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A series of compounds featuring a novel bispiro[indanedione-oxindole-cyclopropane] moiety have been synthesized through a squaramide-catalyzed [2+1] cycloaddition reaction. The tandem Michael-alkylation reaction of 2-arylidene-1,3-indanediones with 3-bromooxindoles furnished the cycloadducts in high yields with excellent diastereo- and enantioselectivities. The ammonium ylide in the catalytic process, as a key intermediate, was revealed by the high-resolution mass spectrometry study.
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Reação de Cicloadição , EstereoisomerismoRESUMO
The first enantioselective formal (3 + 2) cyclocondensation involving α,ß-unsaturated pyrazoleamides as 3-carbon partners was accomplished in a stepwise fashion. The stepwise esterification/Michael addition sequence is promoted by Zn(OTf)2 and quinine-squaramide derivative, respectively. The protocol enables access to spiro-fused pentacyclic spirooxindoles from coumarin-3-formylpyrazoles and 3-hydroxyoxindoles in good to satisfactory overall yields (up to 91%) with excellent dr (all cases >20:1 dr) and high ee values (up to 99%). Mechanistic investigations contributed to shedding light on the enantioselective event of the process.
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Carbono , Cumarínicos , Estereoisomerismo , Esterificação , CatáliseRESUMO
P-type H+ ATPases mediate active H+ efflux from plant cells. They generate a proton motive force across the plasma membrane, providing the free energy to drive the transport of other solutes, partly by coupling to H+ influx. Wegner & Shabala (2020) recently suggested that passive H+ influx can exceed pump-driven efflux due to 'active buffering', that is, cytosolic H+ scavenging and apoplastic H+ generation by metabolism ('biochemical pH clamp'). Charge balance is provided by K+ efflux or anion influx. Here, this hypothesis is extended to net H+ efflux: even though H+ pumping is faster than backflow via symporters and antiporters, a progressive increase in the transmembrane pH gradient is avoided. Cytosolic H+ release is associated with bicarbonate formation from CO2 . Bicarbonate serves as substrate for the PEPCase, catalyzing the reaction from phosphoenolpyruvate to oxaloacetate, which is subsequently reduced to malate. Organic anions such as malate and citrate are released across the plasma membrane and are (partly) protonated in the apoplast, thus limiting pump-induced acidification. Moreover, a 'biophysical pH clamp' is introduced, that is, adjustment of apoplastic/cytosolic pH involving net H+ fluxes across the plasma membrane, while the gradient between compartments is maintained. The clamps are not mutually exclusive but are likely to coexist.
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Células Vegetais , Transporte Biológico , Membrana Celular/metabolismo , Citosol/metabolismo , Concentração de Íons de HidrogênioRESUMO
BACKGROUND: Cardiotocography (CTG) interpretation plays a critical role in prenatal fetal monitoring. However, the interpretation of fetal status assessment using CTG is mainly confined to clinical research. To the best of our knowledge, there is no study on data analysis of CTG records to explore the causal relationships between the important CTG features and fetal status evaluation. METHODS: For analyses, 2126 cardiotocograms were automatically processed and the respective diagnostic features measured by the Sisporto program. In this paper, we aim to explore the causal relationships between the important CTG features and fetal status evaluation. First, we utilized data visualization and Spearman correlation analysis to explore the relationship among CTG features and their importance on fetal status assessment. Second, we proposed a forward-stepwise-selection association rule analysis (ARA) to supplement the fetal status assessment rules based on sparse pathological cases. Third, we established structural equation models (SEMs) to investigate the latent causal factors and their causal coefficients to fetal status assessment. RESULTS: Data visualization and the Spearman correlation analysis found that thirteen CTG features were relevant to the fetal state evaluation. The forward-stepwise-selection ARA further validated and complemented the CTG interpretation rules in the fetal monitoring guidelines. The measurement models validated the five latent variables, which were baseline category (BCat), variability category (VCat), acceleration category (ACat), deceleration category (DCat) and uterine contraction category (UCat) based on fetal monitoring knowledge and the above analyses. Furthermore, the interpretable models discovered the cause factors of fetal status assessment and their causal coefficients to fetal status assessment. For instance, VCat could predict BCat, and UCat could predict DCat as well. ACat, BCat and DCat directly affected fetal status assessment, where ACat was the important causal factor. CONCLUSIONS: The analyses revealed the interpretation rules and discovered the causal factors and their causal coefficients for fetal status assessment. Moreover, the results are consistent with the computerized fetal monitoring and clinical knowledge. Our approaches are conducive to evidence-based medical research and realizing intelligent fetal monitoring.
