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

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

Hamilton-Jacobi quantization of singular Lagrangians with linear velocities

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.Comment: late

EstDZ3: A New Esterolytic Enzyme Exhibiting Remarkable Thermostability

Lipolytic enzymes that retain high levels of catalytic activity when exposed to a variety of denaturing conditions are of high importance for a number of biotechnological applications. In this study, we aimed to identify new lipolytic enzymes, which are highly resistant to prolonged exposure at elevated temperatures. To achieve this, we searched for genes encoding for such proteins in the genomes of a microbial consortium residing in a hot spring located in China. After performing a functional genomic screening on a bacterium of the genus Dictyoglomus, which was isolated from this hot spring after in situ enrichment, we identified a new esterolytic enzyme, termed EstDZ3. Detailed biochemical characterization of the recombinant enzyme, revealed that it constitutes a slightly alkalophilic and highly active esterase against esters of fatty acids with short to medium chain lengths. Importantly, EstDZ3 exhibits remarkable thermostability, as it retained high levels of catalytic activity after exposure to temperatures as high as 95 oC for several hours. Interestingly, EstDZ3 was found to have very little similarity to previously characterized esterolytic enzymes. Computational modelling of the three-dimensional structure of this new enzyme predicted that it exhibits a typical α/β hydrolase fold, which seems to include a subdomain insertion. This insertion is similar to the one present in its closest homologue of known function and structure, the cinnamoyl esterase Lj0536 from Lactobacillus johnsonii. As it was found in the case of Lj0536, this structural feature is expected to be an important determinant of the catalytic properties of EstDZ3. The high levels of esterolytic activity of EstDZ3, combined with its remarkable thermostability and good stability against a wide range of metal ions, organic solvents, and other denaturing agents, render this new enzyme a candidate biocatalyst for high-temperature biotechnological applications

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

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

Serpent: Scalable and Efficient Image Restoration via Multi-scale Structured State Space Models

The landscape of computational building blocks of efficient image restoration architectures is dominated by a combination of convolutional processing and various attention mechanisms. However, convolutional filters, while efficient, are inherently local and therefore struggle with modeling long-range dependencies in images. In contrast, attention excels at capturing global interactions between arbitrary image regions, but suffers from a quadratic cost in image dimension. In this work, we propose Serpent, an efficient architecture for high-resolution image restoration that combines recent advances in state space models (SSMs) with multi-scale signal processing in its core computational block. SSMs, originally introduced for sequence modeling, can maintain a global receptive field with a favorable linear scaling in input size. We propose a novel hierarchical architecture inspired by traditional signal processing principles, that converts the input image into a collection of sequences and processes them in a multi-scale fashion. Our experimental results demonstrate that Serpent can achieve reconstruction quality on par with state-of-the-art techniques, while requiring orders of magnitude less compute (up to $150$ fold reduction in FLOPS) and a factor of up to $5\times$ less GPU memory while maintaining a compact model size. The efficiency gains achieved by Serpent are especially notable at high image resolutions.Comment: 12 pages, 7 figures, under revie