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We examine the properties of oblique coordinates. The coordinates, introduced by Zúñiga et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 055101, (2019)], reduce vibrational mode-mixing and enhance the quality of vibrational assignments in quantum mechanical investigations of two-dimensional model Hamiltonians. Oblique coordinates are obtained by making non-orthogonal rotations of the original coordinates that convert the matrix representation of the quadratic Hamiltonian operator into a block-diagonal matrix where the blocks are distinguished by the total quanta of vibrational excitation. Using techniques for the polar decomposition of matrices, we present a scheme for finding these coordinates for systems of arbitrary dimensions. Several molecular examples are presented that highlight the advantages of these coordinates. [ABSTRACT FROM AUTHOR]

This study investigates the influence of a combined thermal heat flux (imposed by a cone calorimeter) and a compressive loading on the deformation and damage mechanisms within quasi-isotropic carbon fibers reinforced PolyEtherEther Ketone laminates. Thermogravimetric Analyses conducted at increasing heating rates under nitrogen (from 5 to 500°C/min) provide valuable information on the thermal decomposition of C/PEEK that ranges from 550°C to 627°C, with a corresponding mass loss ranging from 20 to 26%. From the thermo-mechanical coupling standpoint, the softening and the thermal decomposition of the PEEK matrix under a 50 kW/m2 heat flux result in the micro-buckling of fibers bundles in matrix-rich areas at the ply scale. Ultimately, it leads to the formation and propagation in the transverse direction of plastic kink bands at the laminates scale. Post-failure observations show that this macroscopic kinking propagates specifically according to the PEEK matrix pyrolysis. [ABSTRACT FROM AUTHOR]

Using a matrix decomposition for sectorial matrices and an AM-GM inequality for singular values, we present a new Rotfel'd type inequality for sectorial matrices, which generalizes and partially improves some results by Zhang. We also give alternative simpler proofs of a main result of a recent paper by Yang, Lu and Chen as well as that by Fu and Liu. [ABSTRACT FROM AUTHOR]

Two new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated with the numerical solution of initial boundary value problems for parabolic partial differential equations in arbitrary spatial dimensions with time-dependent Dirichlet boundary conditions. The new techniques are based on the idea of discretizing the PDE problem at the boundary points as similar as possible to that of the interior points of the domain. These new techniques are considered for the time integration with W-methods based on approximate matrix factorization. By suitably modifying the internal stages of the methods on the boundary points, it is illustrated by numerical testing with time-dependent boundary conditions that the new boundary correction techniques are able to keep the same accuracy and order of convergence that the method reaches in the case of homogeneous boundary conditions. [ABSTRACT FROM AUTHOR]

Robots are projected to affect healthcare services in significant, but unpredictable, ways. Many believe robots will add value to future healthcare, but their arrival has triggered controversy. Debates revolve around how robotics will impact healthcare provision, their effects on the future of labor and caregiver–patient relationships, and ethical dilemmas associated with autonomous machines. This study investigates media representations of healthcare robotics in Norway over a twenty-year period, using a mixed-methods design. Media representations affect public opinion in multiple ways. By assembling and presenting information through stories, they not only set the agenda by broadcasting values, experiences, and expectations about new technologies, but also frame and prime specific understandings of issues. First, we employ an inductive text-mining approach known as "topic modeling," a computational method for eliciting abstract semantic structures from large text corpora. Using Non-Negative Matrix Factorization, we implement a topic model of manifest content from 752 articles, published in Norwegian print media between 1.1.2000 and 2.10.2020, sampled from a comprehensive database for news media (Atekst, Retriever). We complement this computational lens with a more fine-grained, qualitative analysis of content in exemplary texts sampled from each topic. Here, we identify prominent "frames," discursive cues for interpreting how various stakeholders talk about healthcare robotics as a contested domain of policy and practice in a comprehensive welfare state. We also highlight some benefits of this approach for analyzing media discourse and stakeholder perspectives on controversial technologies. [ABSTRACT FROM AUTHOR]

Objective To analyze changes in neuromuscular control during sit-to-stand (STS) in older adults with hallux valgus ( HV) through muscle synergy, and thus to explore the effect of falls in older adults with HV. Methods Four groups of subjects were included in this study, 13 young controls (YC); 12 young HV group ( HVY) ; 14 healthy elderly controls (EC ); and 15 elderly HV group ( HVE ). All subjects completed the STS maneuver in an armless chair, and EMG data were integrated using non-negative matrix factorization to compare muscle synergies in the YC, HVY, EC, and HVE groups; plantar pressures (COP), ground reaction forces (GRF), and fall scores (FES-I) were collected. Results Compared with YC group, HVY, EC, and HVE groups had lower relative activation amplitude of abductor hallucis and lateral gastrocnemius in STS preparation phase ; meanwhile, EC and HVE groups needed more muscle activation to maintain stability of trunk and foot-ankle joints in STS stabilization phase; and HVE group needed more co-contractions of thigh muscles to maintain stability of the knee joint. The COP, FES-I of HVE group was higher than that of the other groups (P < 0.05 ). Conclusion In STS, healthy older adults and older adults with HV required more muscle activation to maintain trunk and ankle stability ; older adults with HV required more co-contraction of the thigh muscles to maintain knee stability; in addition to this, older adults with HV were more prone to falls. [ABSTRACT FROM AUTHOR]

