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Alexander Maier

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YNIMG Journal 2022 Journal Article

Resolving the mesoscopic missing link: Biophysical modeling of EEG from cortical columns in primates

  • Beatriz Herrera
  • Jacob A. Westerberg
  • Michelle S. Schall
  • Alexander Maier
  • Geoffrey F. Woodman
  • Jeffrey D. Schall
  • Jorge J. Riera

Event-related potentials (ERP) are among the most widely measured indices for studying human cognition. While their timing and magnitude provide valuable insights, their usefulness is limited by our understanding of their neural generators at the circuit level. Inverse source localization offers insights into such generators, but their solutions are not unique. To address this problem, scientists have assumed the source space generating such signals comprises a set of discrete equivalent current dipoles, representing the activity of small cortical regions. Based on this notion, theoretical studies have employed forward modeling of scalp potentials to understand how changes in circuit-level dynamics translate into macroscopic ERPs. However, experimental validation is lacking because it requires in vivo measurements of intracranial brain sources. Laminar local field potentials (LFP) offer a mechanism for estimating intracranial current sources. Yet, a theoretical link between LFPs and intracranial brain sources is missing. Here, we present a forward modeling approach for estimating mesoscopic intracranial brain sources from LFPs and predict their contribution to macroscopic ERPs. We evaluate the accuracy of this LFP-based representation of brain sources utilizing synthetic laminar neurophysiological measurements and then demonstrate the power of the approach in vivo to clarify the source of a representative cognitive ERP component. To that end, LFP was measured across the cortical layers of visual area V4 in macaque monkeys performing an attention demanding task. We show that area V4 generates dipoles through layer-specific transsynaptic currents that biophysically recapitulate the ERP component through the detailed forward modeling. The constraints imposed on EEG production by this method also revealed an important dissociation between computational and biophysical contributors. As such, this approach represents an important bridge between laminar microcircuitry, through the mesoscopic activity of cortical columns to the patterns of EEG we measure at the scalp.

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AAAI Conference 2019 Conference Paper

Model-Based Diagnosis of Hybrid Systems Using Satisfiability Modulo Theory

  • Alexander Diedrich
  • Alexander Maier
  • Oliver Niggemann

Currently, detecting and isolating faults in hybrid systems is often done manually with the help of human operators. In this paper we present a novel model-based diagnosis approach for automatically diagnosing hybrid systems. The approach has two parts: First, modelling dynamic system behaviour is done through well-known state space models using differential equations. Second, from the state space models we calculate Boolean residuals through an observer-pattern. The novelty lies in implementing the observer pattern through the use of a symbolic system description specified in satisfiability theory modulo linear arithmetic. With this, we create a static situation for the diagnosis algorithm and decouple modelling and diagnosis. Evaluating the system description generates one Boolean residual for each component. These residuals constitute the fault symptoms. To find the minimum cardinality diagnosis from these symptoms we employ Reiter’s diagnosis lattice. For the experimental evaluation we use a simulation of the Tennessee Eastman process and a simulation of a four-tank model. We show that the presented approach is able to identify all injected faults.

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AAAI Conference 2012 Conference Paper

Learning Behavior Models for Hybrid Timed Systems

  • Oliver Niggemann
  • Benno Stein
  • Asmir Vodencarevic
  • Alexander Maier
  • Hans Kleine Büning

A tailored model of a system is the prerequisite for various analysis tasks, such as anomaly detection, fault identification, or quality assurance. This paper deals with the algorithmic learning of a system’s behavior model given a sample of observations. In particular, we consider real-world production plants where the learned model must capture timing behavior, dependencies between system variables, as well as mode switches—in short: hybrid system’s characteristics. Usually, such model formation tasks are solved by human engineers, entailing the well-known bunch of problems including knowledge acquisition, development cost, or lack of experience. Our contributions to the outlined field are as follows. (1) We present a taxonomy of learning problems related to model formation tasks. As a result, an important open learning problem for the domain of production system is identified: The learning of hybrid timed automata. (2) For this class of models, the learning algorithm HyBUTLA is presented. This algorithm is the first of its kind to solve the underlying model formation problem at scalable precision. (3) We present two case studies that illustrate the usability of this approach in realistic settings. (4) We give a proof for the learning and runtime properties of HyBUTLA.

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