Entire Space Research Articles

Diversity-guided particle swarm optimization with multi-level learning strategy

Particle swarm optimization (termed as PSO) is a metaheuristic algorithm inspired by the swarm intelligence. Since its advent, PSO has been successfully applied to tackle various issues that are hard to optimize. Unfortunately, similar to other evolutionary computation, PSO is also difficult to get rid of the bad luck of premature convergence and local optimization, especially when dealing with complex multimodal issues. Hence, this work proposes a diversity-guided PSO with multi-level learning strategy (DPSO-MLS). To begin with, chaotic opposition-based learning (OBL) is used to generate well-distributed initial particles to speed up convergence process of DPSO-MLS. Subsequently, according to the current swarm diversity, the high-layer learning mechanism enables PSO to explore the entire search space from a global perspective via attractive and repulsive strategies, respectively. Next, according to average fitness value of entire swarm, the low-layer learning strategy fine-tunes the particles search from a local perspective to sustain its diversity. To be specific, in the context of the repulsion phase, the regular varying function (RVF) embedded update strategy is used to block potential local optima so as to continue exploring the potential search space when the particle's fitness is less than the average of swarm, otherwise an alternative mutation scheme is utilized to enrich the swarm diversity. Accordingly, the slowly varying function (SVF) embedded update strategy is applied when the particle's fitness is greater than the average of swarm, otherwise the worst-best example learning based mechanism is exploited to update the worst particle to improve the quality of swarm in the context of the attraction phase. To verify the effectiveness of DPSO-MLS, extensive experiments are conducted and the results show that our proposal is superior or highly competitive to several existing PSOs according to the robustness, convergence rate and solution accuracy.

WS-SSD: Achieving faster 3D object detection for autonomous driving via weighted point cloud sampling

Due to the limited computational resources of the onboard computing devices of autonomous vehicles, the development of lightweight 3D object detectors is essential. Point-based detectors that progressively sample raw point clouds reduce numerous redundant computations and facilitate the implementation of high-speed 3D object detectors. The farthest point sampling based on Euclidean distance (D-FPS) is frequently utilized in point-based 3D detectors for point cloud sampling to reduce computation overhead. D-FPS can ensure uniform point sampling, covering the entire point cloud space as much as possible. The ratio of foreground and background points does not change significantly in the sampling results; hence, foreground objects do not receive sufficient attention. In addition, the number of road reflection points is large, and these points are close to foreground objects, reducing the sampling accuracy for faint objects. We propose weighted farthest point sampling based on Euclidean distance (W-DFPS), which selectively discards some road reflection points in the point sampling process, thus increasing the weight of foreground points in sampling results. It reduces the likelihood of faint objects being lost in the sampling results, such that a small number of sampling points can also cover most foreground objects. W-DFPS replaces D-FPS in the single-stage detector based on instance-aware (IA-SSD), and the network structure is slightly modified, namely the single-stage detector based on weighted sampling (WS-SSD). We evaluate WS-SSD in the KITTI dataset with a single A100 GPU. When the number of sampling points for the first module of WS-SSD is consistent with IA-SSD, the pedestrian detection accuracy is improved by an average of 4.06 compared to IA-SSD. Although the number of sampling points for the first module of WS-SSD is reduced to 25% of IA-SSD, the object detection accuracy remains competitive; it also achieves a state-of-the-art inference speed of 150.76 frames per second (FPS), which is a 46% improvement over IA-SSD.

The Behavior of Sumatera Llourism (Nycticebus coucang) In The Capture Facilities, Primate Animal Study Center LPPM-IPB

Lorises are protected and endangered animals, according to the IUCN, because of poaching, habitat fragmentation, and illegal sales that occur. This study aims to determine the suitability of the cages by observing the behavior and use of the cages space by the sumatera lorises in Primate Animal Study Center. The method used is instantaneous vocal animal sampling with 10-minute intervals. The study results showed locomotion behavior at 46.69%, social behavior at 2.63%, elimination at 1.6%, rest at 25.11%, grooming at 6.16%, foraging at 2.4%, eating at 3.88%, and being alert at 11.53%. Lorises in Primate Animal Study Center use the entire cages space provided to carry out active and inactive activities. The conservation aspect is sufficiently supportive of the housing and feed aspects provided. Even though the feed given is not in accordance with its original habitat, therefore a change in the feed menu is necessary.

