Brute Force Method Research Articles

Notice of Violation of IEEE Publication Principles: VVC/H.266 Intra Mode QTMT Based CU Partition Using CNN

Notice of Violation of IEEE Publication Principles <br><br>“VVC/H. 266 Intra Mode QTMT Based CU Partition Using CNN” <br>by Sameena Javaid, Safdar Rizvi, Muhammad Talha Ubaid, Abdullah Tariq <br>in IEEE Access, April 2022 <br><br>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <br><br>This paper copied content from the article below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. <br><br> “DeepQTMT: A Deep Learning Approach for Fast QTMT-Based CU Partition of Intra-Mode VVC” <br> by Tianyi Li, Mai Xu, Runzhi Tang, Ying Chen, Qunliang Xing <br>in IEEE Transactions on Image Processing, Vol 30, 2021 <br><br> <br/> The latest standard for video coding is versatile video coding (VVC) / H.266 which is developed by the joint video exploration team (JVET). Its coding structure is a multi-type tree (MTT) structure, which consists of two types of trees that are Ternary Tree (TT) and Binary Tree (BT). Due to the use of brute force quest for residual rate-distortion the quad-tree and multi-type tree (QTMT) structure of the coding unit (CU) split and contributes over 98% of the encoding time. This structure is efficient in coding, however, increases computational complexity. The current paper proposes a deep learning technique to predict the QTMT based CU split rather than just the brute-force QTMT method to substantially speed up the time of the encoding process for VVC/H.266 intra mode. In the first phase, we developed an extensive database containing ample CU splitting patterns and various streaming videos. In the second phase, we suggest a multi-level exit CNN (MLE-CNN) model with a redundancy removal mechanism at different levels to determine the CU partition. In the third phase, for the training of MLECNN model we have established the adaptive loss function and analyzing the both unknown number of partition modes and the focus on RD cost minimization. Finally, a variable threshold decision system is established to achieve the targeted low complexity and RD performance. Ultimately experimental findings show that VVC/H.266 encoding time has reduced to 69.11% from 47.91% with insignificant bjontegaard delta bit rate (BDBR) to 2.919% from 1.023% which performs better than the existing futuristic and modern approaches.

Procedure for regularization of bilinear optimal control problems based on a finite-dimensional model

An optimization problem of a linear system of ordinary differential equations on a set of piecewise continuous scalar controls with two-sided restrictions is considered. The cost functional contains the bilinear part (control, state) and a control square with a parameter, which plays the role of a regularization term. An approximate solution of the optimal control problem is carried out on a subset of piecewise constant controls with a non-uniform grid of possible switching points. As a result of the proposed parametrization, reduction to the finite-dimensional problem of quadratic programming was carried out with the parameter in the objective function and the simplest restrictions. In the case of a strictly convex objective function, the finite-dimensional problem can be solved in a finite number of iterations by the method of special points. For strictly concave objective functions, the corresponding problem is solved by simple or specialized brute force methods. In an arbitrary case, parameter conditions and switching points are found at which the objective function becomes convex or concave. At the same time, the corresponding problems of mathematical programming allow a global solution in a finite number of iterations. Thus, the proposed approach allows to approximate the original non-convex variation problem with a finite-dimensional model that allows to find a global solution in a finite number of iterations.

A brute-force code searching for cell of non-identical displacement for CSL grain boundaries and interfaces

