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Design and implementation of bio-inspired camera systems for dynamic environments
No full text현대 카메라 시스템은 다변화 환경에서 효율적이면서도 정확한 광 성능을 구현하 는 요구가 증가하면서, 광 감도, 왜곡 없는 시야각 및 수륙양용 비전 등 다기능 카메라 시스템이 요구되고 있다. 이러한 문제를 해결하기 위해 자연계에서 환경 진화된 시각 시스템의 영상 처리 특성에서 영감을 얻어 효율적인 시각 기능을 모사하는 카메라 시 스템 기술이 주목받고 있다. 본 논문에서는 이러한 자연의 환경 적응 특성을 모사하여 다양한 광 환경에서 효과적으로 작동하는 광학 기능을 갖춘 생체모사형 카메라 시스템 을 탐구한다. 첫째, 나방 눈 표면의 나노구조를 모사하여 설계된 인공 반사 방지 광학 시스템을 제시한다. 이 시스템은 광대역 파장에서 광 투과율을 크게 향상시키는 반사방 지 나노구조를 렌즈 및 필름에 적용하여 저조도 환경에서도 뛰어난 영상 처리 성능을 유지할 수 있는 높은 광 감도 시스템을 구현한다. 둘째, 농게의 독특한 시각 구조를 모사 하여 전방위 전천후 카메라를 개발한다. 3차원으로 배열된 인공 광수용체 구조를 갖는 편평 렌즈 구조를 통해 300도의 넓은 시야각을 확보하였으며, 서로 다른 굴절률을 가진 환경에서도 동일한 영상 처리 성능을 갖는 파노라마 및 수륙양용 시각 구조를 탐구하고 시스템을 구현한다. 셋째, 광 도파관 기술을 개발하여, 인공 겹눈 시각 시스템 내에서 광 정밀 제어를 가능하게 하고, 이를 통해 소형화된 고해상도 광학 시스템을 개발한다. – iii – 본 논문에서 제안한 이러한 생체모사 기술은 기존 카메라 시스템의 한계를 극복하고, 다양한 다변화 환경에서 신뢰할 수 있는 영상 처리 기능을 구현하는 데 기여한다. 또한, 본 논문에서는 이러한 생체모사 기술 구현을 위한 기반 기술과 향후 해결해야 할 과제에 대해서도 논의한다.|Modern camera systems face increasing demands to perform effectively across di- verse environments, requiring solutions to challenges in light sensitivity, field of view, and amphibious vision. To meet these challenges, advanced technologies focus on inte- grating efficient functionalities inspired by natural vision systems, which have evolved highly adaptive imaging capabilities to survival in unpredictable natural habitats. This thesis explores bio-inspired camera systems that emulate these natural adaptations, incorporating advanced optical functionalities for dynamic environments. Firstly, by mimicking the nanostructures on the surface of moth eyes, artificial antireflective op- tical system consists of optical lenses with anti-reflective nanostructures that enhance light sensitivity by significantly increasing transmittance across a wide spectrum of wavelengths. This improvement addresses the challenge of maintaining high perfor- mance in low-light environments. Subsequently, inspired by the fiddler crab’s unique vision system, a flat lens design with a three-dimensionally distributed artificial om- matidia structure achieves an extremely wide field of view, enabling panoramic and amphibious vision, allowing for effective operation across different refractive media. Finally, an efficient optical waveguiding component is developed to provide precise op- tical control within artificial systems, contributing to improved adaptability in precise and compact optical systems. These bio-inspired features enable camera systems to overcome current limitations, delivering reliable optical performance in varied environ- ments. Furthermore, the supportive technologies and remaining challenges necessary to realize these bio-inspired adaptations will be discussed.DoctorAbstract (English)
Abstract (Korean)
List of Contents
List of Tables
List of Figures
1. Introduction 1
1.1 Capture the world from visual information 1
1.2 From conventional optics to adaptive, bio-inspired vision system 2
1.3 Objective and Outline 5
2. Low-light vision: moth-eye inspired antireflective nanostructures 9
2.1 Introduction: Bio-inspired antireflective nanostructures (ARS) for optical enhancement 12
2.2 ARS integration onto optical lenses 16
2.2.1 Optical design and simulation of enhanced transmittance from visible to near infrared 16
2.2.2 Fabrication process of double-sided ARS (DARS) optical lenses 19
2.2.3 System integration and optical performance demonstration 21
2.3 Dual-coated ARS optical film for flexible, robust, and design adaptability 26
2.3.1 Optical design and simulation for dual-coated ARS film 26
2.3.2 Fabrication process for dual-coated ARS optical film 29
2.3.3 Optical and mechanical property 30
2.4 Summary 35
3. Amphibious and panoramic vision: crab-eye inspired artificial compound eye (ACE) camera 37
3.1 Introduction: Bio-inspired amphibious and panoramic vision system 39
3.2 Optical design of amphibious and panoramic ACE camera 41
3.2.1 Amphibious vision: adaptation to semi-terrestrial environments 41
3.2.2 Panoramic vision: optical morphology of the fiddler crab eye 44
3.3 Optical characterization of the amphibious ACE 47
3.3.1 Artificial ommatidium: flat microlens with graded refractive index (g-ML) 47
