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Abstract Culter alburnus is extensively distributed in various rivers and lakes across China. As a widely adaptive fish species, it has significant economic values and special ecological roles. To meet research demands and provide better genomic resources, in this research, a chromosome-level genome assembly was constructed using HiFi long-reads and Hi-C sequencing data. Compared with the published versions, our genome assembly is of higher quality with only 31 gaps and closer to its true structure and sequence. The genome size was 1.052 Gb, with a contig N50 of 32.92 Mb and a scaffold N50 of 43.09 Mb. 55 contigs were anchored to 24 chromosomes on the basis of Hi-C data. A total of 598.23 Mb of repetitive sequences were annotated and 28,228 protein-coding genes were predicted. Additionally, BUSCO assessment indicated assembly and annotation scores of 98.3% and 99.2%, respectively. This high-quality genome will provide scientific support for excavating the species characteristics of C. alburnus and exploring its molecular mechanisms in response to environmental changes and stress.

Abstract Sinosolenaia oleivora (Bivalve, Unionida, Unionidae), is a near-endangered edible mussel. In 2022, it was selected by the Ministry of Agriculture and Rural Affairs as a top-ten aquatic germplasm resource, with potential for industrial development. Using Illumina, PacBio, and Hi-C technology, a high-quality chromosome-level genome of S. oleivora was assembled. The assembled S. oleivora genome spanned 2052.29 Mb with a contig N50 size of 20.36 Mb and a scaffold N50 size of 103.57 Mb. The 302 contigs, accounting for 98.41% of the total assembled genome, were anchored into 19 chromosomes using Hi-C scaffolding. A total of 1171.78 Mb repeat sequences were annotated and 22,971 protein-coding genes were predicted. Compared with the nearest ancestor, a total of 603 expanded and 1767 contracted gene families were found. This study provides important genomic resources for conservation, evolutionary research, and genetic improvements of many economic traits like growth performance.

Ammonia is a common toxicant in aquatic systems and one of the key factors affecting aquaculture. However, data on mollusks’ toxic response and coping mechanisms to ammonia nitrogen, especially freshwater mollusks, are still lacking. In this study, we evaluated the tolerance of a freshwater mollusk Solenaia oleivora to ammonia and investigated its coping mechanisms by combining physiological, metabolic, and transcriptomic analyses in the gills. The acute toxicity test revealed that the LC50–96 h (temperature-20 ℃, pH-7.4) of ammonia in S. oleivora was 63.29 mg/L. The physiological and TUNEL results showed that although 10 mg/L ammonia exposure increased the activities of antioxidant, immune and ammonia detoxification-related enzymes, it still caused oxidative damage and cell apoptosis of gill tissues. A total of 97 differential metabolites (DMs) and 3431 differential expressed genes (DEGs) were identified after ammonia stress. Among them, most DMs and DEGs were involved in immune response, antioxidant, cell apoptosis, carbohydrate metabolism, amino acid metabolism, and lipid metabolism. The enhancement of glycolysis and lipid metabolisms may provide energy for immune response and ammonia detoxification. In addition, glutamine synthesis, alanine synthesis and urea cycle were involved in ammonia nitrogen detoxification in the gill tissue of S. oleivora. Our results indicate that ammonia leads to individual death in S. oleivora, as wells as oxidative damage, cell apoptosis, immune response, and metabolic changes of gill tissues. The findings will provide valuable information to assess the potential ecological risk of environmental ammonia to freshwater mollusks and theoretical guidance for the healthy aquaculture of S. oleivora.

Through-wall radar human body pose recognition technology has broad applications in both military and civilian sectors. Identifying the current pose of targets behind walls and predicting subsequent pose changes are significant challenges. Conventional methods typically utilize radar information along with machine learning algorithms such as SVM and random forests to aid in recognition. However, these approaches have limitations, particularly in complex scenarios. In response to this challenge, this paper proposes a cross-modal supervised through-wall radar human body pose recognition method. By integrating information from both cameras and radar, a cross-modal dataset was constructed, and a corresponding deep learning network architecture was designed. During training, the network effectively learned the pose features of targets obscured by walls, enabling accurate pose recognition (e.g., standing, crouching) in scenarios with unknown wall obstructions. The experimental results demonstrated the superiority of the proposed method over traditional approaches, offering an effective and innovative solution for practical through-wall radar applications. The contribution of this study lies in the integration of deep learning with cross-modal supervision, providing new perspectives for enhancing the robustness and accuracy of target pose recognition.