Atomic simulation of coincidence-site lattice (CSL) grain boundaries (GBs) and interfaces is of importance for understanding GBs in polycrystalline materials and for making functional films. A common process of high-throughput simulation for CSL GBs and interfaces is to explore rigid body translation (RBT) of one crystal respect to the other. Cell of non-identical displacement (CNID) is the minimum cell including all non-identical RBTs in the GB or interface plane and is important for effective sampling. This work proposes an algorithm to compute the CNID of any two-dimensional CSL GB or interface based on a reciprocity relation between the displacement shift complete (DSC) and CSL. Program summaryProgram title: cnidcalCPC Library link to program files:https://doi.org/10.17632/wzy67jd56d.1Code Ocean capsule:https://codeocean.com/capsule/1648641Licensing provisions: MIT licenseProgramming language: Python Nature of problemDetermination of atomic structure of crystalline interfaces and grain boundaries is a key issue for understanding the properties of polycrystalline materials, where atomic simulation has made notable contribution in this field. Simulation of crystalline interfaces often applies a bicrystal model of a coincidence-site lattice (CSL) [1, 2] interface comprising two slabs of crystals which coincides in the interface plane. To determine the most stable structure of this interface model, a main task is often to tailor the initial bicrystal model to obtain many non-identical and non-relaxed structures for subsequent relaxation to explore the energy landscape of the system to find the ‘global minimum’ at 0 K, where one of the most important operations to tailor the model is applying rigid body translation (RBT) [1] of one crystal respect to the other by a vector confined in the interface plane. Because of symmetry of the two crystals, there exist periodicity of this translation vector which is reflected by a special cell called ‘cell of non-identical displacement’ (CNID) [1] which is the minimum cell including all non-identical choices of this vector and is key for effective sampling. Although CNID has a straightforward definition that it is a lattice including both the two overlapping two-dimensional lattices, finding a method capable to determine a primitive basis of CNID in general cases can be non-trivial and there has not been a reported programme capable to do so. Solution methodCNID in nature is a displacement shift complete (DSC) lattice [2]. While there has not been effective reported programme to compute DSC, several programmes have been made to compute CSL [3, 4, 5]. Besides, Grimmer [6] has proposed a mathematical relationship between the DSC and the CSL. In this way, based on a previously reported programme computing the CSL by brute-force method [5] and the relationship between DSC and CSL proposed by Grimmer, we generated a python code to compute CNID. This code is available to compute the CNID of a CSL interface comprising any two lattices if only they coincide even including complex cases involving heterogeneous lattices with difference in both shape and size.

Using surface asperities for efficient random particle overlap detection in the generation of randomly oriented and located particle arrangements

A novel method of detecting overlap between two irregularly shaped virtual particles whose surfaces are described by analytical functions is presented in this study. Utilizing the analytical equation that describes the surface of the particle, the first and second spatial derivatives are used to locate the major surface asperities via the surface curvature. During the particle placement process, detecting overlap between two particles is a crucial, but slow, step. While the asperity check does not detect all cases of overlap between two particles, it leverages the probability that overlap is most likely to occur at a surface asperity. Microstructures are generated using four particle size gradations and three volume fractions to demonstrate the decreased computational time associated with using the asperity overlap detection versus a brute force method. This overlap detection method provides significant increases in efficiency, averaging a speedup of 10 when generating a 40% volume fraction microstructure.

Determining Feature Extraction Parameters for Pulsed Eddy Current Sensor: A Minimisation Problem Approach

Pulsed eddy current (PEC) is an electromagnetic non-destructive testing (NDT) technique mainly used to inspect corrosion in pipelines. Like many other NDT techniques, to quantify pipe wall thickness, a signal feature has to be extracted from the PEC response. The authors’ previous work has exploited the linear relationship of the time-derivative feature to propose an in-situ calibration routine. However, to extract the time-derivative feature, two configuration parameters need to be determined prior to feature extraction. To the authors’ knowledge, none of the previous works explores the determining factors of this configuration parameters, where the current technique is still limited to using brute force method or trial-and-error. This paper brings novelty by formulating the aforementioned problem as a minimisation problem, and solving it using a particle swarm optimisation (PSO) algorithm. The obtained results, compared against brute force method, demonstrate the feasibility and performance improvement of using PSO in determining the configuration parameters. The approach thus presented is validated and the results obtained are justified by analysing the underlying physical system theory.

A propagation-based fault detection and discrimination method and the optimization of sensor deployment

Industrial processes can be affected by faults having a serious impact on operation when not promptly detected and diagnosed. In this paper, a propagation-basedfaultdetectionanddiscrimination(PFDD) method is proposed to develop a strategy for fault diagnosis while in the design phase of a system. The PFDD method constructs the system model using the IntegratedSystemFaultAnalysis(ISFA) technique. Based on the system model, the propagation of hardware and software faults are simulated qualitatively. Given the results of the simulation, the process by which a fault propagates can be characterized using the qualitative features of system variables including the deviation of the system variables from their expected values, the variation of the system variables over time, and the order in which each variable is influenced during the propagation of the fault. The strategy by which a fault can be detected and discriminated is defined using those features. The PFDD method supports the detection and discrimination of faults in both steady states and transient states. Based on the PFDD method, the optimization of sensor deployment in a system is discussed. A brute force algorithm is developed to examine the system’s capability at diagnosing faults and the cost of sensor deployment for all possible configurations of sensors. The optimal sensor deployment strategy can be derived accordingly. However, the brute force method is only applicable to small-scale systems due to its high computational cost. A genetic algorithm is used to optimize sensor deployment in large-scale systems. The PFDD and sensor deployment optimization methods are applied to the Experimental Breeder Reactor II (EBR-II) for verification.