3.3.2 Optical measurement of the g-ML array 50
3.3.3 Fabrication process of the g-ML array 52
3.4 System-level integration for amphibious and panoramic ACE camera 57
3.4.1 Fabrication of the g-ML array for imaging device 57
3.4.2 Three-dimensional integration for imaging device 60
3.5 Imaging demonstration of amphibious and panoramic vision 67
3.5.1 Methodology of the imaging demonstration 67
3.5.2 Imaging demonstration 73
3.5.3 Further advance in imaging performance 80
3.6 Summary 89
4. Amphibious high-resolution (HR) ACE system via fML-based self-aligned waveguide 90
4.1 Introduction: amphibious HR ACE enhanced by self-aligned waveguide 92
4.2 Self-aligned waveguide based on flat microlens (fML) 95
4.2.1 Fabrication method for self-aligned waveguides 95
4.2.2 Validation of self-aligned waveguides integrated with the fML array 98
4.3 Optical characterization of fML integrated with self-aligned waveguide 102
4.3.1 Optical simulations for amphibious imaging performance 102
4.3.2 Comparative evaluation for HR imaging capability 108
4.4 Experimental demonstration of amphibious HR imaging capability 111
4.5 Summary 118
5 Conclusion 119
References 121
Acknowledgements 13
Improved catalytic NO oxidation over Pt supported on sulfuric acid treated TiO2
No full textPromoting the formation of metallic Pt over the catalysts is the key to improving the NO reactivity. In general, TiO2 suppresses the oxidation of Pt by surface acidity and induces the formation of the metallic phase of Pt by Pt-Ti interaction. However, the limited number of acidic sites (–OH) contributes to the formation of large Pt particles, which may lead to the formation of Pt2+ or Pt4+, resulting in performance degradation. In this study, we further formulated the acidic sites of the TiO2 with sulfuric acid treatment (SA-TiO2) to improve catalytic NO oxidation. During the SA treatment, the TiO2 surface is positively charged by the low pH, providing an environment for well-distributed sulfate. In the subsequent introduction of Pt, the increase in acidic sites for Pt adsorption greatly enhanced the dispersion of Pt. During this process, Pt formed bonds with sulfate as [Pt(NH3)4]-SO4. The surface species combined with SO4 and NH3 were decomposed during the calcination process, thereby inhibiting the oxidation of Pt, which promotes the formation of metallic Pt. As a result, highly reactive Pt0 and Pt2+ were further formulated by increasing the acidic sites of SA-TiO2, where the low-temperature NO oxidation performance was improved, regardless of the Pt loading (0.3 to 3 wt.%).FALSEsciescopu
Identification of polymorphs in epitaxial SnO2 thin films deposited on sapphire (0001) substrates
No full textIn this study, synchrotron X-ray diffraction (XRD) and transmission electron microscopy (TEM) methods were combined to identify polymorphs in SnO2 thin films deposited on sapphire (0001) substrates using radio-frequency powder sputtering. A wide range of off-specular Bragg peaks-including higher-order reflections-were examined via high-resolution, in-plane XRD analyses for precise phase identification. Evidently, the orthorhombic columbite (C-SnO2) and tetragonal rutile (R-SnO2) phases coexisted in the as-deposited films. Because both the phases were aligned with their (200) planes along the surface normal, their out-of-plane Q(z) components appeared nearly identical. However, the in-plane Q(x) and Q(y) components were distinguishable. The lattice constants were estimated from the in-plane Bragg peak positions, and the corresponding strain states in ultrathin films (<10 nm) were determined. In the early stage of growth, the C-SnO2 and R-SnO2 domains exhibited opposing strains-compressive and tensile strains, respectively-because of extended domain matching epitaxy, which accommodated lattice mismatch and governed the stabilization of each polymorph. The coexistence of the two phases at the atomic scale was further supported by cross-sectional high-resolution TEM analysis. These findings provide new insights into the strain-driven stabilization of polymorphs and the structural evolution of epitaxial SnO2 thin films on symmetry-mismatched substrates.FALSEsciescopu
Visual Multi-Object Tracking with Re-Identification using Labeled Random Finite Sets