Dictionary learning (DL), implemented via matrix factorization (MF), is commonly used in computational biology to tackle ubiquitous clustering problems. The method is favored due to its conceptual simplicity and relatively low computational complexity. However, DL algorithms produce results that lack interpretability in terms of real biological data. Additionally, they are not optimized for graph-structured data and hence often fail to handle them in a scalable manner. In order to address these limitations, we propose a novel DL algorithm called online convex network dictionary learning (online cvxNDL). Unlike classical DL algorithms, online cvxNDL is implemented via MF and designed to handle extremely large datasets by virtue of its online nature. Importantly, it enables the interpretation of dictionary elements, which serve as cluster representatives, through convex combinations of real measurements. Moreover, the algorithm can be applied to data with a network structure by incorporating specialized subnetwork sampling techniques. To demonstrate the utility of our approach, we apply cvxNDL on 3D-genome RNAPII ChIA-Drop data with the goal of identifying important long-range interaction patterns (long-range dictionary elements). ChIA-Drop probes higher-order interactions, and produces data in the form of hypergraphs whose nodes represent genomic fragments. The hyperedges represent observed physical contacts. Our hypergraph model analysis has the objective of creating an interpretable dictionary of long-range interaction patterns that accurately represent global chromatin physical contact maps. Through the use of dictionary information, one can also associate the contact maps with RNA transcripts and infer cellular functions. To accomplish the task at hand, we focus on RNAPII-enriched ChIA-Drop data from Drosophila Melanogaster S2 cell lines. Our results offer two key insights. First, we demonstrate that online cvxNDL retains the accuracy of classical DL (MF) methods while simultaneously ensuring unique interpretability and scalability. Second, we identify distinct collections of proximal and distal interaction patterns involving chromatin elements shared by related processes across different chromosomes, as well as patterns unique to specific chromosomes. To associate the dictionary elements with biological properties of the corresponding chromatin regions, we employ Gene Ontology (GO) enrichment analysis and perform multiple RNA coexpression studies. Author summary: We introduce a novel method for dictionary learning termed online convex Network Dictionary Learning (online cvxNDL). The method operates in an online manner and utilizes representative subnetworks of a network dataset as dictionary elements. A key feature of online cvxNDL is its ability to work with graph-structured data and generate dictionary elements that represent convex combinations of real data points, thus ensuring interpretability. Online cvxNDL is used to investigate long-range chromatin interactions in S2 cell lines of Drosophila Melanogaster obtained through RNAPII ChIA-Drop measurements represented as hypergraphs. The results show that dictionary elements can accurately and efficiently reconstruct the original interactions present in the data, even when subjected to convexity constraints. To shed light on the biological relevance of the identified dictionaries, we perform Gene Ontology enrichment and RNA-seq coexpression analyses. These studies uncover multiple long-range interaction patterns that are chromosome-specific. Furthermore, the findings affirm the significance of convex dictionaries in representing TADs cross-validated by imaging methods (such as 3-color FISH (fluorescence in situ hybridization)). [ABSTRACT FROM AUTHOR]

During robot-assisted rehabilitation, failure to recognize lower limb movement may efficiently limit the development of exoskeleton robots, especially for individuals with knee pathology. A major challenge encountered with surface electromyography (sEMG) signals generated by lower limb movements is variability between subjects, such as motion patterns and muscle structure. To this end, this paper proposes an sEMG-based lower limb motion recognition using an improved support vector machine (SVM). Firstly, non-negative matrix factorization (NMF) is leveraged to analyze muscle synergy for multi-channel sEMG signals. Secondly, the multi-nonlinear sEMG features are extracted, which reflect the complexity of muscle status change during various lower limb movements. The Fisher discriminant function method is utilized to perform feature selection and reduce feature dimension. Then, a hybrid genetic algorithm-particle swarm optimization (GA-PSO) method is leveraged to determine the best parameters for SVM. Finally, the experiments are carried out to distinguish 11 healthy and 11 knee pathological subjects by performing three different lower limb movements. Results demonstrate the effectiveness and feasibility of the proposed approach in three different lower limb movements with an average accuracy of 96.03% in healthy subjects and 93.65% in knee pathological subjects, respectively. [ABSTRACT FROM AUTHOR]

Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular complex matrices or quasi-upper-triangular real matrices that are equivalent to the original matrices via unitary or, respectively, orthogonal transformations. In general, for theoretical and numerical purposes we often need to reduce, by admissible transformations, a collection of matrices to the Schur form. Unfortunately, such a reduction is not always possible. In this paper we describe all collections of complex (real) matrices that can be reduced to the Schur form by the corresponding unitary (orthogonal) transformations and explain how such a reduction can be done. We prove that this class consists of the collections of matrices associated with pseudoforest graphs. In other words, we describe when the Schur form of a collection of matrices exists and how to find it. [ABSTRACT FROM AUTHOR]

The two-sided Jacobi method for singular value decomposition (SVD) has the advantage of obtaining singular vectors quickly and accurately. In previous research, fast and accurate implementations of the two-sided Jacobi method have been achieved for real matrices. In this study, we implemented SVD for complex matrices using the two-sided Jacobi method. In SVD, given rectangular matrices can be converted into upper-triangular matrices by conducting QR decomposition as a preprocessing step. Then, the upper-triangular matrices are decomposed. In the case where the given matrices are complex, the upper-triangular matrices are complex. Two implementations are proposed: the first requires SVD for complex matrices, whereas the second requires SVD for only real matrices. [ABSTRACT FROM AUTHOR]

Monosynaptic connectivity mapping is crucial for building circuit-level models of neural computation. Two-photon optogenetic stimulation, when combined with whole-cell recording, enables large-scale mapping of physiological circuit parameters. In this experimental setup, recorded postsynaptic currents are used to infer the presence and strength of connections. For many cell types, nearby connections are those we expect to be strongest. However, when the postsynaptic cell expresses opsin, optical excitation of nearby cells can induce direct photocurrents in the postsynaptic cell. These photocurrent artifacts contaminate synaptic currents, making it difficult or impossible to probe connectivity for nearby cells. To overcome this problem, we developed a computational tool, Photocurrent Removal with Constraints (PhoRC). Our method is based on a constrained matrix factorization model which leverages the fact that photocurrent kinetics are less variable than those of synaptic currents. We demonstrate on real and simulated data that PhoRC consistently removes photocurrents while preserving synaptic currents, despite variations in photocurrent kinetics across datasets. Our method allows the discovery of synaptic connections which would have been otherwise obscured by photocurrent artifacts, and may thus reveal a more complete picture of synaptic connectivity. PhoRC runs faster than real time and is available as open source software. Author summary: Mapping the presence and strength of connections between neurons is necessary for understanding how the structure of neural circuits gives rise to their function. Historically, directly measuring these connections has required difficult and time-consuming paired-patch experiments. However, recent developments in the field of two-photon optogenetics enable mapping experiments with much higher throughput. In these new experiments, a single postsynaptic neuron is recorded using an electrode, and a two-photon laser is used to optogenetically activate nearby neurons. When the laser activates a connected presynaptic neuron, the experimenter observes an electrical current on the electrode. The size of the current can then be used to determine the strength of the connection. However, this technique has a drawback: when stimulating near the postsynaptic cell, the laser can directly evoke an electrical current—called a photocurrent—even if no connection is present. This is problematic because it confounds estimates of connectivity. In this work, we developed a computational tool which removes the photocurrent artifact while preserving signals corresponding to true neuronal connections. We expect that this tool will serve as a resource for experimentalists, enabling a more complete picture of synaptic connectivity. [ABSTRACT FROM AUTHOR]

