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Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation
(2022)
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit.
Knowledge of this curve yields a phase dynamics description of the oscillator for arbitrary weak forcing. Similar, though much less studied characteristic, is the amplitude response that can be defined either using an ad hoc approach to amplitude estimation or via the isostable variables.
Here, we discuss the problem of the phase and amplitude response inference from observations using test stimulation. Although PRC determination for noise-free neuronal-like oscillators perturbed by narrow pulses is a well-known task, the general case remains a challenging problem. Even more challenging is the inference of the amplitude response. This characteristic is crucial, e.g. for controlling the amplitude of the collective mode in a network of interacting units-a task relevant to neuroscience. Here, we compare the performance of different techniques suitable for inferring the phase and amplitude response, particularly with application to macroscopic oscillators. We suggest improvements to these techniques, e.g. demonstrating how to obtain the PRC in case of stimuli of arbitrary shape. Our main result is a novel technique denoted by IPID-1, based on the direct reconstruction of the Winfree equation and the analogous first-order equation for isostable dynamics. The technique works for signals with or without well-pronounced marker events and pulses of arbitrary shape; in particular, we consider charge-balanced pulses typical in neuroscience applications. Moreover, this technique is superior for noisy and high-dimensional systems. Additionally, we describe an error measure that can be computed solely from data and complements any inference technique.
Random logic networks
(2021)
We investigate dynamical properties of a quantum generalization of classical reversible Boolean networks. The state of each node is encoded as a single qubit, and classical Boolean logic operations are supplemented by controlled bit-flip and Hadamard operations. We consider synchronous updating schemes in which each qubit is updated at each step based on stored values of the qubits from the previous step. We investigate the periodic or quasiperiodic behavior of quantum networks, and we analyze the propagation of single site perturbations through the quantum networks with input degree one. A nonclassical mechanism for perturbation propagation leads to substantially different evolution of the Hamming distance between the original and perturbed states.
We apply the concepts of relative dimensions and mutual singularities to characterize the fractal properties of overlapping attractor and repeller in chaotic dynamical systems. We consider one analytically solvable example (a generalized baker's map); two other examples, the Anosov-Mobius and the Chirikov-Mobius maps, which possess fractal attractor and repeller on a two-dimensional torus, are explored numerically. We demonstrate that although for these maps the stable and unstable directions are not orthogonal to each other, the relative Renyi and Kullback-Leibler dimensions as well as the mutual singularity spectra for the attractor and repeller can be well approximated under orthogonality assumption of two fractals.
The fundamental sensitivity limit of atomic force microscopy is strongly correlated to the thermal noise of cantilever oscillation. A method to suppress this unwanted noise is to reduce the bandwidth of the measurement, but this approach is limited by the speed of the measurement and the width of the cantilever resonance, commonly defined through the quality factor Q. However, it has been shown that optomechanical resonances in interferometers might affect cantilever oscillations resulting in an effective quality factor Q(eff). When the laser power is sufficiently increased cantilever oscillations might even reach the regime of self-oscillation. In this self-oscillation state, the noise of the system is partially determined by the interaction with laser light far from equilibrium. Here, we show and discuss how tuning of laser power leads to nonlinear optomechanical effects that can dramatically increase the effective quality factor of the cantilever leading to out-of-equilibrium noise. We model the effects using a fourth order nonlinearity of the damping coefficient. Published under an exclusive license by AIP Publishing.
Data-driven expectations for electromagnetic counterpart searches based on LIGO/Virgo public alerts
(2022)
Searches for electromagnetic counterparts of gravitational-wave signals have redoubled since the first detection in 2017 of a binary neutron star merger with a gamma-ray burst, optical/infrared kilonova, and panchromatic afterglow. Yet, one LIGO/Virgo observing run later, there has not yet been a second, secure identification of an electromagnetic counterpart. This is not surprising given that the localization uncertainties of events in LIGO and Virgo's third observing run, O3, were much larger than predicted.
We explain this by showing that improvements in data analysis that now allow LIGO/Virgo to detect weaker and hence more poorly localized events have increased the overall number of detections, of which well-localized, gold-plated events make up a smaller proportion overall.
