Optical fluid and biomolecule transport with thermal fields

A long standing goal is the direct optical control of biomolecules and water for applications ranging from microfluidics over biomolecule detection to non-equilibrium biophysics. Thermal forces originating from optically applied, dynamic microscale temperature gradients have shown to possess great potential to reach this goal. It was demonstrated that laser heating by a few Kelvin can generate and guide water flow on the micrometre scale in bulk fluid, gel matrices or ice without requiring any lithographic structuring. Biomolecules on the other hand can be transported by thermal gradients, a mechanism termed thermophoresis, thermal diffusion or Soret effect. This molecule transport is the subject of current research, however it can be used to both characterize biomolecules and to record binding curves of important biological binding reactions, even in their native matrix of blood serum. Interestingly, thermophoresis can be easily combined with the optothermal fluid control. As a result, molecule traps can be created in a variety of geometries, enabling the trapping of small biomolecules, like for example very short DNA molecules. The combination with DNA replication from thermal convection allows us to approach molecular evolution with concurrent replication and selection processes inside a single chamber: replication is driven by thermal convection and selection by the concurrent accumulation of the DNA molecules. From the short but intense history of applying thermal fields to control fluid flow and biological molecules, we infer that many unexpected and highly synergistic effects and applications are likely to be explored in the future

Recent Developments in Complex and Spatially Correlated Functional Data

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale and complex data by assuming that data are continuous functions, e.g., a realization of a continuous process (curves) or continuous random fields (surfaces), and that each curve or surface is considered as a single observation. Here, we provide an overview of functional data analysis when data are complex and spatially correlated. We provide definitions and estimators of the first and second moments of the corresponding functional random variable. We present two main approaches: The first assumes that data are realizations of a functional random field, i.e., each observation is a curve with a spatial component. We call them 'spatial functional data'. The second approach assumes that data are continuous deterministic fields observed over time. In this case, one observation is a surface or manifold, and we call them 'surface time series'. For the two approaches, we describe software available for the statistical analysis. We also present a data illustration, using a high-resolution wind speed simulated dataset, as an example of the two approaches. The functional data approach offers a new paradigm of data analysis, where the continuous processes or random fields are considered as a single entity. We consider this approach to be very valuable in the context of big data.Comment: Some typos fixed and new references adde

Kirchhoff-Love shell representation and analysis using triangle configuration B-splines

This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff-Love shell in the context of isogeometric analysis (IGA). The Kirchhoff-Love shell formulation requires global $C^1$-continuous basis functions. The nonuniform rational B-spline (NURBS)-based IGA has been extensively used for developing Kirchhoff-Love shell elements. However, shells with complex geometries inevitably need multiple patches and trimming techniques, where stitching patches with high continuity is a challenge. On the other hand, due to their unstructured nature, TCB-splines can accommodate general polygonal domains, have local refinement, and are flexible to model complex geometries with $C^1$ continuity, which naturally fit into the Kirchhoff-Love shell formulation with complex geometries. Therefore, we propose to use TCB-splines as basis functions for geometric representation and solution approximation. We apply our method to both linear and nonlinear benchmark shell problems, where the accuracy and robustness are validated. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff-Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines

Physics-Based Modeling of Nonrigid Objects for Vision and Graphics (Dissertation)

This thesis develops a physics-based framework for 3D shape and nonrigid motion modeling for computer vision and computer graphics. In computer vision it addresses the problems of complex 3D shape representation, shape reconstruction, quantitative model extraction from biomedical data for analysis and visualization, shape estimation, and motion tracking. In computer graphics it demonstrates the generative power of our framework to synthesize constrained shapes, nonrigid object motions and object interactions for the purposes of computer animation. Our framework is based on the use of a new class of dynamically deformable primitives which allow the combination of global and local deformations. It incorporates physical constraints to compose articulated models from deformable primitives and provides force-based techniques for fitting such models to sparse, noise-corrupted 2D and 3D visual data. The framework leads to shape and nonrigid motion estimators that exploit dynamically deformable models to track moving 3D objects from time-varying observations. We develop models with global deformation parameters which represent the salient shape features of natural parts, and local deformation parameters which capture shape details. In the context of computer graphics, these models represent the physics-based marriage of the parameterized and free-form modeling paradigms. An important benefit of their global/local descriptive power in the context of computer vision is that it can potentially satisfy the often conflicting requirements of shape reconstruction and shape recognition. The Lagrange equations of motion that govern our models, augmented by constraints, make them responsive to externally applied forces derived from input data or applied by the user. This system of differential equations is discretized using finite element methods and simulated through time using standard numerical techniques. We employ these equations to formulate a shape and nonrigid motion estimator. The estimator is a continuous extended Kalman filter that recursively transforms the discrepancy between the sensory data and the estimated model state into generalized forces. These adjust the translational, rotational, and deformational degrees of freedom such that the model evolves in a consistent fashion with the noisy data. We demonstrate the interactive time performance of our techniques in a series of experiments in computer vision, graphics, and visualization