Multi-Agent RL Enables Decentralized Spectrum Access in Vehicular Networks

In this paper, we investigate the joint sub-channel and power allocation problem for cellular vehicle-to-everything (V2X) communications, where multiple vehicle-to-infrastructure (V2I) users share the spectrum resources with vehicle-to-vehicle (V2V) users. In particular, a novel channel state information (CSI)-independent decentralized algorithm based on multi-agent reinforcement learning (MARL) is proposed to maximize the sum throughput of V2I links while meeting the latency and reliability requirements of V2V links. Specifically, we implement the individual double dueling deep recurrent Q-networks (D3RQN) and the carefully designed common reward to train the implicitly collaborative agents, through which, each agent optimizes the policy individually based solely on local CSI-independent observations. To handle the non-stationarity induced by multi-agent concurrent learning, we incorporate hysteretic Q-learning and concurrent experience replay trajectory (CERT) to stabilize the training process. Besides, we incorporate the approximate regretted reward (ARR) to alleviate the unstable reward estimation problem caused by shifting environment dynamics. Simulation results demonstrate that the proposed algorithm outperforms the baselines and can achieve close performance compared with the centralized Brute-force method. Furthermore, the proposed CSI-independent design exhibits comparable performance as the CSI-involved version, which sheds some light on the potential to further reduce the signalling overhead of machine learning-based vehicular communication systems.

Securing Smart Cities using LSTM algorithm and lightweight containers against botnet attacks

Smart Cities contains millions of IoT sensors supporting critical applications such as Smart Transport, Buildings, Intelligent Vehicles, and Logistics. A central administrator appointed by the government manages and maintains the security of each node. Smart City relies upon millions of sensors that are heterogeneous and do not support standard security architecture. Different manufacturers have weak protection protocols for their products and do not update their firmware upon newly identified operating systems’ vulnerabilities. Adversaries using brute force methods exploit the lack of inbuilt security systems on IoT devices to grow their bot network. Smart cities require a standard framework combining soft computing and Deep Learning (DL) for device fleet management and complete control of sensor operating systems for absolute security. This paper presents a real-world application for IoT fleet management security using a lightweight container-based botnet detection (C-BotDet) framework. Using a three-phase approach, the framework using Artificial Intelligence detects compromised IoT devices sending malicious traffic on the network. Balena Cloud revokes API keys and prevents a compromised device from infecting other devices to form a more giant botnet. VPN (Virtual Private Network) prevents inter-device communication and routes all malicious traffic through an external server. The framework quickly updates the standard Linux-based operating system IoT device fleet without relying on different manufacturers to update their system security individually. The simulation and analysis of the C-BotDet framework are presented in a practical working environment to demonstrate its implementation feasibility.

Perturbative Analysis of Anisotropic Coaxial Waveguides With Small Eccentricities via Conformal Transformation Optics

This article describes two novel perturbation solutions for the electromagnetic analysis of eccentric coaxial waveguides. Different techniques have been used for solving this type of problem in the past. Most of them rely on solving a complicated transcendental equation obtained from the Graf’s addition theorem or on brute-force numerical methods such as finite differences and finite elements. The proposed approach, instead, employs transformation optics to map the original problem into a problem consisting of a concentric coaxial waveguide filled with an anisotropic and inhomogeneous medium. The corresponding (transformed) wave equation is then solved via a regular perturbation series. This method allows to compute field and wavenumber corrections of the transverse magnetic (TM) and transverse electric (TE) modes for coaxial waveguides with small eccentricities. In addition, another solution is obtained by using the cavity-material perturbation approach for providing the cutoff wavenumbers of TM and TE fields. The proposed perturbation solutions are validated against full-wave finite-element and finite-volume results in several examples.

Subcarrier-pairing entropy loading for digital subcarrier-multiplexing systems with colored-SNR distributions.

