Inherent Structure Research Articles

Leveraging Inherent Structure of Tin Oxide for Efficient Carbonaceous Products Electrosynthesis

AbstractElectrochemical CO2 reduction reaction (CO2RR) holds a great potential for converting CO2 into valuable carbon‐based chemicals and fuels. A promising strategy for enhancing CO2RR performance is the deliberate structural design of electrocatalysts, which can maximize the utilization of inherent structural advantages. In this work, SnO2 nanocubes (NCs) and nanorods (NRs) are synthesized using a surface energy‐driven growth orientation method, where the stable (110) facet and the highly energetic (001) facet constitute the SnO2 nanostructures. Leveraging the inherent structural merits of different facets on SnO2, theoretical calculations reveal that the (001) facet plays a primary role in inhibiting hydrogen evolution reaction (HER), while both (110) and (001) facets are highly favorable for CO2‐to‐formate conversion under the external bias. As a result, SnO2 NCs with a higher facet ratio of (001)/(110) achieve nearly 100% selectivity for the formation of carbonaceous products during CO2RR. More importantly, a maximum partial current density of about 1 A cm−2 with a formate Faradaic efficiency (FE) of over 90% is achieved in a flow cell, distinguishing it from most of the reported Sn‐based electrocatalysts. These results highlight the strategic advantages of leveraging the inherent structure of nanomaterials for efficient CO2RR.

Parameterless Gene-pool Optimal Mixing Evolutionary Algorithms.

When it comes to solving optimization problems with evolutionary algorithms (EAs) in a reliable and scalable manner, detecting and exploiting linkage information, i.e., dependencies between variables, can be key. In this article, we present the latest version of, and propose substantial enhancements to, the Gene-pool Optimal Mixing Evoutionary Algorithm (GOMEA): an EA explicitly designed to estimate and exploit linkage information. We begin by performing a largescale search over several GOMEA design choices to understand what matters most and obtain a generally best-performing version of the algorithm. Next, we introduce a novel version of GOMEA, called CGOMEA, where linkage-based variation is further improved by filtering solution mating based on conditional dependencies. We compare our latest version of GOMEA, the newly introduced CGOMEA, and another contending linkage-aware EA, DSMGA-II, in an extensive experimental evaluation, involving a benchmark set of 9 black-box problems that can only be solved efficiently if their inherent dependency structure is unveiled and exploited. Finally, in an attempt to make EAs more usable and resilient to parameter choices, we investigate the performance of different automatic population management schemes for GOMEA and CGOMEA, de facto making the EAs parameterless. Our results show that GOMEA and CGOMEA significantly outperform the original GOMEA and DSMGA-II on most problems, setting a new state of the art for the field.

Heuristic algorithms for placing geomagnetically induced current blocking devices

We propose a new heuristic approach for solving the challenge of determining optimal placements for geomagnetically induced current blocking devices on electrical grids. Traditionally, these determinations are approached by formulating the problem as mixed-integer nonlinear programming models and solving them using optimization solvers based on the spatial branch-and-bound algorithm. However, computing an optimal solution using the solvers often demands substantial computational time due to their inability to leverage the inherent problem structure. Therefore, in this work we propose a new heuristic approach based on a three-block alternating direction method of multipliers algorithm, and we compare it with an existing stochastic learning algorithm. Both heuristics exploit the structure of the problem of interest. We test these heuristic approaches through extensive numerical experiments conducted on the EPRI-21 and UIUC-150 test systems. The outcomes showcase the superior performance of our methodologies in terms of both solution quality and computational speed when compared with conventional solvers.

Knowledge-aided multi-dictionary block sparsity-aware STAP for airborne polarimetric conformal array radar

Airborne polarimetric conformal array radar has gained increased attention recently. However, the conformal array configuration and polarization factors may lead to non-stationary clutter, which significantly degrades the performance of space–time adaptive processing (STAP), particularly in short-range clutter environments. In this paper, we introduce a knowledge-aided multi-dictionary block sparse Bayesian learning (KA-MDBSBL) algorithm to improve the clutter suppression performance. Using prior knowledge, the proposed algorithm designs multi-dictionary matrices for each training sample, rather than a single dictionary matrix for the cell under test (CUT). We take advantage of the identical clutter profile under each dictionary matrix. In the multi-dictionary case, we enforce shared sparsity in the clutter profiles. Additionally, we utilize the inherent block structure of the dictionary matrix to jointly recover clutter and noise power through a fast convergence learning framework. Subsequently, the clutter plus noise covariance matrix is reconstructed using precisely estimated clutter and noise power, along with the dictionary matrix corresponding to the CUT. Numerical simulations are included to demonstrate the effectiveness and superiority of the proposed algorithm.