리만다양체 상의 비모수적 차원축소방법론

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 통계학과, 2022. 8. 오희석.Over the decades, parametric dimension reduction methods have been actively developed for non-Euclidean data analysis. Examples include Fletcher et al., 2004; Huckemann et al., 2010; Jung et al., 2011; Jung et al., 2012; Zhang et al., 2013. Sometimes the methods are not enough to capture the structure of data. This dissertation presents newly developed nonparametric dimension reductions for data observed on manifold, resulting in more flexible fits. More precisely, the main focus is on the generalizations of principal curves into Riemannian manifold. The principal curve is considered as a nonlinear generalization of principal component analysis (PCA). The dissertation consists of four main parts as follows. First, the approach given in Chapter 3 lie in the same lines of Hastie (1984) and Hastie and Stuetzle (1989) that introduced the definition of original principal curve on Euclidean space. The main contributions of this study can be summarized as follows: (a) We propose both extrinsic and intrinsic approaches to form principal curves on spheres. (b) We establish the stationarity of the proposed principal curves on spheres. (c) In extensive numerical studies, we show the usefulness of the proposed method through real seismological data and real Human motion capture data as well as simulated data on 2-sphere, 4-sphere. Secondly, As one of further work in the previous approach, a robust nonparametric dimension reduction is proposed. To this ends, absolute loss and Huber loss are used rather than L2 loss. The contributions of Chapter 4 can be summarized as follows: (a) We study robust principal curves on spheres that are resistant to outliers. Specifically, we propose absolute-type and Huber-type principal curves, which go through the median of data, to robustify the principal curves for a set of data which may contain outliers. (b) For a theoretical aspect, the stationarity of the robust principal curves is investigated. (c) We provide practical algorithms for implementing the proposed robust principal curves, which are computationally feasible and more convenient to implement. Thirdly, An R package 'spherepc' comprehensively providing dimension reduction methods on a sphere is introduced with details for possible reproducible research. To the best of our knowledge, no available R packages offer the methods of dimension reduction and principal curves on a sphere. The existing R packages providing principal curves, such as 'princurve' and 'LPCM', are available only on Euclidean space. In addition, most nonparametric dimension reduction methods on manifold involve somewhat complex intrinsic optimizations. The proposed R package 'spherepc' provides the state-of-the-art principal curve technique on the sphere and comprehensively collects and implements the existing techniques. Lastly, for an effective initial estimate of complex structured data on manifold, local principal geodesics are first provided and the method is applied to various simulated and real seismological data. For variance stabilization and theoretical investigations for the procedure, nextly, the focus is on the generalization of Kégl (1999); Kégl et al., (2000), which provided the new definition of principal curve on Euclidean space, into generic Riemannian manifolds. Theories including consistency and convergence rate of the procedure by means of empirical risk minimization principle, are further established on generic Riemannian manifolds. The consequences on the real data analysis and simulation study show the promising characteristics of the proposed approach.본 학위 논문은 다양체 자료의 변동성을 더욱 효과적으로 찾아내기 위해, 다양체 자료의 새로운 비모수적 차원축소방법론을 제시하였다. 구체적으로, 주곡선(principal curves) 방법을 일반적인 다양체 공간으로 확장하는 것이 주요 연구 주제이다. 