A subcarrier-pairing entropy loading (SubP-EL) scheme with fairly low complexity is proposed for digital subcarrier-multiplexing (SCM) systems with colored signal-to-noise ratio (SNR) distributions. With the constraint of the target entropy, SubP-EL iteratively optimizes the entropy of subcarriers in pair. After convergence, SubP-EL can approach the optimal performance which is evaluated in simulations and experiments by comparison with the brute-force search method. Meanwhile the complexity of SubP-EL is significantly reduced compared with the brute-force search. In particular, in an 8-subcarrier system with five different SNRs, the complexity of SubP-EL is reduced by approximately a factor of 764, 95 and 13 with the entropy granularities of 0.05 bits/2D-symbol, 0.1 bits/2D-symbol and 0.2 bits/2D-symbol, respectively. The performance of SubP-EL is evaluated in simulations and experiments. In the experiments with 345 km fiber transmissions, the average NGMI gain of SubP-EL over the system without entropy loading is 0.0286 for different optical filtering cases.

Global optimization of default phases for parallel transmit coils for ultra-high-field cardiac MRI.

The development of novel multiple-element transmit-receive arrays is an essential factor for improving B1+ field homogeneity in cardiac MRI at ultra-high magnetic field strength (B0 > = 7.0T). One of the key steps in the design and fine-tuning of such arrays during the development process is finding the default driving phases for individual coil elements providing the best possible homogeneity of the combined B1+-field that is achievable without (or before) subject-specific B1+-adjustment in the scanner. This task is often solved by time-consuming (brute-force) or by limited efficiency optimization methods. In this work, we propose a robust technique to find phase vectors providing optimization of the B1-homogeneity in the default setup of multiple-element transceiver arrays. The key point of the described method is the pre-selection of starting vectors for the iterative solver-based search to maximize the probability of finding a global extremum for a cost function optimizing the homogeneity of a shaped B1+-field. This strategy allows for (i) drastic reduction of the computation time in comparison to a brute-force method and (ii) finding phase vectors providing a combined B1+-field with homogeneity characteristics superior to the one provided by the random-multi-start optimization approach. The method was efficiently used for optimizing the default phase settings in the in-house-built 8Tx/16Rx arrays designed for cMRI in pigs at 7T.

Bounding the number of calling animals with passive acoustics and reliable locations.

When n animal calls are passively detected at n different times, the number of animals producing the sounds is anywhere between one and n unless more information is available. When extremely reliable confidence intervals of location are also available for each call, the upper bound is still n, but a lower bound can be derived. The lower bound exceeds one when it is physically impossible for an animal to travel quickly enough to go from one reliable location to another within the temporal call interval. When many calls are detected, it may be too complicated or numerically prohibitive to determine the minimum number of animals responsible for the calls in space and time by inspection or brute force methods. Instead, it is advantageous to use graph theory. The lower bound for the number of calling animals can be derived using 100% confidence intervals of each call's location. Mathematical theorems guarantee the lower bound is correct: a lesser value is impossible to obtain. Guaranteed bounds for the abundance of calling animals are useful for conservation in the presence of environmental stress and studying behavior.

Power Allocation for Reliable SIC Detection of Rectangular QAM-based NOMA Systems

This paper considers the power allocation for non-orthogonal multiple access (NOMA) users to enable using the successive interference cancellation (SIC) while providing reliable error performance. The derived closed-form expressions are applicable for arbitrary number of NOMA users each of which has a square or rectangular quadrature amplitude modulation (QAM) constellation with arbitrary order. The obtained numerical results show that power assignment process at the transmitter for the superposition process and at the receiver for the SIC process should be performed meticulously because the power difference between the weakest and strongest users can be tremendous when the number of users or the modulation orders increase. Moreover, the derived expressions can be used to reduce the computational complexity that is required to obtain the optimal power coefficients using brute force methods by significantly reducing the search space.