The artificial propagation of the endangered Solenaia oleivora, with unknown fish hosts, was performed via in vitro culture with bighead carp, grass carp, common carp, bovine, and rabbit sera. The effects of glochidium density on transformation rates were evaluated, and the development of juveniles that metamorphosed successfully was documented. The control group had a transformation rate of 0 and a contamination rate of 0. No significant differences were found in the transformation and contamination rates of the bighead carp, grass carp, and common carp serum groups, and their transformation rates were significantly higher, and contamination rates were significantly lower than those of the bovine and rabbit serum groups. Moreover, no significant differences were observed in the transformation rates of glochidia (culture density, 2000–5000 glochidia/dish) in contamination-free conditions. Specimen shell length/height increased from 1.08 ± 0.01 on the first day to 3.08 ± 0.29 during the 13th week. On the basis of anterior and posterior growth differences, juvenile growth was divided into the following three phases: the rapid anterior growth period, distinct anterior and posterior idiophase, and rapid posterior growth period. This study not only provides technological support for the artificial propagation of S. oleivora but also lays a foundation for resource recovery.

The rapid mutations on hemagglutinin (HA) of influenza A virus (IAV) can lead to significant antigenic variance and consequent immune mismatch of vaccine strains. Thus, rapid antigenicity evaluation is highly desired. The subtype-specific antigenicity models have been widely used for common subtypes such as H1 and H3. However, the continuous emerging of new IAV subtypes requires the construction of universal antigenic prediction model which could be applied on multiple IAV subtypes, including the emerging or re-emerging ones. In this study, we presented Univ-Flu, series structure-based universal models for HA antigenicity prediction. Initially, the universal antigenic regions were derived on multiple subtypes. Then, a radial shell structure combined with amino acid indexes were introduced to generate the new three-dimensional structure based descriptors, which could characterize the comprehensive physical–chemical property changes between two HA variants within or across different subtypes. Further, by combining with Random Forest classifier and different training datasets, Univ-Flu could achieve high prediction performances on intra-subtype (average AUC of 0.939), inter-subtype (average AUC of 0.771), and universal-subtype (AUC of 0.978) prediction, through independent test. Results illustrated that the designed descriptor could provide accurate universal antigenic description. Finally, the application on high-throughput antigenic coverage prediction for circulating strains showed that the Univ-Flu could screen out virus strains with high cross-protective spectrum, which could provide in-silico reference for vaccine recommendation.

It is important to detect foodborne pathogens in food and water, such as Listeria monocytogenes (L.monocytrogenes), which can cause foodborne illness in people with compromised immune systems. Volatile organic compounds (VOC) and 3‑hydroxy-2-butanone (3H-2B) produced by L.monocytrogenes can be used as biomarkers for indirect detection of microbial contamination. In this study, the mesoporous ZnO@CO3O4 nanosphere was prepared through the simple hydrothermal synthesis method of ZIF-l-Zn@Co, the cage construction of mesoporous ZnO@CO3O4 nanosphere was remained unchanged after the calcination of the ZIF-l-Zn@Co at 600 °C for 2 h in air. The mesoporous ZnO@CO3O4 nanosphere was selected as the gas sensor showed the strongest response to 3H-2B, and 7–12 times higher than the response of other test gases. In addition, compared with ZnO and Co3O4 single metal oxide gas sensor, the ZnO@CO3O4 sensor possessed better repeatability and stability after repeated repeatability tests under the same conditions.