주곡선은 주성분분석(PCA)의 비선형적 확장 중 하나이며, 본 학위논문은 크게 네 가지의 주제로 이루어져 있다. 첫 번째로, Hastie (1984), Hastie and Stuetzle (1989}의 방법을 임의의 차원의 구면으로 표준적인 방식으로 확장한다. 이 연구 주제의 공헌은 다음과 같다. (a) 임의의 차원의 구면에서 내재적, 외재적인 방식의 주곡선 방법을 각각 제안한다. (b) 본 방법의 이론적 성질(정상성)을 규명한다. (c) 지질학적 자료 및 인간 움직임 자료 등의 실제 자료와 2차원, 4차원 구면위의 시뮬레이션 자료에 본 방법을 적용하여, 그 유용성을 보인다. 두 번째로, 첫 번째 주제의 후속 연구 중 하나로서, 두꺼운 꼬리 분포를 가지는 자료에 대하여 강건한 비모수적 차원축소 방법을 제안한다. 이를 위해, L2 손실함수 대신에 L1 및 휴버(Huber) 손실함수를 활용한다. 이 연구 주제의 공헌은 다음과 같다. (a) 이상치에 민감하지 않은 강건화주곡선(robust principal curves)을 정의한다. 구체적으로, 자료의 기하적 중심점을 지나는 L1 및 휴버 손실함수에 대응되는 새로운 주곡선을 제안한다. (b) 이론적인 측면에서, 강건화주곡선의 정상성을 규명한다. (c) 강건화주곡선을 구현하기 위해 계산이 빠른 실용적인 알고리즘을 제안한다. 세 번째로, 기존의 차원축소방법 및 본 방법론을 제공하는 R 패키지를 구현하였으며 이를 다양한 예제 및 설명과 함께 소개한다. 본 방법론의 강점은 다양체 위에서의 복잡한 최적화 방정식을 풀지않고, 직관적인 방식으로 구현 가능하다는 점이다. R 패키지로 구현되어 제공된다는 점이 이를 방증하며, 본 학위 논문의 연구를 재현가능하게 만든다. 마지막으로, 보다 복잡한 구조를 가지는 다양체 자료의 구조를 추정하기위해, 국소주측지선분석(local principal geodesics) 방법을 우선 제안한다. 이 방법을 실제 지질학 자료 및 다양한 모의실험 자료에 적용하여 그 활용성을 보였다. 다음으로, 추정치의 분산안정화 및 이론적 정당화를 위하여 Kégl (1999), Kégl et al., (2000) 방법을 일반적인 리만다양체로 확장한다. 더 나아가, 방법론의 일치성, 수렴속도와 같은 점근적 성질을 비롯하여 비점근적 성질인 집중부등식(concentration inequality)을 통계적학습이론을 이용하여 규명한다.1 Introduction 1 2 Preliminaries 8 2.1 Principal curves 8 2.1 Riemannian manifolds and centrality on manifold 10 2.1 Principal curves on Riemannian manifolds 14 3 Spherical principal curves 15 3.1 Enhancement of principal circle for initialization 16 3.2 Proposed principal curves 25 3.3 Numerical experiments 34 3.4 Proofs 45 3.5 Concluding remarks 62 4 Robust spherical principal curves 64 4.1 The proposed robust principal curves 64 4.2 Stationarity of robust spherical principal curves 72 4.3 Numerical experiments 74 4.4 Summary and future work 80 5 spherepc: An R package for dimension reduction on a sphere 84 5.1 Existing methods 85 5.2 Spherical principal curves 91 5.3 Local principal geodesics 94 5.4 Application 99 5.5 Conclusion 101 6 Local principal curves on Riemannian manifolds 112 6.1 Preliminaries 116 6.2 Local principal geodesics 118 6.3 Local principal curves 125 6.4 Real data analysis 133 6.5 Further work 133 7 Conclusion 139 A. Appendix 141 A.1. Appendix for Chapter 3 141 A.2. Appendix for Chapter 4 145 A.3. Appendix for Chapter 6 152 Abstract in Korean 176 Acknowledgement in Korean 179박

On the Use of Low-Cost RGB-D Sensors for Autonomous Pothole Detection with Spatial Fuzzy <em>c</em>-Means Segmentation

The automated detection of pavement distress from remote sensing imagery is a promising but challenging task due to the complex structure of pavement surfaces, in addition to the intensity of non-uniformity, and the presence of artifacts and noise. Even though imaging and sensing systems such as high-resolution RGB cameras, stereovision imaging, LiDAR and terrestrial laser scanning can now be combined to collect pavement condition data, the data obtained by these sensors are expensive and require specially equipped vehicles and processing. This hinders the utilization of the potential efficiency and effectiveness of such sensor systems. This chapter presents the potentials of the use of the Kinect v2.0 RGB-D sensor, as a low-cost approach for the efficient and accurate pothole detection on asphalt pavements. By using spatial fuzzy c-means (SFCM) clustering, so as to incorporate the pothole neighborhood spatial information into the membership function for clustering, the RGB data are segmented into pothole and non-pothole objects. The results demonstrate the advantage of complementary processing of low-cost multisensor data, through channeling data streams and linking data processing according to the merits of the individual sensors, for autonomous cost-effective assessment of road-surface conditions using remote sensing technology