Severe ozone (O3) pollution has been recorded in China in recent years. The key precursor, volatile organic compounds (VOCs), is still not well understood in Nanning, which is a less developed city compared to other megacities in China. In this study, a year-long measurement of VOCs was conducted from 1 October 2020 to 30 September 2021, to characterize the ambient variations and apportion the source contributions of VOCs. The daily-averaged concentration of VOCs was measured to be 26.4 ppb, ranging from 3.2 ppb to 136.2 ppb across the whole year. Alkanes and oxygenated VOCs (OVOCs) were major species, contributing 46.9% and 25.2% of total VOC concentrations, respectively. Propane, ethane, and ethanol were the most abundant in Nanning, which differed from the other significant species, such as toluene (3.7 ppb) in Guangzhou, ethylene (3.8 ppb) in Nanjing, and isopentane (5.5 ppb), in Chengdu. The positive matrix factorization (PMF) model resolved six source factors, including vehicular emission (contributing 33% of total VOCs), NG and LPG combustion (19%), fuel burning (17%), solvent use (16%), industry emission (10%), and biogenic emission (5%). This indicated that Nanning was less affected by industrial emission compared with other megacities of China, with industry contributing 12–50%. Ethylene, m/p-xylene, butane, propylene, and isoprene were key species determined by ozone formation potential (OFP) analysis, which should be priority-controlled. The variations in estimated OFP and observed O3 concentrations were significantly different, suggesting that VOC reactivity-based strategies as well as meteorological and NOx effects should be considered collectively in controlling O3 pollution. This study presents a year-long dataset of VOC measurements in Nanning, which gives valuable implications for VOC control in terms of key sources and reactive species and is also beneficial to the formulation of effective ozone control strategies in other less developed regions of China. [ABSTRACT FROM AUTHOR]

Since 2016, the Ministry of Ecology and Environment and the Beijing Municipal Government have adjusted the minimum concentration limit for ambient air dustfall several times, indicating that they attach great importance to dustfall. To grasp the pollution characteristics and sources of dustfall, in this work, the filtration method was used to determine the insoluble dustfall and water-soluble dustfall in the urban area of Beijing. From our analysis, the influence of the meteorological parameters on dustfall was found, and the chemical components of dustfall were determined. The positive matrix factorization (PMF) model was also utilized to analyze the sources of dustfall. The results indicated that the average amount of dustfall in 2021–2022 was 4.4 t·(km2·30 d)−1, and the proportion of insoluble dustfall deposition was 82.4%. Dustfall was positively correlated with the average wind speed and temperature and negatively correlated with the relative humidity and rain precipitation. The impact of the meteorological parameters on insoluble dustfall and water-soluble dustfall was the opposite. The average proportions of crustal material, ions, organic matter, element carbon, trace elements, and unknown components were 48%, 16%, 14%, 1.4%, 0.20%, and 20%, respectively. The proportions of the crustal material and ions were the highest in spring (57%) and summer (37%). The contribution rates of fugitive dust source, secondary inorganic source, mobile source, coal combustion source, snow melting agent source, and other sources were 42.4%, 19.3%, 8.3%, 3.0%, 2.7%, and 24.3%, respectively. This study supported dustfall pollution control by analysing the pollutant characteristics and sources of dustfall from the standpoint of total chemical components. In order to better control dustfall pollution, control measures and evaluation standards for fugitive dust pollution should be formulated. [ABSTRACT FROM AUTHOR]

This paper introduces a new lower-limb rehabilitation machine that meets the rehabilitation needs of hemiplegic patients. First, a left–right independent rotary pedal mechanism was selected to facilitate rehabilitation and adapt to the user's physical condition. Then, a half model of the lower-limb rehabilitation machine is designed and manufactured with ergonomics in mind. As analytical tools, we combine non-negative matrix factorization and non-negative double singular value decomposition to calculate muscle synergy of the walking muscle surface electromyography (sEMG) signal, and use cosine similarity to evaluate the similarity between walking and pedaling activities. By comparing the results of the walking and pedaling experiments, the effectiveness of pedaling in gait rehabilitation is revealed. To further improve the similarity between walking and pedaling, double integration of the sEMG signal is introduced, and the relationship between load input and rotation angle is described for the first time using Fourier series. The results of the experiment confirmed that more than half of the 10 subjects performed pedaling exercises similar to walking using Fourier series loading compared to pedaling exercises with normal constant loading. This loading parameter may have the potential to improve rehabilitation efficiency for many subjects compared to the usual exercise. [ABSTRACT FROM AUTHOR]

Similarity of point patterns is critical to geographic information retrieval. Many methods depend on measuring the similarity between point patterns within the spatial database. However, previous researches mainly focus on point density which is only one aspect of point patterns. A point distribution can be complex by its numerous alignments of point groups, which usually imply different geographical meanings in reality. In this paper, we propose a new method that uses image analysis techniques to comprehensively consider the characteristics of a point pattern. Specifically, given a set of point datasets falling in the same region, our method first generates the point intensity surfaces to transform the original vector space to raster space; then, the method constructs a matrix to describe all the pattern-related information. Finally, the point pattern similarity is calculated by decomposing this matrix into the lower-order representation and the factorized basis features. Due to the use of matrix decomposition, the proposed method has the merits that it can eliminate noises from the original data and assess the similarity of two patterns with emphasis on their major features. As a case study, our method is effective in discovering regularity from the taxi pick-up/drop-off point datasets. [ABSTRACT FROM AUTHOR]

In environments with a low signal-to-reverberation ratio (SRR) characterized by fluctuations in clutter number and distribution, particle filter-based tracking methods may experience significant fluctuations in the posterior probability of existence. This can lead to interruptions or even loss of the target trajectory. To address this issue, an adaptive PF-based tracking method (APF) with joint reverberation suppression is proposed. This method establishes the state space model under the Bayesian framework and implements it through particle filtering. To keep the weak target echoes, all the non-zero entries contained in the sparse matrix processed by the low-rank and sparsity decomposition (LRSD) are treated as the measurements. The prominent feature of this approach is introducing an adaptive measurement likelihood ratio (AMLR) into the posterior update step, which solves the problem of unstable tracking due to the strong fluctuation in the number of point measurements per frame. The proposed method is verified by four shallow water experimental datasets obtained by an active sonar with a uniform horizontal linear array. The results demonstrate that the tracking frame success ratio of the proposed method improved by over 14% compared with the conventional PF tracking method. [ABSTRACT FROM AUTHOR]

Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m × n matrices. The theory of operator spaces provides a set up which describes 4 norm optimal factorizations of Grothendieck's sort. It is shown that 3 of the optimal factorizations are uniquely determined and the remaining one is unique in some cases. [ABSTRACT FROM AUTHOR]

We consider the core blocks corresponding to the Hecke algebras of type B over a field of arbitrary characteristic. To each core block, we associate two non-negative integers which determine the indexing of the Specht modules and simple modules in the block, the weight of the block, the multicharge of the algebra (up to a shift) and the block decomposition matrix. [ABSTRACT FROM AUTHOR]

