With recent advancements in next-generation data storage, especially in biological molecule-based storage, insertion, deletion, and substitution (IDS) error-correcting codes have garnered increased attention. However, a universal method for designing tailored IDS-correcting codes across varying channel settings remains underexplored. We present an autoencoder-based approach, THEA-code, aimed at efficiently generating IDS-correcting codes for complex IDS channels. In the work, a disturbance-based discretization is proposed to discretize the features of the autoencoder, and a simulated differentiable IDS channel is developed as a differentiable alternative for IDS operations. These innovations facilitate the successful convergence of the autoencoder, producing channel-customized IDS-correcting codes that demonstrate commendable performance across complex IDS channels, particularly in realistic DNA-based storage channels.

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance remain open, making the invention of a novel IDS-correcting code a hard task. Furthermore, current studies on single-IDS-correcting code misalign with the requirements of applications which necessitates the correcting of multiple errors. Compromise solutions have involved shortening codewords to reduce the chance of multiple errors. However, the code rates of existing codes are poor at short lengths, diminishing the overall storage density. In this study, a novel method is introduced for designing high-code-rate single-IDS-correcting codewords through deep Levenshtein distance embedding. A deep learning model is utilized to project the sequences into embedding vectors that preserve the Levenshtein distances between the original sequences. This embedding space serves as a proxy for the complex Levenshtein domain, within which algorithms for codeword search and segment correcting is developed. While the concept underpinning this approach is straightforward, it bypasses the mathematical challenges typically encountered in code design. The proposed method results in a code rate that outperforms existing combinatorial solutions, particularly for designing short-length codewords.

Efficient computation or approximation of Levenshtein distance, a widely-used metric for evaluating sequence similarity, has attracted significant attention with the emergence of DNA storage and other biological applications. Sequence embedding, which maps Levenshtein distance to a conventional distance between embedding vectors, has emerged as a promising solution. In this paper, a novel neural network-based sequence embedding technique using Poisson regression is proposed. We first provide a theoretical analysis of the impact of embedding dimension on model performance and present a criterion for selecting an appropriate embedding dimension. Under this embedding dimension, the Poisson regression is introduced by assuming the Levenshtein distance between sequences of fixed length following a Poisson distribution, which naturally aligns with the definition of Levenshtein distance. Moreover, from the perspective of the distribution of embedding distances, Poisson regression approximates the negative log likelihood of the chi-squared distribution and offers advancements in removing the skewness. Through comprehensive experiments on real DNA storage data, we demonstrate the superior performance of the proposed method compared to state-of-the-art approaches.

Graph Convolutional Network (GCN) is an important method for learning graph representations of nodes. For large-scale graphs, the GCN could meet with the neighborhood expansion phenomenon, which makes the model complexity high and the training time long. An efficient solution is to adopt graph sampling techniques, such as node sampling and random walk sampling. However, the existing sampling methods still suffer from aggregating too many neighbor nodes and ignoring node feature information. Therefore, in this paper, we propose a new subgraph sampling method, namely, Similarity-Aware Random Walk (SARW), for GCN with large-scale graphs. A novel similarity index between two adjacent nodes is proposed, describing the relationship of nodes with their neighbors. Then, we design a sampling probability expression between adjacent nodes using node feature information, degree information, neighbor set information, etc. Moreover, we prove the unbiasedness of the SARW-based GCN model for node representations. The simplified version of SARW (SSARW) has a much smaller variance, which indicates the effectiveness of our subgraph sampling method in large-scale graphs for GCN learning. Experiments on six datasets show our method achieves superior performance over the state-of-the-art graph sampling approaches for the large-scale graph node classification task.

Storing information in DNA molecules is of great interest because of its advantages in longevity, high storage density, and low maintenance cost. A key step in the DNA storage pipeline is to efficiently cluster the retrieved DNA sequences according to their similarities. Levenshtein distance is the most suitable metric on the similarity between two DNA sequences, but it is inferior in terms of computational complexity and less compatible with mature clustering algorithms. In this work, we propose a novel deep squared Euclidean embedding for DNA sequences using Siamese neural network, squared Euclidean embedding, and chi-squared regression. The Levenshtein distance is approximated by the squared Euclidean distance between the embedding vectors, which is fast calculated and clustering algorithm friendly. The proposed approach is analyzed theoretically and experimentally. The results show that the proposed embedding is efficient and robust.

In recent years, the non-biological applications of DNA molecules have made considerable progress; most of these applications were performed in vitro, involving biochemical operations such as synthesis, amplification and sequencing. Because errors may occur with specific sequence patterns or experimental instruments, these biochemical operations are not completely reliable. Modeling errors in these biochemical procedures is an interesting research topic. For example, researchers have proposed several methods to avoid the known vulnerable sequence patterns in the study of storing binary information in DNA molecules. However, there are few end-to-end methods to evaluate these biochemical errors with regard to the DNA sequences. In this article, based on the data generated by a DNA storage research, we use artificial neural networks to predict whether a DNA sequence tends to cause errors in biochemical operations. Through comparative experiments and hyperparameter optimization, we analyze the known and potential problems in the research process. As a result, an end-to-end method to model the biochemical errors of DNA molecules in vitro through a computer system is proposed.