SSA: Subset sum approach to protein β-sheet structure prediction

The three-dimensional structures of proteins provide their functions and incorrect folding of its β-strands can be the cause of many diseases. There are two major approaches for determining protein structures: computational prediction and experimental methods that employ technologies such as Cryo-electron microscopy. Due to experimental methods’s high costs, extended wait times for its lengthy processes, and incompleteness of results, computational prediction is an attractive alternative. As the focus of the present paper, β-sheet structure prediction is a major portion of overall protein structure prediction. Prediction of other substructures, such as α-helices, is simpler with lower computational time complexities. Brute force methods are the most common approach and dynamic programming is also utilized to generate all possible conformations. The current study introduces the Subset Sum Approach (SSA) for the direct search space generation method, which is shown to outperform the dynamic programming approach in terms of both time and space. For the first time, the present work has calculated both the state space cardinality of the dynamic programming approach and the search space cardinality of the general brute force approaches. In regard to a set of pruning rules, SSA has demonstrated higher efficiency with respect to both time and accuracy in comparison to state-of-the-art methods.

Comparison of source apportionment approaches and analysis of non-linearity in a real case model application

Abstract. The response of particulate matter (PM) concentrations to emission reductions was analysed by assessing the results obtained with two different source apportionment approaches. The brute force (BF) method source impacts, computed at various emission reduction levels using two chemical transport models (CAMx and FARM), were compared with the contributions obtained with the tagged species (TS) approach (CAMx with the PSAT module). The study focused on the main sources of secondary inorganic aerosol precursors in the Po Valley (northern Italy): agriculture, road transport, industry and residential combustion. The interaction terms between different sources obtained from a factor decomposition analysis were used as indicators of non-linear PM10 concentration responses to individual source emission reductions. Moreover, such interaction terms were analysed in light of the free ammonia / total nitrate gas ratio to determine the relationships between the chemical regime and the non-linearity at selected sites. The impacts of the different sources were not proportional to the emission reductions, and such non-linearity was most relevant for 100 % emission reduction levels compared with smaller reduction levels (50 % and 20 %). Such differences between emission reduction levels were connected to the extent to which they modify the chemical regime in the base case. Non-linearity was mainly associated with agriculture and the interaction of this source with road transport and, to a lesser extent, with industry. Actually, the mass concentrations of PM10 allocated to agriculture by the TS and BF approaches were significantly different when a 100 % emission reduction was applied. However, in many situations the non-linearity in PM10 annual average source allocation was negligible, and the TS and BF approaches provided comparable results. PM mass concentrations attributed to the same sources by TS and BF were highly comparable in terms of spatial patterns and quantification of the source allocation for industry, transport and residential combustion. The conclusions obtained in this study for PM10 are also applicable to PM2.5.

Developing an Android-Based City Tour App using Evolutionary Algorithm

Traveling around a city and making transit in certain areas is called a city tour. Furthermore, determining the optimal city tour route can be considered as a traveling salesman problem. There are many kinds of algorithms to solve this, one of which is the Genetic Algorithm (GA). In developing the City Tour application, a platform is needed to be taken to various places anywhere and anytime. Finally, we developed an application that runs on mobile devices. This application is built on the Android platform so that its use can be more efficient. Furthermore, it can be concluded that the GA applied to the Android-based City Tour Application is reliable to determine city tour routes; this is evidenced by comparing GA with the brute force method, where GA provides optimum results with less running time.

Assessing uncertainty for classified mixed model prediction

Classified mixed model prediction (CMMP) is a new method that has embedded the traditional mixed model prediction (MMP) with a modern flavour. The basic idea is to first identify a class among the training data that matches the potential class corresponding to the new observations, whose associated mixed effect is of interest for prediction. Once such a matching is established, the MMP method can be utilized to make more accurate prediction that takes into account the subject-level differences. In this paper, we consider estimation of the mean squared prediction error (MSPE) of CMMP. A recently proposed Sumca method is implemented. Sumca combines analytic and Monte-Carlo approaches, leading to a second-order unbiased estimator of the MSPE. The performance of Sumca is investigated via simulation studies and comparisons are made with alternative methods. The simulation study shows that a brute-force bootstrap method performs almost as well as Sumca, while a naive approach and a Prasad-Rao estimator at the matched index are significantly inferior to Sumca. A real-data application is considered. Remarks and recommendation are offered.