Many important biological facts have been found as single-cell RNA sequencing (scRNA-seq) technology has advanced. With the use of this technology, it is now possible to investigate the connections among individual cells, genes, and illnesses. For the analysis of single-cell data, clustering is frequently used. Nevertheless, biological data usually contain a large amount of noise data, and traditional clustering methods are sensitive to noise. However, acquiring higher-order spatial information from the data alone is insufficient. As a result, getting trustworthy clustering findings is challenging. We propose the Cauchy hyper-graph Laplacian non-negative matrix factorization (CHLNMF) as a unique approach to address these issues. In CHLNMF, we replace the measurement based on Euclidean distance in the conventional non-negative matrix factorization (NMF), which can lessen the influence of noise, with the Cauchy loss function (CLF). The model also incorporates the hyper-graph constraint, which takes into account the high-order link among the samples. The CHLNMF model's best solution is then discovered using a half-quadratic optimization approach. Finally, using seven scRNA-seq datasets, we contrast the CHLNMF technique with the other nine top methods. The validity of our technique was established by analysis of the experimental outcomes. [ABSTRACT FROM AUTHOR]

Chronic kidney disease (CKD) is a complex disorder that causes a gradual loss of kidney function, affecting approximately 9.1% of the world's population. Here, we use a soft-clustering algorithm to deconstruct its genetic heterogeneity. First, we selected 322 CKD-associated independent genetic variants from published genome-wide association studies (GWAS) and added association results for 229 traits from the GWAS catalog. We then applied nonnegative matrix factorization (NMF) to discover overlapping clusters of related traits and variants. We computed cluster-specific polygenic scores and validated each cluster with a phenome-wide association study (PheWAS) on the BioMe biobank (n = 31,701). NMF identified nine clusters that reflect different aspects of CKD, with the top-weighted traits signifying areas such as kidney function, type 2 diabetes (T2D), and body weight. For most clusters, the top-weighted traits were confirmed in the PheWAS analysis. Results were found to be more significant in the cross-ancestry analysis, although significant ancestry-specific associations were also identified. While all alleles were associated with a decreased kidney function, associations with CKD-related diseases (e.g., T2D) were found only for a smaller subset of variants and differed across genetic ancestry groups. Our findings leverage genetics to gain insights into the underlying biology of CKD and investigate population-specific associations. [ABSTRACT FROM AUTHOR]

The effective segmentation of clouds and cloud shadows is crucial for surface feature extraction, climate monitoring, and atmospheric correction, but it remains a critical challenge in remote sensing image processing. Cloud features are intricate, with varied distributions and unclear boundaries, making accurate extraction difficult, with only a few networks addressing this challenge. To tackle these issues, we introduce a multi-scale receptive field aggregation network (MRFA-Net). The MRFA-Net comprises an MRFA-Encoder and MRFA-Decoder. Within the encoder, the net includes the asymmetric feature extractor module (AFEM) and multi-scale attention, which capture diverse local features and enhance contextual semantic understanding, respectively. The MRFA-Decoder includes the multi-path decoder module (MDM) for blending features and the global feature refinement module (GFRM) for optimizing information via learnable matrix decomposition. Experimental results demonstrate that our model excelled in generalization and segmentation performance when addressing various complex backgrounds and different category detections, exhibiting advantages in terms of parameter efficiency and computational complexity, with the MRFA-Net achieving a mean intersection over union (MIoU) of 94.12% on our custom Cloud and Shadow dataset, and 87.54% on the open-source HRC_WHU dataset, outperforming other models by at least 0.53% and 0.62%. The proposed model demonstrates applicability in practical scenarios where features are difficult to distinguish. [ABSTRACT FROM AUTHOR]

Neuroblastoma is the most common extracranial solid tumor in children. It is a highly heterogeneous tumor consisting of different subcellular types and genetic abnormalities. Literature data confirm the biological and clinical complexity of this cancer, which requires a wider availability of gene targets for the implementation of personalized therapy. This paper presents a study of neuroblastoma samples from primary tumors of untreated patients. The focus of this analysis is to evaluate the impact that the inflammatory process may have on the pathogenesis of neuroblastoma. Eighty-eight gene profiles were selected and analyzed using a non-negative matrix factorization framework to extract a subset of genes relevant to the identification of an inflammatory phenotype, whose targets (PIK3CG, NFATC2, PIK3R2, VAV1, RAC2, COL6A2, COL6A3, COL12A1, COL14A1, ITGAL, ITGB7, FOS, PTGS2, PTPRC, ITPR3) allow further investigation. Based on the genetic signals automatically derived from the data used, neuroblastoma could be classified according to stage rather than as a "cold" or "poorly immunogenic" tumor. [ABSTRACT FROM AUTHOR]

• We present a shortcut in the compositional analysis of plastic waste. • The separation system's influence on the homogeneity and performance is examined. • Both HDPE samples display good material performance and a homogeneous composition. • PP and LDPE from post source separation display slightly more heterogeneity. • Multivariate FTIR data evaluation is a fast and informative analysis method. Whether plastic packaging waste is disposed of in different bins (source separation, S) or in a single bin (post source separation, P) is generally assumed to impact the waste stream's quality. To elucidate this question, we evaluated the quality of LDPE, HDPE, and PP plastic waste from both separation systems (S and P) through a concise analytical strategy. The materials received similar treatment after collection (e.g., washing, NIR-sorting). A multivariate approach to ATR-FTIR spectroscopy was developed to assess their material composition and the effect of washing. Results were complemented by TGA, DSC, and py-GC/MS analysis. The material performance was investigated by a lab-scale extrusion and granulation, followed by an assessment of the mechanical properties and the melt volume rate. Our study reveals the HDPE materials to be of good quality, regardless of their source. For LDPE and PP, the P-materials are fractionally more contaminated after washing. Both PP-materials display poor material performance with highly fluctuating elongations-at-break (between 30 % and 380 %). S-LDPE was found to contain more polymeric impurities than P-LDPE. We conclude that the quality depends strongly on the material type and on the treatment after collection (washing, sorting). The multivariate approach to FTIR data evaluation we propose aims at simplifying the quality evaluation of polyolefin waste plastics and may serve as a basis for future work in this field. [ABSTRACT FROM AUTHOR]

