Matrix Factorization Research Articles

Evaluation of the potentially toxic elements and radionuclides in the soil sample of Novaya Zemlya in the Arctic Circle

The study presented here elucidate the concentrations of radionuclides and potentially toxic elements in the soil samples around the Novaya Zemlya in the Russian Arctic zone, determined using HPGe gamma spectrometry, inductively coupled plasma optical emission spectrometry and direct mercury analyzer. The average detected concentrations for 226Ra, 232Th, 40K, 235U and 137Cs were 36.40, 46.06, 768, 2.06 and 4.71 Bq/kg, respectively. At many sampling sites, the concentrations of potentially toxic elements (Zn, Cu, Pb, Cd, Ni, and Cr) were higher than the natural levels. Positive Matrix Factorization analysis revealed the contribution of oil dumps (32%), natural sources (16%), bird colonies (32%) and atmospheric deposition (20%) for elevated elements content. In the case of radionuclides, the natural occurring contamination (38%) was primary source followed by dumped material (32%) and bird colonies (30%). The radiological risk from radionuclides was relatively high, yet still under permissible levels. For potentially toxic elements, Fe was predominant non-carcinogenic pollutant and Ni emerged as major carcinogenic contaminant. Keeping in view the high content of some elements, future studies are required to keep the human and ecological risk low, and to establish scientific grounds for the contribution of settled bird species. The findings of the study advance the present knowledge about the contamination of the study area and lays the path for further effort.

Single cell atlas reveals multilayered metabolic heterogeneity across tumour types

Metabolic reprogramming plays a pivotal role in cancer progression, contributing to substantial intratumour heterogeneity and influencing tumour behaviour. However, a systematic characterization of metabolic heterogeneity across multiple cancer types at the single-cell level remains limited. We integrated 296 tumour and normal samples spanning six common cancer types to construct a single-cell compendium of metabolic gene expression profiles and identify cell type-specific metabolic properties and reprogramming patterns. A computational approach based on non-negative matrix factorization (NMF) was utilised to identify metabolic meta-programs (MMPs) showing intratumour heterogeneity. In-vitro cell experiments were conducted to confirm the associations between MMPs and chemotherapy resistance, as well as the function of key metabolic regulators. Survival analyses were performed to assess clinical relevance of cellular metabolic properties. Our analysis revealed shared glycolysis upregulation and divergent regulation of citric acid cycle across different cell types. In malignant cells, we identified a colorectal cancer-specific MMP associated with resistance to the cuproptosis inducer elesclomol, validated through in-vitro cell experiments. Furthermore, our findings enabled the stratification of patients into distinct prognostic subtypes based on metabolic properties of specific cell types, such as myeloid cells. This study presents a nuanced understanding of multilayered metabolic heterogeneity, offering valuable insights into potential personalized therapies targeting tumour metabolism. National Key Research and Development Program of China (2021YFA1300601). National Natural Science Foundation of China (key grants 82030081 and 81874235). The Shenzhen High-level Hospital Construction Fund and Shenzhen Basic Research Key Project (JCYJ20220818102811024). The Lam Chung Nin Foundation for Systems Biomedicine.

Improvement of E-commerce Recommender System Using Hybridization of Bert, Matrix Factorization and Attention Mechanism

Improvement of E-commerce Recommender System Using Hybridization of Bert, Matrix Factorization and Attention Mechanism

A survey on feature extraction and learning techniques for link prediction in homogeneous and heterogeneous complex networks

Complex networks are commonly observed in several real-world areas, such as social, biological, and technical systems, where they exhibit complicated patterns of connectedness and organised clusters. These networks have intricate topological characteristics that frequently elude conventional characterization. Link prediction in complex networks, like data flow in telecommunications networks, protein interactions in biological systems, and social media interactions on platforms like Facebook, etc., is an essential element of network analytics and presents fresh research challenges. Consequently, there is a growing emphasis in research on creating new link prediction methods for different network applications. This survey investigates several strategies related to link prediction, ranging from feature extraction based to feature learning based techniques, with a specific focus on their utilisation in dynamic and developing network topologies. Furthermore, this paper emphasises on a wide variety of feature learning techniques that go beyond basic feature extraction and matrix factorization. It includes advanced learning-based algorithms and neural network techniques specifically designed for link prediction. The study also presents evaluation results of different link prediction techniques on homogeneous and heterogeneous network datasets, and provides a thorough examination of existing methods and potential areas for further investigation.

