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AimsBy associating features with orthonormal bases, we analyse the values of the extracted features for the daily biweekly growth rates of COVID-19 confirmed cases and deaths on national and continental levels. MethodsBy adopting the concept of Fourier coefficients, we analyse the inner products with respect to temporal and spatial frequencies on national and continental levels. The input data are the global time series data with 117 countries over 109 days on a national level; and 6 continents over 447 days on a continental level. Next, we calculate the Euclidean distance matrices and their average variabilities, which measure the average discrepancy between one feature vector and all others. Then we analyse the temporal and spatial variabilities on a national level. By calculating the temporal inner products on a continental level, we derive and analyse the similarities between the continents. ResultsOn the national level, the daily biweekly growth rates bear higher similarities in the time dimension than the ones in the space dimension. Furthermore, there exists a strong concurrency between the features for biweekly growth rates of cases and deaths. As far as the trends of the features are concerned, the features are stabler on the continental level, and less predictive on the national level. In addition, there are very high similarities between all the continents, except Asia. ConclusionsThe features for daily biweekly growth rates of cases and deaths are extracted via orthonormal frequencies. By tracking the inner products for the input data and the orthonormal features, we could decompose the evolutionary results of COVID-19 into some fundamental frequencies. Though the frequency-based techniques are applied, the interpretation of the features should resort to other methods. By analysing the spectrum of the frequencies, we reveal hidden patterns of the COVID-19 pandemic. This would provide some preliminary research merits for further insightful investigations. It could also be used to predict future trends of daily biweekly growth rates of COVID-19 cases and deaths.

Free-electron lasers provide a source of x-ray pulses short enough and intense enough to drive nonlinearities in molecular systems. Impulsive interactions driven by these x-ray pulses provide a way to create and probe valence electron motions with high temporal and spatial resolution. Observing these electronic motions is crucial to understand the role of electronic coherence in chemical processes. A simple nonlinear technique for probing electronic motion, impulsive stimulated x-ray Raman scattering (ISXRS), involves a single impulsive interaction to produce a coherent superposition of electronic states. We demonstrate electronic population transfer via ISXRS using broad bandwidth (5.5eV full width at half maximum) attosecond x-ray pulses produced by the Linac Coherent Light Source. The impulsive excitation is resonantly enhanced by the oxygen 1s→2π^{*} resonance of nitric oxide (NO), and excited state neutral molecules are probed with a time-delayed UV laser pulse.

The widespread use of nanostructures and nanomaterials has opened up a whole new realm of challenges in thermal management, but also leads to possibilities for energy conversion, storage, and generation, in addition to numerous other technological applications. At the microscale and below, standard thermal measurement techniques reach their limits, and several novel methods have been developed to overcome these limitations. Among the most recent, contactless photothermal methods have been widely used and have proved their advantages in terms of versatility, temporal and spatial resolution, and even sensitivity in some situations. Among them, thermoreflectance and Raman thermometry have been used to measure the thermal properties from bulk materials to thin films, multilayers, suspended structures, and nanomaterials. This Tutorial presents the principles of these two techniques and some of their most common implementations. It expands to more advanced systems for spatial mapping and for probing of non-Fourier thermal transport. Finally, this paper concludes with discussing the limitations and perspectives of these techniques and future directions in nanoscale thermometry. I. INTRODUCTION, ICN2 is supported by the Severo Ochoa program from the Spanish Research Agency (AEI, Grant No. SEV-2017-0706) and by the CERCA Programme/Generalitat de Catalunya. ICN2 authors acknowledge support from the Spanish MICINN Project SIP (No. PGC2018-101743-B-I00) and the H2020 European FET Open project PHENOMEN (No. GA 713450). E.C.-A. acknowledges financial support from EU Project NANOPOLY (No. GA 289061). The NTNU authors are supported by the Research Council of Norway through the FRINATEK Project No. 251068 with the title: “Engineering Metal-Polymer Interface for Enhanced Heat Transfer.”

Quantum fluids of light are an emerging tool employed in quantum many-body physics. Their amazing properties and versatility allow using them in a wide variety of fields including gravitation, quantum information and simulation. However the implications of the quantum nature of light in the nonlinear optical propagation are still missing many features. We theoretically predict classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear medium. By using the so called Gamow vectors, we show that the quadratures of a coherent state get squeezed and that a maximal squeezing power exists. Our analysis holds true for temporal and spatial optical propagation in highly nonlocal regime. These results open a new scenario in quantum photon fluids and may lead to novel applications in fields like metrology and analogues of quantum gravity., 6 pages, 2 figures