Dimension reduction has been used to visualise the distribution of multidimensional microbiome data, but the composite variables calculated by the dimension reduction methods have not been widely used to investigate the relationship of the human gut microbiome with lifestyle and disease. In the present study, we applied several dimension reduction methods, including principal component analysis, principal coordinate analysis (PCoA), non-metric multidimensional scaling (NMDS), and non-negative matrix factorization, to a microbiome dataset from 186 subjects with symptoms of allergic rhinitis (AR) and 106 controls. All the dimension reduction methods supported that the distribution of microbial data points appeared to be continuous rather than discrete. Comparison of the composite variables calculated from the different dimension reduction methods showed that the characteristics of the composite variables differed depending on the distance matrices and the dimension reduction methods. The first composite variables calculated from PCoA and NMDS with the UniFrac distance were strongly associated with AR (FDR adjusted P = 2.4 × 10–4 for PCoA and P = 2.8 × 10–4 for NMDS), and also with the relative abundance of Bifidobacterium and Prevotella. The abundance of Bifidobacterium was also linked to intake of several nutrients, including carbohydrate, saturated fat, and alcohol via composite variables. Notably, the association between the composite variables and AR was much stronger than the association between the relative abundance of individual genera and AR. Our results highlight the usefulness of the dimension reduction methods for investigating the association of microbial composition with lifestyle and disease in clinical research. [ABSTRACT FROM AUTHOR]

Anti-cancer response of cell lines to drugs is in urgent need for individualized precision medical decision-making in the era of precision medicine. Measurements with wet-experiments is time-consuming and expensive and it is almost impossible for wide ranges of application. The design of computational models that can precisely predict the responses between drugs and cell lines could provide a credible reference for further research. Existing methods of response prediction based on matrix factorization or neural networks have revealed that both linear or nonlinear latent characteristics are applicable and effective for the precise prediction of drug responses. However, the majority of them consider only linear or nonlinear relationships for drug response prediction. Herein, we propose a Dual Branch Deep Neural Matrix Factorization (DBDNMF) method to address the above-mentioned issues. DBDNMF learns the latent representation of drugs and cell lines through flexible inputs and reconstructs the partially observed matrix through a series of hidden neural network layers. Experimental results on the datasets of Cancer Cell Line Encyclopedia (CCLE) and Genomics of Drug Sensitivity in Cancer (GDSC) show that the accuracy of drug prediction exceeds state-of-the-art drug response prediction algorithms, demonstrating its reliability and stability. The hierarchical clustering results show that drugs with similar response levels tend to target similar signaling pathway, and cell lines coming from the same tissue subtype tend to share the same pattern of response, which are consistent with previously published studies. Author summary: As is known, the phenotype of cancer is closely related to gene expression in the human body. In the era of precision medicine, an increasing amount of anti-cancer drug response data is urgently needed for individualized therapy. Measurements with wet-experiments are time-consuming and costly, and computational methods are necessary. Existing methods mainly focused predominantly on linear or nonlinear relationships between cells and drugs for prediction. However, it has been shown that both linear and nonlinear relationships could contribute to more precise response prediction. Here, we propose a Dual Branch Deep Neural Matrix Factorization (DBDNMF) method to better use both linear and nonlinear relationships and the experimental results show that it outperforms state-of-the-art algorithms. Our results suggest that drugs showing similar response levels tend to target similar signaling pathways while cell lines sharing similar response patterns tend to come from the same tissue subtype. The analysis of experimental results may benefit medical decision-making. [ABSTRACT FROM AUTHOR]

In recent years, the tropical polynomial factorization problem, the tropical matrix decomposition problem, and the tropical multivariate quadratic equation solving problem have been proved to be NP-hard. Some asymmetric cryptographic systems based on tropical semirings have been proposed, but most of them are insecure and have been successfully attacked. In this paper, a new key exchange protocol and a new encryption protocol are proposed based on the difficulty of finding the multiple exponentiation problem of the tropical Jones matrices. The analysis results indicate that our protocol can resist various existing attacks. The complexity of attacking an MEP by adversaries is raised due to the larger number of combinations in the tropical Jones matrices compared to regular matrix polynomials. Furthermore, the index semiring is the non-negative integer cyclic matrix semiring, leading to a higher efficiency in key generation. [ABSTRACT FROM AUTHOR]

We propose a heuristic method to solve polynomial matrix equations of the type ∑ k = 1 m a k X k = B , where a k are scalar coefficients and X and B are square matrices of order n. The method is based on the decomposition of the B matrix as a linear combination of the identity matrix and an idempotent, involutive, or nilpotent matrix. We prove that this decomposition is always possible when n = 2 . Moreover, in some cases we can compute solutions when we have an infinite number of them (singular solutions). This method has been coded in MATLAB and has been compared to other methods found in the existing literature, such as the diagonalization and the interpolation methods. It turns out that the proposed method is considerably faster than the latter methods. Furthermore, the proposed method can calculate solutions when diagonalization and interpolation methods fail or calculate singular solutions when these methods are not capable of doing so. [ABSTRACT FROM AUTHOR]

Collaborative filtering (CF), a fundamental technique in personalized Recommender Systems, operates by leveraging user–item preference interactions. Matrix factorization remains one of the most prevalent CF-based methods. However, recent advancements in deep learning have spurred the development of hybrid models, which extend matrix factorization, particularly with autoencoders, to capture nonlinear item relationships. Despite these advancements, many proposed models often neglect dynamic changes in the rating process and overlook user features. This paper introduces IUAutoTimeSVD++, a novel hybrid model that builds upon autoTimeSVD++. By incorporating item–user features into the timeSVD++ framework, the proposed model aims to address the static nature and sparsity issues inherent in existing models. Our model utilizes a contractive autoencoder (CAE) to enhance the capacity to capture a robust and stable representation of user-specific and item-specific features, accommodating temporal variations in user preferences and leveraging item characteristics. Experimental results on two public datasets demonstrate IUAutoTimeSVD++'s superiority over baseline models, affirming its effectiveness in capturing and utilizing user and item features for temporally adaptive recommendations. [ABSTRACT FROM AUTHOR]

Hybrid receptor models overestimate the contribution of background areas (no specific emission sources), like the Yellow Sea in Korea. This study aimed to improve model performances using Advanced Concentration Emission and Retention Time Weighted Trajectory (ACERWT). ACERWT was combined with a positive matrix factorization (PMF), back trajectory, and Regional Emission Inventory in Asia (REAS). The PMF receptor model used one year of data from Korea's Central Air Environment Research Center. In the PMF receptor model, eight sources (dust/soil, secondary nitrate, biomass burning, vehicles, secondary sulfate, industry, coal combustion and sea salt) influenced PM2.5 pollution at the receptor site (Daejeon, Korea). Secondary sulfate was the most dominant source, followed by secondary nitrate and vehicle sources. ACERWT results showed high contributions from China, Japan, and Korean regions, while the contribution from the Yellow Sea was significantly lower. Several regions, such as the eastern and south-eastern areas of China, the southern area of Taiwan, the western area of Tokyo, and the central area of Korea, showed high contributions due to large-scale emission facilities and industrial complexes. In this study, the ACERWT model significantly improved its performance regarding regional contributions to PM2.5 pollution at the receptor site. [ABSTRACT FROM AUTHOR]