Exposure to food additive mixtures and type 2 diabetes risk in the NutriNet-Santé cohort

Abstract Background So far, the safety evaluation of food additives has been performed substance by substance, while in real life, millions of individuals are exposed to mixtures of food additives daily. According to preliminary experimental data, some of these chemicals, alone and/or in synergy are suspected to impact metabolic health. The objective of this study was to investigate for the first time the associations between exposure to mixtures of food additives and type 2 diabetes (T2D) risk in a large prospective cohort of French adults. Methods Participants (n = 108,783, 79.2% women, mean age=42.4 years, SD = 14.6) from the NutriNet-Santé cohort (2009-2024) completed repeated 24h-dietary records, detailing industrial product brands. Additive exposure was assessed using composition databases and laboratory assays. Five mixtures of additives were identified through non-negative matrix factorisation (NMF). Associations between these mixtures and the risk of T2D were characterised using multivariable proportional hazards Cox models adjusted for known risk factors. Findings 1115 participants were identified with T2D during follow-up. Two additive mixtures were associated with increased T2D risk. The first mixture included higher exposure to modified starches E14xx, pectins E440, guar gum E412, carrageenan E407, and polyphosphates E452 (HRper 1SD increment=1.11 [1.05-1.18]), p < 0.0001). The second mixture comprised citric acid E330, sodium citrates E331, phosphoric acid E338, sulphite ammonia caramel E150d, acesulfame-K E950, aspartame E951, sucralose E955 and arabic gum E414 (HR1SD=1.13 [1.08-1.18]), p < 0.0001). Interpretation This large prospective cohort study revealed direct associations between T2D risk and exposure to two food additive mixtures. Molecular epidemiology and experimental studies will be necessary to depict underlying mechanisms and potential cocktail effects. Key messages • Consumed together, widely used food additives may contribute to T2D aetiology, shedding light on the detrimental impact of highly processed foods on metabolic health. • This study highlights positives associations between T2D risk and exposure to two food additive mixtures.

Matrix Factorization and Prediction for High-Dimensional Co-Occurrence Count Data via Shared Parameter Alternating Zero Inflated Gamma Model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

Collaborative filtering recommendation based on K-nearest neighbor and non-negative matrix factorization algorithm

Collaborative filtering recommendation based on K-nearest neighbor and non-negative matrix factorization algorithm

Enhanced Assessment of Water Quality and Pollutant Source Apportionment Using APCS-MLR and PMF Models in the Upper Reaches of the Tarim River

To evaluate the pollution sources and dynamics of the upper reaches of the Tarim River, 10 typical sampling points were selected, and 23 water quality parameters from 2020 to 2022 were analyzed using one-way analysis of variance, the comprehensive Water Quality Identification Index (WQI), and Principal Component Analysis (PCA). The pollution status, sources, and contribution rates of water quality were investigated using the Absolute Principal Component-Multiple Linear Regression Model (APCS-MLR) and Positive Matrix Factorization (PMF). The results indicated that the water quality parameters of dissolved oxygen (DO), chemical oxygen demand (CODMn), biochemical oxygen demand after 5 days (BOD5), total nitrogen (TN), total phosphorus (TP), fluoride ions (F-), and ammonia-nitrogen (NH3-N) in the upper reaches of the Tarim River exceed standards, with noticeable spatial variations observed for each parameter. The water quality evaluation grades in the upper reaches of Tarim River primarily indicate “moderate” and “good” levels, with DO, TN, NH3-N, and electrical conductivity (EC) being the key parameters influencing variations in water quality. The source analysis results from APCS-MLR and PMF yielded similar outcomes, identifying six potential pollution sources. Among these, soil weathering, livestock and poultry breeding, and agricultural activities exhibited higher contribution rates. Specifically, the contribution rates for these sources according to APCS-MLR were 44.11%, 19.63%, and 11.67%, respectively; while according to PMF they are 24.08%, 17.88%, and 27.54%, respectively. Furthermore, industrial pollution sources contributed at a rate of 6.01% according to APCS-MLR, while urban living sources contributed at a rate of 2.13%. However, based on PMF analysis, the contribution rates for industrial pollution sources increased significantly to 16.71%. Additionally, APCS-MLR identified natural sources as contributing at a rate of 16.45%, whereas PMF suggested that a combination of agricultural activities and natural sources contributed at a lower rate of only 9.52%. In conclusion, the water quality within the upper reaches of the Tarim River is predominantly satisfactory. Nonetheless, localized pollution, primarily attributable to human activities, presents a substantial challenge. These observations provide critical insights into improving and protecting the fragile water quality of the Tarim River.