Advanced Hyperspectral Image Analysis: Superpixelwise Multiscale Adaptive T-HOSVD for 3D Feature Extraction.

Hyperspectral images (HSIs) possess an inherent three-order structure, prompting increased interest in extracting 3D features. Tensor analysis and low-rank representations, notably truncated higher-order SVD (T-HOSVD), have gained prominence for this purpose. However, determining the optimal order and addressing sensitivity to changes in data distribution remain challenging. To tackle these issues, this paper introduces an unsupervised Superpixelwise Multiscale Adaptive T-HOSVD (SmaT-HOSVD) method. Leveraging superpixel segmentation, the algorithm identifies homogeneous regions, facilitating the extraction of local features to enhance spatial contextual information within the image. Subsequently, T-HOSVD is adaptively applied to the obtained superpixel blocks for feature extraction and fusion across different scales. SmaT-HOSVD harnesses superpixel blocks and low-rank representations to extract 3D features, effectively capturing both spectral and spatial information of HSIs. By integrating optimal-rank estimation and multiscale fusion strategies, it acquires more comprehensive low-rank information and mitigates sensitivity to data variations. Notably, when trained on subsets comprising 2%, 1%, and 1% of the Indian Pines, University of Pavia, and Salinas datasets, respectively, SmaT-HOSVD achieves impressive overall accuracies of 93.31%, 97.21%, and 99.25%, while maintaining excellent efficiency. Future research will explore SmaT-HOSVD's applicability in deep-sea HSI classification and pursue additional avenues for advancing the field.

FCAN : Speech emotion recognition network based on focused contrastive learning

Traditional speech emotion recognition (SER) models predominantly utilize cross-entropy loss for supervised optimization. Yet, given the limited size of SER datasets, relying solely on cross-entropy loss does not adequately capture the intricacies within the data. Moreover, conventional contrastive learning techniques, though improving performance, do not completely harness the inherent data structure across samples. To surmount these limitations, we introduce an innovative emotion recognition network founded on focused contrastive learning. Our model employs bidirectional gated recurrent unit (GRU) networks to seize critical contextual dependencies. By integrating an attention mechanism, we adeptly merge the contextual features of dialogues with individual utterance attributes, forming a comprehensive multi-stage feature fusion framework. This strategy extracts more elaborate emotional features from the constrained dataset. Additionally, by amalgamating the focal loss function into our training protocol, we mitigate imbalanced sample issues to a degree. We further refine our contrastive loss function by enacting a weighted strategy for intra-dialogue category assignments, where higher penalty weights are ascribed to harder-to-identify categories, thus incentivizing the model to concentrate on distinguishing subtler category differences. This refinement significantly bolsters the model’s proficiency in learning various emotional feature distributions, thereby enhancing its emotion recognition capabilities. Experimental validation on IEMOCAP and MELD benchmark datasets underpins our model’s superiority.

Formation of core-shell structure MnCo2O4 microspheres and as a bifunctional catalyst for zinc-air batteries

Efficient and stable bifunctional catalysts, facilitating oxygen reduction and oxygen evolution, play a pivotal role in energy conversion and storage fields. In this paper, four core-shell MnCo2O4 catalyst samples are prepared by controlling different solvent heating time, which are 0.5 h, 2 h, 6 h, and 12 h, respectively. The subsequent tests indicate that the sample with a 6 h not only has an ideal core-shell structure, but also exhibits favorable performance. The unique core-shell structure and favorable electrochemical performance are mainly attributed to the prepared precursor spheres. The microspheres have an inherent core-shell structure. Detailed studies of the morphological variations of MnCo2O4 catalysts with the different solvent heating time are performed using transmission electron microscopy and field emission scanning electron microscopy. Furthermore, we analyze the potential formation mechanism of the core-shell structure MnCo2O4 catalyst. The obtained core-shell structured MnCo2O4 catalysts provide a new way for the preparation of cathode catalyst for zinc-air batteries.