Source impact and contribution analysis of ambient ozone using multi-modeling approaches over the Pearl River Delta region, China

Quantification of source impacts and contributions is a key element for the design of effective air pollution control policies. In this study, O3 source impacts and contributions were comprehensively assessed over the Pearl River Delta (PRD) region of China using brute-force method (BFM), response surface modeling with BFM (RSM-BFM) and differential method (RSM-DM) respectively, high-order decoupled direct method (HDDM), and ozone source apportionment technology (OSAT). The multi-modeling comparison results indicated that under typical nonlinear atmospheric conditions during the O3 formation, BFM, RSM-BFM, and HDDM seemed to be appropriate for assessing the impact of single source emissions; however, the results of HDDM could deviate from those of BFM when the emission reduction ratio was higher than 50 %. Under multi-source control scenarios, the results of source contribution analyses obtained from RSM-DM and OSAT were reasonably well, but the performance of OSAT was limited by its capability in representing the nonlinearity of O3 response to emission reductions of its precursors, particularly NOx. The results of this pilot study in the PRD showed that the RSM-DM appeared to replicate the nonlinearity of O3 chemistry reasonably well (e.g., O3 disbenefits due to local NOx emission reductions in Guangzhou city). Based on the source contribution results, on-road mobile (including both NOx and VOC emissions) and industrial process (mainly VOC emissions) sources were identified as two major contribution sectors by both RSM-DM and OSAT, contributing an average of 31.5 % and 11.4 % (estimated by RSM-DM) and 29.2 % and 13.0 % (estimated by OSAT) respectively to O3 formation in 9 cities of the PRD. Therefore, the reinforced emission reductions on NOx and VOC from on-road mobile and industrial process sources in the central cities (i.e., Guangzhou, Foshan, Dongguan, Shenzhen, and Zhongshan) were suggested to effectively mitigate the ambient O3 levels in the PRD.

Rapid algorithm for covariance ellipsoid model based collision warning of space objects

The recent decades have witnessed a tremendous growth in the number of satellites and debris in space, leading to an increasingly high risk of collision between space objects. Collision warning aims at assessing the collision risk between space objects and attempts to identify possible collisions in order for satellites to perform evasive maneuvers in advance. Current collision warning methods are based on the computation of collision probability and comparison with some tolerance threshold. Such a threshold is usually set according to experience. In contrast, this paper proposes to use covariance ellipsoid with a user defined Mahalanobis distance to represent the most possible region in which the relative position vector distributes. Zero vector represents the collision event, and once it enters this ellipsoid, a collision warning occurs. A collision warning function along with a definite threshold is then formulated based on this criterion. Moreover, in order to rapidly predict the possible collision intervals, a self-adaptive Hermite interpolation technique is applied to approximate the collision warning function by piecewise cubic polynomials for efficient roots finding. Finally, the proposed collision warning criterion has been evaluated in several collision scenarios. Comparison experiments are also conducted with the brute force method and analytical propagators. The simulation shows that the calculation of collision warning interval based on the proposed criterion is effective, and the self-adaptive Hermite interpolation method performs high efficiency and accuracy.

Local and transboundary transport contributions to the wintertime particulate pollution in the Guanzhong Basin (GZB), China: A case study

Heavy haze with high levels of fine particulate matters (PM2.5) frequently engulfs the Guanzhong Basin (GZB) in northwestern China during wintertime. Although it is an enclosed basin with a narrow opening to the east, prevailing easterly winds during heavy haze episodes have a large potential to bring air pollutants to the GZB from the two highly polluted neighboring provinces of Shanxi and Henan (SX&HN). The source-oriented WRF-Chem model simulations of a persistent and heavy haze episode that occurred in the GZB from December 6 to 21, 2016, reveal that local emissions dominate PM2.5 concentrations in the GZB, with an average near-surface PM2.5 contribution of about 56.0% during the episode. The transboundary transport of emissions from SX&HN accounts for around 22.2% of the total PM2.5 in the GZB. Furthermore, with the deterioration of the air quality in the GZB from being slightly polluted to severely polluted in terms of hourly PM2.5 concentration, transboundary transport of emissions from SX&HN plays an increasingly important role in the particulate pollution, with the average PM2.5 contribution increasing from 8.0% to 27.5%. Compared with the source-oriented method (SOM), the brute force method (BFM) overestimates the contribution of GZB local emissions and transboundary transport of emissions from SX&HN to the total PM2.5 in the GZB. In addition, the BFM-estimated NH3 contribution of transboundary transport of emissions from SX&HN is negative, indicating the limitation of the BFM in source apportionment. Our results suggest that cooperative emission mitigation strategies with neighboring provinces are beneficial for lowering the particulate pollution in the GZB, particularly under severely polluted conditions.