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We previously proposed the first nontrivial examples of a code having support $t$-designs for all weights obtained from the Assmus-Mattson theorem and having support $t'$-designs for some weights with some $t'>t$. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus-Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code $\mathcal{G}_{24}$.

In this paper we generalize Dillon's switching method to characterize the exact $c$-differential uniformity of functions constructed via this method. More precisely, we modify some PcN/APcN and other functions with known $c$-differential uniformity in a controllable number of coordinates to render more such functions. We present several applications of the method in constructing PcN and APcN functions with respect to all $c\neq 1$. As a byproduct, we generalize some result of [Y. Wu, N. Li, X. Zeng, {\em New PcN and APcN functions over finite fields}, Designs Codes Crypt. 89 (2021), 2637--2651]. Computational results rendering functions with low differential uniformity, as well as, other good cryptographic properties are sprinkled throughout the paper.

Linear mixed models (LMMs) are instrumental for regression analysis with structured dependence, such as grouped, clustered, or multilevel data. However, selection among the covariates--while accounting for this structured dependence--remains a challenge. We introduce a Bayesian decision analysis for subset selection with LMMs. Using a Mahalanobis loss function that incorporates the structured dependence, we derive optimal linear coefficients for (i) any given subset of variables and (ii) all subsets of variables that satisfy a cardinality constraint. Crucially, these estimates inherit shrinkage or regularization and uncertainty quantification from the underlying Bayesian model, and apply for any well-specified Bayesian LMM. More broadly, our decision analysis strategy deemphasizes the role of a single "best" subset, which is often unstable and limited in its information content, and instead favors a collection of near-optimal subsets. This collection is summarized by key member subsets and variable-specific importance metrics. Customized subset search and out-of-sample approximation algorithms are provided for more scalable computing. These tools are applied to simulated data and a longitudinal physical activity dataset, and demonstrate excellent prediction, estimation, and selection ability.

Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. In this paper, we construct more general generator polynomials for two classes of MDS symbol-pair codes with code length $lp$. Based on repeated-root cyclic codes, we derive all MDS symbol-pair codes of length $3p$, when the degree of the generator polynomials is no more than 10. We also give two new classes of (almost maximal distance separable) AMDS symbol-pair codes with the length $lp$ or $4p$ by virtue of repeated-root cyclic codes. For length $3p$, we derive all AMDS symbol-pair codes, when the degree of the generator polynomials is less than 10. The main results are obtained by determining the solutions of certain equations over finite fields.

Generalized pair weights of linear codes are generalizations of minimum symbol-pair weights, which were introduced by Liu and Pan \cite{LP} recently. Generalized pair weights can be used to characterize the ability of protecting information in the symbol-pair read wire-tap channels of type II. In this paper, we introduce the notion of generalized $b$-symbol weights of linear codes over finite fields, which is a generalization of generalized Hamming weights and generalized pair weights. We obtain some basic properties and bounds of generalized $b$-symbol weights which are called Singleton-like bounds for generalized $b$-symbol weights. As examples, we calculate generalized weight matrices for simplex codes and Hamming codes. We provide a necessary and sufficient condition for a linear code to be a $b$-symbol MDS code by using the generator matrix and the parity check matrix of this linear code. Finally, a necessary and sufficient condition of a linear isomorphism preserving $b$-symbol weights between two linear codes is obtained. As a corollary, we get the classical MacWilliams extension theorem when $b=1$.

Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature is becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, Chignolin and Bovine Pancreatic Trypsin Inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.

Images can convey rich semantics and induce various emotions in viewers. Recently, with the rapid advancement of emotional intelligence and the explosive growth of visual data, extensive research efforts have been dedicated to affective image content analysis (AICA). In this survey, we will comprehensively review the development of AICA in the recent two decades, especially focusing on the state-of-the-art methods with respect to three main challenges -- the affective gap, perception subjectivity, and label noise and absence. We begin with an introduction to the key emotion representation models that have been widely employed in AICA and description of available datasets for performing evaluation with quantitative comparison of label noise and dataset bias. We then summarize and compare the representative approaches on (1) emotion feature extraction, including both handcrafted and deep features, (2) learning methods on dominant emotion recognition, personalized emotion prediction, emotion distribution learning, and learning from noisy data or few labels, and (3) AICA based applications. Finally, we discuss some challenges and promising research directions in the future, such as image content and context understanding, group emotion clustering, and viewer-image interaction.

In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation 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) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism 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. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.

Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.