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We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
We present two methods for reducing multidimensional information to one dimension for ease of understand or analysis while maintaining statistical power. While not new, dimensional reduction is not greatly used in high-energy physics and…
In the past fifteen years mathematical models for microelectromechanical systems (MEMS) have been the subject of several studies, in particular due to the interesting qualitative properties they feature. Still most research is devoted to an…
Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
We derive finite-dimensional quantum mechanics from a single ontological principle, that \emph{existence is constituted by distinguishability}, together with two structural commitments: finite capacity $N$ (parametric input) and…
Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…
We provide a unified framework to obtain numerically certain quantities, such as the distribution function, absolute moments and prices of financial options, from the characteristic function of some (unknown) probability density function…
The Kalman canonical form for quantum linear systems was derived in \cite{ZGPG18}. The purpose of this paper is to present an alternative derivation by means of a Gramian matrix approach. Controllability and observability Gramian matrices…
Effective and efficient forecasting relies on identification of the relevant information contained in past observations -- the predictive features -- and isolating it from the rest. When the future of a process bears a strong dependence on…
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…