We present simulations of the next two LIGO/Virgo/KAGRA observing runs, O4 and O5, that are grounded in the statistics of O3 public alerts. To illustrate the significant impact that the updated predictions can have, we study the follow-up strategy for the Zwicky Transient Facility. Realistic and timely forecasting of gravitational-wave localization accuracy is paramount given the large commitments of telescope time and the need to prioritize which events are followed up.
We include a data release of our simulated localizations as a public proposal planning resource for astronomers.
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.
Comb-like geometric constraints leading to emergence of the time-fractional Schrödinger equation
(2021)
This paper presents an overview over several examples, where the comb-like geometric constraints lead to emergence of the time-fractional Schrodinger equation. Motion of a quantum object on a comb structure is modeled by a suitable modification of the kinetic energy operator, obtained by insertion of the Dirac delta function in the Laplacian. First, we consider motion of a free particle on two- and three-dimensional comb structures, and then we extend the study to the interacting cases. A general form of a nonlocal term, which describes the interactions of the particle with the medium, is included in the Hamiltonian, and later on, the cases of constant and Dirac delta potentials are analyzed. At the end, we discuss the case of non-integer dimensions, considering separately the case of fractal dimension between one and two, and the case of fractal dimension between two and three. All these examples show that even though we are starting with the standard time-dependent Schrodinger equation on a comb, the time-fractional equation for the Green's functions appears, due to these specific geometric constraints.
We present the discovery of a new double-detonation progenitor system consisting of a hot subdwarf B (sdB) binary with a white dwarf companion with a P (orb) = 76.34179(2) minutes orbital period. Spectroscopic observations are consistent with an sdB star during helium core burning residing on the extreme horizontal branch. Chimera light curves are dominated by ellipsoidal deformation of the sdB star and a weak eclipse of the companion white dwarf. Combining spectroscopic and light curve fits, we find a low-mass sdB star, M (sdB) = 0.383 +/- 0.028 M (circle dot) with a massive white dwarf companion, M (WD) = 0.725 +/- 0.026 M (circle dot). From the eclipses we find a blackbody temperature for the white dwarf of 26,800 K resulting in a cooling age of approximate to 25 Myr whereas our MESA model predicts an sdB age of approximate to 170 Myr. We conclude that the sdB formed first through stable mass transfer followed by a common envelope which led to the formation of the white dwarf companion approximate to 25 Myr ago. Using the MESA stellar evolutionary code we find that the sdB star will start mass transfer in approximate to 6 Myr and in approximate to 60 Myr the white dwarf will reach a total mass of 0.92 M (circle dot) with a thick helium layer of 0.17 M (circle dot). This will lead to a detonation that will likely destroy the white dwarf in a peculiar thermonuclear supernova. PTF1 J2238+7430 is only the second confirmed candidate for a double-detonation thermonuclear supernova. Using both systems we estimate that at least approximate to 1% of white dwarf thermonuclear supernovae originate from sdB+WD binaries with thick helium layers, consistent with the small number of observed peculiar thermonuclear explosions.
The study addresses the question, if observed changes in terms of Arctic-midlatitude linkages during winter are driven by Arctic Sea ice decline alone or if the increase of global sea surface temperatures plays an additional role. We compare atmosphere-only model experiments with ECHAM6 to ERA-Interim Reanalysis data. The model sensitivity experiment is implemented as a set of four combinations of sea ice and sea surface temperature boundary conditions. Atmospheric circulation regimes are determined and evaluated in terms of their cyclone and blocking characteristics and changes in frequency during winter. As a prerequisite, ECHAM6 reproduces general features of circulation regimes very well. Tropospheric changes induced by the change of boundary conditions are revealed and further impacts on the large-scale circulation up into the stratosphere are investigated. In early winter, the observed increase of atmospheric blocking in the region between Scandinavia and the Urals are primarily related to the changes in sea surface temperatures. During late winter, we f nd a weakened polar stratospheric vortex in the reanalysis that further impacts the troposphere. In the model sensitivity study a climatologically weakened polar vortex occurs only if sea ice is reduced and sea surface temperatures are increased together. This response is delayed compared to the reanalysis. The tropospheric response during late winter is inconclusive in the model, which is potentially related to the weak and delayed response in the stratosphere. The model experiments do not reproduce the connection between early and late winter as interpreted from the reanalysis. Potentially explaining this mismatch, we identify a discrepancy of ECHAM6 to reproduce the weakening of the stratospheric polar vortex through blocking induced upward propagation of planetary waves.