With the decrease in biodiversity in freshwater ecosystems, the monitoring of fish has become a current research hotspot. The eDNA-based method has been applied to a variety of single-type water systems (i.e., rivers, lakes, or oceans), but it has not been applied to river–lake-connected systems. We collected eDNA from water samples from the Changjiang River–Shijiu Lake connected system (including the lake area, river channel, and river section) and discussed the fish diversity characteristics of the connected system. A total of 180 samples were collected, and the fish community was analyzed using eDNA metabarcoding of the mitochondrial 12 s region. We finally identified 66 taxa of fish, including one at the order level, two at the family level, 9 at the subfamily level, 20 at the genus level, and 34 annotated to the species level. The number of fish species in the river–lake connected system was greater than that in a single-type water system. The lake area, river channel, and river section had a high degree of overlap in fish composition, and the maximum number of fish was in the river section. There was no significant difference in α diversity index among the three types of waters, but there were significant differences in fish relative abundance, which was dominated by different species. The distribution of three migratory fish (Elopichthys bambusa, Ctenopharyngodon idella, and Hypophthalmichthyinae sp.) accorded with the unique life history migration strategy in the middle and lower reaches of the Changjiang River. Our results provide detailed data on fish diversity and have important implications for the long-term management and conservation of river–lake connected systems in the lower reaches of the Changjiang River. Our research further proves that eDNA can be used to monitor the biodiversity of river–lake connected systems and reflect their spatial characteristics. As a continuously explored method, eDNA shows great potential in the study of fish diversity in river–lake systems.

In this paper, an electrochemical sensing platform based on gold nanoparticle modified carbon nanofiber (CNF@AuNPs) as working electrode is proposed for the high sensitivity and selective determination of metronidazole. Meanwhile, the sensor has a large linear response range from 0.1 to 2000 μM, the limit of detection for metronidazole (MNZ) is as low as 0.024 μM. The sensor is simple to prepare and reproducible, and it shows good results in MNZ analysis of tap water.

The genetic diversity in the naked carp (Gymnocypris przewalskii) of China is threatened by climate change, human activities, as well as natural factors, eliciting conservation concerns. To explore the genetic aspects of G. przewalskii, the genetic diversity, genetic structure, population differentiation, and historical demography of 566 representative individuals from seven geographically distinct ranges of Qinghai Lake were evaluated by mitochondrial DNA cytochrome oxidase subunit I (COI) and D-loop sequences. Estimates of genetic parameters showed that the seven populations of G. przewalskii had high levels of haplotype diversity (0.50243–0.94620) and low levels of nucleotide diversity (0.00079–0.00624). Haplotype genealogy indicated there was no obvious phylogenetic pattern between haplotypes. Both markers denoted the absence of population genetic structure [the genetic differentiation coefficient F-statistics (Fst) < 0] and the presence of high genetic flow (COI: 0.9731–1.0441; D-loop: 0.9480–1.0398). The mismatch between the distribution and neutrality tests supported the evidence of population expansion, which occurred during the late middle Pleistocene [COI: 0.36–0.108 MYA (Million Years Ago); D-loop: 0.497–0.165 MYA]. Furthermore, this work illustrated two simple, reliable, and inexpensive molecular markers for analysis of genetic diversity, while the sensitivity of the mitochondrial D-loop region as a reflection of genetic diversity in G. przewalskii is higher than that of the COI gene.

The removal of the net enclosure has been used as a lake management strategy in various regions of China as ecological development is given more attention. Nevertheless, little is known about the substantive impact of this measure on fish communities in inland lakes. To this end, the fish community composition and structural features after the removal of the net enclosure in Gehu Lake were explored and evaluated in this study from 2021 to 2022 and compared to the investigation before the net enclosure removal from 2017 to 2018. Belonging to 7 orders, 10 families, and 46 species, a total of 17,151 fish were collected, with pelagic, sedentary, and omnivorous species dominating. In comparison, the number of species increased by 10 after removal, and fish alpha diversity increased. The Index of Relative Importance (IRI) revealed that the composition of dominating species remained constant, including Coilia nasus, Hypophthalmichthys molitrix, and Hypophthalmichthys nobilis; Parabramis pekinensis, Megalobrama amblycephal, and Culter mongolicus were upgraded from common species to general species. Culter alburnus, Hemiculter bleekeri, and Pseudobrama simoni were downgraded from general species to common species. Elopichthys bambusa had become a common species (IRI = 109.35), which was not discovered before removal. According to the hierarchical clustering (HC) and non-metric multidimensional sequencing (NMDS), the fish community of the northern reserve was highly aggregated. As the Abundance Biomass Comparison (ABC) curve and biodiversity index indicated, the fish community structure of the whole lake was in a state of moderate anthropogenic disturbance with reduced stability, while that of the northern reserve was in a state of light anthropogenic disturbance with greater stability. The number of fish species increased in this survey compared to the period before removal, species and dominant species composition altered dramatically, and total lake stability declined. This study demonstrates that the fish diversity in Gehu Lake increased after the removal of the net enclosure. Meanwhile, the stability of the fish community structure was decreased temporarily. Lake restoration is a long-term process, and the underlying impact of the removal of the net enclosure still requires continuous monitoring and further studies.

