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A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I…
The state $\rho$ of a quantum system can be represented by a vector $\mathbf{P}_{\mathcal{M}}(\rho)$ of outcome probabilities for a set of measurements $\mathcal{M}$. Such representations appear throughout physics, for example, in quantum…
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence…
A class of polynomial dynamical systems called complex-balanced are locally stable and conjectured to be globally stable. In general, complex-balancing is not a robust property, i.e., small changes in parameter values may result in the loss…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate…
General wisdom tells us that if two quantum states are ``macroscopically distinguishable'' then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
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…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for…
We explore set-stabilizability by constrained controls, and both controllability and stabilizability can be regarded as the special case of set-stabilizability. We not only clarify how to define an equilibrium point of Schr$\ddot{o}$dinger…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from Copenhagen to many worlds are critically revisited. The difficulties for intuitive models of quantum physics are pointed…
Difficulties and discomfort with the interpretation of quantum mechanics are due to differences in language between it and classical physics. Analogies to The Special Theory of Relativity, which also required changes in the basic worldview…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…