Related papers: Modeling Hierarchical System with Operads

We demonstrate that hidden long range order is always present in the gapped phases of interacting fermionic systems on one dimensional lattices. It is captured by correlation functions of appropriate nonlocal charge and/or spin operators,…

Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive, meaning that they require direct access to underlying…

We consider the estimation of approximate factor models for time series data, where strong serial and cross-sectional correlations amongst the idiosyncratic component are present. This setting comes up naturally in many applications, but…

In this paper we present a hierarchical multi-rate control architecture for nonlinear autonomous systems operating in partially observable environments. Control objectives are expressed using syntactically co-safe Linear Temporal Logic…

Genomic instability, the propensity of aberrations in chromosomes, plays a critical role in the development of many diseases. High throughput genotyping experiments have been performed to study genomic instability in diseases. The output of…

A hierarchical approach to the construction of compound distributions for process-induced faults in IC manufacture is proposed. Within this framework, the negative binomial distribution and the compound binomial distribution are treated as…

Systematic testing of object-oriented software turned out to be much more complex than testing conventional software. Especially the highly incremental and iterative development cycle demands both many more changes and partially implemented…

In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…

In this paper the interactions between component failures are quantified and the interaction matrix and interaction network are obtained. The quantified interactions can capture the general propagation patterns of the cascades from…

Nowadays, the consequences of failure and downtime of distributed systems have become more and more severe. As an obvious solution, these systems incorporate protection mechanisms to tolerate faults that could cause systems failures and…

Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object…

Fractional ordered dynamical systems (FODS) are being studied in the present due to their innate qualitative and quantitative properties and their applications in various fields. The Jerk system, which is a system involving three…

As AI agents powered by large language models (LLMs) increasingly use external tools for high-stakes decisions, a critical reliability question arises: how do errors propagate across sequential tool calls? We introduce the first theoretical…

We propose a methodology to detect and isolate link failures in a weighted and directed network of identical multi-input multi-output LTI systems when only the output responses of a subset of nodes are available. Our method is based on the…

We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one correspondence with the nodes of the Hierarchical Tucker…

We propose an error-disturbance relation for general observables on finite dimensional Hilbert spaces based on operational notions of error and disturbance. For two-dimensional systems we derive tight inequalities expressing the trade-off…

Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer…

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…