Genesis of the Floquet Hofstadter butterfly

We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Hofstadter spectrum is analyzed for different regimes of the driving frequency. For lower frequencies, resonances of various copies of the spectrum lead to intricate formations of topological gaps. In the Landau-level regime, new wing-like gaps emerge upon reducing the driving frequency, thus revealing the possibility of dynamically tuning the formation of the Hofstadter butterfly. In this regime, an effective model may be analytically derived, which allows us to retrace the energy levels that exhibit avoided crossings and ultimately lead to gap structures with a wing-like shape. At high frequencies, we find that gaps open for various fluxes at $E=0$, and upon increasing the amplitude of the driving, gaps also close and reopen at other energies. The topological invariants of these gaps are calculated and the resulting spectrum is elucidated. We suggest opportunities for experimental realization and discuss similarities with Landau-level structures in non-driven systems.Comment: 8 pages, 4 figure

Cheryl's Birthday

We present four logic puzzles and after that their solutions. Joseph Yeo designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for 'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other knowledge puzzles, and that can also be found on the webpage http://personal.us.es/hvd/lightbulb.html dedicated to the book.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Deep Multi-instance Networks with Sparse Label Assignment for Whole Mammogram Classification

Mammogram classification is directly related to computer-aided diagnosis of breast cancer. Traditional methods rely on regions of interest (ROIs) which require great efforts to annotate. Inspired by the success of using deep convolutional features for natural image analysis and multi-instance learning (MIL) for labeling a set of instances/patches, we propose end-to-end trained deep multi-instance networks for mass classification based on whole mammogram without the aforementioned ROIs. We explore three different schemes to construct deep multi-instance networks for whole mammogram classification. Experimental results on the INbreast dataset demonstrate the robustness of proposed networks compared to previous work using segmentation and detection annotations.Comment: MICCAI 2017 Camera Read

The hybrid-order topology of weak topological insulators

We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a hidden crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators.Comment: 10 pages, 5 figure

Estimating the Soil Temperature Profile from a single Depth Observation: A simple Empirical Heatflow Solution

Two field data sets are used to model near-surface soil temperature profiles in a bare soil. It is shown that the commonly used solutions to the heat flow equations by Van Wijk perform well when applied at deeper soil layers, but result in large errors when applied to near surface layers, where more extreme variations in temperature occur. The reason for this is that these approaches do not consider heat sources or sinks below the surface. This paper proposes a new approach for modeling the surface soil temperature profiles from a single observation depth. This approach consists of two parts: 1) modeling an instantaneous ground flux profile based on net radiation and the ground heat flux at 5 cm depth; and 2) use of this ground heat flux profile to extrapolate a single temperature observation to a complete surface temperature profile. The new model is validated under different field and weather conditions showing low RMS errors of 1-3 K for wet to dry conditions. Finally, the proposed model is tested under limitations in input data that are associated with remote sensing applications. It is shown that these limitations result in only small increases in the overall error. This approach may be useful for satellite-based global energy balance applications. Copyright 2008 by the American Geophysical Union

Fermionic statistics in the strongly correlated limit of Density Functional Theory

Exact pieces of information on the adiabatic connection integrand $W_{\lambda}[\rho]$, which allows to evaluate the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit ($\lambda\to\infty$, where $\lambda$ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the fermionic statistics at large coupling $\lambda$, both numerical and theoretical, confirming that spin effects enter at orders $\sim e^{-\sqrt{\lambda}}$

A Logic of Blockchain Updates

Blockchains are distributed data structures that are used to achieve consensus in systems for cryptocurrencies (like Bitcoin) or smart contracts (like Ethereum). Although blockchains gained a lot of popularity recently, there is no logic-based model for blockchains available. We introduce BCL, a dynamic logic to reason about blockchain updates, and show that BCL is sound and complete with respect to a simple blockchain model

Playing cards with Hintikka An introduction to dynamic epistemic logic

This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in Hintikka’s ‘Knowledge and Belief ’ (1962) give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates