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Easy-hard phase transition in parameter estimation for optical waveguides.

ABSTRACT: The determination of the parameters of cylindrical optical waveguides, e.g. the diameters [Formula: see text] of r layers of (semi-) transparent optical fibres, can be executed by inverse evaluation of the scattering intensities that emerge under monochromatic illumination. The inverse problem can be solved by optimising the mismatch [Formula: see text] between the measured and simulated scattering patterns. The global optimum corresponds to the correct parameter values. The mismatch [Formula: see text] can be seen as an energy landscape as a function of the diameters. In this work, we study the structure of the energy landscape for different values of the complex refractive indices [Formula: see text], for [Formula: see text] and [Formula: see text] layers. We find that for both values of r, depending on the values of [Formula: see text], two very different types of energy landscapes exist, respectively. One type is dominated by one global minimum and the other type exhibits a multitude of local minima. From an algorithmic viewpoint, this corresponds to easy and hard phases, respectively. Our results indicate that the two phases are separated by sharp phase-transition lines and that the shape of these lines can be described by one "critical" exponent b, which depends slightly on r. Interestingly, the same exponent also describes the dependence of the number of local minima on the diameters. Thus, our findings are comparable to previous theoretical studies on easy-hard transitions in basic combinatorial optimisation or decision problems like Travelling Salesperson and Satisfiability. To our knowledge our results are the first indicating the existence of easy-hard transitions for a real-world optimisation problem of technological relevance.

SUBMITTER: Claussen G

PROVIDER: S-EPMC7562953 | biostudies-literature | 2020 Oct

REPOSITORIES: biostudies-literature

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Easy-hard phase transition in parameter estimation for optical waveguides.

Claussen Gunnar G Hartmann Alexander K AK

Scientific reports 20201015 1

The determination of the parameters of cylindrical optical waveguides, e.g. the diameters [Formula: see text] of r layers of (semi-) transparent optical fibres, can be executed by inverse evaluation of the scattering intensities that emerge under monochromatic illumination. The inverse problem can be solved by optimising the mismatch [Formula: see text] between the measured and simulated scattering patterns. The global optimum corresponds to the correct parameter values. The mismatch [Formula: s ...[more]

PMID: 33060751

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Project description:An optical impedance spectroscopy (OIS) technique based on a single-mode electro-active-integrated optical waveguide (EA-IOW) was developed to investigate electron-transfer processes of redox adsorbates. A highly sensitive single-mode EA-IOW device was used to optically follow the time-dependent faradaic current originated from a submonolayer of cytochrome c undergoing redox exchanges driven by a harmonic modulation of the electric potential at several dc bias potentials and at several frequencies. To properly retrieve the faradaic current density from the ac-modulated optical signal, we introduce here a mathematical formalism that (i) accounts for intrinsic changes that invariably occur in the optical baseline of the EA-IOW device during potential modulation and (ii) provides accurate results for the electro-chemical parameters. We are able to optically reconstruct the faradaic current density profile against the dc bias potential in the working electrode, identify the formal potential, and determine the energy-width of the electron-transfer process. In addition, by combining the optically reconstructed faradaic signal with simple electrical measurements of impedance across the whole electrochemical cell and the capacitance of the electric double-layer, we are able to determine the time-constant connected to the redox reaction of the adsorbed protein assembly. For cytochrome c directly immobilized onto the indium tin oxide (ITO) surface, we measured a reaction rate constant of 26.5 s(-1). Finally, we calculate the charge-transfer resistance and pseudocapacitance associated with the electron-transfer process and show that the frequency dependence of the redox reaction of the protein submonolayer follows as expected the electrical equivalent of an RC-series admittance diagram. Above all, we show here that OIS with single-mode EA-IOW's provide strong analytical signals that can be readily monitored even for small surface-densities of species involved in the redox process (e.g., fmol/cm(2), 0.1% of a full protein monolayer). This experimental approach, when combined with the analytical formalism described here, brings additional sensitivity, accuracy, and simplicity to electro-chemical analysis and is expected to become a useful tool in investigations of redox processes.

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Easy-hard phase transition in parameter estimation for optical waveguides.

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Easy-hard phase transition in parameter estimation for optical waveguides.

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