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Cardiotocografia , Frequência Cardíaca Fetal , Feminino , Monitorização Fetal , Humanos , GravidezRESUMO
Complex, multigenic biological traits are shaped by the emergent interaction of proteins being the main functional units at the molecular scale. Based on a phenomenological approach, algorithms for quantifying two different aspects of emergence were introduced (Wegner and Hao in Progr Biophys Mol Biol 161:54-61, 2021) describing: (i) pairwise reciprocal interactions of proteins mutually modifying their contribution to a complex trait (denoted as weak emergence), and (ii) formation of a new, complex trait by a set of n 'constitutive' proteins at concentrations exceeding individual threshold values (strong emergence). The latter algorithm is modified here to take account of protein redundancy with respect to a complex trait ('full redundancy'). Irreducibility is considered a necessary and sufficient criterion for strong biological emergence; if one constitutive protein is missing, or its concentration drops below the threshold the trait is lost. A definition based on 'unpredictability' is dismissed, because this criterion is irrelevant for the evolution of a complex trait, and apparent unpredictability may rather reflect our basic deficits in understanding unless we can provide an unequivocal proof for it. The phenomenological approach advocated here allows to identify hidden rules according to which strongly emergent traits may be organized. This is of high value for understanding the evolution of complex traits which seems to require the saltational advent of all constitutive proteins 'in one turn' to arrive at a functional trait providing for an improved fitness of the organism. Rather than being a purely random process, it may be guided by fundamental structural principles.
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Algoritmos , Evolução Biológica , FenótipoRESUMO
Soil salinization is a major threat to global food security and the biodiversity of natural ecosystems. To adapt to salt stress, plants rely on ROS-mediated signalling networks that operate upstream of a broad array of physiological and genetic processes. A key player in ROS signalling is NADPH oxidase, a plasma-membrane-bound enzyme encoded by RBOH genes. In this study, we have conducted a comprehensive bioinformatic analysis of over 50 halophytic and glycophytic species to link the difference in the kinetics of ROS signalling between contrasting species with the abundance and/or structure of NADPH oxidases. The RBOH proteins were predicted in all the tested plant lineages except some algae species from the Rhodophyta, Chlorophyta and Streptophyta. Within the glycophytic group, the number of RBOH copies correlated negatively with salinity stress tolerance, suggesting that a reduction in the number of RBOH isoforms may be potentially related to the evolution of plant salinity tolerance. While halophytes did not develop unique protein families during evolution, they evolved additional phosphorylation target sites at the N-termini of NADPH oxidases, potentially modulating enzyme activity and allowing more control over their function, resulting in more efficient ROS signalling and adaptation to saline conditions.
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NADPH Oxidases/fisiologia , Plantas Tolerantes a Sal/enzimologia , Evolução Biológica , NADPH Oxidases/genética , Tolerância ao Sal/genética , Tolerância ao Sal/fisiologia , Plantas Tolerantes a Sal/genética , Plantas Tolerantes a Sal/fisiologiaRESUMO
Precision oncology involves effectively selecting drugs for cancer patients and planning an effective treatment regimen. However, for Molecular targeted drug, using genomic state of the drug target to select drugs has limitations. Many patients who could benefit from molecularly targeted drugs, but they are being missed due to the insufficient labelling ability of the existing target genes. For non-specific chemotherapy drugs, most of the first-line anticancer drugs do not have biomarkers to guide doctor make treatment regimen. Furthermore, it is important to determine a long-term treatment plan based on the patient's genomic data during tumor evolution. Therefore, it is necessary to establish a tumor drug sensitivity prediction model, which can assist doctors in designing a personalized tumor treatment regimen. This paper proposed a novel model to predict tumor drug sensitivity including targeted drugs and non-specific chemotherapy drugs. This model uses statistical methods based on Bimodal distribution to select multimodal genetic data to solve dimensional challenges and reduce noise and to establish a classification model to predict the effectiveness of the drug in the tumor cell line using machine learning. The experimental test 87 molecular targeted drugs and non-specific chemotherapy drugs. The results show that the method can effectively predict the sensitivity of tumor drugs with an average sensitivity of 0.98 and specificity of 0.97. This model is worth to promotion. If it can be successfully used in clinical trials, it will effectively assist doctors to develop personalized cancer treatment programs and expand the application of molecularly targeted drugs.
