Some Single and Combined Operations on Formal Languages: Algebraic Properties and Complexity

In this thesis, we consider several research questions related to language operations in the following areas of automata and formal language theory: reversibility of operations, generalizations of (comma-free) codes, generalizations of basic operations, language equations, and state complexity. Motivated by cryptography applications, we investigate several reversibility questions with respect to the parallel insertion and deletion operations. Among the results we obtained, the following result is of particular interest. For languages L1, L2 ⊆ Σ∗, if L2 satisfies the condition L2ΣL2 ∩ Σ+L2Σ+ = ∅, then any language L1 can be recovered after first parallel-inserting L2 into L1 and then parallel-deleting L2 from the result. This property reminds us of the definition of comma-free codes. Following this observation, we define the notions of comma codes and k-comma codes, and then generalize them to comma intercodes and k-comma intercodes, respectively. Besides proving all these new codes are indeed codes, we obtain some interesting properties, as well as several hierarchical results among the families of the new codes and some existing codes such as comma-free codes, infix codes, and bifix codes. Another topic considered in this thesis are some natural generalizations of basic language operations. We introduce block insertion on trajectories and block deletion on trajectories, which properly generalize several sequential as well as parallel binary language operations such as catenation, sequential insertion, k-insertion, parallel insertion, quotient, sequential deletion, k-deletion, etc. We obtain several closure properties of the families of regular and context-free languages under the new operations by using some relationships between these new operations and shuffle and deletion on trajectories. Also, we obtain several decidability results of language equation problems with respect to the new operations. Lastly, we study the state complexity of the following combined operations: L1L2∗, L1L2R, L1(L2 ∩ L3), L1(L2 ∪ L3), (L1L2)R, L1∗L2, L1RL2, (L1 ∩ L2)L3, (L1 ∪ L2)L3, L1L2 ∩ L3, and L1L2 ∪ L3 for regular languages L1, L2, and L3. These are all the combinations of two basic operations whose state complexities have not been studied in the literature

6 Access Methods and Query Processing Techniques

The performance of a database management system (DBMS) is fundamentally dependent on the access methods and query processing techniques available to the system. Traditionally, relational DBMSs have relied on well-known access methods, such as the ubiquitous B +-tree, hashing with chaining, and, in som

Prediction of the Size Distributions of Methanol-Ethanol Clusters Detected in VUV Laser/Time-of-flight Mass Spectrometry

The size distributions and geometries of vapor clusters equilibrated with methanol−ethanol (Me−Et) liquid mixtures were recently studied by vacuum ultraviolet (VUV) laser time-of-flight (TOF) mass spectrometry and density functional theory (DFT) calculations (Liu, Y.; Consta, S.; Ogeer, F.; Shi, Y. J.; Lipson, R. H. Can. J. Chem. 2007, 85, 843−852). On the basis of the mass spectra recorded, it was concluded that the formation of neutral tetramers is particularly prominent. Here we develop grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) frameworks to compute cluster size distributions in vapor mixtures that allow a direct comparison with experimental mass spectra. Using the all-atom optimized potential for liquid simulations (OPLS-AA) force field, we systematically examined the neutral cluster size distributions as functions of pressure and temperature. These neutral cluster distributions were then used to derive ionized cluster distributions to compare directly with the experiments. The simulations suggest that supersaturation at 12 to 16 times the equilibrium vapor pressure at 298 K or supercooling at temperature 240 to 260 K at the equilibrium vapor pressure can lead to the relatively abundant tetramer population observed in the experiments. Our simulations capture the most distinct features observed in the experimental TOF mass spectra: Et3H+ at m/z = 139 in the vapor corresponding to 10:90% Me−Et liquid mixture and Me3H+ at m/z = 97 in the vapors corresponding to 50:50% and 90:10% Me−Et liquid mixtures. The hybrid GCMC scheme developed in this work extends the capability of studying the size distributions of neat clusters to mixed species and provides a useful tool for studying environmentally important systems such as atmospheric aerosols