Efficient preparation of anisotropic cellulose sponge from cotton stalks: An excellent material for separation applications

Water pollution and solid waste resource reuse demand immediate attention and research. Here, we present a method to create anisotropic cellulose sponges from cotton stalk waste. Using the inherent structure of cotton stalks, we selectively remove lignin and hemicellulose via acid and alkali pretreatment. This process yields cellulose sponges with a natural pore structure. Our findings demonstrate that these sponges retain the original pore configuration of cotton stalks, providing excellent connectivity and compressibility due to their unique anisotropic three-dimensional structure. Moreover, these sponges exhibit exceptional super-hydrophilic and underwater super-oleophobic properties, with underwater oil contact angles exceeding 150° for all tested oils. External pressure can reduce the pore size of the cellulose sponge, facilitating the gravity-driven separation and removal of dyes and emulsions. Remarkably, removal efficiencies for Methylene Blue (MB), Congo Red (CR), water-in-oil (w/o) emulsions, and oil-in-water (o/w) emulsions exceed 99 %, 97 %, 99 %, and 99 %, respectively, highlighting superior removal and recyclability. Further investigation into the mechanisms of dye and emulsion removal employs X-ray photoelectron spectroscopy (XPS) characterization and molecular dynamics (MD) simulation. These insights lay the groundwork for the efficient recycling and resource utilization of waste cotton stalks, offering promising applications in water purification.

APPLYING HYPERGRAPHS TO STUDIES IN QUANTITATIVE BIOLOGY

The objective of this research is to demonstrate hypergraph versatility and applicability for modeling diverse biological systems. The inherent structure of hypergraphs allows for encoding of higher-order feature interactions, providing a flexible framework for efficient models that can enhance our understanding of physical phenomena and one that can be generalized across various datasets. By adopting innovative methods including centrality measure and populations of models rather than singular instances, biases and overfitting tendencies are mitigated, again presenting promise for application across a broad spectrum of biological systems. Furthermore, emphasis is placed on the significance of probabilistic distribution analysis in elucidating threshold selection and feature relevance while maintaining high levels of accuracy. Our results demonstrate the advantages of hypergraph models on two different datasets; with the first on gene expression and the identification of outlier genes and the second on classifying starch grains. There is significant scope in the application of the hypergraph to a wider class of biological systems, with the potential to improve understanding of the biological processes.

Stable and Durable Superhydrophobic Cotton Fabrics Prepared via a Simple 1,4-Conjugate Addition Reaction for Ultrahigh Efficient Oil-Water Separation.

Superhydrophobic materials used for oil-water separation have received wide attention. However, the simple and low-cost strategy for making durable superhydrophobic materials remains a major challenge. Here, this work reports that stable and durable superhydrophobic cotton fabrics can be prepared using a simple two-step impregnation process. Silica nanoparticles are surface modified by hydrolysis condensation of 3-aminopropyltrimethoxysilane (APTMS). 1,4-conjugate addition reaction between the acrylic group of cross-linking agent pentaerythritol triacrylate (PETA) and the amino group of octadecylamine (ODA) forms a covalent cross-linked rough network structure. The long hydrophobic chain of ODA makes the cotton fabric exhibit excellent superhydrophobic properties, and the water contact angle (WCA) of the fabric surface reaches 158°. The modified cotton fabric has good physical and chemical stability, self-cleaning, and anti-fouling. At the same time, the modified fabric shows excellent oil/water separation efficiency (98.16% after 20 cycles) and ultrahigh separation flux (15413.63 L m-2 h-1) due to its superhydrophobicity, superoleophilicity, and inherent porous structure. The method provides a broad prospect in the future diversification applications of oil/water separation and oil spill cleaning.

A generalizable framework for low-rank tensor completion with numerical priors

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically considered exploiting the numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. Despite the existence of some individual works which consider ad hoc numerical priors for specific tasks, no generalizable frameworks for incorporating numerical priors have appeared. We present the Generalized CP Decomposition Tensor Completion (GCDTC) framework, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account. We test GCDTC by further proposing the Smooth Poisson Tensor Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose performance exceeds current state-of-the-arts by considerable margins in the task of non-negative tensor completion, exemplifying GCDTC’s effectiveness. Our code is open-source.