Heavy metals in roadside soil along an expressway connecting two megacities in China: Accumulation characteristics, sources and influencing factors.

Transportation is widely recognized as a significant contributor to heavy metal (HM) pollution in roadside soils. A better understanding of HM pollution in soils near expressways is crucial, particularly given the rapid expansion of expressway transportation in China in recent years. In this study, 329 roadside topsoil samples were collected along the Beijing-Tianjin Expressway, which connects two megacities in China. Chemical analysis showed that HM concentrations in the soil samples were generally below national limits. The mean pollution index (Pi) values for As, Cr, Cu, Ni, Pb, and Zn ranged from 0.94 to 1.01, while Cd and Hg exhibited slightly higher mean Pi values of 1.19 and 1.13, respectively. The Nemerow integrated pollution index values for all samples ranged from 0.71 to 4.97, with a mean of 1.26. This suggests a slight enrichment of HM above natural background levels, especially for Cd and Hg. Source apportionment using positive matrix factorization revealed that natural sources contributed the most to soil HMs (64.51 %), followed by agricultural sources (19.15 %), traffic sources (9.77 %), and industrial sources (6.57 %). The Shapley additive explanation analysis, based on the random forest model, identified soil organic carbon, deep soil HM content, altitude, total soil K2O, urbanization composite impact index, and total soil P as primary influencing factors. This indicates that the impact of transportation on roadside soils along the Beijing-Tianjin Expressway is currently relatively limited. The prominent influence of soil properties and altitude underscored the importance of "transport" and "receptor" in the soil HMs accumulation process at the local scale. These findings provide critical data and a scientific basis for decision-makers to develop policies for expressway design and roadside soil protection.

Effect of foot type on electromyography characteristics and synergy of lower limb muscles during running

The foot structure is associated with different running mechanics. The central nervous system is responsible for using the muscles through synergies during locomotion. The purpose of the present study was to examine the effect of foot structure on the electromyography factors and the synergy of the selected muscles of the lower extremity. Tibialis anterior, extensor digitorum longus, peroneus longus, soleus, biceps femoris, vastus lateralis, gastrocnemius lateralis and medialis muscles activity of 60 barefoot recreational runners with different foot structures was recorded while running at a speed of 3.3 m/s. Muscle activity was measured in the running cycle. Besides, muscle synergies were extracted using non-negative matrix factorization algorithm. The results showed that there were differences between groups with different foot type in muscle activity under different phases of running in some muscles. Furthermore, the findings indicated that the number of synergies was similar in different groups and the relative weight of muscles was not different across groups. In conclusion, despite the difference in muscle activity under different phases of the running cycle, muscle synergies are similar among the groups. This can indicate similar control by the central nervous system in runners with different arch structures while running and the observed changes in muscle activity can be attributed to the type of forces exerted on the body, the length-tension relationship, and changes in the direction of the lower limbs in people with different arch structures.

Non-Negative Matrix Factorization with Averaged Kurtosis and Manifold Constraints for Blind Hyperspectral Unmixing

The Nonnegative Matrix Factorization (NMF) algorithm and its variants have gained widespread popularity across various domains, including neural networks, text clustering, image processing, and signal analysis. In the context of hyperspectral unmixing (HU), an important task involving the accurate extraction of endmembers from mixed spectra, researchers have been actively exploring different regularization techniques within the traditional NMF framework. These techniques aim to improve the precision and reliability of the endmember extraction process in HU. In this study, we propose a novel HU algorithm called KMBNMF, which introduces an average kurtosis regularization term based on endmember spectra to enhance endmember extraction, additionally, it integrates a manifold regularization term into the average kurtosis-constrained NMF by constructing a symmetric weight matrix. This combination of these two regularization techniques not only optimizes the extraction process of independent endmembers but also improves the part-based representation capability of hyperspectral data. Experimental results obtained from simulated and real-world hyperspectral datasets demonstrate the competitive performance of the proposed KMBNMF algorithm when compared to state-of-the-art algorithms.