No full text본 논문은 베이즈 필터링(Bayesian filtering)을 통해 객체 출현 및 재출현 그리고 가림 현상과 같은 문제를 해결하는 향상된 온라인 비주얼 다중 객체 추적(multi-object tracking)을 기법을 소개한다. 먼저, 객체의 사라짐 및 재출현 문제 해결을 위해, 라벨링 된 확률 유한 집합(labeled random finite set) 필터링 알고리즘을 제안한다. 이는 객체 관리를위해객체들의특징을활용하고,객체검출(detection)에대해선형시간복잡도로 작동하는새로운모델을포함한다.또한,궤적의겹침과크기를고려한퍼지(fuzzy)검출 모델이 가림 현상(occlusion) 처리를 개선하며, 계산 시간을 최소화하기 위해 근사화된 필터도함께제시된다.다음장에서는제안하는다중객체추적알고리즘을 2D이미지에 서실제 3D좌표로확장한다.이접근법은단안카메라의 2D검출들을통합함으로써 3D 다중 객체 추적을 향상시키고, 카메라 재구성 시 검출기 재학습의 필요성을 제거한다. 이를통해트랙초기화및종료,재식별,가림현상처리를단일베이즈필터링재귀로통 합하고, 나아가 객체의 특징, 운동 데이터, 기하학적 가림 모델을 활용하여 제안 기법의 효율성을 높인다. 마지막으로, 2D 바운딩 박스 검출만을 사용하여 실시간 다중 카메라 다중 객체 추적(multi-camera multi-object tracking)을 위한 빠른 온라인 알고리즘이 고 안된다. 이 방법은 다중 센서(multi-sensor) generalized labeled multi-Bernoulli 필터를 – iii – 낮은복잡도와정확도손실없이구현가능하게하고,동적카메라구성에대한강건함을 보여준다.|This dissertation introduces advanced methods for online visual multi-object track- ing (MOT), addressing challenges like object appearance-reappearance and occlusion, using Bayesian filtering techniques. We first introduce an algorithm that leverages la- beled random finite set (LRFS) filtering to tackle disappearance and reappearance issues, incorporating a novel model that utilizes object features to manage reappearing objects with linear complexity relative to the number of detections. A fuzzy detection model is also introduced to enhance occlusion handling by considering track overlaps and sizes. To reduce computational time, we propose an approximation of this filter. In the next chapter, we extend our proposed multi-object tracking algorithm from 2D images to 3D real-world coordinates. More specifically, this approach enhances 3D multi-object tracking by integrating 2D detections from monocular cameras, elim- inating the need for detector retraining upon camera reconfiguration. This solution combines track initiation/termination, re-identification, and occlusion handling into a single Bayes filtering recursion, with improved efficiency through feature and kinematic incorporation, and a geometric occlusion model. In the last chapter, a rapid online al- gorithm is presented for real-time multi-camera multi-object tracking, using only 2D bounding box detections. This method simplifies the Multi-Sensor Generalized La- beled Multi-Bernoulli (MS-GLMB) filter to achieve a low-complexity implementation, demonstrating faster performance without accuracy loss, and robustness to dynamic camera configurations.DoctorAbstract (English) i
Abstract (Korean) iii
List of Contents v
List of Tables viii
List of Figures xii
List of Algorithms xviii
1 Introduction 1
2 Visual Multi-Object Tracking with
Re-Identification and Occlusion Handling using Labeled Random Fi-
nite Sets 5
2.1 Abstract 5
2.2 Introduction 6
2.3 Related Work 9
2.3.1 Visual Multi-Object Tracking 9
2.3.2 Visual RFS-based Localization and Tracking 10
2.4 Dynamic and Measurement Models 11
2.4.1 Multi-Object Dynamic and Appearance Model 12
2.4.2 Measurement Model with Occlusion 13
2.4.3 Fuzzy Detection Model 15
2.5 Bayesian Multi-Object Filtering Solutions 19
2.5.1 The Exact Filtering Recursion 20
2.5.2 The GLMB Filter 21
2.5.3 The LMB Filter 23
2.5.4 Track Initialization and Re-ID 25
2.5.5 Multi-Object Estimator 27
2.6 Implementation Details 28
2.6.1 Object Dynamic Representation 28
2.6.2 Single-Object Detection Model 29
2.6.3 Hypothesis Truncation for GLMB/LMB Filters 30
2.7 Experiments 32
2.7.1 Evaluation of Tracking Accuracy 33
2.7.2 Evaluation of Efficiency 40
2.7.3 Ablation Studies 42
2.7.4 Fuzzy Rules Analysis 44
2.7.5 Limitation 45
2.8 Details on Filtering Recursions 46
2.8.1 Exact Filtering Recursion 46
2.8.2 GLMB Filtering Recursion 47
2.8.3 LMB Filtering Recursion 48
2.9 OSPA(2) Metric 48
2.10 Conclusion 50
3 Track Initialization and Re-Identification for 3D Multi-View Multi-
Object Tracking 51
3.1 Abstract 51
3.2 Introduction 52
3.3 Related Works 55
3.3.1 Visual Multi-Object Detection 55
3.3.2 Visual Multi-Object Tracking 57
3.4 Bayesian Multi-View MOT 59
3.4.1 Object Dynamic Model 60
3.4.2 Multi-View Measurement Model 63
3.4.3 Bayesian Multi-View MOT Filter 67
3.5 Approximate MV-MOT Filter 68
3.5.1 Multi-View GLMB Recursion 69
3.5.2 Occlusion Modeling 71
3.5.3 Adaptive Birth Modeling 74
3.6 Experimental Results 78
3.6.1 Performance Evaluation 82
3.6.2 Benchmarking Against Ideal Trackers 88