Self-Assembled Micelles Based on Ginsenoside Rg5 for the Targeted Treatment of PTX-Resistant Tumors.

Paclitaxel (PTX) is one of the first-line drugs for prostate cancer (PC) treatment. However, the poor water solubility, inadequate specific targeting ability, multidrug resistance, and severe neurotoxicity are far from being fully resolved, despite diverse PTX formulations in the market, such as the gold-standard PTX albumin nanoparticle (Abraxane) and polymer micelles (Genexol-PM). Some studies attempting to solve the multiple problems of chemotherapy delivery fall into the trap of an extremely complicated formulation design and sacrifice druggability. To better address these issues, this study designed an efficient, toxicity-reduced paclitaxel-ginsenoside polymeric micelle (RPM). With the aid of the inherent amphiphilic molecular structure and pharmacological effects of ginsenoside Rg5, the prepared RPM enhances the water solubility and active targeting of PTX, inhibiting chemotherapy resistance in cancer cells. Moreover, the polymeric micelles demonstrated favorable anti-inflammatory and neuroprotective effects, providing ideas for the development of new clinical anti-PC preparations.

Self-hydrogen transfer hydrogenolysis of β-O-4 bonds in lignin model compounds over NiCu/Al2O3 catalyst

Hydrogenolysis of β-O-4 linkages in lignin to produce aromatic compounds is attractive but challenging. Currently, external hydrogen source like hydrogen gas or hydrogen-donor solvent is necessary during hydrogenolysis, leading to high cost and low selectivity of products. Herein, a NiCu/Al2O3 catalyst was prepared for self-hydrogen transfer hydrogenolysis (SHTH) of Cβ-O bond using inherent CαH-OH structure as H-source. A β-O-4 model compound, 2-phenoxy-1-phenethanol, was completely transformed into acetophenone and phenol at 220 ℃ under 1 MPa N2 for 2h. The SHTH reaction proceeded through a dehydrogenation reaction followed by a hydrogenolysis reaction. Hydrogen radicals released from CαH-OH group generated a “hydrogen pool” on the catalyst surface, which inserted into the formed β-O-4 ketone intermediate to cleave the Cβ-O bond. The catalyst presented outstanding reusability and universality during the SHTH reaction. Moreover, the methoxy groups at aryl positions impeded the SHTH process, and the steric effect was related to the amount and position of methoxy groups. This study realizes the utilization of structural hydrogen from lignin model compounds for its Cβ-O bond cleavage, providing an economical and sustainable method toward lignin valorization.

Improving Hyperspectral Image Classification with Compact Multi-Branch Deep Learning

The progress in hyperspectral image (HSI) classification owes much to the integration of various deep learning techniques. However, the inherent 3D cube structure of HSIs presents a unique challenge, necessitating an innovative approach for the efficient utilization of spectral data in classification tasks. This research focuses on HSI classification through the adoption of a recently validated deep-learning methodology. Challenges in HSI classification encompass issues related to dimensionality, data redundancy, and computational expenses, with CNN-based methods prevailing due to architectural limitations. In response to these challenges, we introduce a groundbreaking model known as “Crossover Dimensionality Reduction and Multi-branch Deep Learning” (CMD) for hyperspectral image classification. The CMD model employs a multi-branch deep learning architecture incorporating Factor Analysis and MNF for crossover feature extraction, with the selection of optimal features from each technique. Experimental findings underscore the CMD model’s superiority over existing methods, emphasizing its potential to enhance HSI classification outcomes. Notably, the CMD model exhibits exceptional performance on benchmark datasets such as Salinas Scene (SC), Pavia University (PU), Kennedy Space Center (KSC), and Indian Pines (IP), achieving impressive overall accuracy rates of 99.35% and 99.18% using only 5% of the training data.

