COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION

This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice

Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the structure of the ground truth signal, the severity of the degradation, the implicit bias of the reconstruction model and the complex interactions between the above factors. This results in natural sample-by-sample variation in the difficulty of a reconstruction task, which is often overlooked by contemporary techniques. Recently, diffusion-based inverse problem solvers have established new state-of-the-art in various reconstruction tasks. However, they have the drawback of being computationally prohibitive. Our key observation in this paper is that most existing solvers lack the ability to adapt their compute power to the difficulty of the reconstruction task, resulting in long inference times, subpar performance and wasteful resource allocation. We propose a novel method that we call severity encoding, to estimate the degradation severity of noisy, degraded signals in the latent space of an autoencoder. We show that the estimated severity has strong correlation with the true corruption level and can give useful hints at the difficulty of reconstruction problems on a sample-by-sample basis. Furthermore, we propose a reconstruction method based on latent diffusion models that leverages the predicted degradation severities to fine-tune the reverse diffusion sampling trajectory and thus achieve sample-adaptive inference times. We utilize latent diffusion posterior sampling to maintain data consistency with observations. We perform experiments on both linear and nonlinear inverse problems and demonstrate that our technique achieves performance comparable to state-of-the-art diffusion-based techniques, with significant improvements in computational efficiency.Comment: 14 pages, 6 figures, preliminary versio

Geometrical Spinoptics and the Optical Hall Effect

33 pages. Two subsections and new references added. To appear in the Journal of Geometry and PhysicsGeometrical optics is extended so as to provide a model for spinning light rays via the coadjoint orbits of the Euclidean group characterized by color and spin. This leads to a theory of ``geometrical spinoptics'' in refractive media. Symplectic scattering yields generalized Snell-Descartes laws that include the recently discovered optical Hall effect

Questionable and Unquestionable in Quantum Mechanics

We derive the basic postulates of quantum physics from a few very simple operational assumptions based exclusively on the relative frequencies of observable events (measurement operations and measurement outcomes). We isolate a notion which can be identified with the system's own state, in the sense that it characterizes the system's probabilistic behavior against all possible measurement operations. We investigate some important features of the possible states of the system. All those investigations remain within the framework of classical Kolmogorovian probability theory, meaning that any physical system (traditionally categorized as classical or quantum) that can be described in operational terms can be described within classical Kolmogorovian probability theory. In the second part of the paper we show that anything that can be described in operational terms can, if we wish, be represented in the Hilbert space quantum mechanical formalism. The outcomes of each measurement can be represented by a system of pairwise orthogonal closed subspaces spanning the entire Hilbert space; the states of the system can be represented by pure state operators, and the probabilities of the outcomes can be reproduced by the usual trace formula. Each real valued quantity can be associated with a suitable self-adjoint operator, such that the possible measurement results are the eigenvalues and the outcome events are represented by the eigenspaces, according to the spectral decomposition of the operator in question. This suggests that the basic postulates of quantum theory are in fact analytic statements: they do not tell us anything about a physical system beyond the fact that the system can be described in operational terms. This is almost true. At the end of the paper we discuss a few subtle points where the representation we obtained is not completely identical with standard quantum mechanics.Comment: 40 page

Blockchain Technology Adoption: Implications and Challenges

According to the World Economic Forum, by 2025 10% of the world’s GDP (currently about $100 trillion) may be on blockchain. Blockchain technology is described as a distributed ledger technology (DLT) underpinned by five fundamental principles: decentralization, peer-to-peer transmission; transparency with pseudonymity; irreversibility of records; and computational logic. Despite blockchain’s transformative potential, it is unclear how Blockchain applications are implemented across industries and product/service categories. The purpose of the paper is to discuss the general challenges, risks, and implications related to blockchain implementation and adoption by the private and public sectors. We discuss how blockchain should overcome multiple barriers–technological, governance, organizational and social–for its widespread adoption. Mainly, the regulatory uncertainty, scalability and performance, interoperability, data privacy, security, legacy systems and the skills gap barriers to adoption are examined. Moreover, the socioeconomic implications of blockchain are discussed mainly the financial, economic, social and institutional impacts

Skeleton in the Euclidean closet

Euclidean automata have been introduced in Kornai [Kor14a] to model a phenomenon known as "being in conflicted states". This brief note gives a further look on Euclidean automata and takes the rst steps in studying skeleta and representability and the logical characterization of languages accepted by Euclidean automata