DNA 오리가미 구조체의 형상 설계를 위한 기계적 응력 조절 기술

학위논문(박사)--서울대학교 대학원 :공과대학 기계항공공학부,2020. 2. 김도년.In this thesis, we describe two design strategies that engineer mechanical stress to program static or dynamic conformations of the DNA origami structure. DNA origami nanotechnology facilitated the self-assembly of DNA strands into any conceivable shape encoded by their rationally designed sequences. Mechanics-based design approaches have played an important role in improving the structural diversity of the DNA origami structures. Due to low twist controllability and limited reconfiguration mode, however, they have still limitations in achievable diversity or complexity in structural shapes and their reconfigurations and their applications. To this end, first, we developed a design strategy for fine control of twisted DNA origami structures by considering not only amount of geometrical perturbations but also their arrangements within the structures. With the configurational design of geometrical perturbations, we can program various distributions of the mechanical stress enabling a fine control over twist rate of DNA origami structures. Second, we developed a design strategy that transforms a two-dimensional structure into three-dimensional supercoiled one on demand. We employed the topological invariant property to convert a simple twist deformation into complex bending one leading to supercoiling of the DNA origami structure. We expect that our mechanical stress programming strategies can be utilized to design DNA origami structures with desired shapes or reconfiguration motions and enhance the performance of functional structures.본 학위논문은 목표하는 정적 및 동적 형상을 지닌 DNA 오리가미 구조 제작을 위한 기계적 응력 조절 기술에 기반한 설계방법을 제시한다. DNA 오리가미 나노기술은 DNA 가닥들의 자가조립 과정을 통해 기존에 제작이 어려웠던 다양한 형상의 나노구조물을 손쉽게 만들 수 만들 수 있다. 이를 활용해 목표 형상의 나노구조물을 만들기 위해 다양한 설계 방법들이 제시되어 왔다. 이중 역학적 원리에 기반한 설계 방법은 구조 내부에 의도적으로 기계적 스트레스를 발생시켜 구조의 비틀림, 굽힘 등을 정량적으로 조절할 수 있게 만들어, 제작 가능한 형상의 범주를 넓히는데 크게 기여하였다. 하지만 기존 방법들은 세밀한 비틀림 형상 제어가 어렵다는 점 그리고 제한된 종류의 형상변화만이 가능하다는 문제점으로 인해 목표 형상을 지닌 정적 혹은 동적 구조의 제작 및 이러한 구조들의 활용에 어려움이 존재한다. 이에 해결책으로써 본 연구는 다음과 같은 기계적 응력 조절 기술들을 제시한다. 첫째, 구조 내 기하학적 섭동의 분포 설계 통해 DNA 오리가미 구조물의 세밀한 비틀림 형상 조절을 위한 설계 방법을 제시한다. 이를 이용한 구조 내 변형 에너지의 조절을 통해, 미세한 비틀림 형상 조절이 가능해진다. 둘째, 단순한 2차원 구조물을 복잡한 3차원 형상의 구조물로 변환시키는 형상 변환 메커니즘을 제안한다. 양끝이 이어진 닫힌 구조가 지닌 위상학적 불변성을 이용해, 국부적 비틀림을 전역적 굽힘 변형으로 변환시킴으로써, DNA 오리가미 구조의 슈퍼코일링 현상을 제시한다. 이러한 기계적 응력 조절 기술들은 원하는 형상 및 변화 움직임을 지닌 DNA 나노구조물의 설계에 활용되어 기능성 나노구조물들의 성능을 향상시키는데 기여할 것이라고 기대된다.Abstract 1 Table of contents 3 List of tables 5 List of figures 6 Chapter 1. Introduction 9 1.1. Research background 9 1.1.1. DNA origami nanotechnology 9 1.1.2. Self-assembly of DNA origami structure 12 1.1.3. Structural motifs 14 1.1.4. Computational design and analysis tools 16 1.2. Design strategy for DNA Origami structure 18 1.2.1. Lattice-based design 18 1.2.2. Flexible hinge-assisted design 19 1.2.3. Mechanical stress-assisted design 20 1.3. Research motivation 23 1.4. Thesis overview 25 Chapter 2. Methodology 28 2.1. Computational modeling and analysis 28 2.1.1. FE simulation for DNA origami structures 28 2.1.2. MD simulation for DNA origami structures 30 2.2. Fabrication and characterization 31 2.2.1. Self-assembly of DNA origami structures. 31 2.2.2. Agarose gel electrophoresis. 32 2.2.3. AFM imaging 33 2.2.4. TEM imaging 34 Chapter 3. Mechanical stress engineering for fine shape control 35 3.1. Limitation in the design of twisted structures 35 3.2. Configurational design approach 37 3.3. Twist angle variation 41 3.4. Fine control over twist rate 68 3.5. Twist control assisted by mechanical relaxation using gaps 76 3.6. Summary 83 Chapter 4. Mechanical stress engineering for shape reconfiguration 84 4.1. Limitation in the reconfiguration mechanisms 84 4.2. Buckling-induced homeomorphic transformation 86 4.3. Supercoiling of the 6HB ring 91 4.4. Computational analysis of the buckling-induced supercoiling 104 4.5. Reconfiguration control by local defects 110 4.6. Summary 112 Chapter 5. Concluding remark 113 Appendix 115 A1. Calculation of twist angles of 6HB structures 115 A2. Relation between twist angle and trans-ratio (TR) 118 A3. FE simulation of a coiling of a dsDNA ring 120 Bibliography 122 국 문 초 록 132 Acknowledgments 134Docto