The C-BixSnSb composite toward fast-charging and long-life sodium-ion batteries

Sodium ion batteries (SIBs) fitted with high-rate and high-capacity anodes are attractive for their higher energy density and faster charging capability. However, it is still a challenge to develop high-energy SIBs with high power and long life, due to the sluggish kinetic and limited Na+ insertion in electrode materials. The inherent crystal structure and constituent element are two important factors to resolve the critical issues faced above. Taking the merits of layer-structure and middle-entropy, herein, we proposed and designed a high ion-conductive composite combing with ternary alloy and layered BixSnSb@C nanofibers, which eliminate ion migration barriers while maintaining the structural framework for superior rate property and cycle stability. Used as anode for SIBs, the multiphase BixSnSb@C with adjustable Bi content exhibits excellent Na storage capability as compared to their single phase counterpart. Specially, up to a rate of 132C (50 A g−1), the capacity is still as high as 400 mAh g−1, meanwhile, after 5000 charge and discharge cycles at a current density of 12C, the capacity still maintains 85 % of its initial capacity, which outperform the individual Bi- or SnSb-based materials. The superior electrochemical performances originate from the middle-entropy nature and layer structure of BiSnSb alloy, which can provide more channels for fast Na+ transport, and accommodate large volume changes. Besides, the activity energy and ions transport resistance of Na+ in different composites were evaluated. Furthermore, the full-cell coupled with NaNi1/3Fe1/3Mn1/3O2 as cathode was formed and a capacity retention of ∼80 % is realized in 100 cycles. The results show that the BixSnSb@C is a potential anode for fast-charging Na-ion batteries and could be used to guide the design of multi-component alloy-base anodes.

Study on the disinfection effect of chlorine dioxide disinfectant (ClO2) on dental unit waterlines and its in vitro safety evaluation

BackgroundEnsuring the safety of dental unit waterlines (DUWLs) has become a pivotal issue in dental care practices, focusing on the health implications for both patients and healthcare providers. The inherent structure and usage conditions of DUWLs contribute to the risk of biofilm formation and bacterial growth, highlighting the need for effective disinfection solutions.The quest for a disinfection method that is both safe for clinical use and effective against pathogens such as Staphylococcus aureus and Escherichia coli in DUWLs underscores the urgency of this research.MaterialsChlorine dioxide disinfectants at concentrations of 5, 20, and 80 mg/L were used to treat biofilms of S. aureus and E. coli cultured in DUWLs. The disinfection effectiveness was assessed through bacterial counts and culturing. Simultaneously, human skin fibroblast cells were treated with the disinfectant to observe changes in cell morphology and cytotoxicity. Additionally, the study included corrosion tests on various metals (carbon steel, brass, stainless steel, aluminum, etc.).ResultsExperimental results showed that chlorine dioxide disinfectants at concentrations of 20 mg/L and 80 mg/L significantly reduced the bacterial count of S. aureus and E. coli, indicating effective disinfection. In terms of cytotoxicity, higher concentrations were more harmful to cellular safety, but even at 80 mg/L, the cytotoxicity of chlorine dioxide remained within controllable limits. Corrosion tests revealed that chlorine dioxide disinfectants had a certain corrosive effect on carbon steel and brass, and the degree of corrosion increased with the concentration of the disinfectant.ConclusionAfter thorough research, we recommend using chlorine dioxide disinfectant at a concentration of 20 mg/L for significantly reducing bacterial biofilms in dental unit waterlines (DUWLs). This concentration also ensures satisfactory cell safety and metal corrosion resistance.

Highly efficient thermal conductivity of polyarylene ether nitrile composites via the introduction of hybrid fillers and tailored cross-linked structure

Polymer dielectrics with high thermal conductivity (λ) and excellent insulating properties are of interest in miniaturized and integrated electronic devices. However, most polymers are unable to fulfill this need due to their inherent structure. In this work, a polymer alloy with balanced thermal conductive and dielectric properties was successfully prepared by polyarylene ether nitrile(PEN), bisphthalonitrile-microsphere@boron nitride nanosheets(Bm@BNNS), and silicon carbide whisker (SiCws) at different scales. Specifically, introduction of Bm@BNNS fillers with core-shell structure into PEN resins results in heterogeneous interfaces, which effectively reduces the agglomeration and dosage of BNNS and synergistically improves the λ and dielectric performance. Besides, it has high breakdown strength (Eb) and high energy storage density (242.26 kV/mm, 1.66J/cm3) when filled with only 4.37 vol% BNNS compared to pure PEN. Furthermore, effects of one-dimensional SiCws at different scales on formation of heat-conduction pathways and electrical insulation properties of PEN/Bm@BNNS composites were investigated. The findings display that PEN/Bm@BNNS/SiCws composites with large size SiCws (7.81 vol%) achieved a high λ of 2.376 W/m.K, which was 135.24 % and 87.09 % higher than pure PEN and PEN/Bm@BNNS composites, respectively. Thus, the thermal conductive pathways are constructed by line-plate structure (SiCws-BNNS), and insulating performance primarily on the core-shell structure (Bm@BNNS). Besides, the novel PEN/Bm@BNNS/SiCws hybrid materials are together with a low coefficient of thermal expansion of 38–89 ppm/°C and high Tg of 220 °C. Thus, it gives a promising insight to achieve highly λ polymer-based insulating film materials used for high-temperature-resistant fields.