In deep learning, the vanilla stochastic gradient descent (SGD) and SGD with heavy-ball momentum (SGDM) methods have a wide range of applications due to their simplicity and great generalization. This paper uses an exponential scaling method to realize a smooth and stable transition from SGDM to SGD, which combines the advantages of the fast training speed of SGDM and the accurate convergence of SGD (named TSGD). We also provide some theoretical results on the convergence of this algorithm. At the same time, we take advantage of the learning rate warmup strategy’s stability and the learning rate decay strategy’s high accuracy. A warmup–decay learning rate strategy with double exponential functions is proposed (named 2ExpLR). The experimental results on different datasets for the proposed algorithms indicate that the accuracy is improved significantly and that the training is faster and more stable.

Salinity is an important ecological factor affecting the osmolality of aquatic animals. Solenaia oleivora is an endemic and economically important freshwater shellfish in China. However, its osmotic response and osmoregulatory mechanisms under high salinity stress are still unclear. In this study, S. oleivora was exposed to saline water (salinity: 2.2‰) for 3 h, 6 h, 12 h, 24 h, and 48 h, and then the changes in osmolality, ion concentrations, free amino acid (FAA) content, Na+/K+-ATPase (NKA) activity, and gill histology were analyzed. The hemolymph osmolality increased from 3 h after salinity stress and stabilized between 24–48 h. Na+ in the hemolymph increased from 24 h after salinity stress, and Cl− increased from 3 h. The content of total FAAs in the hemolymph increased after salinity stress. The content of alanine, glycine, glutamine, proline, and other FAAs increased after salinity stress. NKA activity in the gill, hepatopancreases, adductor muscle, and axe foot decreased during 3–48 h of salinity stress. The gill filament space increased and the number of gill cilia decreased after salinity stress. Principal component analysis (PCA) showed that the first two principal components (PC1 and PC2) cumulatively explained 77.6% of the total variation. The NKA activity was positively associated with PC1, while the ion concentration and most FAAs were negatively associated with PC1. Thus, these results indicated that S. oleivora is an osmoconformer, and inorganic ions, FAA, NKA, and gill structure changes play an important role in its osmoregulation.

Using systemic, periodic surveys from 2015 to 2019, population distribution, speculated age and habitat preference were analyzed to assess the living status for the Silver Carp (Hypophthalmichthys molitrix) in the lower Yangtze River. Small Silver Carps became more temporarily abundant in spring and autumn, and the catch per unit effort (CPUE) fluctuated yearly. Spatially, going from Anqing (AQ) to Changshu (CS), Silver Carps in the 200 mm standard length(SL) group became less abundant, whereas those in the 400–600 mm and >600 mm SL groups steadily increased. According to the Von Bertalanffy growth equation, the Silver Carp exhibits isometric growth, and the inflection point of SL and body weight (BW) were 564.01mm and 2948.31g, respectively, with a growth characteristic index (φ) of 5.0655. The fish dominant age range was 0+ to 5 years, reflecting the young age composition of the fish. Furthermore, the habitat survey findings revealed that the Silver Carp has the different preference on habitat selection in different life history. Juvenile Silver Carps were comparatively staying in the lower Yangtze River, where there exists a relatively stable bifurcated river. Adult fishes were mostly found in the CS and Nantong(NT) section where the river is wide and the food is rich. When compared with the historical survey data, it was found that the Silver Carp live in the AQ through NT section. The living status and perspective of the Silver Carp in the lower reach of the Yangtze River were clarified, and future work should be more concerned with the strengthening of conservation and the restoration of adequate habitat.

