Mixed-precision methods offer the potential to achieve better performance while maintaining accuracy comparable to that of high-precision formats. However, the adoption of mixed precision—particularly with 16-bit formats—in scientific computing remains limited due to precision truncation.

Large language models (LLMs), representing a breakthrough advancement in artificial intelligence, have demonstrated substantial application value and development potential in bioinformatics research, particularly showing significant progress in the processing and analysis of complex biological data. This comprehensive review systematically examines the development and applications of LLMs in bioinformatics, with particular emphasis on their advancements in protein and nucleic acid structure prediction, omics analysis, drug design and screening, and biomedical literature mining. This work highlights the distinctive capabilities of LLMs in end-to-end learning and knowledge transfer paradigms. Additionally, this paper thoroughly discusses the major challenges confronting LLMs in current applications, including key issues such as model interpretability and data bias. Furthermore, this review comprehensively explores the potential of LLMs in cross-modal learning and interdisciplinary development. In conclusion, this paper aims to systematically summarize the current research status of LLMs in bioinformatics, objectively evaluate their advantages and limitations, and provide insights and recommendations for future research directions, thereby positioning LLMs as essential tools in bioinformatics research and fostering innovative developments in the biomedical field.

Due to the increasing size of datasets and complexity of models, distributed machine learning is becoming increasingly important. Among the various components of distributed machine learning frameworks, the all-reduce operation holds significant importance, particularly in terms of communication costs among computing nodes. The all-reduce operation distributes to all nodes one or more reductions of data symbols from all nodes. This operation is used in distributed machine learning for aggregating data from computing nodes during the training and synchronizing the results among all computing nodes. This paper considers a distributed system consisting of computing nodes which are connected with each other via one-hop links. The data symbols are encoded and stored in the computing nodes. This paper focuses on the so-called all-linear-reduce operation which distributes to all nodes one or more linear combinations of data symbols from all nodes. This paper aims to determine the optimal bandwidth for the linear all-reduce operation, for an arbitrarily given distributed system. We propose a universal all-linear-reduce operation, which has been proven to achieve the optimal bandwidth in some cases.

Real-world distributed storage systems (DSSs) are heterogeneous because storage nodes may have unequal per-symbol storage costs, and network links may have unequal per-symbol transmission costs. For some general classes of heterogeneous DSSs, the optimal tradeoff between storage and repair costs achievable by functional repair codes is known (at least numerically). However, it is unclear whether exact-repair codes can achieve any point of such an optimal storage-repair tradeoff curve, especially at the point of the minimum storage cost. In this paper, we provide an affirmative answer to the question by constructing the so-called heterogeneous minimum storage repair (HMSR) codes for both the average and worst-case repair costs. To optimize storage and repair costs, a heterogeneous DSS may need to adopt irregular array codes and repair a node by downloading unequal numbers of symbols from helper nodes. However, our results show that for almost all heterogeneous DSSs, exact-repair HMSR codes are regular array codes covering an adequately chosen set of nodes. Specifically, exact-repair HMSR codes are designed by stacking conventional MSR codes and applying different repair schemes to different layers. Still, this does not work for every heterogeneous DSS. It is proven that using regular or linear irregular array codes for constructing exact-repair HMSR codes is insufficient in some cases.

The Asymmetrical Numeral Systems (ANS) coding has received significant attention in well-integrated compression systems. One particularly insightful technique that has emerged is the interleaved ANS coder (IAC), which substantially enhances the throughput by using multiple encoders and decoders. However, IAC has a limitation that even a single bit error in the compressed bitstream may diffuse across multiple decoders, resulting in many symbols to be incorrectly decoded. In this paper, we propose a parallel method to mitigate the diffusion for a class of error patterns, by limiting the errors to affect only a single decoder. The simulation results show that compared with IAC, our proposal can reduce the average number of incorrectly decoded symbols by about 50% while maintaining comparable encoding and decoding throughput.

In an erasure-coded distributed storage system (DSS), requesting a file requires downloading information from multiple storage nodes, called servers, which leads to cross-server network traffic. The cross-server transmission cost can be reduced if these servers are equipped with extra memory to cache some information about the files. This paper considers the so-called cache-aided DSS (CADSS), where each server is connected to several caching proxies through a shared link, and studies the transmission cost incurred by file requests. For simplicity, we focus on a CADSS in which the servers are connected via a one-hop link, and each server is connected to the same number of caching proxies. When the caching proxies receive file requests, a server first downloads some symbols from the other servers, called the helper servers, and then broadcasts some symbols to the caching proxies. For a single server, the maximum number of symbols downloaded from the helper nodes (respectively broadcast to its caching proxies) normalized by the file size is called the cross-server (respectively local) reads. This paper first optimizes the cross-server and local reads separately. Whether from the perspective of optimizing cross-server or local reads, a CADSS can be interpreted as an equivalent single-server caching system but with different system parameters. This paper analyzes the optimal tradeoff between the cross-server and local reads. It is shown that the optimal cross-server and local reads can be achieved simultaneously for some parameters, while a tradeoff exists for some other parameters. We characterize the two extreme points of the optimal tradeoff curve and derive the optimal tradeoff for some specific parameters.