Synchronization-based semi-supervised data streams classification with label evolution and extreme verification delay

The critical need for classifying streaming data arises from its widespread use in real-world industries, where analyzing continuous, dynamic, and evolving data streams accurately and promptly is essential for informed decision-making and gaining predictive insights. Existing research mainly focuses on abundant supervision, overlooking the scarcity and delayed availability of labels, which can vary in timing. Addressing this, the article introduces a new learning method that employs a synchronization-based core support extraction technique. This technique is designed to manage changing concepts and delayed partial labeling by extracting key data points that act as pseudo-labels. Thanks to the concept of synchronization, these extracted key data points accurately represent the inherent local cluster structure in an intuitive manner and better maintain the class structure. Consequently, these pseudo-labels are utilized for classifying future incoming data batches. Furthermore, the method incorporates a knowledge base to summarize and represent all incoming streaming data. Building upon this knowledge base, an ensemble model for classification and an efficient new class detector are proposed. Both operate in a local fashion to ensure robust learning, even in complex class distributions. Evaluations on benchmark datasets reveal a consistent performance lead, surpassing established algorithms by up to 10%, achieving state-of-the-art results.

GTE: a graph learning framework for prediction of T-cell receptors and epitopes binding specificity.

The interaction between T-cell receptors (TCRs) and peptides (epitopes) presented by major histocompatibility complex molecules (MHC) is fundamental to the immune response. Accurate prediction of TCR-epitope interactions is crucial for advancing the understanding of various diseases and their prevention and treatment. Existing methods primarily rely on sequence-based approaches, overlooking the inherent topology structure of TCR-epitope interaction networks. In this study, we present $GTE$, a novel heterogeneous Graph neural network model based on inductive learning to capture the topological structure between TCRs and Epitopes. Furthermore, we address the challenge of constructing negative samples within the graph by proposing a dynamic edge update strategy, enhancing model learning with the nonbinding TCR-epitope pairs. Additionally, to overcome data imbalance, we adapt the Deep AUC Maximization strategy to the graph domain. Extensive experiments are conducted on four public datasets to demonstrate the superiority of exploring underlying topological structures in predicting TCR-epitope interactions, illustrating the benefits of delving into complex molecular networks. The implementation code and data are available at https://github.com/uta-smile/GTE.

Calibrating Spatial Stratified Heterogeneity for Heavy-Tailed Distributed Data

The phenomena with within-strata characteristics that are more similar than between-strata characteristics are ubiquitous (e.g., land-use types and image classifications). It can be summarized as spatial stratified heterogeneity (SSH), which is measured and attributed using the geographical detector (Geodetector) q-statistic. SSH is typically calibrated by stratification and hundreds of algorithms have been developed. Little is discussed about the conditions of the methods. In this work, a novel stratification method based on head/tail breaks is introduced for the purpose of better capturing the SSH of geographical variables with a heavy-tailed distribution. Compared to conventional sample-based stratifications, the presented approach is a population-based optimized stratification that indicates an underlying scaling property in geographical spaces. It requires no prior knowledge or auxiliary variables and supports a naturally determined number of strata instead of being subjectively preset. In addition, our approach reveals the inherent hierarchical structure of geographical variables, characterizes its dominant components across all scales, and provides the potential to make the stratification meaningful and interpretable. The advantages were illustrated by several case studies in natural and social sciences. The proposed approach is versatile and flexible so that it can be applied for the stratification of both geographical and nongeographical variables and is conducive to advancing SSH-related studies as well. This study provides a new way of thinking for advocating spatial heterogeneity or scaling law and advances our understanding of geographical phenomena.