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Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect…
We study macroscopic observables defined as the total value of a physical quantity over a collection of quantum systems. We show that previous results obtained for infinite ensemble of identically prepared systems lead to incorrect…
In quantum theory, physically measurable quantities of a microscopic system are represented by self-adjoint operators. However, not all of the self-adjoint operators correspond to measurable quantities. The superselection rule is a…
Observations in Quantum Mechanics are subject to complex restrictions arising from the principle of energy conservation. Determining such restrictions, however, has been so far an elusive task, and only partial results are known. In this…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The measurement of human behavior remains a central challenge across the behavioral sciences. Traditional approaches typically rely on passive observation of responses collected under static or weakly controlled conditions, limiting the…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
Measurement data provides a precise and detailed description of components within a complex system but it is rarely used directly as a component of a system model. In this paper we introduce a model-based representation of measurement data…
In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
In this paper it is showed that if a time-varying uncertain system is robustly completely detectable then there exists an estimator for this system, i.e. we can estimate asymptotically the state vector of the system. Moreover, if a…
The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for non-linear quantum mechanical…