Brown carbon (BrC) is a new term for organic aerosol (OA) with strong absorption ability from the visible to ultraviolet (UV) wavelengths, which plays a vital role in atmospheric visibility and climate change. Herein, we report field measurements from 1 March 2020 to 28 February 2021, sampled at urban Suzhou, Yangtze River Delta (YRD), China, to investigate the optical properties and sources of BrC. By analyzing the seasonal characteristics of the absorption of BrC at 370 nm (babs370), babs370 was found to be the highest (9.0 ± 7.2 Mm−1) in winter and the lowest (5.1 ± 3.3 Mm−1) in summer, respectively. The absorption Ångström exponent (AAE) value of BrC in winter was 1.22 ± 0.05, followed by 1.21 ± 0.05, 1.20 ± 0.05, and 1.19 ± 0.05 for fall, spring, and summer, respectively. The mass absorption cross-section (MAC) of secondary organic carbon (SOC) was 3.3 ± 0.2 m2g−1 in spring, 2.9 ± 0.1 m2g−1 in summer, 4.3 ± 0.1 m2g−1 in fall, and 2.8 ± 0.2 m2g−1 in winter, significantly lower than that of primary organic carbon (POC) at 370 nm, suggesting the aging process could weaken the light absorption of BrC. Five different BrC factors were identified by the positive matrix factorization (PMF) analysis, including biomass-burning-related, vehicle-related, sulfate-related, nitrate-related, and dust-related factors, which on average account for 7.4%, 73.4%, 11.9%, 1.9%, and 5.4% of babs370, respectively. Potential Source Contribution Factor (PSCF) analysis showed that those high babs370 periods were mainly contributed by air mass from the south. Moreover, for the influence degree of the potential source areas, the sequence was winter > spring > fall > summer. Our results improve the understanding of BrC in an important industrial city in YRD, which could reduce the uncertainty of the prediction of its climate effect in this region. [ABSTRACT FROM AUTHOR]

Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (eRPCA$$ {e}^{\mathrm{RPCA}} $$), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient eRPCA$$ {e}^{\mathrm{RPCA}} $$ decomposition, under either its natural or canonical parametrization. The effectiveness of eRPCA$$ {e}^{\mathrm{RPCA}} $$ is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area. [ABSTRACT FROM AUTHOR]

Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary signed graphs, and therefore to arbitrary symmetric matrices. We show that for an arbitrary symmetric matrix, a positive fraction of eigenbases satisfy a generalized version of known nodal bounds for un-signed (that is classical) graphs. We do this through an explicit decomposition. Moreover, we show that with high probability, the number of nodal domains of a bulk eigenvector of the adjacency matrix of a signed Erdős-Rényi graph is |$\Omega (n/\log n)$| and |$o(n)$|⁠. [ABSTRACT FROM AUTHOR]

Background: Longitudinal magnetic resonance imaging (MRI) has been proposed for tracking the progression of Alzheimer's disease (AD) through the assessment of brain atrophy. Objective: Detection of brain atrophy patterns in patients with AD as the longitudinal disease tracker. Methods: We used a refined version of orthonormal projective non-negative matrix factorization (OPNMF) to identify six distinct spatial components of voxel-wise volume loss in the brains of 83 subjects with AD from the ADNI3 cohort relative to healthy young controls from the ABIDE study. We extracted non-negative coefficients representing subject-specific quantitative measures of regional atrophy. Coefficients of brain atrophy were compared to subjects with mild cognitive impairment and controls, to investigate the cross-sectional and longitudinal associations between AD biomarkers and regional atrophy severity in different groups. We further validated our results in an independent dataset from ADNI2. Results: The six non-overlapping atrophy components represent symmetric gray matter volume loss primarily in frontal, temporal, parietal and cerebellar regions. Atrophy in these regions was highly correlated with cognition both cross-sectionally and longitudinally, with medial temporal atrophy showing the strongest correlations. Subjects with elevated CSF levels of TAU and PTAU and lower baseline CSF Aβ42 values, demonstrated a tendency toward a more rapid increase of atrophy. Conclusions: The present study has applied a transferable method to characterize the imaging changes associated with AD through six spatially distinct atrophy components and correlated these atrophy patterns with cognitive changes and CSF biomarkers cross-sectionally and longitudinally, which may help us better understand the underlying pathology of AD. [ABSTRACT FROM AUTHOR]

Polycystic ovarian syndrome (PCOS) is commonly diagnosed in adolescence, and information about the condition is often shared online. We aimed to assess the extent, content, and engagement of PCOS-related information across social media platforms. We performed a cross-sectional content analysis of PCOS-related posts on TikTok, Instagram, and Reddit. Top PCOS posts were collected from TikTok and Instagram (N = 100). Two researchers independently coded all posts using a codebook including symptoms, interventions, and qualities. Logistic regression assessed the relationship between user engagement and creator conflicts of interest. On Reddit, posts from 2020 to 2022 (N = 34,208) were collected. Topic modeling using latent Dirichlet allocation and non-negative matrix factorization (NMF) was applied to discover topics in the textual data. PCOS content received high engagement across all platforms, with an average of 1.8 million views on TikTok. "Weight" and "Diet" were the most frequently mentioned topics on TikTok and Instagram, and interactions with medical providers were discussed in 30% of posts. A financial conflict of interest was present in 45% of TikTok posts and 89% of Instagram posts. NMF identified 15 coherent topics, including symptoms, interventions, interactions with the medical system, and information-seeking. Reddit posts under "Symptom Management" received the most comments. PCOS content is present and pervasive across social media platforms, suggesting the ability of information from non-clinician sources to reach and engage with a large population using novel modes of health information sharing. Further studies of this content will allow for a deeper understanding of patient perceptions, misconceptions, and knowledge of PCOS, with the potential to inform patient-centered counseling. [ABSTRACT FROM AUTHOR]

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user–item interaction matrix into user and item latent matrices. Because the model typically learns each interaction independently, it may overlook the underlying shared dependencies between users and items, resulting in less stable and interpretable recommendations. Based on these insights, we propose "Hierarchical Matrix Factorization" (HMF), which incorporates clustering concepts to capture the hierarchy, where leaf nodes and other nodes correspond to users/items and clusters, respectively. Central to our approach, called hierarchical embeddings, is the additional decomposition of the latent matrices (embeddings) into probabilistic connection matrices, which link the hierarchy, and a root cluster latent matrix. The embeddings are differentiable, allowing simultaneous learning of interactions and clustering using a single gradient descent method. Furthermore, the obtained cluster-specific interactions naturally summarize user–item interactions and provide interpretability. Experimental results on ratings and ranking predictions show that HMF outperforms existing MF methods, in particular achieving a 1.37 point improvement in RMSE for sparse interactions. Additionally, it was confirmed that the clustering integration of HMF has the potential for faster learning convergence and mitigation of overfitting compared to MF, and also provides interpretability through a cluster-centered case study. [Display omitted] • Recommender model to capture user/item hierarchies simultaneously in factorization. • Hierarchical embeddings are optimized with a single gradient descent method. • Obtained clusters capable of summarizing of interactions and providing interpretation. • Possibility of being robust to sparse interactions due to its hierarchical structure. • Presentation of a case study summarizing preferences on a cluster-by-cluster basis. [ABSTRACT FROM AUTHOR]