VISCOSITY SOLUTIONS TO THE INFINITY LAPLACIAN EQUATION WITH SINGULAR NONLINEAR TERMS

Abstract In this paper, we study the singular boundary value problem $$ \begin{align*} \begin{cases} \Delta_\infty^h u=\lambda f(x,u,Du) \quad &\mathrm{in}\; \Omega, \\ u>0\quad &\mathrm{in}\; \Omega,\\ u=0 \quad &\mathrm{on} \;\partial\Omega, \end{cases} \end{align*} $$ where $\lambda>0$ is a parameter, $h>1$ and $\Delta _\infty ^h u=|Du|^{h-3} \langle D^2uDu,Du \rangle $ is the highly degenerate and h-homogeneous operator related to the infinity Laplacian. The nonlinear term $f(x,t,p):\Omega \times (0,\infty )\times \mathbb {R}^{n}\rightarrow \mathbb {R}$ is a continuous function and may exhibit singularity at $t\rightarrow 0^{+}$ . We establish the comparison principle by the double variables method for the general equation $\Delta _\infty ^h u=F(x,u,Du)$ under some conditions on the term $F(x,t,p)$ . Then, we establish the existence of viscosity solutions to the singular boundary value problem in a bounded domain based on Perron’s method and the comparison principle. Finally, we obtain the existence result in the entire Euclidean space by the approximation procedure. In this procedure, we also establish the local Lipschitz continuity of the viscosity solution.

From Pagoda to Pavilion: The Transition of Spatial Logic and Visual Experience of Multi-Story Buddhist Buildings in Medieval China

Pagodas and pavilions (ge 閣) are the most popular and representative multi-story buildings since Buddhism was introduced to China. While providing visitors with a new visual experience, they have also largely reshaped the urban space and skyline in medieval China. The former originated from India and Central Asia and was transformed in China, developing a unique style; The latter originated more from the creation of Chinese architects and became a model of typical Chinese-style Buddhist architecture. Briefly, the pagoda matured earlier than the pavilion, and continuously developed while maintaining its basic style; the pavilion-style Buddhist architecture gradually developed later and finally matured after the Tang and Song dynasties (618–1276), partially presenting a different spatial logic from the pagoda, and bringing a new visual experience. In my opinion, although the pavilion may not necessarily be as large as the pagoda in terms of volume and absolute height, it can provide believers with greater visual impact in the internal space for worship, due to the cross-story giant Buddhist statues; the closer integration of Buddha statues and architecture makes it replace or share the core position of the pagoda in some monasteries and even become the visual center of the entire religious space. Due to the existence of the pavilion, viewers can not only worship the Buddhist statues on a two-dimensional plane or by looking up at the statues from the bottom, but have also gained a three-dimensional perspective, to worship directly at the Buddha’s shoulders, neck, and head. In the Buddhist grottoes, the layout of the early single-layer or multi-layer horizontally distribution of caves on cliff was also changed due to the excavation of the cross-layer giant statue grottoes, covered by multi-story pavilion-style buildings, providing viewers with a visual experience similar to that of the pavilions of great statues. Additionally, there is a new visual experience of worshiping the Buddha in a vertical circle, in cases such as Bamiyan and the Leshan Giant Buddha.

Moduli of Continuity in Metric Models and Extension of Livability Indices

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function ϕ. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modeling of livability indices in North American cities.

A family of robust chaotic S-unimodal maps based on the Gaussian function

This research paper introduces a family of one-dimensional S-unimodal maps based on the Gaussian function, designed to exhibit robust chaos across a wide range of parameters. These maps are developed to display robust chaos by avoiding multiple fixed points that are primarily responsible for the coexisting attractors in 1D maps. The parameter space analysis reveals that chaotic behaviour is sustained across the entire parameter space, except for a very narrow region. The study employs a comprehensive computational approach, including quantitative measures such as sample entropy, Lyapunov exponent, and invariant measures. The uniformly higher values of sample entropy, uniform positive values of the Lyapunov exponent, and the existence of invariant measures in a region of parameter space confirm the presence of robust chaos in these maps. Such a promising class of robust chaotic maps may be potentially used in diverse fields such as chaos-based cryptography, pseudo-random number generation, communication systems, and more.

GreenNAS: A Green Approach to the Hyperparameters Tuning in Deep Learning

This paper discusses the challenges of the hyperparameter tuning in deep learning models and proposes a green approach to the neural architecture search process that minimizes its environmental impact. The traditional approach of neural architecture search involves sweeping the entire space of possible architectures, which is computationally expensive and time-consuming. Recently, to address this issue, performance predictors have been proposed to estimate the performance of different architectures, thereby reducing the search space and speeding up the exploration process. The proposed approach aims to develop a performance predictor by training only a small percentage of the possible hyperparameter configurations. The suggested predictor can be queried to find the best configurations without training them on the dataset. Numerical examples of image denoising and classification enable us to evaluate the performance of the proposed approach in terms of performance and time complexity.

Multi-objective optimization of daylight illuminance indicators and energy usage intensity for office space in Tehran by genetic algorithm

One of the important categories in office spaces is the control of daylight and energy consumption. By controlling natural light, it is possible to provide uniform light in the entire space, sufficient daylight, and visual comfort for office workers. In many cases, this important issue can be resolved by choosing the right shading. In this study, the aim is to investigate the significance of some important parameters such as DoS (Depth of Shading), FO (Facade Offset), FSoS (Flip Start of Shading), LoS (Location of Shading), WWR (Window to Wall Ratio), CoS (Count of Shading), AoS (Angle of Shading), and HoW (Height of Window) in the optimal design of shading for an office environment in Tehran. For this purpose, eight variables have been designed and the aim is to improve the indicators of Energy Usage Intensity (EUI), Spatial Daylight Autonomy(sDA), Daylight Glare Probability (DGP), and Tc (Thermal comfort) in the office space. For optimization in the grasshopper environment, Wallacei’s algorithm was used. Then, the algorithm provides a set of optimal points. Then a point was selected as optimal by the WSM (Weighted Sum Method) method. According to the input variables that are DoS, FO, FSoS, LoS, WWR, CoS, AoS, and HoW its optimal point values are 0.4, 0, Up, Horizontal, 80, 5, 30, 0.5, respectively. The results show that the values of sDA, DGP, EUI, and Tc were improved by 43.6%, 52.77%, 13.9, and 3.696%, respectively, before and after shading optimization. Also, the annual glare and the hottest and coldest day of the year were checked where there were around 500(cd/m2) and 200(cd/m2) reduction of glare value in winter and summer seasons, respectively. Finally, the value of Useful Daylight Illuminance (UDI)before and after the installation of the optimal shading was 25.8 and 68.4, respectively.

Data-driven ensemble optimal compensation control for partially known delayed and persistently disturbed nonlinear systems

In almost all industrial processes, the development of an accurate mathematical model that comprehensively characterizes the regulated system poses a substantial obstacle. Diverse factors, such as unidentified system components and time-varying external disturbances, contribute to this phenomenon. This can result in a disparity between the model and the plant and thereby compromising the performance of the designed controller. In this study, a novel data-driven ensemble optimal compensation control framework is proposed for partially known nonlinear systems with state delays and structural disturbances. Initially, the estimated system model is leveraged to construct a robust fuzzy model predictive controller (RFMPC) based on the Lyapunov–Krasovskii functional (LKF), ensuring the input-to-state stability (ISS) of the plant. Then, a reinforcement learning (RL)-based compensator is assembled to gradually minimize the model-plant mismatch across the entire state space. To streamline the training process of the compensator and facilitate its stability, a dynamic network update scheme is devised, incorporating a moving average gradient calculation method and a learning rate tuning strategy. Furthermore, comparative discussions with some prevalent methods are demonstrated. With the established control framework, the performance of the RFMPC can be securely enhanced, and convergence is ensured within a narrow proximity to equilibrium, despite time-varying perturbation dynamics. By integrating this approach with deep learning (DL) methods, the efficacy of numerous industrial processes could be significantly improved. A numerical simulation and a discretized continuous-time stirring tank reactor (CSTR) example validate the effectiveness and benefits of the proposed control strategy.

Experimental investigation of walking drops: Wave field and interaction with slit structures.

While bouncing walking silicone oil droplets (walkers) do show many quantumlike phenomena, the original, most intriguing, double-slit experiment with walkers has been shown to be an overinterpretation of data. Several experiments and numerical simulations have proven that for at least some parameter region there is no randomness. Still, true randomness was claimed to be observed in an experiment on chaotically bouncing walkers. Also, most of the available phase space has not been investigated. The main goal of this paper is therefore to look for true interference and chaos in the entire phase space. Recently, we made an extensive investigation of drops interacting with slits, but still in a limited range. However, the outcome was always deterministic and only incidentally mimicked the statistics of the corresponding quantum case. We also showed that the extra interference, already seen by others, in the double-slit case was caused by reflection of waves from the outlet of the unused slit after passage and thus was not a true double-slit effect. A new theoretical treatment of bouncing drop dynamics has since given analytic relations for the associated wave field, leading to a proposal for criteria for the possible occurrence of true interference in the double-slit experiment. Satisfying these criteria, requires working close to the onset of the Faraday instability, with two spatial conditions favoring slow walkers, and a temporal condition favoring fast walkers. The regions of high velocity, where the walkers bounce periodically, and of very low velocity, with chaotically bouncing walkers, have not been comprehensively investigated so far. We have therefore looked at these regions, probing the limits for interaction with slits. Furthermore, noting that a short transit time is essential to fulfill the criteria, experiments were done using double-slit barriers only 0.5 and 2mm broad. Nowhere was true interference or a chaotic response found. As the theory has implications for many of the observed quantumlike phenomena involving walkers as, e.g., tunneling and interaction between drops, we have measured the spatial and temporal decay of the wave field. A comparison with the theory shows very good agreement but leads to a reformulation of the above-mentioned criteria.

Bio-Inspired Jumping Spider Optimization for Controller Tuning/ Parameter Estimation of an Uncertain Aerodynamic MIMO System

The practical near impossibility of empirical attempts in estimating optimal controller gains makes the use of metaheuristics strategies inevitable to automatically obtain these gains by an iterative, heuristic simulation procedure. The convergence of the gains values to the local or global solutions occur with ease. In designing controllers for the Twin-Rotor MIMO System (TRMS), Jumping Spider Optimization Algorithm (JSOA), a novel neoteric population-based bio-inspired metaheuristic approach is used to obtain optimum values for the Proportional, Integral and Derivative (PID) controllers. With the k,p,i controller gains as the decision variables, the JSOA solution to a nonlinear multi-objective optimization problem subject to some intrinsic constraints spawned optimal values for the controllers’ variables. Counter to other algorithms (deterministic and stochastic) that get caught in local minima, JSOA evolved a solution after searchingly rummaging the entire solution search space in a vectorized fashion for an optimal value. Compared with several other versatile controllers (using GA, PSO, Pattern Search and Simulated Annealing), statistical results obtained showed JSOA technique provided a unique solution and found the gains of the PID controllers, marginally in relation to the others (optimization methods).

Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold

Because of their applications, the study of piecewise-linear differential systems has become increasingly important in recent years. This type of system already exists to model many different natural phenomena in physics, biology, economics, etc. As is well known, the study of the qualitative theory of piecewise differential systems focuses mainly on limit cycles. Most papers studying the problem of existence and the maximum number of limit cycles of piecewise differential systems have precisely considered planar systems. However, few papers have examined this problem in [Formula: see text]. In this paper, our main goal is to examine a class of discontinuous piecewise differential systems in [Formula: see text], where we consider the unit sphere as the separation surface that divides the entire space into two regions, each one has a linear vector field analogous to planar center. In general, it is hard to determine an exact upper bound for the number of limit cycles that a class of differential systems can exhibit. We prove that this class of differential systems can have at most four limit cycles. We show that there are examples of such differential systems with exactly 1, 2, 3 and 4 limit cycles.

On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity

We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlinearity of the form: − Δ u = λ u p − u q in R N + 1 , where 0 < q < p < 1 and λ ∈ R. The approach is based on the Nehari manifold method supplemented by a one-sided constraint given through the functional of the suitable Pohozaev identity. The limit value of the parameter λ, where the approach is applicable, corresponds to the existence of periodic in one variable and compactly supported in the other variables least energy solutions. This value is found through the extrem values of nonlinear generalized Rayleigh quotients and the so-called curve of the critical exponents of p, q. Important properties of the solutions are derived for suitable ranges of the parameters, such as that they are not trivial with respect to the periodic variable and do not coincide with compactly supported solutions on the entire space R N + 1 .

