Control Synthesis for Permutation-Symmetric High-Dimensional Systems With Counting Constraints

General-purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this paper, we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably correct controllers for systems with tens of thousands of states. The key ingredients of the solution are an aggregate abstraction procedure for mildly heterogeneous systems and a formulation of counting constraints as linear inequalities

Self-Assembly of DNA-Coated Particles: Experiment, Simulation and Theory

The bottom-up assembly of material architectures with tunable complexity, function, composition, and structure is a long sought goal in rational materials design. One promising approach aims to harnesses the programmability and specificity of DNA hybridization in order to direct the assembly of oligonucleotide-functionalized nano- and micro-particles by tailoring, in part, interparticle interactions. DNA-programmable assembly into three-dimensionally ordered structures has attracted extensive research interest owing to emergent applications in photonics, plasmonics and catalysis and potentially many other areas. Progress on the rational design of DNA-mediated interactions to create useful two-dimensional structures (e.g., structured films), on the other hand, has been rather slow. In this thesis, we establish strategies to engineer a diversity of 2D crystalline arrangements by designing and exploiting DNA-programmable interparticle interactions. We employ a combination of simulation, theory and experiments to predict and confirm accessibility of 2D structural diversity in an effort to establish a rational approach to 2D DNA-mediated particle assembly.We start with the experimental realization of 2D DNA-mediated assembly by decorating micron-sized silica particles with covalently attached single-stranded DNA through a two-step reaction. Subsequently, we elucidate sensitivity and ultimate controllability of DNA-mediated assembly—specifically the melting transition from dispersed singlet particles to aggregated or assembled structures—through control of the concentration of commonly employed nonionic surfactants. We relate the observed tunability to an apparent coupling with the critical micelle temperature in these systems. Also, both square and hexagonal 2D ordered particle arrangements are shown to evolve from disordered aggregates under appropriate annealing conditions defined based upon pre-established melting profiles. Subsequently, the controlled mixing of complementary ssDNA functionality on individual particles (‘multi-flavoring’) as opposed to functionalization of particles with the same type of ssDNA (‘uni-flavoring’) is explored as a possible design handle for tuning interparticle interactions and, thereby, accessing diverse structures. We employ a combination of simulations, theory, and experimental validation toward establishing ‘multi-flavoring’ as a rational design strategy. Firstly, MD simulations are carried out using effective pair potentials to describe interparticle interactions that are representative of different degrees of ssDNA ‘multi-flavoring’. These simulations reveal the template-free assembly of a diversity of 2D crystal polymorphs that is apparently tunable by controlling the relative attractive strengths between like and unlike functionalized particles. The resulting phase diagrams predict conditions (i.e., strengths of relative interparticle interactions) for obtaining crystalline phases with lattice symmetries ranging among square, alternating string hexagonal, random hexagonal, rhombic, honeycomb, and even kagome.Finally, these model findings are translated to experiments, in which binary microparticles are decorated with a tailored mixture of two different complementary ssDNA strands as a straight-forward means to realize tunable particle interactions. Guided by simple statistical mechanics and the detailed MD simulations, ‘multi-flavoring’ and control of solution phase particle stoichiometry resulted in experimental realization of structurally diverse 2D microparticle assemblies consistent with predictions, such as square, pentagonal and hexagonal lattices (honeycomb, kagome). The combined simulation, theory, and experimental findings reveal how control of interparticle interactions via DNA-functionalized particle “multi-flavoring” can lead to an even wider range of accessible colloidal crystal structures. The 2D experiments coupled with the model predictions may be used to provide new fundamental insight into nano- or microparticle assembly in three dimensions

Can ChatGPT be used to generate scientific hypotheses?

We investigate whether large language models can perform the creative hypothesis generation that human researchers regularly do. While the error rate is high, generative AI seems to be able to effectively structure vast amounts of scientific knowledge and provide interesting and testable hypotheses. The future scientific enterprise may include synergistic efforts with a swarm of "hypothesis machines", challenged by automated experimentation and adversarial peer reviews

Power network and smart grids analysis from a graph theoretic perspective

The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study. In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness. The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9