Assessing Scientific Text Similarity: A Novel Approach Utilizing Non-Negative Matrix Factorization and Bidirectional Encoder Representations from Transformer

The patent serves as a vital component of scientific text, and over time, escalating competition has generated a substantial demand for patent analysis encompassing areas such as company strategy and legal services, necessitating fast, accurate, and easily applicable similarity estimators. At present, conducting natural language processing(NLP) on patent content, including titles, abstracts, etc., can serve as an effective method for estimating similarity. However, the traditional NLP approach has some disadvantages, such as the requirement for a huge amount of labeled data and poor explanation of deep-learning-based model internals, exacerbated by the high compression of patent content. On the other hand, most knowledge-based deep learning models require a vast amount of additional analysis results as training variables in similarity estimation, which are limited due to human participation in the analysis part. Thus, in this research, addressing these challenges, we introduce a novel estimator to enhance the transparency of similarity estimation. This approach integrates a patent’s content with international patent classification (IPC), leveraging bidirectional encoder representations from transformers (BERT), and non-negative matrix factorization (NMF). By integrating these techniques, we aim to improve knowledge discovery transparency in NLP across various IPC dimensions and incorporate more background knowledge into context similarity estimation. The experimental results demonstrate that our model is reliable, explainable, highly accurate, and practically usable.

Muscle synergies during the walk-run and run-walk transitions.

Muscular synergies could represent the patterns of muscular activation used by the central nervous system (CNS) to simplify the production of movement. Studies in walking-running transitions described up to nine synergy modules, and an earlier activation of flexor and extension ankle muscular groups compared to running or walking. Our project aims to study the behaviour of muscle synergies in different stance and swing variations of walking-running (WRT) and running-walking (RWT) transitions. Twenty-four trained men participated in this study. A variable speed protocol on a treadmill was developed to record the activity of 14 muscle during walking, running and relative transitions. The protocol was based on five ramps of 50 seconds each around±10 and 20% of the WRT speed. WRT and RWT were identified according to an abrupt change of the duty factor. Analysing surface electromyography using non-negative matrix factorization (NMF) we obtained synergy modules and temporal activation profiles. Alpha threshold for statistical tests set at 0.05. We described four different transition strides, two for increasing speed transitions, and two for decreasing speed transitions. Four to six synergy modules were found in each condition. According to the maximum cosine similarity results, the two identified WRT conditions shared five modules, while the two RWT conditions shared four modules. WRT and RWT overall shared 4.33±0.58 modules. The activation profiles and centres of activation revealed differences among conditions. Transition occurred at step level, and transition strides were composed by walk-like and run-like steps. Compared with previous studies in running and walking, both transitions needed earlier activation of a comparable number of synergy modules. Synergies were affected by acceleration: during RWT the need to dissipate energy, to decrease the speed, was achieved by increasing the number of co-activating muscles. This was reflected in fewer synergy modules and different activation profiles compared to WRT. We believe that our results could be enforced in different applied fields, like clinical gait analysis, physiotherapy and rehabilitation, where plans including co-activation of specific muscular groups could be useful. Gait transitions are common in different sports, and therefore also application in training and sport science would be possible.

A self-organizing map clustering adaptive artificial neural network model for analysis critical success factors in different phases of MTO projects case study: electrical equipment manufacturer and supplier in Iran

