Ushering in a New Era for King’s Conceptual System and Theory of Goal Attainment

The COVID-19 pandemic has ushered in a new era for nurses and healthcare. King’s conceptual framework continues to provide a practical theoretical underpinning for nurse-client interactions in virtual care spaces that are now a pervasive part of the interacting systems framework. The author in this article discusses the current applications and future opportunities for applications of King’s work in practice, education, and research.

Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds

Correctness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems. Recent developments of computing and communication grids for radio broadcasting, cellular networks, communication subsystems of supercomputers, specialized grids for numerical methods and networks on chips require verification of protocols for any number of devices. For analysis of computing and communication grid structures, a new class of infinite Petri nets has been introduced and studied for more than 10 years. Infinite Petri nets were also applied for simulating cellular automata. Rectangular, triangular and hexagonal grids on plane, hyper cube and hyper torus in multidimensional space have been considered. Composing and solving in parametric form infinite Diophantine systems of linear equations allowed us to prove the protocol properties for any grid size and any number of dimensions. Software generators of infinite Petri net models have been developed. Special classes of graphs, such as a graph of packet transmission directions and a graph of blockings, have been introduced and studied. Complex deadlocks have been revealed and classified. In the present paper, infinite Petri nets are divided into two following kinds: a single infinite construct and an infinite set of constructs of specified size (and number of dimensions). Finally, the paper discusses possible future work directions.

Dynamical symmetry breaking through AI: The dimer self-trapping transition

The nonlinear dimer obtained through the nonlinear Schrödinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective [Formula: see text] model. In this later context, the self-trapping transition is an initial condition-dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition that has been investigated analytically and mathematically is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of this work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the nondegenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.

On intermediate statistics across many-body localization transition

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

Relaxation of Some Confusions about Confounders

This work is about observational causal discovery for deterministic and stochastic dynamic systems. We explore what additional knowledge can be gained by the usage of standard conditional independence tests and if the interacting systems are located in a geodesic space.