The unmixing of hyperspectral data is a hot topic in the field of remote sensing. However, in presence of various types of noise, especially the noisy channels, the performance of unmixing approaches is seriously deteriorated. To enhance the robustness of the unmixing method is a subject worth studying. This paper presents a robust unmixing method based on the recently-proposed multilinear mixing model, where the l2,1norm is adopted in the loss function to suppress the influence of noise. The sparseness of abundance is also considered to improve the parameter estimation. The resulting optimization problem is solved by the alternating direction multiplier method (ADMM). Experiments on both synthetic and real images demonstrate the performance of the proposed unmixing strategy.

To improve the classification performance in the context of hyperspectral image (HSI) processing, many works have been developed based on two common strategies, namely, the spatial–spectral information integration and the utilization of neural networks. However, both strategies typically require more training data than the classical algorithms, aggregating the shortage of labeled samples. In this letter, we propose a novel framework that organically combines the spectrum-based deep metric learning (DML) model and the conditional random field (CRF) algorithm. The DML model is supervised by the center loss to produce spectrum-based features that gather more tightly in Euclidean space within classes. The CRF with Gaussian edge potentials, which is first proposed for image segmentation tasks, is introduced to give the pixel-wise classification over the HSI by utilizing both the geographical distances between pixels and the Euclidean distances between the features produced by the DML model. The proposed framework is trained by spectral pixels at the DML stage and utilizes the half handcrafted spatial features at the CRF stage. This settlement alleviates the shortage of training data to some extent. Experiments on two real HSIs demonstrate the advantages of the proposed method in terms of both classification accuracy and computation cost.

In this paper, we propose a spectral-spatial feature extraction and classification framework based on an artificial neuron network in the context of hyperspectral imagery. With limited labeled samples, only spectral information is exploited for training and spatial context is integrated posteriorly at the testing stage. Taking advantage of recent advances in face recognition, a joint supervision symbol that combines softmax loss and center loss is adopted to train the proposed network, by which intraclass features are gathered while interclass variations are enlarged. Based on the learned architecture, the extracted spectrum-based features are classified by a center classifier. Moreover, to fuse the spectral and spatial information, an adaptive spectral-spatial center classifier is developed, where multiscale neighborhoods are considered simultaneously, and the final label is determined using an adaptive voting strategy. Finally, experimental results on three well-known data sets validate the effectiveness of the proposed methods compared with the state-of-the-art approaches.

The shortage of training samples remains one of the main obstacles in applying the neural networks to the hyperspectral images classification. To fuse the spatial and spectral information, pixel patches are often utilized to train a model, which may further aggregate this problem. In the existing works, an artificial neural network (ANN) model supervised by centerloss (ANNC) was introduced. Training merely with spectral information, the ANNC yields discriminative spectral features suitable for the subsequent classification tasks. In this paper, we propose a novel convolutional neural network (CNN)-based spatial feature fusion (CSFF) algorithm, which allows a smart integration of spatial information to the spectral features extracted by ANNC. As a critical part of CSFF, a CNN-based discriminant model is introduced to estimate whether two pixels belong to the same class. At the testing stage, by applying the discriminant model to the pixel pairs generated by a test pixel and each of its neighbors, the local structure is estimated and represented as a customized convolutional kernel. The spectral-spatial feature is generated by a convolutional operation between the estimated kernel and the corresponding spectral features within a local region. The final label is determined by classifying the resulting spectral-spatial feature. Without increasing the number of training samples or involving pixel patches at the training stage, the CSFF framework achieves the state of the art by declining 20%-50% classification failures in experiments on three well-known hyperspectral images.

Given a sequence $s=(s_1,s_2,\ldots )$ of positive integers, the notion of inversion sequences with respect to $s$, or $s$-inversion sequences, was introduced by Savage and Schuster in their study of lecture hall polytopes. A sequence $(e_1,e_2,\ldots,e_n)$ of nonnegative integers is called an $s$-inversion sequence of length $n$ if $0\leq e_i < s_i$ for $1\leq i\leq n$. Let $I_n$ be the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\ldots)$---that is, $s_{2i-1}=2i-1$ and $s_{2i}=4i$ for $i\geq1$---and let $P_n$ be the set of signed permutations on the multiset $\{1^2,2^2,\ldots,n^2\}$. Savage and Visontai conjectured that the descent number over $P_n$ is equidistributed with the ascent number over $I_{2n}$. In this paper, we give a proof of this conjecture by using $P$-partitions of type $B$. (Lin independently obtained a proof based on recurrence relations.) Moreover, we find a set of signed permutations over which the descent number is equidistributed with the ascent number over $I_{2n-1}$. Let $I'_n$ be the set of $s$-inversion sequences of length $n$ for $s=(2,2,6,4,10,6,\ldots)$; that is, $s_{2i-1}=4i-2$ and $s_{2i}=2i$ for $i\geq1$. We also find two sets of signed permutations over which the descent number is equidistributed with the ascent number over $I'_n$, depending on the parity of $n$.