3.6.3 Ablation Study 89
3.7 Conclusion 92
4 A Fast Online Algorithm for 3D Multi-Camera Multi-Object Track-
ing 94
4.1 Abstract 94
4.2 Introduction 95
4.3 Related Works 96
4.4 The Fast 3D Multi-Object Tracking Algorithm 98
4.4.1 Track Prediction 99
4.4.2 Data Association and Track Update 101
4.4.3 Track Initialization and Termination 106
4.5 Algorithm Implementation 107
4.6 Derivation from the Multi-Sensor GLMB Filter 113
4.7 Experimental Results 115
4.7.1 Performance Evaluation 118
4.7.2 Benchmarking Against 3D-Training-Based Methods 120
4.7.3 Ablation Study 122
4.8 Conclusions 124
Summary 125
Bibliography 127
A Abbreviations 144
Acknowledgements 14
Biodegradable, ionic thermoelectric composites via self-assembly of dipeptides and deep eutectic solvents
No full textThe growing demand for biodegradable conductive composites is driven by the need to mitigate electronic waste and advance bioelectronics for healthcare applications. Self-assembled peptide composites, particularly diphenylalanine (FF) derivatives, represent a promising class of materials for such electronics due to their inherent biodegradability and ease of hybridization with functional materials. However, the integration of ionic species with these peptides is often limited by the disruption of non-covalent interactions between FF derivatives. In this study, we developed biodegradable, ionic thermoelectric composites by co-assembling Fmoc-FF with deep eutectic solvents (DESs) composed of choline chloride (ChCl) and ethylene glycol (EG). Spectroscopic analyses revealed that Fmoc-FF formed eutectogels through pi-pi interactions between Fmoc groups, resulting in a highly porous colloidal network. The Fmoc-FF eutectogels exhibited an ionic conductivity of up to 47.5 mS center dot cm-1 and a Seebeck coefficient of 7.39 mV center dot K-1, making them suitable for heat harvesting. Additionally, they were entirely degraded within 48 h under proteolytic conditions, confirming their biodegradability. The eutectogels also displayed self-healing and shear-thinning behaviors, highlighting compatibility with additive manufacturing techniques for device integration.TRUEsciescopu
Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet
No full textWe report on numerical simulations of the two-dimensional spin-1 Blume-Capel ferromagnet embedded in a triangular lattice. Utilizing a range of Monte Carlo and finite-size scaling techniques, we explore several critical aspects along the crystal field-temperature (Δ,T) transition line. Wang-Landau simulations measuring the joint density of states in combination with the method of field mixing allow us to probe the phase coexistence curve in high resolution, determining the tricritical point (Δt,Tt) with improved accuracy and verifying the tricritical exponents. Extensive multicanonical simulations identifying transition points across the phase diagram characterize the Ising universality class for ΔΔt, a finite-size scaling analysis is dedicated to revealing the first-order signature in the surface tension that linearly increases upon lowering the temperature deeper into the first-order transition regime. Finally, a comprehensive picture of the phase diagram for the model is presented, collecting transition points obtained from the combined numerical approach in this study and previous estimates in the literature. © 2025 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.TRUEscopu
Molecular engineering of redox electrolytes for size-matched interfacial coupling with microporous carbon in redox-enhanced electrochemical capacitors
No full textRedox-enhanced electrochemical capacitors (redox ECs), leveraging soluble organic redox-active species, exceed traditional electric double-layer capacitors (EDLCs) in achieving higher energy density and delivering stable power output. While prior studies have predominantly focused on improving redox EC performance by enhancing the solubility of redox-active species, solubility alone is insufficient to fully unlock their potential. A critical yet underexplored factor is the interfacial compatibility between organic redox species and electrode surfaces. This limitation contrasts sharply with the well-established strategies in EDLCs, where capacitance optimization has been rigorously