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This paper investigates the structural functional observability (SFO) and structural output controllability (SOC) of a class of systems with generically diagonalizable state matrices and explores the associated minimal sensor and actuator…

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for…

In many problems, agents cooperate locally so that a leader or fusion center can infer the state of every agent from probing the state of only a small number of agents. Versions of this problem arise when a fusion center reconstructs an…

Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…

Empirical analyses of ordinal outcomes using repeated cross-sectional data rely on marginal distributions, leaving the joint distribution unobserved and the sources of distributional change unidentified. This paper develops a framework to…

We study the problem of tracking an object moving through a network of wireless sensors. In order to conserve energy, the sensors may be put into a sleep mode with a timer that determines their sleep duration. It is assumed that an asleep…

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…

To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring…

In this work, we study minimum data rate tracking of a dynamical system under a neuromorphic event-based sensing paradigm. We begin by bridging the gap between continuous-time (CT) system dynamics and information theory's causal rate…

Many observers can simultaneously measure different parts of an environment of a quantum system in order to find out its state. To study this problem we generalize the formalism of conditional master equations to the multiple observer case.…

The aim of this chapter is to introduce the concept of regional boundary exponential reduced observability in connection with the sensors characterizations on a sub-region on boundary of the considered domain boundary. More precisely, we…

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that {multiple} sensors have been deployed and that the sensors are subject to resource…

Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…

Understanding how neural dynamics shape cognitive experiences remains a central challenge in neuroscience and psychiatry. Here, we present a novel framework leveraging state-to-output controllability from dynamical systems theory to model…

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

This paper introduces the new concepts of Functional Controllability and Functional Stabilizability, and establishes their duality with Functional Observability and Functional Detectability, respectively. A Generalized Separation Principle…

Synchronization plays a fundamental role in healthy cognitive and motor function. However, how synchronization depends on the interplay between local dynamics, coupling and topology and how prone to synchronization a network with given…

Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult…

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…