Related papers: Modeling Hierarchical System with Operads
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
This paper deals with the fault detection and isolation (FDI) problem for linear structured systems in which the system matrices are given by zero/nonzero/arbitrary pattern matrices. In this paper, we follow a geometric approach to verify…
Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing…
This is a complementary document to the paper presented in [1], to provide more detailed proofs for some results. The main paper addresses the problem of trajectory tracking control of autonomous rotorcraft in operation scenarios where only…
The ability to reason with multiple hierarchical structures is an attractive and desirable property of sequential inductive biases for natural language processing. Do the state-of-the-art Transformers and LSTM architectures implicitly…
Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…
We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…
Identifying the cause of a system-level failure in a cyber-physical system (CPS) can be like tracing a needle in a haystack. This paper approaches the problem by assuming that the CPS has been designed compositionally and that each…
This paper introduces different views for understanding problems and faults with the goal of defining a method for the formal specification of systems. The idea of Layered Fault Tolerant Specification (LFTS) is proposed to make the method…
Higher order parametric level correlations in disordered systems with broken time-reversal symmetry are studied by mapping the problem onto a model of coupled Hermitian random matrices. Closed analytical expression is derived for parametric…
Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via…
This paper is an introduction to a series of papers in which we give combinatorial models for certain important operads (including A-infinity and E-infinity operads, the little n-cubes operads, and the framed little disks operad) and…
Model-based safety analysis approaches aim at finding critical failure combinations by analysis of models of the whole system (i.e. software, hardware, failure modes and environment). The advantage of these methods compared to traditional…
We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently the class of operator systems that are associated with…
In this paper the focus is on the relationship between the occurrence of failures in a (directed or undirected) network of linear single integrator agents and the presence of jump discontinuities in the derivatives of the network output.…
This paper evaluates methods of hierarchical skill analysis developed in aerospace to the problem of surgical skill assessment and modeling. The analysis employs tool motion data of Fundamental of Laparoscopic Skills (FLS) tasks collected…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
This paper introduces an integrated system designed to enhance the explainability of fault diagnostics in complex systems, such as nuclear power plants, where operator understanding is critical for informed decision-making. By combining a…