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Antineoplásicos/farmacologia , Biomarcadores Tumorais/antagonistas & inibidores , Técnicas de Apoio para a Decisão , Genômica , Aprendizado de Máquina , Neoplasias/tratamento farmacológico , Medicina de Precisão , Biomarcadores Tumorais/genética , Biomarcadores Tumorais/metabolismo , Linhagem Celular Tumoral , Tomada de Decisão Clínica , Bases de Dados Genéticas , Ensaios de Seleção de Medicamentos Antitumorais , Regulação Neoplásica da Expressão Gênica , Humanos , Modelos Estatísticos , Terapia de Alvo Molecular , Neoplasias/genética , Neoplasias/metabolismo , Farmacogenética , Transdução de SinaisRESUMO
Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, causal discovery based on a constraint approach could recover the causal structures from passive observational data in general cases, and had shown extensive prospects in numerous real world applications. However, when the graph was sufficiently large, it did not work well. To alleviate this problem, an improved causal structure learning algorithm named brain storm optimization (BSO), is presented in this paper, combining K2 with brain storm optimization (K2-BSO). Here BSO is used to search optimal topological order of nodes instead of graph space. This paper assumes that dataset is generated by conforming to a causal diagram in which each variable is generated from its parent based on a causal mechanism. We designed an elaborate distance function for clustering step in BSO according to the mechanism of K2. The graph space therefore was reduced to a smaller topological order space and the order space can be further reduced by an efficient clustering method. The experimental results on various real-world datasets showed our methods outperformed the traditional search and score methods and the state-of-the-art genetic algorithm-based methods.
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Algoritmos , Aprendizado de Máquina , Modelos Teóricos , HumanosRESUMO
MOTIVATION: Genome-wide association studies (GWASs) are commonly applied on human genomic data to understand the causal gene combinations statistically connected to certain diseases. Patients involved in these GWASs could be re-identified when the studies release statistical information on a large number of single-nucleotide polymorphisms. Subsequent work, however, found that such privacy attacks are theoretically possible but unsuccessful and unconvincing in real settings. RESULTS: We derive the first practical privacy attack that can successfully identify specific individuals from limited published associations from the Wellcome Trust Case Control Consortium (WTCCC) dataset. For GWAS results computed over 25 randomly selected loci, our algorithm always pinpoints at least one patient from the WTCCC dataset. Moreover, the number of re-identified patients grows rapidly with the number of published genotypes. Finally, we discuss prevention methods to disable the attack, thus providing a solution for enhancing patient privacy. AVAILABILITY AND IMPLEMENTATION: Proofs of the theorems and additional experimental results are available in the support online documents. The attack algorithm codes are publicly available at https://sites.google.com/site/zhangzhenjie/GWAS_attack.zip. The genomic dataset used in the experiments is available at http://www.wtccc.org.uk/ on request.
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Algoritmos , Privacidade Genética , Estudo de Associação Genômica Ampla , Genoma Humano , Genótipo , Humanos , Polimorfismo de Nucleotídeo ÚnicoRESUMO
In multi-instance nonparallel plane learning (NPL), the training set is comprised of bags of instances and the nonparallel planes are trained to classify the bags. Most of the existing multi-instance NPL methods are proposed based on a twin support vector machine (TWSVM). Similar to TWSVM, they use only a single plane to generalize the data occurrence of one class and do not sufficiently consider the boundary information, which may lead to the limitation of their classification accuracy. In this article, we propose a multi-instance nonparallel tube learning (MINTL) method. Distinguished from the existing multi-instance NPL methods, MINTL embeds the boundary information into the classifier by learning a large-margin-based ϵ -tube for each class, such that the boundary information can be incorporated into refining the classifier and further improving the performance. Specifically, given a K -class multi-instance dataset, MINTL seeks K ϵ -tubes, one for each class. In multi-instance learning, each positive bag contains at least one positive instance. To build up the ϵk -tube of class k , we require that each bag of class k should have at least one instance included in the ϵk -tube. Moreover, except for one instance included in the ϵk -tube, the remaining instances in the positive bag may include positive instances or irrelevant instances, and their labels are unavailable. A large margin constraint is presented to assign the remaining instances either inside the ϵk -tube or outside the ϵk -tube with a large margin. Substantial experiments on real-world datasets have shown that MINTL obtains significantly better classification accuracy than the existing multi-instance NPL methods.
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This paper focuses on the problem of semi-supervised domain adaptation for time-series forecasting, which is underexplored in literature, despite being often encountered in practice. Existing methods on time-series domain adaptation mainly follow the paradigm designed for static data, which cannot handle domain-specific complex conditional dependencies raised by data offset, time lags, and variant data distributions. In order to address these challenges, we analyze variational conditional dependencies in time-series data and find that the causal structures are usually stable among domains, and further raise the causal conditional shift assumption. Enlightened by this assumption, we consider the causal generation process for time-series data and propose an end-to-end model for the semi-supervised domain adaptation problem on time-series forecasting. Our method can not only discover the Granger-Causal structures among cross-domain data but also address the cross-domain time-series forecasting problem with accurate and interpretable predicted results. We further theoretically analyze the superiority of the proposed method, where the generalization error on the target domain is bounded by the empirical risks and by the discrepancy between the causal structures from different domains. Experimental results on both synthetic and real data demonstrate the effectiveness of our method for the semi-supervised domain adaptation method on time-series forecasting.
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Conditional independence (CI) testing is an important problem, especially in causal discovery. Most testing methods assume that all variables are fully observable and then test the CI among the observed data. Such an assumption is often untenable beyond applications dealing with, e.g., psychological analysis about the mental health status and medical diagnosing (researchers need to consider the existence of latent variables in these scenarios); and typically adopted latent CI test schemes mainly suffer from robust or efficient issues. Accordingly, this article investigates the problem of testing CI between latent variables. To this end, we offer an auxiliary regression-based CI (AReCI) test by taking the measured variable as the surrogate variable of the latent variables to conduct the regression over the latent variables under the linear causal models, in which each latent variable has some certain measured variables. Specifically, given a pair of latent variables LX and LY , and a corresponding latent variable set LO , [Formula: see text] holds if and only if [Formula: see text] and [Formula: see text] are statistically independent, where A' and A'' are the two disjoint subset of the measured variable for the corresponding latent variables, A'{LO} â©A''{LO} = ∅ , and ω1 is a parameter vector characterized from the cross covariance between A{LX} and A'{LO} , and ω2 is a parameter vector characterized from the cross covariance between A{LY} and A''{LO} . We theoretically show that the AReCI test is capable of addressing both Gaussian and non-Gaussian data. In addition, we find that the well-known partial correlation test can be seen as a special case of the AReCI test. Finally, we devise a causal discovery method by using the AReCI test as the CI test. The experimental results on synthetic and real-world data illustrate the effectiveness of our method.
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To solve the problem of ice condensation and adhesion, it is urgent to develop new anti-icing and deicing technologies. This study presented the development of a highly efficient photothermal-enhanced superhydrophobic PDMS/Ni@Ti3C2Tx composite film (m-NMPA) fabricated cost-effectively and straightforwardly. This film was fabricated utilizing PDMS as a hydrophobic agent, adhesive, and surface protector, while Ni@Ti3C2Tx as a magnetic photothermal filler innovatively. Through a simple spraying method, the filler is guided by a strong magnetic field to self-assemble into an eyelash-like microstructure array. The unique structure not only imparts superhydrophobic properties to the surface but also constructs an efficient "light-capturing" architecture. Remarkably, the m-NMPA film demonstrates outstanding superhydrophobic passive anti-icing and efficient photothermal active deicing performance without the use of fluorinated chemicals. The micro-/nanostructure of the film forms a gas layer, significantly delaying the freezing time of water. Particularly under extreme cold conditions (-30 °C), the freezing time is extended by a factor of 7.3 compared to the bare substrate. Furthermore, under sunlight exposure, surface droplets do not freeze. The excellent photothermal performance is attributed to the firm anchoring of nickel particles on the MXene surface, facilitating effective "point-to-face" photothermal synergy. The eyelash-like microarray structure enhances light-capturing capability, resulting in a high light absorption rate of 98%. Furthermore, the microstructure aids in maintaining heat at the uppermost layer of the surface, maximizing the utilization of thermal energy for ice melting and frost thawing. Under solar irradiation, the m-NMPA film can rapidly melt approximately a 4 mm thick ice layer within 558 s and expel the melted water promptly, reducing the risk of secondary icing. Additionally, the ice adhesion force on the surface of the m-NMPA film is remarkably low, with an adhesion strength of approximately 4.7 kPa for a 1 × 1 cm2 ice column. After undergoing rigorous durability tests, including xenon lamp weathering test, pressure resistance test, repeated adhesive tape testing, xenon lamp irradiation, water drop impact testing, and repeated brushing with hydrochloric acid and particles, the film's surface structure and superhydrophobic performance have remained exceptional. The photothermal superhydrophobic passive anti-icing and active deicing technology in this work rely on sustainable solar energy for efficient heat generation. It presents broad prospects for practical applications with advantages such as simple processing method, environmental friendliness, outstanding anti-icing effects, and exceptional durability.
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Multiview clustering (MVC) has been widely studied in machine learning and data mining for its capability of improving clustering performance by fusing the information from multiview data. In the past decade, a large number of MVC methods have made impressive progress, but most of them suffer from computational burdens, especially in large-scale tasks. Binary MVC (BMVC) is proposed to address this issue by representing the large-scale high-dimensional dataset as a group of consensus and low-dimensional binary codes. However, current BMVC-based approaches generate the clustering by executing binary k -means on the obtained binary codes, which fail to capture the embedded geometric information, leading to poor clustering performance. In addition, parameter selection is another "mission impossible" in unsupervised learning tasks including MVC. To tackle these challenges, a framework of multiview clustering via partitioning the signed prototype graph (SPGMVC) is proposed in this work. The SPGMVC framework offers several contributions. First, SPGMVC is designed as a unified framework for MVC. It combines effective technologies, such as consensus binary coding, code compression (CC), signed prototype graph (SPG) partitioning, and prototype-based cluster assignment. Second, SPGMVC partitions the signed graph (SG) based on the relationships between positive and negative edges. By capturing the underlying structure of the data, this partitioning strategy improves clustering accuracy (ACC). CC techniques are applied to reduce the graph's scale, enabling further partitioning and enhancing computational efficiency. Third, SPGMVC employs an alternate minimizing strategy to efficiently handle the optimization problem. This strategy has nearly linear time and space complexity with respect to the data volume, making it suitable for large-scale tasks. Fourth, SPGMVC proposes an automatic parameter selection strategy, eliminating the need for extensive parameter exploration. Comprehensive experiments illustrate the superiority of our model. The implementation of SPGMVC is available at: https://github.com/gepingyang/PSGMVC.
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Soft elastomer composites are promising functional materials for engineer interfaces, where the miniaturized electronic devices have triggered increasing demand for effective heat dissipation, high fracture energy, and antifatigue fracture. However, such a combination of these properties can be rarely met in the same elastomer composites simultaneously. Here a strategy is presented to fabricate a soft, extreme fracture tough (3316 J m-2) and antifatigue fracture (1052.56 J mâ»2) polydimethylsiloxane/aluminum elastomer composite. These outstanding properties are achieved by optimizing the dangling chains and spherical aluminum fillers, resulting in the combined effects of crack pinning and interfacial slippage. The dangling chains that lengthen the polymer chains between cross-linked points pin the cracks and the rigid fillers obstruct the cracks, enhancing the energy per unit area needed for fatigue failure. The dangling chains also promote polymer/filler interfacial slippage, enabling effective deflection and blunting of an advancing crack tip, thus enhancing mechanical energy dissipation. Moreover, the elastomer composite exhibits low thermal resistance (≈0.12 K cm2 W-1), due to the formation of a thermally conductive network. These remarkable characteristics render this elastomer composite promising for application as a thermal interface material in electronic devices.
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Temporal recommendation which recommends items to users with consideration of time information has been of wide interest in recent years. But huge event space, highly sparse user activities and time-heterogeneous dependency of temporal behaviors make it really challenging to learn the temporal patterns for high-quality recommendation. In this paper, aiming to handle these challenges, especially the time-heterogeneous characteristic of user's temporal behaviors, we proposed the Neural-based Time-heterogenous Markov Transition (NeuralTMT) model. Firstly, users' temporal behaviors are mathematically simplified as the third-order Markov transition tensors. And then a linear co-factorization model which learns the time-evolving user/item factors from these tensors is proposed. Furthermore, the model is extended to the neural-based learning framework (NeuralTMT), which is more flexible and able to capture time-heterogeneous temporal patterns via nonlinear neural network mappings and attention techniques. Extensive experiments on four datasets demonstrate that NeuralTMT performs significantly better than the state-of-the-art baselines. And the proposed method is fundamentally inspired by factorization techniques, which may also provide some interesting ideas on the connection of tensor factorization and neural-based sequential recommendation methods.