Based on the generalized matrix eigenvalue decomposition technique, two kinds of basis functions are constructed, which are simultaneously orthogonal in both L 2 - and H 1 -inner products, and lead to diagonal systems for second order problems. Then we construct mixed Legendre-Laguerre spectral element methods for solving high oscillation or steep gradient solutions problems on unbounded domains, which reduce the non-zero entries of linear systems and computational cost. We also analyze the optimal convergence of numerical solutions and describe its numerical implementation. Numerical experiments exhibit the effectiveness and accuracy of the suggested approaches. [ABSTRACT FROM AUTHOR]

Let A be a complex matrix. The question when a generalized column constrained inverse coincides with a generalized row constrained inverse was answered, which lead to the generalized constrained inverse of A was introduced and this inverse coincides with the weak group inverse. Moreover, the "distance" between the generalized constrained inverse and the inverse along two matrices was given, that is, the generalized constrained inverse of A coincides with the (Ak, (Ak)*A)-inverse of A, where k is the index of A. [ABSTRACT FROM AUTHOR]

In 2020, Cossu and Zanardo raised a problem on the idempotent factorization of singular matrices in the form ( p z z ¯ ‖ z ‖ / p ) , where p is a prime integer which is irreducible but not prime in the ring of integers O K , with K a real quadratic number field, and z ∈ O K is such that 〈 p , z 〉 is a non-principal ideal. In this paper, we provide some classes of matrices that factor in a prescribed way and some other classes that do not. We further show that there are matrices in the above form that cannot be written as a product of two idempotent matrices. [ABSTRACT FROM AUTHOR]

This paper proposes a dual-channel speech separation method based on spatial estimation via sparse Bayesian inference (SBI) and nonnegative matrix factorization (NMF). The spatial information estimated by traditional compressed sensing (CS) models is insufficient when two microphones receive limited columns of mixed signals. Considering the sparsity of peak values in the cross-correlation spectrum between two received signals, the proposed method builds a new CS model based on cross-correlation spectrum and applies SBI algorithm to solve this model to improve the estimation accuracy of spatial information. Combined the spatial information with the spectral features decomposed by NMF, NMF coefficient matrix masks belonging to individual source are generated for pre-separation. To mitigate retained potential interference components, a post-separation processing stage is designed using an expectation maximization (EM) algorithm based on a Gaussian mixture model (GMM). The estimated spatial information and binary time–frequency masks are used for parameter initialization of the EM algorithm. The experimental results using real-world speech data show that the proposed method can achieve better separation performance compared to various existing methods. [ABSTRACT FROM AUTHOR]

In recent years, many cities have taken measures to reduce volatile organic compounds (VOCs), an important precursor of ozone (O 3), to alleviate O 3 pollution in China. 116 VOC species were measured by online and offline methods in the urban area of Jiaozuo from May to October in 2021 to analyze the compositional characteristics. VOC sources were analyzed by a positive matrix factorization (PMF) model, and the sensitivity of ozone generation was determined by ozone isopleth plotting research (OZIPR) simulation. The results showed that the average volume concentration of total VOCs was 30.54 ppbv and showed a bimodal feature due to the rush-hour traffic in the morning and at nightfall. The most dominant VOC groups were oxygenated VOCs (OVOCs, 29.3%) and alkanes (26.7%), and the most abundant VOC species were acetone and acetylene. However, based on the maximum incremental reactivity (MIR) method, the major VOC groups in terms of ozone formation potential (OFP) contribution were OVOCs (68.09 µg/m3, 31.5%), aromatics (62.90 µg/m3, 29.1%) and alkene/alkynes (54.90 µg/m3, 25.4%). This indicates that the control of OVOCs, aromatics and alkene/alkynes should take priority. Five sources of VOCs were quantified by PMF, including fixed sources of fossil fuel combustion (27.8%), industrial processes (25.9%), vehicle exhaust (19.7%), natural and secondary formation (13.9%) and solvent usage (12.7%). The empirical kinetic modeling approach (EKMA) curve obtained by OZIPR on O 3 exceedance days indicated that the O 3 sensitivity varied in different months. The results provide theoretical support for O 3 pollution prevention and control in Jiaozuo. [ABSTRACT FROM AUTHOR]

• Characteristics, sources and health risks of PM 2.5 -bound elements were explored. • The accumulated cancer risk exceeded the threshold of 10−6. • Dust was the leading source, but traffic source was the main contributor of risks. • Serious health risks caused by trace elements existed in special events. To gain a comprehensive understanding of sources and health risks of trace elements in an area of China with high population densities and low PM 2.5 concentrations, 15 trace elements (Al, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, As, Sn, Ba, Pb) in PM 2.5 were monitored from December 2020 to November 2021 in a representative city, Xiamen. The concentrations of trace elements in Xiamen displayed an obvious seasonal variation and were dominated by K, Fe, Al, Ca and Zn. Based on Positive Matrix Factorization analysis, source appointment revealed that the major sources of trace elements in Xiamen were traffic, dust, biomass and firework combustion, industrial manufacture and shipping emission. According to health risk assessment combined with the source appointment results, it indicated that the average noncarcinogenic risk was below the threshold and cancer risk of four hazardous metals (Cr, Ni, As, Pb) exceeded the threshold (10−6). Traffic-related source had almost half amount of contribution to the health risk induced by PM 2.5 -bound trace elements. During the dust transport period or Spring Festival period, the health risks exceeded an acceptable threshold even an order of magnitude higher, suggesting that the serious health risks still existed in low PM 2.5 environment at certain times. Health risk assessment reminded that the health risk reduction in PM 2.5 at southeastern China should prioritize traffic-related hazardous trace elements and highlighted the importance of controlling vehicles emissions in the future. [ABSTRACT FROM AUTHOR]