PurposeThe purpose of this paper is to investigate the benefit of critical success factors (CSFs) clustering in different phases of make-to-order (MTO) projects and develop standards for management.Design/methodology/approachThis study is based on a questionnaire survey. First of all, collecting data by structured interviews, relying on a questionnaire and second from leader contractors who are active in the engineering and steel industry (in Iran). So, the requirements and objective of the research are presented to the top management of MTO projects to gain their support in data collection. Then 20 CSFs were identified by the literature review so a questionnaire survey was prepared for the CSFs assessment and interview with the experts. Finally analyzing the importance and performance of CSFs in project phases and cluster them in different project phases with self-organizing map as one of the artificial neural network (ANN) approaches due to high predictive accuracy. Review the research result with the top management of MTO project and examine the results obtained from neural networks and validation indices.FindingsCluster analysis shows that the implementation phase is the most important stage in MTO organizations and the other phases like feasibility and start-up, design and planning, delivery and end-phase should be also considered as effective phases in determining the level of organization performance. Different industries with additional data at different periodic times will verify the result. Furthermore, testing the other ANN model will improve risk analysis and could shift this classification approach to a regression type.Research limitations/implicationsThe main limitation of the research is related to the sample. Research findings are limited to the time of data collection so validity is limited to the mentioned time. Different industries with additional data will verify the result. Furthermore, testing different ANN models such as K-MEANS, non-negative matrix factorization (NMF) analyses will improve risk analysis and could meet different classification results to find gaps.Practical implicationsIn this paper, CSF and project phase dimensions are viewed together which is necessary to meet better results for simplifying social and economic benefits. Merge the new findings and latest technologies could prepare the best results and enable managers to create a better framework or implement key factors for minimizing waste.Originality/valueThis paper moves the definition of MTO organizations beyond measuring cost, complexity and financial variables by clustering CSFs in different phases of projects. So, the results enable managers to use this concept in their daily production to minimize waste and could be implemented to efficiently choose factors.

A spatial matrix factorization method to characterize ecological assemblages as a mixture of unobserved sources: An application to fish eDNA surveys

Abstract Understanding how ecological assemblages vary in space and time is essential for advancing our knowledge of biodiversity dynamics and ecosystem functioning. Metabarcoding of environmental DNA (eDNA) is an efficient method for documenting biodiversity changes in both marine and terrestrial ecosystems. However, current methods fail to detect and display the biodiversity structure within and between eDNA samples limiting ecological and biogeographical interpretations. We present a spatial matrix factorization method that identifies optimal eDNA sample assemblages—called pools—assuming that taxonomic unit composition is based on a fixed number of unknown sources. These sources, in turn, represent taxonomic units sharing similar habitat properties or characteristics. The method aims to reduce the multi‐taxa composition structure into a low number of dimensions defined by these sources. This method is inspired by admixture analysis in population genetics. Using a marine fish eDNA survey on 263 sampling stations detecting 2888 molecular operational taxonomic units (MOTUs), we apply this method to analyse the biogeography and mixing patterns of fish assemblages at regional and large scales. At large scale, our analysis reveals six primary pools of fish samples characterized by distinct biogeographic patterns, with some mixtures between these pools. We identify pools composed of unique sources, corresponding to distinct and more isolated regions such as the Mediterranean and Scotia Seas. We also identify pools composed of a greater mix of sources, corresponding to geographically connected areas, such as tropical regions. Additionally, we identify the taxa underpinning the formation of each pool. In the regional analysis of Mediterranean eDNA samples, our method successfully identifies different pools, allowing the detection of not only geographic gradients but also human‐induced gradients corresponding to protection levels. Spatial matrix factorization adds a new method in community ecology, where each sample is considered as a mixture of K unobserved sources, to assess the dissimilarity of ecological assemblages revealing environmental and human‐induced gradients. Beyond the study of fish eDNA samples, this method has the potential to shed new light on any biodiversity survey and provide new bioindicators of global change.

Graph Regularized Sparse L2,1 Semi‐Nonnegative Matrix Factorization for Data Reduction

ABSTRACTNon‐negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi‐Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts‐based data representations to include mixed‐sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF‐related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new SNF algorithm that utilizes the noise‐insensitive norm. We provide monotonic convergence analysis of the SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed‐sign datasets as well as several randomized mixed‐sign matrices to demonstrate the performance superiority of SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels.

Leveraging user’s preference and social circle for personalized recommendation via matrix factorization with sub-linear convergence rate

Recommender systems aim to filter information effectively and recommend useful sources to match users’ requirements. However, the exponential growth of information in recent social networks may cause low prediction accuracy for recommendation systems. This article proposes a unified personalized recommendation architecture referred to as PSRec, which incorporates user preference and social relationship into matrix factorization framework. Specifically, PSRec generates two collections for textual reviews and contextual information respectively, and performs preference learning for each user via the Latent Dirichlet Allocation topic model. Moreover, PSRec exploits the inner relations within the social circle for recommendation, including direct trust relationship and indirect trust relationship. Additionally, it’s certificated that PSRec can converge at a sub-linear rate via theoretical analysis. Experimental results over DoubanMovie, CiaoDVDs and Yelp demonstrate the superiority of the proposed PSRec, which can achieve significant improvements and provide much better user experience while compared with other benchmark models.

