Related papers: On algebraic time-derivative estimation and deadbe…

In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…

Many types of detectors, such as cathode strip chambers and some MPGDs, allow us to reconstruct track positions by induced strip charges. There are two main types of algebraic methods for this reconstruction: center of gravity methods and…

We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…

As an alternative to the popular balanced truncation method, the cross Gramian matrix induces a class of balancing model reduction techniques. Besides the classical computation of the cross Gramian by a Sylvester matrix equation, an…

We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite as well…

The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…

A method for selecting a graphical model for $p$-vector-valued stationary Gaussian time series was recently proposed by Matsuda and uses the Kullback-Leibler divergence measure to define a test statistic. This statistic was used in a…

This paper presents a method for jointly estimating the state, input, and parameters of linear systems in an online fashion. The method is specially designed for measurements that are corrupted with non-Gaussian noise or outliers, which are…

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

The importance of state estimation in fluid mechanics is well-established; it is required for accomplishing several tasks including design/optimization, active control, and future state prediction. A common tactic in this regards is to rely…

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…

A symbolic approach to decentralized set-valued state estimation and prediction for systems that admit a hybrid state machine representations is proposed. The decentralized computational scheme represents a conj unction of a finite number…

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…

This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive…

Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the…