On a new class of progressive waves in Yang–Mills fields with SU(2) symmetry

In the present paper, a new class of wave solutions to the Yang-Mills equations with SU(2) symmetry is considered. They describe the propagation of non-Abelian transverse progressive waves. In the case under consideration, the problem is reduced to six nonlinear partial differential equations. Their solutions are sought in a special form that allows them to be satisfied. The found exact wave solutions to the considered Yang-Mills equations do not have singularities in the entire space and have finite energies that can take any positive value. The obtain results can be used to detect non-Abelian progressive waves in space.

Multi-objective continuous review inventory policy using MOPSO and TOPSIS methods

In the dynamic business environment of today, decision-making involves considering various conflicting aspects. Inventory planning problems aim to determine how much and when to order products to satisfy customer demand at the lowest possible cost while maintaining a desirable service level. These problems can be formulated as a MOPSO algorithm, which is used to handle multiple objectives in a continuous review stochastic inventory control system (r, Q). Unfortunately, most multi-objective inventory models have been solved by aggregating objectives using specific weights or by optimizing only one objective and treating the others as constraints. Considering the complexity of real-world inventory control problems, which involves conflicting objectives such as minimizing cost and maximizing service level, the need arises to employ more precise optimizers that can generate better and more diverse non-dominated solutions of reorder point and order size system. In this paper multi-criteria decision-making framework that combines MOPSO algorithm and TOPSIS method to generate a Pareto front of non-dominated solutions and rank them based on decision makers' preferences. Initially, the original MOPSO is applied to the multi-objective inventory control problem, and then the mutation operator is integrated into the MOPSO to maintain diversity in the swarm and explore the entire search space. Next, the leader selection strategy called the geographically-based system (Grids) is replaced by the crowding distance factor to choose the global optimal particle as a leader. Additionally, the ε-dominance concept is employed to limit the archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. In conclusion, this work not only pioneers a cutting-edge approach to multi objective inventory control but also underscores its practical value. By facilitating the generation of superior solutions that cater to diverse decision-maker preferences, our methodology resonates deeply with real-world challenges and sets a new benchmark for effective inventory planning.

Examining Differential Item Functioning from a Multidimensional IRT Perspective.

Differential item functioning (DIF) is a standard analysis for every testing company. Research has demonstrated that DIF can result when test items measure different ability composites, and the groups being examined for DIF exhibit distinct underlying ability distributions on those composite abilities. In this article, we examine DIF from a two-dimensional multidimensional item response theory (MIRT) perspective. We begin by delving into the compensatory MIRT model, illustrating and how items and the composites they measure can be graphically represented. Additionally, we discuss how estimated item parameters can vary based on the underlying latent ability distributions of the examinees. Analytical research highlighting the consequences of ignoring dimensionally and applying unidimensional IRT models, where the two-dimensional latent space is mapped onto a unidimensional, is reviewed. Next, we investigate three different approaches to understanding DIF from a MIRT standpoint: 1. Analytically Uniform and Nonuniform DIF: When two groups of interest have different two-dimensional ability distributions, a unidimensional model is estimated. 2. Accounting for complete latent ability space: We emphasize the importance of considering the entire latent ability space when using DIF conditional approaches, which leads to the mitigation of DIF effects. 3. Scenario-Based DIF: Even when underlying two-dimensional distributions are identical for two groups, differing problem-solving approaches can still lead to DIF. Modern software programs facilitate routine DIF procedures for comparing response data from two identified groups of interest. The real challenge is to identify why DIF could occur with flagged items. Thus, as a closing challenge, we present four items (Appendix A) from a standardized test and invite readers to identify which group was favored by a DIF analysis.

Criteria for Davies irreducibility of Markovian quantum dynamics

The dynamics of Markovian open quantum systems are described by Lindblad master equations, generating a quantum dynamical semigroup. An important concept for such systems is (Davies) irreducibility, i.e. the question whether there exist non-trivial invariant subspaces. Steady states of irreducible systems are unique and faithful, i.e. they have full rank. In the 1970s, Frigerio showed that a system is irreducible if the Lindblad operators span a self-adjoint set with trivial commutant. We discuss a more general and powerful algebraic criterion, showing that a system is irreducible if and only if the multiplicative algebra generated by the Lindblad operators La and the operator iH+∑aLa†La , involving the Hamiltonian H, is the entire operator space. Examples for two-level systems, show that a change of Hamiltonian terms as well as the addition or removal of dissipators can render a reducible system irreducible and vice versa. Examples for many-body systems show that a large class of spin chains can be rendered irreducible by dissipators on just one or two sites. Additionally, we discuss the decisive differences between (Davies) reducibility and Evans reducibility for quantum channels and dynamical semigroups which has lead to some confusion in the recent physics literature, especially, in the context of boundary-driven systems. We give a criterion for quantum reducibility in terms of associated classical Markov processes and, lastly, discuss the relation of the main result to the stabilization of pure states and argue that systems with local Lindblad operators cannot stabilize pure Fermi-sea states.

Dynamic Model Inference of Gene Regulatory Network based on Hybrid Parallel Genetic Algorithm and Threshold Qualification Method

Gene regulation is the process by which various substances in cells regulate the behaviour of gene expression, thereby controlling almost all cellular activities. Therefore, studying gene regulation not only helps to uncover the internal laws governing life processes but also plays a crucial role in predicting, diagnosing, treating, and designing drugs for genetic diseases. By utilizing multi-source biological information such as gene expression profiles, transcription factor information, and protein interaction data, a network model can be developed to depict the regulatory relationships between genes, facilitating further research. To address the limitations of traditional gene regulatory network construction methods, a novel dynamic model has been created by combining hybrid genetics and threshold restriction. This model comprises two parts: solution space reduction and parameter fitting. During solution space reduction, singular value decomposition is employed to define a mathematically feasible gene regulatory network, reducing unnecessary calculations. Subsequently, the control genes of each gene are constrained within a certain range using threshold limitation, enhancing computational efficiency while adhering to bioinformatics principles. In the parameter fitting phase, parallel genetic algorithms are utilized to expediently optimize the entire solution space. The mountain climbing method is then applied to solve problems meticulously within a limited scope, improving calculation accuracy. In this study, this approach was applied to establish genetic regulatory systems for complex skin melanoma and type 2 diabetes. Through comparison with actual networks, the validity of the method was confirmed. Compared to traditional genetic and particle swarm optimization methods, the effectiveness of the proposed method was verified. This paper models the intricate mechanism of gene regulation and elucidates the regulatory process involving genes, proteins, and small biological molecules in greater detail than other models, aligning more closely with intracellular dynamics laws.

A new injection method for identifying the subpopliteal recess of the knee.

The posterolateral region of the knee has a complex and diverse anatomy. Hydrarthrosis of the knee can potentially communicate with other parts of the joint space. The joint fluid distribution reflects anatomical communications between synovial spaces. To observe the continuity between the knee joint cavity and the surrounding bursa, we devised a dissection method with a new injection agent, an eosin-containing congealed liquid that spreads uniformly over the entire space. The purpose of this study was to perform a detailed examination of the subpopliteal recess (SPR) where a bursa connects to the knee joint capsule. We also reported the advantages of this new injection agent compared with conventional materials (latex and epoxy resin). Twenty-two formalin-fixed cadavers (34 knees), two N-vinyl-pyrrolidone (NVP)-fixed cadavers (4 knees), and two cadavers (3 knees) fixed by Thiel's method were used. After filling the knee joint space and SPR with eosin congealed liquid, the specimens were dissected to investigate the morphology of the SPR. In addition, three different types of injection agents were assessed. The SPR extended distally along the popliteus tendon. The SPR length was 22.64 ± 11.38 mm from the upper end of the lateral tibial condyle to the lower end of the depression. The existence of a fabellofibular ligament made the SPR significantly longer, but abrasion of the femoral articular cartilage did not affect the SPR. Furthermore, the relationship between the popliteus muscle and the SPR was classified into three types (types 1-3). Types 2 and 3 in which the SPR extended to the proximal tibiofibular joint may cause instability of the knee joint. The eosin congealed liquid was highly useful in many aspects, such as fluidity and injection workability. The new dissection method with eosin congealed liquid provides insights into the anatomy of the posterior lateral knee, which are useful for radiological diagnoses and clinical treatments.