Topological Properties and Broadcasting Algorithmsof the Generalized-Star Cube

Abstract—In this research, another version of the star cube called the generalized-star cube, GSC(n, k, m), is presented as a three level interconnection topology. GSC(n, k, m) is a product graph of the (n, k)-star graph and the m-dimensional hypercube (m-cube). It can be constructed in one of two ways: to replace each node in an m-cube with an (n, k)-star graph, or to replace each node in an (n, k)-star graph with an m-cube. Because there are three parameters m, n, and k, the network size of GSC(n, k, m) can be changed more flexibly than the star graph, star-cube, and (n, k)-star graph. We first investigate the topological properties of the GSC(n, k, m), such as the node degree, diameter, average distance, and cost. Also, the regularity and node symmetry of the GSC(n, k, m) are derived.Then, we illustrate the broadcasting algorithms for both of the single-port and all-port models. To develop these algorithms, we use the spanning binomial tree, the neighbourhood broadcasting algorithm, and the minimum dominating set. The complexities of the broadcasting algorithms are also examined

Algorithms and complexity analyses for some combinational optimization problems

The main focus of this dissertation is on classical combinatorial optimization problems in two important areas: scheduling and network design. In the area of scheduling, the main interest is in problems in the master-slave model. In this model, each machine is either a master machine or a slave machine. Each job is associated with a preprocessing task, a slave task and a postprocessing task that must be executed in this order. Each slave task has a dedicated slave machine. All the preprocessing and postprocessing tasks share a single master machine or the same set of master machines. A job may also have an arbitrary release time before which the preprocessing task is not available to be processed. The main objective in this dissertation is to minimize the total completion time or the makespan. Both the complexity and algorithmic issues of these problems are considered. It is shown that the problem of minimizing the total completion time is strongly NP-hard even under severe constraints. Various efficient algorithms are designed to minimize the total completion time under various scenarios. In the area of network design, the survivable network design problems are studied first. The input for this problem is an undirected graph G = (V, E), a non-negative cost for each edge, and a nonnegative connectivity requirement ruv for every (unordered) pair of vertices &ruv. The goal is to find a minimum-cost subgraph in which each pair of vertices u,v is joined by at least ruv edge (vertex)-disjoint paths. A Polynomial Time Approximation Scheme (PTAS) is designed for the problem when the graph is Euclidean and the connectivity requirement of any point is at most 2. PTASs or Quasi-PTASs are also designed for 2-edge-connectivity problem and biconnectivity problem and their variations in unweighted or weighted planar graphs. Next, the problem of constructing geometric fault-tolerant spanners with low cost and bounded maximum degree is considered. The first result shows that there is a greedy algorithm which constructs fault-tolerant spanners having asymptotically optimal bounds for both the maximum degree and the total cost at the same time. Then an efficient algorithm is developed which finds fault-tolerant spanners with asymptotically optimal bound for the maximum degree and almost optimal bound for the total cost

MFCS\u2798 Satellite Workshop on Cellular Automata

For the 1998 conference on Mathematical Foundations of Computer Science (MFCS\u2798) four papers on Cellular Automata were accepted as regular MFCS\u2798 contributions. Furthermore an MFCS\u2798 satellite workshop on Cellular Automata was organized with ten additional talks. The embedding of the workshop into the conference with its participants coming from a broad spectrum of fields of work lead to interesting discussions and a fruitful exchange of ideas. The contributions which had been accepted for MFCS\u2798 itself may be found in the conference proceedings, edited by L. Brim, J. Gruska and J. Zlatuska, Springer LNCS 1450. All other (invited and regular) papers of the workshop are contained in this technical report. (One paper, for which no postscript file of the full paper is available, is only included in the printed version of the report). Contents: F. Blanchard, E. Formenti, P. Kurka: Cellular automata in the Cantor, Besicovitch and Weyl Spaces K. Kobayashi: On Time Optimal Solutions of the Two-Dimensional Firing Squad Synchronization Problem L. Margara: Topological Mixing and Denseness of Periodic Orbits for Linear Cellular Automata over Z_m B. Martin: A Geometrical Hierarchy of Graph via Cellular Automata K. Morita, K. Imai: Number-Conserving Reversible Cellular Automata and Their Computation-Universality C. Nichitiu, E. Remila: Simulations of graph automata K. Svozil: Is the world a machine? H. Umeo: Cellular Algorithms with 1-bit Inter-Cell Communications F. Reischle, Th. Worsch: Simulations between alternating CA, alternating TM and circuit families K. Sutner: Computation Theory of Cellular Automat

