Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice

We present an exact real-space renormalization group (RSRG) method for evaluating the dynamic structure factor of an infinite one-dimensional quasiperiodic period-doubling (PD) lattice. We observe that for every normal mode frequency of the chain, the dynamic structure factor $S(q,\omega)$ always exhibits periodicity with respect to the wave vector $q$ and the presence of such periodicity even in absence of translational invariance in the system is quite surprising. Our analysis shows that this periodicity in $S(q,\omega)$ actually indicates the presence of delocalized phonon modes in the PD chain. The Brillouin Zones of the lattice are found to have a hierarchical structure and the dispersion relation gives both the acoustic as well as optical branches. The phonon dispersion curves have a nested structure and we have shown that it is actually the superposition of the dispersion curves of an infinite set of periodic lattices.Comment: 9 pages, 3 postscript figures, REVTeX, To appear in Phys. Rev. B (1 February 1998-I

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences

We comment on some recent investigations on the electronic properties of models associated to the Thue-Morse chain and point out that their conclusions are in contradiction with rigorously proven theorems and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.Comment: 15,CPT-94/P.3003,tex,

Trace and antitrace maps for aperiodic sequences, their extensions and applications

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.Comment: 13 pages, REVTeX, now also includes applications to electronic systems, some references adde

Future-ai:International consensus guideline for trustworthy and deployable artificial intelligence in healthcare

Despite major advances in artificial intelligence (AI) for medicine and healthcare, the deployment and adoption of AI technologies remain limited in real-world clinical practice. In recent years, concerns have been raised about the technical, clinical, ethical and legal risks associated with medical AI. To increase real world adoption, it is essential that medical AI tools are trusted and accepted by patients, clinicians, health organisations and authorities. This work describes the FUTURE-AI guideline as the first international consensus framework for guiding the development and deployment of trustworthy AI tools in healthcare. The FUTURE-AI consortium was founded in 2021 and currently comprises 118 inter-disciplinary experts from 51 countries representing all continents, including AI scientists, clinicians, ethicists, and social scientists. Over a two-year period, the consortium defined guiding principles and best practices for trustworthy AI through an iterative process comprising an in-depth literature review, a modified Delphi survey, and online consensus meetings. The FUTURE-AI framework was established based on 6 guiding principles for trustworthy AI in healthcare, i.e. Fairness, Universality, Traceability, Usability, Robustness and Explainability. Through consensus, a set of 28 best practices were defined, addressing technical, clinical, legal and socio-ethical dimensions. The recommendations cover the entire lifecycle of medical AI, from design, development and validation to regulation, deployment, and monitoring. FUTURE-AI is a risk-informed, assumption-free guideline which provides a structured approach for constructing medical AI tools that will be trusted, deployed and adopted in real-world practice. Researchers are encouraged to take the recommendations into account in proof-of-concept stages to facilitate future translation towards clinical practice of medical AI

FUTURE-AI: International consensus guideline for trustworthy and deployable artificial intelligence in healthcare

Despite major advances in artificial intelligence (AI) for medicine and healthcare, the deployment and adoption of AI technologies remain limited in real-world clinical practice. In recent years, concerns have been raised about the technical, clinical, ethical and legal risks associated with medical AI. To increase real world adoption, it is essential that medical AI tools are trusted and accepted by patients, clinicians, health organisations and authorities. This work describes the FUTURE-AI guideline as the first international consensus framework for guiding the development and deployment of trustworthy AI tools in healthcare. The FUTURE-AI consortium was founded in 2021 and currently comprises 118 inter-disciplinary experts from 51 countries representing all continents, including AI scientists, clinicians, ethicists, and social scientists. Over a two-year period, the consortium defined guiding principles and best practices for trustworthy AI through an iterative process comprising an in-depth literature review, a modified Delphi survey, and online consensus meetings. The FUTURE-AI framework was established based on 6 guiding principles for trustworthy AI in healthcare, i.e. Fairness, Universality, Traceability, Usability, Robustness and Explainability. Through consensus, a set of 28 best practices were defined, addressing technical, clinical, legal and socio-ethical dimensions. The recommendations cover the entire lifecycle of medical AI, from design, development and validation to regulation, deployment, and monitoring. FUTURE-AI is a risk-informed, assumption-free guideline which provides a structured approach for constructing medical AI tools that will be trusted, deployed and adopted in real-world practice. Researchers are encouraged to take the recommendations into account in proof-of-concept stages to facilitate future translation towards clinical practice of medical AI