An Analysis of Online Classes Tweets Using Gephi: Inputs for Online Learning

The conduct of online classes has emerged as one of the major changes in the educational landscape at the onset of COVID-19. Its implementation has been met by varying reactions that have become evident in social media, particularly on Twitter. This paper analyzed #onlineclasses tweets of Filipino users using network analysis through Gephi and NodeXL software. The resulting network has 2,278 users and 998 interactions with many groups of small interactions among users, and low clustering coefficient and modularity values. The users in the top 8 communities in the network talk about the challenges brought about by online classes and the opportunities that online networks offer. Hence, the network of #OnlineClasses tweets can be described as a community cluster. Smaller groups of users who engaged in aspects of online classes emerge in the network, signifying that Filipinos have differing points of view about the topic. Sentiment sharing through social networks provides an avenue for sharing challenges and building communities that help address challenges for online learning in the pandemic.

Resonance free domain for a system of Schrödinger operators with energy-level crossings

We consider a [Formula: see text] system of 1D semiclassical differential operators with two Schrödinger operators in the diagonal part and small interactions of order [Formula: see text] in the off-diagonal part, where [Formula: see text] is a semiclassical parameter and [Formula: see text] is a constant larger than [Formula: see text]. We study the absence of resonance near a non-trapping energy for both Schrödinger operators in the presence of crossings of their potentials. The width of resonances is estimated from below by [Formula: see text] and the coefficient [Formula: see text] is given in terms of the directed cycles of the generalized bicharacteristics induced by two Hamiltonians.

Orthogonal Operators: Applications, Origin and Outlook

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

Orthogonal Operators: Applications, Origin and Outlook

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

Interaction instability of localization in quasiperiodic systems

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Absence of dynamical localization in interacting driven systems

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.

Next-near-neighbour interactions with Al in Li+- and Rb+-exchanged Na+β-aluminas, detected by synchrotron X-ray absorption spectroscopy

Synchrotron X-ray absorption near-edge structure (XANES) spectroscopy studies have been carried out on the electronic and crystal structure environments around the Al atom in Na+β-alumina and in two β-aluminas with Na+exchanged by Li+and Rb+. The aim is to define the type of interaction, if any, existing between the Al located in the `spinel block' and the fast-conducting cations in the `conduction plane'. Na+β′′-alumina has also been studied for comparison. All β-alumina spectra differ from that of α-alumina (corundum) by showing additional features due to the presence of tetrahedral Al. Moreover, they all show a much greater degree of local disorder. There are definite, but small, interactions between tetrahedral Al (and, possibly, also octahedral Al) in the `spinel block' and the Na+and Rb+cations in the `conduction plane'; Na+and Rb+β-aluminas have similar AlK-edge XANES features, but with intensities that change in relation to the weight of the `conduction plane' atom. Despite differences in composition and structure, Na+β′′-alumina shows the same behaviour, thus confirming the substantial similarity of the Al local environments. Li+-exchanged β-alumina has an AlK-edge XANES spectrum that apparently differs from all others, but actually conveys the same basic information. Indeed, interaction between Al and Li is much greater than in any other β-alumina because Li+moves laterally off the `conduction plane' to become close to a facing tetrahedral Al, and strongly interacts with it. Thus, this study also draws attention to the fact that β-aluminas react differently to alkali exchange.