Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

Uniformities for the convergence in law and in probability

The convergence (X _n, Y_n)0 is investigated and characterized for probability metrics which metrize convergence in distribution or in probability. Some related metrics are also considered.     

Semi-Supervised Cross-Subject Emotion Recognition Based on Stacked Denoising Autoencoder Architecture Using a Fusion of Multi-Modal Physiological Signals

In recent decades, emotion recognition has received considerable attention. As more enthusiasm has shifted to the physiological pattern, a wide range of elaborate physiological emotion data features come up and are combined with various classifying models to detect one’s emotional states. To circumvent the labor of artificially designing features, we propose to acquire affective and robust representations automatically through the Stacked Denoising Autoencoder (SDA) architecture with unsupervised pre-training, followed by supervised fine-tuning. In this paper, we compare the performances of different features and models through three binary classification tasks based on the Valence-Arousal-Dominance (VAD) affection model. Decision fusion and feature fusion of electroencephalogram (EEG) and peripheral signals are performed on hand-engineered features; data-level fusion is performed on deep-learning methods. It turns out that the fusion data perform better than the two modalities. To take advantage of deep-learning algorithms, we augment the original data and feed it directly into our training model. We use two deep architectures and another generative stacked semi-supervised architecture as references for comparison to test the method’s practical effects. The results reveal that our scheme slightly outperforms the other three deep feature extractors and surpasses the state-of-the-art of hand-engineered features.     

An Algorithm Framework for Drug-Induced Liver Injury Prediction Based on Genetic Algorithm and Ensemble Learning

In the process of drug discovery, drug-induced liver injury (DILI) is still an active research field and is one of the most common and important issues in toxicity evaluation research. It directly leads to the high wear attrition of the drug. At present, there are a variety of computer algorithms based on molecular representations to predict DILI. It is found that a single molecular representation method is insufficient to complete the task of toxicity prediction, and multiple molecular fingerprint fusion methods have been used as model input. In order to solve the problem of high dimensional and unbalanced DILI prediction data, this paper integrates existing datasets and designs a new algorithm framework, Rotation-Ensemble-GA (R-E-GA). The main idea is to find a feature subset with better predictive performance after rotating the fusion vector of high-dimensional molecular representation in the feature space. Then, an Adaboost-type ensemble learning method is integrated into R-E-GA to improve the prediction accuracy. The experimental results show that the performance of R-E-GA is better than other state-of-art algorithms including ensemble learning-based and graph neural network-based methods. Through five-fold cross-validation, the R-E-GA obtains an ACC of 0.77, an F1 score of 0.769, and an AUC of 0.842.     

Gabor Analysis on Finite Product of Cyclic Groups

We present a complete characterization of Gabor frame operators on finite dimensional Hilbert space $L^2(\Gamma)$, where $\Gamma = \mathbb{Z}_{m_1} \times \mathbb{Z}_{m_2} \times \dots \times \mathbb{Z}_{m_p}$ and $m_1,m_2,\dots,m_p$ are positive integers. The notion of generalized $B$-modulation and generalized $B$-translation is introduced and some significant properties of the generalized pseudo $B$-Gabor like frames are discussed.     

Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics

In Phys. Lett. A 313 (2003) 343 we have found that the self-reciprocal Hankel transformation (HT) is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations' transformation in quantum mechanics.     

Deep Multilabel Multilingual Document Learning for Cross-Lingual Document Retrieval

Cross-lingual document retrieval, which aims to take a query in one language to retrieve relevant documents in another, has attracted strong research interest in the last decades. Most studies on this task start with cross-lingual comparisons at the word level and then represent documents via word embeddings, which leads to insufficient structure information. In this work, the cross-lingual comparison at the document level is achieved through the cross-lingual semantic space. Our method, MDL (deep multilabel multilingual document learning), leverages a six-layer fully connected network to project cross-lingual documents into a shared semantic space. The semantic distances can be calculated when the cross-lingual documents are transformed into embeddings in semantic space. The supervision signals are automatically extracted from the data and then used to construct the semantic space via a linear classifier. The ambiguity of manual labels could be avoided and the multilabel supervision signals can be acquired instead of a single label. The representation of the semantic space is enriched by multilabel supervision signals, which improves the discriminative ability of the embeddings. The MDL is easy to extend to other fields since it does not depend on specific data. Furthermore, MDL is more efficient than the models training all languages jointly, since each language is trained individually. Experiments on Wikipedia data showed that the proposed method outperforms the state-of-the-art cross-lingual document retrieval methods.     

一类非线性边值问题正解的存在性

本文运用锥上的不动点理论,讨论了一类与一阶导函数有关的二阶奇性混合边值问题的正解存在性．     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Statistical replacement for systems with delta-correlated fluctuations

Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable.