Search Results (66)

Protein function emerges from dynamic conformational changes, yet structure prediction methods provide only static snapshots. While AlphaFold3 (AF3) predicts protein structures, the potential for extracting dynamic information from its ensemble predictions has remained underexplored. Here, we demonstrate that AF3 structural ensembles contain substantial dynamic information that correlates remarkably well with molecular dynamics simulations (MD). We developed ChronoSort, a novel algorithm that organizes static structure predictions into temporally coherent trajectories by minimizing structural differences between neighboring frames. Through systematic analysis of four diverse protein targets, we show that root-mean-square fluctuations derived from AF3 ensembles can correlate strongly with those from MD (r = 0.53 to 0.84). Principal component analysis reveals that AF3 predictions capture the same collective motion patterns observed in molecular dynamics trajectories, with eigenvector similarities significantly exceeding random distributions. ChronoSort trajectories exhibit structural evolution profiles comparable to MD. These findings suggest that modern AI-based structure prediction tools encode conformational flexibility information that can be systematically extracted without expensive MD. We provide ChronoSort as open-source software to enable broad community adoption. This work offers a novel approach to extracting functional insights from structure prediction tools in minutes, with significant implications for synthetic biology, protein engineering, drug discovery, and structure–function studies. Full article

This paper focuses on the inverse extremal eigenvalue problem (IEEP) and a special inverse singular value problem (ISVP). First, a bordered tridiagonal matrix is constructed from the extremal eigenvalues of its leading principal submatrices and an eigenvector. Then, based on the previous construction, a Lefkovitch-type matrix is constructed from a particular set of singular values and a singular vector. Sufficient conditions are established for the existence of a symmetric bordered tridiagonal matrix, while the nonsymmetric case is also addressed. Finally, numerical examples illustrating these constructions derived from the main results are presented. Full article

This study proposes a rapid method for identifying the geographical origin of Poria by combining Raman spectroscopy with an improved PCA algorithm—multi-matrix projection discrimination analysis. Poria samples from four Chinese provinces—Yunnan, Anhui, Shaanxi, and Hubei—were analyzed. Four datasets were constructed, each containing 25 Raman spectra per origin, with an additional 10 spectra per origin reserved as independent test sets. PCA was then separately applied to the spectral dataset of each origin to derive its respective eigenvector matrix. For each test spectrum, four reconstructed spectra were generated by projecting it onto the eigenvector matrices of the four origins. The origin was determined by identifying the one with the minimum Euclidean distance between the test spectrum and its reconstructions. When the first six principal components were used for model construction, the test set accuracy reached 97.5%, significantly outperforming the optimized PCA–SVM model, which achieved an accuracy of 85%. These results demonstrate that Raman spectroscopy, combined with the multi-matrix projection discrimination method based on PCA, can effectively capture the fingerprint information of Poria and accurately determine its geographical origin. Full article

Consistency indices quantify the degree of transitivity and proportionality violations in a pairwise comparison matrix (PCM), forming a cornerstone of the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). Several methods have been proposed to compute consistency, including those based on the maximum eigenvalue, dot product, Jaccard index, and the Bose index. However, these methods often overlook two critical aspects: (i) vector projection or directional alignment, and (ii) the weight or importance of individual elements within a pointwise evaluative structure. The first limitation is particularly impactful. Adjustments made during the consistency improvement process affect the final priority vector disproportionately when heavily weighted elements are involved. Although consistency may improve numerically through such adjustments, the resulting priority vector can deviate significantly, especially when the true vector is known. This indicates that approaches neglecting projection and weighting considerations may yield internally consistent yet externally incompatible vectors, thereby compromising the validity of the analysis. This study builds on the idea that consistency and compatibility are intrinsically related; they are two sides of the same coin and should be considered complementary. To address these limitations, it introduces a novel metric, the Consistency Index G (CI-G) based on the compatibility index G. This measure evaluates how well the columns of a PCM align with its principal eigenvector, using CI-G as a diagnostic component. The proposed approach not only refines consistency measurement but also enhances the accuracy and reliability of derived priorities. Full article

This paper proposes a structure-aware compression technique for efficient compression of high-resolution synthetic aperture radar (SAR)-based point clouds by quantitatively analyzing the directional characteristics of local structures. The proposed method computes the angular difference between the principal eigenvector of each point and those of its neighboring points, selectively removing points with low contribution to directional preservation and retaining only structurally significant feature points. The method demonstrates superior information preservation performance through various compression evaluation metrics such as entropy, peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM). Additionally, the SHREC’19 human mesh dataset is employed to further assess the generality and robustness of the proposed approach. The results show that the proposed method can maximize data efficiency while preserving the core information of the point cloud through a novel directionality-based structural preservation strategy. Full article

Semi-annual climate oscillations in the Western Hemisphere (20 S–35 N, 150 W–20 E) were studied via empirical orthogonal function (EOF) eigenvector loading patterns and principal component time scores from 1980 to 2023. The spatial loading maximum for 850 hPa zonal wind extended from the north Atlantic to the east Pacific; channeling was evident over the southwestern Caribbean. The eigenvector loading maximum for precipitation reflected an equatorial trough, while the semi-annual SST formed a dipole with loading maxima in upwelling zones off Angola (10 E) and Peru (80 W). Weakened Caribbean trade winds and strengthened tropical convection correlated with a warm Atlantic/cool Pacific pattern (R = 0.46). Wavelet spectral analysis of principal component time scores found a persistent 6-month rhythm disrupted only by major El Nino Southern Oscillation events and anomalous mid-latitude conditions associated with negative-phase Arctic Oscillation. Historical climatologies revealed that 6-month cycles of wind, precipitation, and sea temperature were tightly coupled in the Western Hemisphere by heat surplus in the equatorial ocean diffused by meridional overturning Hadley cells. External forcing emerged in early 2010 when warm anomalies over Canada diverted the subtropical jet, suppressing subtropical trade winds and evaporative cooling and intensifying the equatorial trough across the Western Hemisphere. Climatic trends of increased jet-stream instability suggest that the semi-annual amplitude may grow over time. Full article

This study presents a novel method for characterizing galaxy clusters by integrating statistical classification techniques with an optimized adaptation of the red sequence approach. The proposed algorithm employs Gaussian mixture models to analyze the distribution of three key variables: r magnitude, $g–r$ color index, and redshift z. To enhance cluster discrimination, we incorporate Mahalanobis distance metrics and modify the conventional red sequence technique by adopting the principal eigenvector as the slope of the cluster. A sample of 114 galaxy groups and clusters within the redshift range $0.002<z<0.45$ was used to validate the method. Comparative analyses demonstrate that the proposed approach achieves comparable or, in certain cases, superior performance in cluster characterization relative to the standard red sequence technique. These results highlight the algorithm’s potential as a robust tool for the exploratory identification and initial parameter determination of galaxy clusters, particularly in large-scale surveys. The methodology bridges statistical rigor with established astrophysical techniques, offering a promising avenue for advancing cluster detection in observational cosmology. Full article

With the Multi-Criteria Decision-Making (MCDM) problems becoming increasingly complex, traditional MCDM methods cannot effectively handle ambiguous, incomplete, or uncertain data. While several novel types of MCDM methods have been proposed to address this limitation, they fail to consider the potentially complex interactions among decision criteria. An effective capacity identification methodology is definitely needed to conquer this issue. In this paper, we develop a novel unsupervised method for identifying 2-additive capacities by means of Principal Component Analysis (PCA) and Kendall’s correlation coefficient. During the process, some significant results are achieved. Firstly, the Shapley values of decision criteria are derived by using the PCA, through a combination of the variance contribution rate of each Principal Component (PC) and its corresponding eigenvector. Secondly, Kendall’s correlation coefficient stemmed from the decision data created to help identify the Shapley interaction index for each pair of criteria by unsupervised learning. The optimization model equipped with a new form of monotonicity conditions is then established to further determine the optimal Shapley interaction index. With these two kinds of indices, a desired monotone 2-additive capacity is finally identified in an objective and efficient manner. Numerical experiments demonstrate that our proposal can adequately consider the importance of criteria and accurately identify the types of Shapley interaction indices between criteria, and is thus able to produce more convincing and logical results compared with other unsupervised identification methods. Full article

The accurate measurement of pulverized coal concentration (PCC) is crucial for optimizing the production efficiency and safety of coal-fired power plants. Traditional microwave attenuation methods typically rely on a single frequency for analysis while neglecting valuable information in the frequency domain, making them susceptible to the varying sensitivity of the signal at different frequencies. To address this issue, we proposed an innovative frequency selection method based on principal component analysis (PCA) and orthogonal matching pursuit (OMP) algorithms and implemented a multi-frequency microwave sensing system for PCC measurement. This method transcended the constraints of single-frequency analysis by employing a developed hardware system to control multiple working frequencies and signal paths. It measured insertion loss data across the sensor cross-section at various frequencies and utilized PCA to reduce the dimensionality of high-dimensional full-path insertion loss data. Subsequently, the OMP algorithm was applied to select the optimal frequency signal combination based on the contribution rates of the eigenvectors, enhancing the measurement accuracy through multi-dimensional fusion. The experimental results demonstrated that the multi-frequency microwave sensing system effectively extracted features from the high-dimensional PCC samples and selected the optimal frequency combination. Filed experiments conducted on five coal mills showed that, within a common PCC range of 0–0.5 kg/kg, the system achieved a minimum mean absolute error (MAE) of 1.41% and a correlation coefficient of 0.85. These results indicate that the system could quantitatively predict PCC and promptly detect PCC fluctuations, highlighting its immediacy and reliability. Full article

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system’s parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results. Full article

In this paper, a new multidimensional Takagi–Sugeno (T-S) identification technique is proposed for multivariable nonlinear systems. In this technique, multidimensional membership functions are designed using concepts from solid mechanics. The design of membership functions is carried out in multidimensional space, defining the principal axes from the eigenvectors of the inertia matrix, and it has the characteristic of dividing the space into regions with the same inertia. These regions are analyzed to define the center of gravity for each rule. Illustrative examples of multivariable nonlinear systems, such as a thermal mixing process and a binary distillation column, are selected to evaluate the effectiveness of the proposed method. The proposed method is compared with traditional T-S identification that uses one-dimensional membership functions and shows a reduction in the relative identification error and the algorithm execution time. Additionally, the proposed method prevents rules from being positioned outside the system’s range, thereby avoiding the generation of unnecessary rules. Full article

Inhibiting MDM2-p53 interaction is considered an efficient mode of cancer treatment. In our current study, Gaussian-accelerated molecular dynamics (GaMD), deep learning (DL), and binding free energy calculations were combined together to probe the binding mechanism of non-peptide inhibitors K23 and 0Y7 and peptide ones PDI6W and PDI to MDM2. The GaMD trajectory-based DL approach successfully identified significant functional domains, predominantly located at the helixes α2 and α2’, as well as the β-strands and loops between α2 and α2’. The post-processing analysis of the GaMD simulations indicated that inhibitor binding highly influences the structural flexibility and collective motions of MDM2. Calculations of molecular mechanics–generalized Born surface area (MM-GBSA) and solvated interaction energy (SIE) not only suggest that the ranking of the calculated binding free energies is in agreement with that of the experimental results, but also verify that van der Walls interactions are the primary forces responsible for inhibitor–MDM2 binding. Our findings also indicate that peptide inhibitors yield more interaction contacts with MDM2 compared to non-peptide inhibitors. Principal component analysis (PCA) and free energy landscape (FEL) analysis indicated that the piperidinone inhibitor 0Y7 shows the most pronounced impact on the free energy profiles of MDM2, with the piperidinone inhibitor demonstrating higher fluctuation amplitudes along primary eigenvectors. The hot spots of MDM2 revealed by residue-based free energy estimation provide target sites for drug design toward MDM2. This study is expected to provide useful theoretical aid for the development of selective inhibitors of MDM2 family members. Full article

Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation. Full article

This work develops a new method for vector data augmentation. The proposed method applies principal component analysis (PCA), determines the eigenvectors of a set of training vectors for a machine learning (ML) method and uses them to generate the distilled vectors. The training and PCA-distilled vectors have the same dimension. The user chooses the number of vectors to be distilled and augmented to the set of training vectors. A statistical approach determines the lowest number of vectors to be distilled such that when augmented to the original vectors, the extended set trains an ML classifier to achieve a required accuracy. Hence, the novelty of this study is the distillation of vectors with the PCA method and their use to augment the original set of vectors. The advantage that comes from the novelty is that it increases the statistics of ML classifiers. To validate the advantage, we conducted experiments with four public databases and applied four classifiers: a neural network, logistic regression and support vector machine with linear and polynomial kernels. For the purpose of augmentation, we conducted several distillations, including nested distillation (double distillation). The latter notion means that new vectors were distilled from already distilled vectors. We trained the classifiers with three sets of vectors: the original vectors, original vectors augmented with vectors distilled by PCA and original vectors augmented with distilled PCA vectors and double distilled by PCA vectors. The experimental results are presented in the paper, and they confirm the advantage of the PCA-distilled vectors increasing the classification statistics of ML methods if the distilled vectors augment the original training vectors. Full article

This paper has proposed a comprehensive indicator based on principal component analysis (PCA) for diagnosing the state of anaerobic digestion. Various state and performance variables were monitored under different operational modes, including start-up, interruption and resumption of substrate supply, and impulse organic loading rates. While these individual variables are useful for estimating the state of anaerobic digestion, they must be interpreted by experts. Coupled indicators combine these variables with the effect of offering more detailed insights, but they are limited in their universal applicability. Time-series eigenvalues reflected the anaerobic digestion process occurring in response to operational changes: Stable states were identified by eigenvalue peaks below 1.0, and they had an average below 0.2. Slightly perturbed states were identified by a consistent decrease in eigenvalue peaks from a value of below 4.0 or by observing isolated peaks below 3.0. Disturbed states were identified by repeated eigenvalue peaks over 3.0, and they had an average above 0.6. The long-term persistence of these peaks signals an increasing kinetic imbalance, which could lead to process failure. Ultimately, this study demonstrates that time-series eigenvalue analysis is an effective comprehensive indicator for identifying kinetic imbalances in anaerobic digestion. Full article