demonstrated through the precise matching of electrolyte ion size with electrode pore size. Here, we systematically investigate interfacial interactions by tailoring the molecular size of viologen derivatives through substituent modifications, enabling precise adjustments at the angstrom scale to achieve optimal compatibility with porous carbon electrodes. Our findings reveal that redox EC performance-spanning capacity, rate capability, and self-discharge characteristics-is strongly governed by the size matching between viologen derivatives and carbon pore structures. Notably, butyl viologen (BV), when paired with microporedominant activated carbon (MSC30; pore size <0.8 nm), achieves optimal cell performance with exceptional cycle stability over 10,000 cycles.FALSEsciescopu
AI-Guided Design of Ternary Eutectic Electrolytes: Dual Regulation of Zn²⁺ Solvation and Hydrogen-Bond Network for Interfacial Stability and Low Temperature Zn-Ion Batteries
No full textAqueous Zn-ion batteries (AZIBs) are emerging as a promising solution for large-scale grid energy storage due to their low manufacturing cost, intrinsic safety, recyclability, and minimal environmental impact, positioning them as viable alternatives to flammable organic-electrolyte-based batteries. However, challenges such as water-triggered parasitic reactions, dendrite growth, and limited low- temperature performance hinder commercialization. Electrolyte engineering, particularly through additive-based approaches, has shown promise in addressing these challenges by modifying Zn2+ solvation structures to suppress parasitic reactions and stabilize the Zn anode during cycling. High donor number (DN) additives have been recognized for their effectiveness in enhancing cell performance, yet their identification relies on trial-and-error processes, owing to the uncharacterized properties of many candidate materials. In this study, a deep learning model is employed to predict DN-related properties for over 1,000,000 samples. By systematically screening materials based on structural and functional criteria, the study identifies N,N-dimethylmethanesulfonamide (DMMSA) as an advanced material. Using DMMSA, a ternary eutectic electrolyte (TEE) composed of hydrated Zn(ClO4)2·6H2O, DMMSA, and H2O is developed as a next-generation alternative to conventional aqueous electrolytes. Experimental and theoretical analyses confirm that DMMSA regulates the Zn2+ solvation structure and reorganizes the hydrogen bond network, effectively inhibiting parasitic reactions and enabling stable operation at low temperatures. The inert methyl groups of DMMSA, attributed to an "end-capping effect", disrupt chain- like hydrogen bonds between H2O molecules, thereby improving ionic conductivity and enhancing low- temperature performance. This electrolyte achieves a remarkable cycle life of 4,842 hours of cycling at 0.5 mA cm-2 and an areal capacity of 0.5 mAh cm-2 in Zn//Zn cells. By integrating AI-assisted material discovery with experimental and theoretical validation, our approach offers a pathway to accelerate advancements in battery technology and foster innovative solutions for the industry’s future.MasterAbstract ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 5
Contents ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 7
List of Figures ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 8
Ⅰ. Introduction ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 10
Ⅱ. Result and discussion ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 14
Ⅱ.1. Challenges in AZIBs and Electrolyte Optimization ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 14
Ⅱ.2. Analysis of physicochemical properties and Zn2+ solvation structures ․․․․․․․․․․․․․․․․․․․․․․․ 17
Ⅱ.3. Suppressing water decomposition at Zn metal ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 21
Ⅱ.4. Uniform Zn deposition morphology ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 23
Ⅱ.5. Low-temperature and full-cell performance ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 26
Ⅲ. Experimental Section ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 40
Ⅳ. Reference ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 43
Acknowledgement ․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․․ 4