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Aprendizado de Máquina , Redes Neurais de Computação , AprendizagemRESUMO
Causal discovery from observational data is an important but challenging task in many scientific fields. A recent line of work formulates the structure learning problem as a continuous constrained optimization task using an algebraic characterization of directed acyclic graphs (DAGs) and the least-square loss function. Though the least-square loss function is well justified under the standard Gaussian noise assumption, it is limited if the assumption does not hold. In this work, we theoretically show that the violation of the Gaussian noise assumption will hinder the causal direction identification, making the causal orientation fully determined by the causal strength as well as the variances of noises in the linear case and by the strong non-Gaussian noises in the nonlinear case. Consequently, we propose a more general entropy-based loss that is theoretically consistent with the likelihood score under any noise distribution. We run extensive empirical evaluations on both synthetic data and real-world data to validate the effectiveness of the proposed method and show that our method achieves the best in structure Hamming distance, false discovery rate (FDR), and true-positive rate (TPR) matrices.
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Scheduling is significant in improving the production efficiency and reducing delivery delays for manufacturing enterprises. Unlike the flexible job-shop scheduling problem, two special constraints are encountered in real-world power supply manufacturing systems: 1) periodic maintenance and 2) mandatory outsourcing. As the characteristics of these constraints are not considered in existing scheduling algorithms, schedules generated by most existing approaches are not optimal or even conflict with these constraints. In this article, a self-organizing neural scheduler (SoNS) is proposed to overcome this limitation. A long short-term memory encoder is developed to transform the variable-length structural information into fixed-length feature vectors. Moreover, the reinforcement learning model is proposed to automatically select policies for improving candidate schedules. To validate the effectiveness of the proposed algorithm, extensive experiments are conducted on over 300 problem instances. The nonparametric Kruskal-Wallis tests confirm that the proposed algorithm outperforms several state-of-the-art methods in terms of effectiveness and robustness within a limited computational budget. It demonstrates that the proposed SoNS can solve scheduling problems with the periodic maintenance and mandatory outsourcing constraints effectively.
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Automated tuning can significantly improve productivity and save the costs of manual operation in the microwave filter manufacturing industry. This article proposes a mathematical model of scattering data optimization to find the accurate coupling matrix for multiple-version microwave filters, a core step of automated microwave filter tuning. For the large-scale problem of coupling coefficient combination, we propose a decision set decomposition strategy that evenly divides the entire frequency interval into several subintervals according to the correlation between scattering data. With this strategy, we design a microscale (small-size subsets of the decomposed decision set) searching algorithm, which solves each suboptimization problem by searching the decision subset instead of the entire decision set. To verify the validity of the proposed algorithm for multiple-version microwave filters, experiments are conducted on three versions of microwave filters from a real-world production line, including the two-port eighth-order, ninth-order, and tenth-order microwave filters. Experimental results show that the proposed model is feasible within the industrial error for the multiversion microwave filter tuning problem. Besides, the proposed algorithm outperforms the state-of-the-art optimization algorithms in the coupling matrix optimization problem.
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Nonlinear causal discovery with high-dimensional data where each variable is multidimensional plays a significant role in many scientific disciplines, such as social network analysis. Previous work majorly focuses on exploiting asymmetry in the causal and anticausal directions between two high-dimensional variables (a cause-effect pair). Although there exist some works that concentrate on the causal order identification between multiple variables, i.e., more than two high-dimensional variables, they do not validate the consistency of methods through theoretical analysis on multiple-variable data. In particular, based on the asymmetry for the cause-effect pair, if model assumptions for any pair of the data are violated, the asymmetry condition will not hold, resulting in the deduction of incorrect order identification. Thus, in this article, we propose a causal functional model, namely high-dimensional deterministic model (HDDM), to identify the causal orderings among multiple high-dimensional variables. We derive two candidates' selection rules to alleviate the inconvenient effects resulted from the violated-assumption pairs. The corresponding theoretical justification is provided as well. With these theoretical results, we develop a method to infer causal orderings for nonlinear multiple-variable data. Simulations on synthetic data and real-world data are conducted to verify the efficacy of our proposed method. Since we focus on deterministic relations in our method, we also verify the robustness of the noises in simulations.