Agricultural nonpoint source pollution is a critical issue that causes eutrophication in water bodies, due to the application of fertilizers. The traditional rice-fish coculture systems may develop a novel sustainable agriculture. The present study was undertaken to understand the ecological mechanisms of integrated fish farming especially water chemistry, dynamics of plankton, and benthic populations and their community compositions. In the rice-fish coculture system (RF), the total nitrogen in the water was higher compared to the rice monoculture system (RM), but significantly lower than in conventional fertilized rice farming. Dissolved oxygen (DO) presented a significant “Month x Treatment” interaction (p

The intelligent transportation system (ITS) is inseparable from people’s lives, and the development of artificial intelligence has made intelligent video surveillance systems more widely used. In practical traffic scenarios, the detection and tracking of vehicle targets is an important core aspect of intelligent surveillance systems and has become a hot topic of research today. However, in practical applications, there is a wide variety of targets and often interference factors such as occlusion, while a single sensor is unable to collect a wealth of information. In this paper, we propose an improved data matching method to fuse the video information obtained from the camera with the millimetre-wave radar information for the alignment and correlation of multi-target data in the spatial dimension, in order to address the problem of poor recognition alignment caused by mutual occlusion between vehicles and external environmental disturbances in intelligent transportation systems. The spatio-temporal alignment of the two sensors is first performed to determine the conversion relationship between the radar and pixel coordinate systems, and the calibration on the timeline is performed by Lagrangian interpolation. An improved Hausdorff distance matching algorithm is proposed for the data dimension to calculate the similarity between the data collected by the two sensors, to determine whether they are state descriptions of the same target, and to match the data with high similarity to delineate the region of interest (ROI) for target vehicle detection.

Low-head dams are a ubiquitous human disturbance in headwater streams. The effects of low-head dams on stream fish assemblages have gathered increasing interest in the past 20 years; whereas, the effects remain controversial among the existing studies. In this study, we collected fishes from 58 impoundments created by low-head dams and 58 reference free-flowing segments below or above dams within headwater streams of four basins in Wannan Mountains, China. We used the beta diversity, including taxonomic and functional indices based on species composition and species traits, respectively, to quantify the degree to which fish assemblages were altered by low-head dams by comparing pairwise assemblages between impoundment and reference free-flowing segment for each dam surveyed. We aimed to assess whether taxonomic and functional beta diversities varied across the 58 low-head dams surveyed and how beta diversities related to local habitat, landscape conditions, and dam size measures. We found that both taxonomic and functional beta diversities showed quite high spatial variation, with the coefficient of variance of 54.47% and 76.74%, which were dominated by species turnover (68.8%) and functional nestedness (62.8%), respectively. Taxonomic beta diversity, functional beta diversity and functional turnover rate significantly varied across basins, and taxonomic turnover and nestedness rates significantly varied between reference types (i.e., free-flowing segments below vs. above dams). We also found that taxonomic beta diversity, functional beta diversity, and functional turnover rates significantly related to local habitat and/or landscape conditions. Environmental factors explained more spatial variances in functional diversity than taxonomic diversity. Our results suggest that the effects of low-head dams on fish assemblages vary spatially across different dams and relates to environmental factors. In addition, our results highlight the need for reliable approaches for assessing the effects of low-head dams on stream fish assemblages.

Early prevention and monitoring of Ralstonia solanacearum (Rs) on nightshade is extremely critical for potent prevention and treatment of bacterial wilt disease. We developed two kinds of lateral flow immunochromatographic strip (LFICS) using gold nanoparticles (GNPs) and fluorescein isothiocyanate (FITC) for rapid diagnosis of plant bacterial wilt, caused by Ralstonia solanacearum (Rs), which both were based on double antibody sandwich method. Three monoclonal antibodies (McAb) highly specific to Rs were obtained by cell fusion and screening after four times of immunization with the strain GIM 1.76. Under optimized conditions, the limit of detection (LOD) with GNPs and FITC were 104 colony forming units per millilitre (CFU/mL) and 106 CFU/mL respectively, then the range detection correspondingly were 104–109 CFU/mL and 106–109 CFU/mL. On top of that, the developed immunoassay could be used for spot and point-of-care testing Rs on tomato seed, ginger seed, casuarina seed and display no cross-reaction with 43 other phytopathogenic strains that also could infect plants so as to cause plants diseases. These results demonstrated that we sucessfully developed two simple, effective and sensitive strips for monitoring bacterial wilt infection. Meanwhile, this is the first report about LFICS labelled by FITC for rapid detection of Rs, and it is the first time conformed that the sensitive of the LFICS with GNPs is significantly higher than FITC.

