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The Boltzmann-Shannon Index (BSI) for clustered continuous data is introduced as a normalized measure that captures the relationship between geometry-based and frequency-based probability distributions defined over the clusters. In essence,…
Application of interpretable machine learning techniques on medical datasets facilitate early and fast diagnoses, along with getting deeper insight into the data. Furthermore, the transparency of these models increase trust among…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
The investigation of ergodicity or lack thereof in isolated quantum many-body systems has conventionally focused on the description of the reduced density matrices of local subsystems in the contexts of thermalization, integrability, and…
In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…
With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…
Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and…
We pose an engineering challenge of controlling an Ensemble of Energy Devices via coordinated, implementation-light and randomized on/off switching as a problem in Non-Equilibrium Statistical Mechanics. We show that Mean Field Control} with…
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
Ensemble learning combines several individual models to obtain a better generalization performance. In this work we present a practical method for estimating the joint power of several classifiers. It differs from existing approaches which…
We present a new algorithm for learning unknown governing equations from trajectory data, using and ensemble of neural networks. Given samples of solutions $x(t)$ to an unknown dynamical system $\dot{x}(t)=f(t,x(t))$, we approximate the…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
The dynamics of fermionic many-body systems is investigated in the framework of Boltzmann-Langevin (BL) stochastic one-body approaches. Within the recently introduced BLOB model, we examine the interplay between mean-field effects and…
Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of…
We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…
Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions.…