fixed features, in real practice the features may be evolvable. For example, features of data gathered by limited-lifespan sensors will change when these sensors are substituted by new ones. In this paper, we propose a novel learning paradigm: \emph{Feature Evolvable Streaming Learning} where old features would vanish and new features would occur. Rather than relying on only the current features, we attempt to recover the vanished features and exploit it to improve performance. Specifically, we learn two models from the recovered features and the current features, respectively. To benefit from the recovered features, we develop two ensemble methods. In the first method, we combine the predictions from two models and theoretically show that with the assistance of old features, the performance on new features can be improved. In the second approach, we dynamically select the best single prediction and establish a better performance guarantee when the best model switches. Experiments on both synthetic and real data validate the effectiveness of our proposal

Compare Contact Model-based Control and Contact Model-free Learning: A Survey of Robotic Peg-in-hole Assembly Strategies

In this paper, we present an overview of robotic peg-in-hole assembly and analyze two main strategies: contact model-based and contact model-free strategies. More specifically, we first introduce the contact model control approaches, including contact state recognition and compliant control two steps. Additionally, we focus on a comprehensive analysis of the whole robotic assembly system. Second, without the contact state recognition process, we decompose the contact model-free learning algorithms into two main subfields: learning from demonstrations and learning from environments (mainly based on reinforcement learning). For each subfield, we survey the landmark studies and ongoing research to compare the different categories. We hope to strengthen the relation between these two research communities by revealing the underlying links. Ultimately, the remaining challenges and open questions in the field of robotic peg-in-hole assembly community is discussed. The promising directions and potential future work are also considered