• ON particles increased as NO x enhancement at night. • ON particles were mainly produced via heterogeneous reactions between NO x and organics. • The decrease of ON particles was associated with photo-bleaching effect. Organic nitrogen (ON) compounds play a significant role in the light absorption of brown carbon and the formation of organic aerosols, however, the mixing state, secondary formation processes, and influencing factors of ON compounds are still unclear. This paper reports on the mixing state of ON-containing particles based on measurements obtained using a high-performance single particle aerosol mass spectrometer in January 2020 in Guangzhou. The ON-containing particles accounted for 21% of the total detected single particles, and the particle count and number fraction of the ON-containing particles were two times higher at night than during the day. The prominent increase in the content of ON-containing particles with the enhancement of NO x mainly occurred at night, and accompanied by high relative humidity and nitrate, which were associated with heterogeneous reactions between organics and gaseous NO x and/or NO 3 radical. The synchronous decreases in ON-containing particles and the mass absorption coefficient of water-soluble extracts at 365 nm in the afternoon may be associated with photo-bleaching of the ON species in the particles. In addition, the positive matrix factorization analysis found five factors dominated the formation processes of ON particles, and the nitrate factor (33%) mainly contributed to the production of ON particles at night. The results of this study provide unique insights into the mixing states and secondary formation processes of the ON-containing particles. [Display omitted] [ABSTRACT FROM AUTHOR]

A reformulation of the Ornstein–Zernike equation for a homogeneous isotropic fluid composed of m species, with spherical symmetry, is formally derived. Based on a factorization of matrices of composed functions, this reformulation provides an interesting new set of functions. As a test to this reformulation, the resulting equations are solved for a binary mixture of hard spheres and compared to those obtained from the standard solution of the Ornstein–Zernike equation and with molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Heavy metal(loid)s (HMs) pollution has become a common and complex problem in industrial parks due to rapid industrialization and urbanization. Here, soil and groundwater were sampled from a retired industrial park to investigate the pollution characteristics of HMs. Results show that Ni, Pb, Cr, Zn, Cd, and Cu were the typical HMs in the soil. Source analysis with the positive matrix factorization model indicates that HMs in the topsoil stemmed from industrial activities, traffic emission, and natural source, and the groundwater HMs originated from industrial activities, groundwater-soil interaction, groundwater-rock interaction, and atmosphere deposition. The sequential extraction of soil HMs reveals that As and Hg were mainly distributed in the residue fraction, while Ni, Pb, Cr, Zn, Cd, and Cu mainly existed in the mobile fraction. Most HMs either in the total concentration or in the bioavailable fraction preferred to retain in soil as indicated by their high soil-water partitioning coefficients (K d), and the K d values were correlated with soil pH, groundwater redox potential, and dissolved oxygen. The relative stable soil-groundwater circumstance and the low active fraction contents limited the vertical migration of soil HMs and their release to groundwater. These findings increase our knowledge about HMs pollution characteristics of traditional industrial parks and provide a protocol for HMs pollution scrutinizing in large zones. [Display omitted] [ABSTRACT FROM AUTHOR]

Recommender Systems (RS) are a vital part of companies with an active participation on the web. These companies require strategies that allow them to take advantage of product ratings from users in order to provide future recommendations to other users. In the last decade, several algorithms have been developed for movie recommendation, with Matrix Factorization algorithm being one of the most popular algorithms. Our approach is to evaluate the performance of this recommendation algorithm in scenarios where underlying social networks, which characterize certain types of interactions between users, can be inferred. In particular, the MovieLens dataset is used, which consists of approximately 100,000 ratings by 671 users on 9066 movies, during the period from 29 March 1996 to 24 September 2018. [ABSTRACT FROM AUTHOR]

Background: Alzheimer's disease (AD) is an irreversible primary brain disease with insidious onset. The rise of imaging genetics research has led numerous researchers to examine the complex association between genes and brain phenotypes from the perspective of computational biology. Methods: Given that most previous studies have assumed that imaging data and genetic data are linearly related and are therefore unable to explore their nonlinear relationship, our study applied a joint depth semi-supervised nonnegative matrix decomposition (JDSNMF) algorithm to solve this problem. The JDSNMF algorithm jointly decomposed multimodal imaging genetics data into both a standard basis matrix and multiple feature matrices. During the decomposition process, the coefficient matrix A multilayer nonlinear transformation was performed using a neural network to capture nonlinear features. Results: The results using a real dataset demonstrated that the algorithm can fully exploit the association between strongly correlated image genetics data and effectively detect biomarkers of AD. Our results might provide a reference for identifying biologically significant imaging genetic correlations, and help to elucidate disease-related mechanisms. Conclusions: The diagnostic model constructed by the top features of the three modality data sets mined by the algorithm has high accuracy, and these features are expected to become new therapeutic targets for AD. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce a new series of Legendre basis functions by using the matrix decomposition technique, which are simultaneously orthogonal in both L 2 - and H 1 -inner products. Then, we construct efficient space-time spectral method for linear Sobolev equation using spectral approximation in space and multi-domain collocation approximation in time, which can be implemented in a synchronous parallel fashion. Next, we propose a novel Legendre spectral element method for solving nonlinear Sobolev equation with Burgers' type term, which reduce the non-zero entries of linear systems and computational cost. Some rigorous error estimates are carried out for one-dimensional Sobolev equation. Numerical experiments illustrate the effectiveness and accuracy of the suggested approaches. [ABSTRACT FROM AUTHOR]

Time-dependent photodetachment action spectra for the linear hydrocarbon anions C4H− and C6H− are investigated using the cryogenic Double ElectroStatic Ion Ring ExpEriment. The radiative cooling characteristics of these ions on the millisecond to seconds timescale are characterized by monitoring changes in their spectra as the ions cool by spontaneous infrared (IR) emission. The average cooling rates, extracted using Non-negative Matrix Factorization, are fit with 1/e lifetimes of 19 ± 2 and 3.0 ± 0.2 s for C4H− and C6H−, respectively. The cooling rates are successfully reproduced using a simple harmonic cascade model of IR emission. The ultraslow radiative cooling dynamics determined in this work provide important data for understanding the thermal cooling properties of linear hydrocarbon anions and for refining models of the formation and destruction mechanisms of these anions in astrochemical environments. [ABSTRACT FROM AUTHOR]

The significance of community structure in complex networks, such as social, biological, and online networks, has been widely recognized. Detecting communities in social media networks typically relies on two sources of information: the network's topological structure and node attributes. Incorporating rich node content attribute information poses both flexibility and challenges for community detection. Traditional approaches either focus on mining one information source or linearly combining results from both sources, which fails to effectively fuse the information. This paper introduces a practical collaborative learning approach that explores the multi-dimensional attribute characteristics of nodes to facilitate community division. By leveraging graphical matrix decomposition, the proposed algorithm, CDGMF, improves the effectiveness and robustness of community detection. Experimental results demonstrate the method's ability to effectively utilize node attribute information for guiding community detection, resulting in higher-quality community divisions. [ABSTRACT FROM AUTHOR]