Based on the Reed-Muller (RM) transform, this paper proposes a Reed-Solomon (RS) encoding/erasure decoding algorithm for any number of parities. Specifically, we first generalize the previous RM-based syndrome calculation, which allows only up to seven parities, to support any number of parities. Then we propose a general encoding/erasure decoding algorithm. The proposed encoding algorithm eliminates the operations in solving linear equations, and this improves the computational efficiency of existing RM-based RS algorithms. In terms of erasure decoding, this paper employs the generalized RM-based syndrome calculation and lower–upper (LU) decomposition to accelerate the computational efficiency. Analysis shows that the proposed encoding/erasure decoding algorithm approaches the complexity of$\lfloor \lg T \rfloor + 1$XORs per data bit with$N$increasing, where$T$and$N$denote the number of parities and codeword length respectively. To highlight the advantage of the proposed RM-based algorithms, the implementations with Single Instruction Multiple Data (SIMD) technology are provided. Simulation results show that the proposed algorithms are competitive, as compared with other cutting-edge implementations.

In this paper, the problem of designing the maximum-distance-separable (MDS) array codes for repairing a single node failure in a distributed storage system (DSS) is addressed. We consider the class of heterogeneous DSSs which can be represented as a fully connected storage network consisting of links having possibly different per-symbol transmission costs and assume that the repair process only allows a single-hop transmission from any helper node to a failed node. First, we consider the repair cost of a failed node to be the total transmission cost from all helper nodes incurred by the repair process. For a storage network represented by a complete weighted graph with the weights being the persymbol transmission costs, we derive a repair cost lower bound of every node. Somewhat surprisingly, even for a storage network represented by a complete weighted graph with time-varying weights, we can also construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes. Next, we consider the repair cost of a failed node to be the worst-case transmission cost over all helper nodes incurred by the repair process. For a storage network represented by a static complete weighted graph, we derive a lower bound on the repair cost of every node and construct a single optimal-repair-cost MDS array code that can achieve the repair cost lower bounds of all nodes.

In this paper, we consider two rack-aware storage systems. First, large-scale rack-aware storage system, which is very common in large-scale storage system, is a rack-aware storage system where all sizes of racks are at least the number of redundant nodes. For such storage system, we prove that any Maximum Distance Separable (MDS) codes can have optimal inter-rack repair bandwidth and give a closed-form representation of all repair schemes with optimal inter-rack repair bandwidth. Furthermore, we show that the optimal repair access and optimal inter-rack repair bandwidth can be attained simultaneously for such storage system. Second, we investigate the rack-aware storage system of all racks with the same size, which is called uniform rack-aware storage system. We prove that, except the trivial cases, we cannot attain optimal inter-rack repair bandwidth and optimal repair access for such storage system at the same time. Specifically, we establish the lower bound of repair access for a repair scheme with optimal interrack repair bandwidth, which is tight for some parameters, and also the tight lower bound of inter-rack repair bandwidth for a repair scheme with optimal repair access.

Regenerating codes are designed to reduce the repair bandwidth (access bandwidth) for rebuilding a fail node in an erasure-coded storage system. In practical systems, the fail node is not rebuilt immediately. Before its rebuilding, the data originally stored in the failed node might be accessed by the system. Hence, accessing the data in the failed disk (degraded read) with low latency is crucial for any practical storage system. In this work, to solve this problem, a new class of the regenerating codes based on the maximum distance separable (MDS) array codes is defined, named the MDS array code with the property of degraded read friendly (DRF). For the DRF MDS array codes with 2 redundant nodes and the sub-packetization level of 2, the lower bound of their access bandwidth is derived. A class of the DRF MDS array codes that achieves the derived bound is given to solidify the achievability of the proposed lower bound.

In this paper, we consider the update bandwidth in distributed storage systems (DSSs). The update bandwidth, which measures the transmission efficiency of the update process in DSSs, is defined as the average amount of data symbols transferred in the network when the data symbols stored in a node are updated. This paper contains the following contributions. First, we establish the closed-form expression of the minimum update bandwidth attainable by irregular array codes. Second, after defining a class of irregular array codes, called Minimum Update Bandwidth (MUB) codes, which achieve the minimum update bandwidth of irregular array codes, we determine the smallest code redundancy attainable by MUB codes. Third, the code parameters, with which the minimum code redundancy of irregular array codes and the smallest code redundancy of MUB codes can be equal, are identified, which allows us to define MR-MUB codes as a class of irregular array codes that simultaneously achieve the minimum code redundancy and the minimum update bandwidth. Fourth, we introduce explicit code constructions of MR-MUB codes and MUB codes with the smallest code redundancy. Fifth, we establish a lower bound of the update complexity of MR-MUB codes, which can be used to prove that the minimum update complexity of irregular array codes may not be achieved by MR-MUB codes. Last, we construct a class of$(n = k + 2, k)$vertical maximum-distance separable (MDS) array codes that can achieve all of the minimum code redundancy, the minimum update bandwidth and the optimal repair bandwidth of irregular array codes.

In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove lower bounds of encoding circuit size required in the encoding of (punctured) Hadamard codes and (extended) Hamming codes. Then the encoding algorithms for (extended) Hamming codes are presented to achieve the derived lower bounds.

In this paper, we consider the update bandwidth in distributed storage systems. The update bandwidth is defined as the bandwidth when the data storage in a node is updated. The minimum update bandwidth for irregular array codes is provided. Further, we minimize the code redundancy when the update bandwidth is minimal. Finally, we introduce a class of vertical MDS codes that minimizes both update bandwidth and code redundancy.