팽창률 조절이 가능한 등방성 조직 팽창 기술

학위논문(박사)--서울대학교 대학원 :자연과학대학 화학부,2020. 2. 이연.Tissue expansion techniques physically expand swellable hydrogel-embedded biological specimens to overcome the resolution limit of conventional light microscopy. As the benefits of expansion come at the expense of signal concentration, imaging volume and time, and mechanical integrity of the sample, the optimal expansion ratio may widely differ depending on the experiment. However, existing expansion methods offer only fixed expansion ratios that cannot be easily adjusted to balance the gain and loss associated with expansion. In this thesis, I describe a hydrogel conversion-based expansion method, that enables easy adjustment of the expansion ratio for individual needs, simply by changing the duration of a alkaline hydrolysis step. This method, termed ZOOM (an acronym for Zoom by hydrOgel cOnversion Microscopy), isotropically expands samples up to 8-fold in a single expansion process. ZOOM preserves biomolecules for post-processing labellings and supports multi-round expansion for the imaging of a single sample at multiple zoom factors. ZOOM can be flexibly and scalably applied to nanoscale imaging of diverse samples, ranging from cultured cells to thick tissues, as well as bacteria, exoskeletal Caenorhabditis elegans, and human brain samples.조직 팽창 기술은 광학 현미경의 해상 한계를 극복하기 위해 생물체 조직 시편을 팽윤성 하이드로겔 내에 포매시켜 팽창시키는 기술이다. 이러한 조직 팽창 기술은 팽창률이 증가할수록 해상도가 개선되는 장점을 갖는 한편 팽창률 증가에 따라 이미징 면적이 증가하여 전체적인 이미징 시간이 증가하고, 팽창에 따른 형광 표지 신호 희석 혹은 시편의 강성 저하 등의 단점을 갖게 된다. 따라서 최적의 팽창 배율은 실험의 목적이나 관측 대상에 따라 다르게 결정된다. 하지만 2015년 MIT의 Ed Boyden 교수 연구팀에 의해 개발된 Expansion microscopy (ExM) 기술을 필두로 현재까지 개발된 조직 팽창 기술들은 모두 고정된 배율로만 조직을 팽창시킬 수 있어, 경우에 따라 이미징 효율이 크게 저하되고 있는 실정이다. 특히 3차원 조직 이미징의 경우 이미징 시간의 증가나 형광 표지 신호 희석 등의 단점이 기하급수적으로 영향을 미쳐, 팽창률 최적화를 가능하게 하는 팽창률 조절 기술 개발이 절대적으로 필요한 상황이라고 볼 수 있다. 본 학위 논문에서는 이러한 기술적 단점을 극복할 수 있는 새로운 조직 팽창 기술에 대해 서술하였다. ZOOM (Zoom by hydrOgel cOnversion Microscopy) 이라 명명한 본 기술은 알칼리 가수분해를 통해 손쉽게 팽창률을 조절할 수 있는 기반 기술이며, 이론적으로 면역 형광법에서 구현할 수 있는 최대 해상도까지 이를 수 있는 팽창 배율인 8배까지 팽창률을 자유롭게 조절할 수 있는 기술이다. ZOOM 프로세스를 통해 팽창률을 점진적으로 증가시켜 가며 다양한 세포 및 조직의 3차원 팽창 형태를 확인해 본 결과, 팽창률이 증가하여도 구조적 뒤틀림 현상 없이 등방성 팽창률을 유지하며, 점진적으로 해상도를 개선할 수 있음을 확인하였고, 반복적으로 ZOOM 프로세스를 적용하여도 지속적으로 항체 염색이 가능하여 유의한 항원결정기의 유실이 발생하지 않음을 확인하였다. 이러한 ZOOM 기술은 배양 세포부터 두꺼운 마우스 조직까지 적용이 가능하였고, 각 종별 특성을 고려한 공정 조건의 미세 조정을 통해 박테리아, 선충 및 인간의 뇌 조직에 이르기 까지 매우 광범위한 생물체 조직에 성공적으로 확대 적용이 가능하였다.1. Introduction. 1 2. Results. 4 2.1. Theoretical considerations for the expansion of hydrogel-tissue hybrids. 4 2.2. Hydrogel conversion-based tissue expansion strategy enables easy tuning of the expansion ratio. 5 2.3. Isotropic and preservative expansion with improved mechanical properties 7 2.4. Nanoscale imaging of diverse subcellular structures from ZOOMed cultured cells. 12 2.5. Nanoscale imaging of subcellular and cellular features from ZOOMed neural tissues 14 2.6. ZOOMing into C. elegans, bacteria, and human clinical samples 16 3. Discussion 18 4. Experimental Section 22 4.1. Reagents 22 4.2. Cell culture 24 4.3. Animals 25 4.4. Stereotaxic surgery 26 4.5. Mouse perfusion. 26 4.6. C. elegans culture. 27 4.7. Postmortem human brain tissue 27 4.8. NMR analysis 27 4.9. Hydrogel embedding 28 4.10. Hydrogel conversion. 31 4.11. Immunostaining. 31 4.12. Expansion, mounting, and imaging. 32 4.13. Expansion factor measurement. 33 4.14. Measurement error quantification. 34 4.15. Line profile intensity and FWHM analysis. 35 4.16. Neurofilament tracing. 35 4.17. Tissue shrinkage test. 36 4.18. Compressive strength measurement. 36 4.19. Statistics and reproducibility 37 5. References. 38 Mathematica script for RMS error measurement. 74Docto