Drug-resistant cases of human immunodeficiency virus (HIV) nucleoside reverse transcriptase inhibitors (NRTI) are constantly accumulating due to the frequent mutations of the reverse transcriptase (RT). Predicting the potential drug resistance of HIV-1 NRTIs could provide instructions for the proper clinical use of available drugs. In this study, a novel proteochemometric (PCM) model was constructed to predict the drug resistance between six NRTIs against different variants of RT. Forty-seven dominant mutation sites were screened using the whole protein of HIV-1 RT. Thereafter, the physicochemical properties of the dominant mutation sites can be derived to generate the protein descriptors of RT. Furthermore, by combining the molecular descriptors of NRTIs, PCM modeling can be constructed to predict the inhibition ability between RT variants and NRTIs. The results indicated that our PCM model could achieve a mean AUC value of 0.946 and a mean accuracy of 0.873 on the external validation set. Finally, based on PCM modeling, the importance of features was calculated to reveal the dominant amino acid distribution and mutation patterns on RT, to reflect the characteristics of drug-resistant sequences.

Listeria monocytogenes (LM) is a gram-positive facultative intracellular pathogen that could stimulate host to produce inflammatory response, cell-mediated immunity, and humoral immunity. In this study, an attenuated live vector vaccine for Aeromonas hydrophila (AH) named EGDeABdd-dat-ompW was successfully constructed using an attenuated vector named EGDeABdd, in which dal, dat, actA, and inlB genes were deleted from wild-type LM-EGDe. To construct EGDeABdd-dat-ompW, a recombinant plasmid pERL3-dat-ompW obtained by inserting the dat gene from EGDe and outer membrane protein gene ompW from AH into pERL3 plasmid was transformed into EGDeABdd cell. The safety and immunogenicity of EGDeABdd-dat-ompW as an attenuated vector vaccine for delivery of OMPW were assessed through analyzing invasion to Caco-2 cells and mice, cytokine production of macrophagocyte and mouse splenocytes, and T-cell proliferation of mouse splenocytes. Serum titers against AH and the immunoprotective effect of the vaccine to mice were also measured after intravenous injection with vaccine for four times. The results showed that the live vector vaccine EGDeABdd-dat-ompW for AH exhibited high attenuation in invading Caco-2 cells and mice than did EGDe. Real-time PCR (RT-PCR) showed that cytokines (e.g., TNF-α, IL-6, and IL-1β from macrophages; and IL-6 and IFN-γ from mouse splenocytes) had significantly increased after immunization by EGDeABdd-dat-ompW. Meanwhile, the vaccine could induce the production of CD3+CD4+ and CD3+CD8+ T-cell proliferation of mice and generate effective immunoprotection against lethal challenge of 20 × LD50 AH. All these results indicated that the attenuated EGDeABdd-dat could be used as a live vector for the delivery of the exogenous gene, not only possessing safety but also providing high immunogenicity. The successful application in the AH vaccine further showed that it could be used in other fields such as vaccines in cancer or infectious diseases.

Alcohol abuse is a major public health crisis. Relative evidences supported that the gut microbiota (GM) played an important role in central nervous system (CNS) function, and the composition of them had changed after alcohol drinking. We sought to explore the changes of GM in alcohol dependence. In our study, the GM of mice with alcohol administration was detected through analyzed 16S rRNA gene sequencing and the fecal metabolites were analyzed by LC-MS. The microbial diversity was significantly higher in the alcohol administration group, the abundance of phylum Firmicutes and its class Clostridiales were elevated, meanwhile the abundance of Lachnospiraceae, Alistipes, and Odoribacter showed significant differences among the three groups. Based on LC-MS results, bile acid, secondary bile acid, serotonin and taurine level had varying degrees of changes in alcohol model. From paraffin sections, tissue damage was observed in liver and colon. These findings provide direct evidence that alcohol intake affects the composition of GM, enable a better understanding of the function of GM in the microbiota-gut-brain (MGB) axis, and give a new thought for alcohol addiction treatment.

The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing. In this paper, we introduce novel dual relationships between the GHR calculus and multivariate real calculus, in order to provide a new, simpler proof of the GHR derivative rules. This further reinforces the theoretical foundation of the GHR calculus and provides a convenient methodology for generic extensions of real- and complex-valued learning algorithms to the quaternion domain.

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

The online gradient method has been widely used in training neural networks. We consider in this paper an online split-complex gradient algorithm for complex-valued neural networks. We choose an adaptive learning rate during the training procedure. Under certain conditions, by firstly showing the monotonicity of the error function, it is proved that the gradient of the error function tends to zero and the weight sequence tends to a fixed point. A numerical example is given to support the theoretical findings.