Application of time series and multivariate statistical models for water quality assessment and pollution source apportionment in an Urban River, New Jersey, USA.

Water quality monitoring reveals changing trends in the environmental condition of aquatic systems, elucidates the prevailing factors impacting a water body, and facilitates science-backed policymaking. A 2020 hiatus in water quality data tracking in the Lower Passaic River (LPR), New Jersey, has created a 5-year information gap. To gain insight into the LPR water quality status during this lag period and ahead, water quality indices computed with 16-year historical data available for 12 physical, chemical, nutrient, and microbiological parameters were used to predict water quality between 2020 and 2025 using seasonal autoregressive moving average (ARIMA) models. Average water quality ranged from good to very poor (34 ≤ µWQI ≤ 95), with noticeable spatial and seasonal variations detected in the historical and predicted data. Pollution source tracking with the positive matrix factorization (PMF) model yielded significant R2 values (0.9 < R2 ≤ 1) for the input parameters and revealed four major LPR pollution factors, i.e., combined sewer systems, surface runoff, tide-influenced sediment resuspension, and industrial wastewater with pollution contribution rates of 23-30.2% in the upstream and downstream study areas. Significant correlation of toxic metals, nutrients, and sewage indicators suggest similarities in their sources.

An Improved Nonnegative Matrix Factorization Algorithm Combined with K-Means for Audio Noise Reduction

Clustering algorithms have the characteristics of being simple and efficient and can complete calculations without a large number of datasets, making them suitable for application in noise reduction processing for audio module mass production testing. In order to solve the problems of the NMF algorithm easily getting stuck in local optimal solutions and difficult feature signal extraction, an improved NMF audio denoising algorithm combined with K-means initialization was designed. Firstly, the Euclidean distance formula of K-means has been improved to extract audio signal features from multiple dimensions. Combined with the initialization strategy of K-means decomposition, the initialization dictionary matrix of the NMF algorithm has been optimized to avoid getting stuck in local optimal solutions and effectively improve the robustness of the algorithm. Secondly, in the sparse coding part of the NMF algorithm, feature extraction expressions are added to solve the problem of noise residue and partial spectral signal loss in audio signals during the operation process. At the same time, the size of the coefficient matrix is limited to reduce operation time and improve the accuracy of feature extraction in high-precision audio signals. Then, comparative experiments were conducted using the NOIZEUS and NOISEX-92 datasets, as well as random noise audio signals. This algorithm improved the signal-to-noise ratio by 10–20 dB and reduced harmonic distortion by approximately −10 dB. Finally, a high-precision audio acquisition unit based on FPGA was designed, and practical applications have shown that it can effectively improve the signal-to-noise ratio of audio signals and reduce harmonic distortion.

Transcriptome dynamics in developing leaves from C3 and C4 Flaveria species.

C4 species have evolved more than 60 times independently from C3 ancestors. This multiple and parallel evolution of the complex C4 trait suggests common underlying evolutionary mechanisms, which could be identified by comparative analysis of closely related C3 and C4 species. Efficient C4 function depends on a distinctive leaf anatomy that is characterised by enlarged, chloroplast-rich bundle sheath cells and narrow vein spacing. To elucidate the molecular mechanisms that generate the Kranz anatomy, we analysed a developmental series of leaves from the C4 plant Flaveria bidentis and the closely related C3 species Flaveria robusta by comparing anatomies and transcriptomes. Vascular density measurements of all nine leaf developmental stages identified three leaf anatomical zones whose proportions vary with respect to the developmental stage. We then deconvoluted the transcriptome datasets using non-negative matrix factorisation, which identified four distinct transcriptome patterns in the growing leaves of both species. By integrating the leaf anatomy and transcriptome data, we were able to correlate the different transcriptional profiles with different developmental zones in the leaves. These comparisons revealed an important role for auxin metabolism, in particular auxin homeostasis (conjugation and deconjugation), in establishing the high vein density typical of C4 species.