Entangled graphs on surfaces in space

In the chemical world, as well as the physical, strands get tangled. When those strands form loops, the mathematical discipline of ‘knot theory’ can be used to analyse and describe the resultant tangles. However less has been studied about the situation when the strands branch and form entangled loops in either finite structures or infinite periodic structures. The branches and loops within the structure form a ‘graph’, and can be described by mathematical ‘graph theory’, but when graph theory concerns itself with the way that a graph can fit in space, it typically focuses on the simplest ways of doing so. Graph theory thus provides few tools for understanding graphs that are entangled beyond their simplest spatial configurations. This thesis explores this gap between knot theory and graph theory. It is focussed on the introduction of small amounts of entanglement into finite graphs embedded in space. These graphs are located on surfaces in space, and the surface is chosen to allow a limited amount of complexity. As well as limiting the types of entanglement possible, the surface simplifies the analysis of the problem – reducing a three-dimensional problem to a two-dimensional one. Through much of this thesis, the embedding surface is a torus (the surface of a doughnut) and the graph embedded on the surface is the graph of a polyhedron. Polyhedral graphs can be embedded on a sphere, but the addition of the central hole of the torus allows a certain amount of freedom for the entanglement of the edges of the graph. Entanglements of the five Platonic polyhedra (tetrahedron, octahedron, cube, dodecahedron, icosahedron) are studied in depth through their embeddings on the torus. The structures that are produced in this way are analysed in terms of their component knots and links, as well as their symmetry and energy. It is then shown that all toroidally embedded tangled polyhedral graphs are necessarily chiral, which is an important property in biochemical and other systems. These finite tangled structures can also be used to make tangled infinite periodic nets; planar repeating subgraphs within the net can be systematically replaced with a tangled version, introducing a controlled level of entanglement into the net. Finally, the analysis of entangled structures simply in terms of knots and links is shown to be deficient, as a novel form of tangling can exist which involves neither knots nor links. This new form of entanglement is known as a ravel. Different types of ravels can be localised to the immediate vicinity of a vertex, or can be spread over an arbitrarily large scope within a finite graph or periodic net. These different forms of entanglement are relevant to chemical and biochemical self-assembly, including DNA nanotechnology and metal-ligand complex crystallisation

Visual Servoing

The goal of this book is to introduce the visional application by excellent researchers in the world currently and offer the knowledge that can also be applied to another field widely. This book collects the main studies about machine vision currently in the world, and has a powerful persuasion in the applications employed in the machine vision. The contents, which demonstrate that the machine vision theory, are realized in different field. For the beginner, it is easy to understand the development in the vision servoing. For engineer, professor and researcher, they can study and learn the chapters, and then employ another application method

Minimizing Movement for Target Coverage and Network Connectivity in Mobile Sensor Networks

PublishedJournal Article© 2014 IEEE. Coverage of interest points and network connectivity are two main challenging and practically important issues of Wireless Sensor Networks (WSNs). Although many studies have exploited the mobility of sensors to improve the quality of coverage andconnectivity, little attention has been paid to the minimization of sensors' movement, which often consumes the majority of the limited energy of sensors and thus shortens the network lifetime significantly. To fill in this gap, this paper addresses the challenges of the Mobile Sensor Deployment (MSD) problem and investigates how to deploy mobile sensors with minimum movement to form a WSN that provides both target coverage and network connectivity. To this end, the MSD problem is decomposed into two sub-problems: the Target COVerage (TCOV) problem and the Network CONnectivity (NCON) problem. We then solve TCOV and NCON one by one and combine their solutions to address the MSD problem. The NP-hardness of TCOV is proved. For a special case of TCOV where targets disperse from each other farther than double of the coverage radius, an exact algorithm based on the Hungarian method is proposed to find the optimal solution. For general cases of TCOV, two heuristic algorithms, i.e., the Basic algorithm based on clique partition and the TV-Greedy algorithm based on Voronoi partition of the deployment region, are proposed to reduce the total movement distance ofsensors. For NCON, an efficient solution based on the Steiner minimum tree with constrained edge length is proposed. Thecombination of the solutions to TCOV and NCON, as demonstrated by extensive simulation experiments, offers a promising solutionto the original MSD problem that balances the load of different sensors and prolongs the network lifetime consequently.This work is supported in part by the National Science Foundation of China (Grant Nos. 61232001, 61103203, 61173169, and 61173051), the Major Science & Technology Research Program for Strategic Emerging Industry of Hunan (Grant No. 2012GK4054), and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 14C0030)