Multi-train trajectory optimisation to maximise rail network energy efficiency under travel-time constraints

Optimising the trajectories of multiple interacting trains to maximise energy efficiency is a difficult, but highly desirable, problem to solve. A bespoke genetic algorithm has been developed for the multi-train trajectory optimisation problem and used to seek a near-optimal set of control point distances for multiple trains, such that a weighted sum of the time and energy objectives is minimised. Genetic operators tailored to the problem are developed including a new mutation operation and the insertion and deletion pairs of control points during the reproduction process. Compared with published results, the new GA was shown to increase the quality of solutions found by an average of 27.6% and increase consistency by a factor of 28. This allows more precise control over the relative priority given to achieving time targets or increasing energy efficiency

Study and development of techniques for automatic control of remote manipulators

An overall conceptual design for an autonomous control system of remote manipulators which utilizes feedback was constructed. The system consists of a description of the high-level capabilities of a model from which design algorithms are constructed. The autonomous capability is achieved through automatic planning and locally controlled execution of the plans. The operator gives his commands in high level task-oriented terms. The system transforms these commands into a plan. It uses built-in procedural knowledge of the problem domain and an internal model of the current state of the world

c-di-GMP modulates type IV MSHA pilus retraction and surface attachment in Vibrio cholerae.

Biofilm formation by Vibrio cholerae facilitates environmental persistence, and hyperinfectivity within the host. Biofilm formation is regulated by 3',5'-cyclic diguanylate (c-di-GMP) and requires production of the type IV mannose-sensitive hemagglutinin (MSHA) pilus. Here, we show that the MSHA pilus is a dynamic extendable and retractable system, and its activity is directly controlled by c-di-GMP. The interaction between c-di-GMP and the ATPase MshE promotes pilus extension, whereas low levels of c-di-GMP correlate with enhanced retraction. Loss of retraction facilitated by the ATPase PilT increases near-surface roaming motility, and impairs initial surface attachment. However, prolonged retraction upon surface attachment results in reduced MSHA-mediated surface anchoring and increased levels of detachment. Our results indicate that c-di-GMP directly controls MshE activity, thus regulating MSHA pilus extension and retraction dynamics, and modulating V. cholerae surface attachment and colonization

Machine learning and inferencing for the decomposition of speech mixtures

In this dissertation, we present and evaluate a novel approach for incorporating machine learning and inferencing into the time-frequency decomposition of speech signals in the context of speaker-independent multi-speaker pitch tracking. The pitch tracking performance of the resulting algorithm is comparable to that of a state-of-the-art machine-learning algorithm for multi-pitch tracking while being significantly more computationally efficient and requiring much less training data. Multi-pitch tracking is a time-frequency signal processing problem in which mutual interferences of the harmonics from different speakers make it challenging to design an algorithm to reliably estimate the fundamental frequency trajectories of the individual speakers. The current state-of-the-art in speaker-independent multi-pitch tracking utilizes 1) a deep neural network for producing spectrograms of individual speakers and 2) another deep neural network that acts upon the individual spectrograms and the original audio’s spectrogram to produce estimates of the pitch tracks of the individual speakers. However, the implementation of this Multi-Spectrogram Machine- Learning (MS-ML) algorithm could be computationally intensive and make it impractical for hardware platforms such as embedded devices where the computational power is limited. Instead of utilizing deep neural networks to estimate the pitch values directly, we have derived and evaluated a fault recognition and diagnosis (FRD) framework that utilizes machine learning and inferencing techniques to recognize potential faults in the pitch tracks produced by a traditional multi-pitch tracking algorithm. The result of this fault-recognition phase is then used to trigger a fault-diagnosis phase aimed at resolving the recognized fault(s) through adaptive adjustment of the time-frequency analysis of the input signal. The pitch estimates produced by the resulting FRD-ML algorithm are found to be comparable in accuracy to those produced via the MS-ML algorithm. However, our evaluation of the FRD-ML algorithm shows it to have significant advantages over the MS-ML algorithm. Specifically, the number of multiplications per second in FRD-ML is found to be two orders of magnitude less while the number of additions per second is about the same as in the MS-ML algorithm. Furthermore, the required amount of training data to achieve optimal performance is found to be two orders of magnitude less for the FRD-ML algorithm in comparison to the MS-ML algorithm. The reduction in the number of multiplications per second means it is more feasible to implement the MPT solution on hardware platforms with limited computational power such as embedded devices rather than relying on Graphics Processing Units (GPUs) or cloud computing. The reduction in training data size makes the algorithm more flexible in terms of configuring for different application scenarios such as training for different languages where there may not be a large amount of training data