Michael Sebek

Ivo Herman, Dan Martinec, Zdeněk Hurák et al.

We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix - the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H-infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.

Ivo Herman, Dan Martinec, Zdeněk Hurák et al.

We consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the open-loop transfer function of the vehicle contains two or more integrators and the Fiedler eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain - the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller the predecessor following strategy.

Ivo Herman, Dan Martinec, Michael Sebek

This paper considers transfer functions in consensus systems where agents have identical SISO dynamics of arbitrary order. The interconnecting structure is a directed graph. The transfer functions for various inputs and outputs are presented in simple product forms with a similar structure of the numerator and the denominator. This structure combines the network properties and the agent model in an explicit way. The link between a higher-order and a single-integrator dynamics is shown and the polynomials of the transfer function in the single-integrator system are related to the graph properties. These properties also allow to generalize a result on the minimal dimension of the controllable subspace to the directed graphs.

Michael Sebek

We present an extension of state-feedback pole placement for quaternionic systems, based on companion forms and the Ackermann formula. For controllable single-input quaternionic LTI models, we define a companion polynomial that annihilates its companion matrix, characterize spectra via right-eigenvalue similarity classes, and prove coefficient-matching design in controllable coordinates. We then derive a coordinate-free Ackermann gain expression valid for real target polynomials, and state its scope and limitations. Short examples demonstrate correctness, practical use, and numerical simplicity.

Michael Sebek

We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error dynamics through right-eigenvalue similarity classes. We also give an Ackermann-type formula for real-coefficient target polynomials, where polynomial evaluation is similarity-equivariant. The resulting recipes place observer poles directly over quaternions and clarify when companion-coordinate updates and one-shot Ackermann formulas remain valid.

Gordana Ispirova, Michael Sebek, Giulia Menichetti

This chapter explores the evolution, classification, and health implications of food processing, while emphasizing the transformative role of machine learning, artificial intelligence (AI), and data science in advancing food informatics. It begins with a historical overview and a critical review of traditional classification frameworks such as NOVA, Nutri-Score, and SIGA, highlighting their strengths and limitations, particularly the subjectivity and reproducibility challenges that hinder epidemiological research and public policy. To address these issues, the chapter presents novel computational approaches, including FoodProX, a random forest model trained on nutrient composition data to infer processing levels and generate a continuous FPro score. It also explores how large language models like BERT and BioBERT can semantically embed food descriptions and ingredient lists for predictive tasks, even in the presence of missing data. A key contribution of the chapter is a novel case study using the Open Food Facts database, showcasing how multimodal AI models can integrate structured and unstructured data to classify foods at scale, offering a new paradigm for food processing assessment in public health and research.

Ayan Chatterjee, Robin Walters, Zohair Shafi et al.

Identifying novel drug-target interactions (DTI) is a critical and rate limiting step in drug discovery. While deep learning models have been proposed to accelerate the identification process, we show that state-of-the-art models fail to generalize to novel (i.e., never-before-seen) structures. We first unveil the mechanisms responsible for this shortcoming, demonstrating how models rely on shortcuts that leverage the topology of the protein-ligand bipartite network, rather than learning the node features. Then, we introduce AI-Bind, a pipeline that combines network-based sampling strategies with unsupervised pre-training, allowing us to limit the annotation imbalance and improve binding predictions for novel proteins and ligands. We illustrate the value of AI-Bind by predicting drugs and natural compounds with binding affinity to SARS-CoV-2 viral proteins and the associated human proteins. We also validate these predictions via docking simulations and comparison with recent experimental evidence, and step up the process of interpreting machine learning prediction of protein-ligand binding by identifying potential active binding sites on the amino acid sequence. Overall, AI-Bind offers a powerful high-throughput approach to identify drug-target combinations, with the potential of becoming a powerful tool in drug discovery.