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Given two finite abstract simplicial complexes A and B, one can define a new simplicial complex on the set of simplicial maps from A to B. After adding two technicalities, we call this complex Homsc(A, B). We prove the following dichotomy: For a fixed finite abstract simplicial complex B, either Homsc(A, B) is always a disjoint union of contractible spaces or every finite CW-complex can be obtained up to a homotopy equivalence as Homsc(A, B) by choosing A in a right way. We furthermore show that the first case is equivalent to the existence of a nontrivial social choice function and that in this case, the space itself is homotopy equivalent to a discrete set. Secondly, we give a generalization to finite relational structures and show that this dichotomy coincides with a complexity theoretic dichotomy for constraint satisfaction problems, namely in the first case, the problem is in P and in the second case NP-complete. This generalizes a result from [SW24] respectively arXiv:2307.03446 [cs.CC]

On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively definable relations are a natural intermediate concept which extends primitive positive definability by infinite conjunctions. We consider for every convex set $S\subset \mathbb{R}^n$ the structure of the real numbers $\mathbb{R}$ with addition, scalar multiplication, constants, and additionally the relation $S$. We prove that depending on $S$, the set of all relations with an infinitary primitive positive definition in this structure equals one out of six possible sets. This dependency gives a natural partition of the convex sets into six nonempty classes. We also give an elementary geometric description of the classes and a description in terms of linear maps. The classification also implies that there is no locally closed clone between the clone of affine combinations and the clone of convex combinations., Comment: 48 pages

Topological defects are ubiquitous, they manifest in a wide variety of systems such as liquid crystals, magnets or superconductors. The recent quest for nonabelian anyons in condensed matter physics stimulates the interest for topological defects since they can be hosted in vortices in quantum magnets or topological superconductors. In addition to these vortex defects, in this study we propose to investigate edge dislocations in 2D magnets as new building blocks for topological physics since they can be described as vortices in the structural phase field. Here we demonstrate the existence of higher order topological dislocations within the higher order moir\'e pattern of the van der Waals 2D magnet CrCl3 deposited on Au(111). Surprizingly, these higher order dislocations arise from ordinary simple edge dislocations in the atomic lattice of CrCl3. We provide a theoretical framework explaining the higher order dislocations as vortex with a winding Chern number of 2. We expect that these original defects could stabilize some anyons either in a 2D quantum magnet or within a 2D superconductor coupled to it.

Epitaxial strain has emerged as a powerful tool to tune magnetic and ferroelectric properties in functional materials such as in multiferroic perovskite oxides. Here, we use first-principles calculations to explore the evolution of magnetic interactions in the antiferromagnetic multiferroic BiFeO$_3$ (BFO), one of the most promising multiferroics for future technology. The epitaxial strain in BFO(001) oriented film is varied between $\varepsilon_{xx,yy}$ $\in$ $[-2\%, +2\%]$. We find that both strengths of the exchange interaction and Dzyaloshinskii-Moriya interaction (DMI) decrease linearly from compressive to tensile strain whereas the uniaxial magnetocrystalline anisotropy follows a parabolic behavior which lifts the energy degeneracy of the (111) easy plane of bulk BFO. From the trends of the magnetic interactions we can explain the destruction of cycloidal order in compressive strain as observed in experiments due to the increasing anisotropy energy. For tensile strain, we predict that the ground state remains unchanged as a function of strain. By using the domain wall (DW) energy, we envision the region where isolated chiral magnetic texture might occur as function of strain i.e. where the DW and the spin spiral energy are equal. This transition between $-1.5\%$ and $-0.5\%$ of strain should allow topologically stable magnetic states such as antiferromagnetic skyrmions and merons to occur. Hence, our work should trigger experimental and theoretical investigations in this range of strain.

Magnetic skyrmions have raised high hopes for future spintronic devices. For many applications it would be of great advantage to have more than one metastable particle-like texture available. The coexistence of skyrmions and antiskyrmions has been proposed in inversion symmetric magnets with exchange frustration. However, so far only model systems have been studied and the lifetime of coexisting metastable topological spin structures has not been obtained. Here, we predict that skyrmions and antiskyrmions with diameters below 10 nm can coexist at zero magnetic field in a Rh/Co bilayer on the Ir(111) surface -- an experimentally feasible system. We show that the lifetimes of metastable skyrmions and antiskyrmions in the ferromagnetic ground state are above one hour for temperatures up to 75 K and 48 K, respectively. The entropic contribution to the nucleation and annihilation rates differs for skyrmions and antiskyrmions. This opens the route to thermally activated creation of coexisting skyrmions and antiskyrmions in frustrated magnets with Dzyaloshinskii-Moriya interaction.

X-ray phase-contrast imaging offers enhanced sensitivity for weakly-attenuating materials, such as breast and brain tissue, but has yet to be widely implemented clinically due to high coherence requirements and expensive x-ray optics. Speckle-based phase contrast imaging has been proposed as an affordable and simple alternative; however, obtaining high-quality phase-contrast images requires accurate tracking of sample-induced speckle pattern modulations. This study introduced a convolutional neural network to accurately retrieve sub-pixel displacement fields from pairs of reference (i.e., without sample) and sample images for speckle tracking. Speckle patterns were generated utilizing an in-house wave-optical simulation tool. These images were then randomly deformed and attenuated to generate training and testing datasets. The performance of the model was evaluated and compared against conventional speckle tracking algorithms: zero-normalized cross-correlation and unified modulated pattern analysis. We demonstrate improved accuracy (1.7 times better than conventional speckle tracking), bias (2.6 times), and spatial resolution (2.3 times), as well as noise robustness, window size independence, and computational efficiency. In addition, the model was validated with a simulated geometric phantom. Thus, in this study, we propose a novel convolutional-neural-network-based speckle-tracking method with enhanced performance and robustness that offers improved alternative tracking while further expanding the potential applications of speckle-based phase contrast imaging.

The electrical control of magnons opens up new ways to transport and process information for logic devices. In magnetoelectrical multiferroics, the Dzyaloshinskii-Moriya (DM) interaction directly allow for such a control and, hence, is of major importance. We determine the origin and the strength of the (converse) spin current DM interaction in the R3c bulk phase of the multiferroic BiFeO3 based on density functional theory. Our data supports only the existence of one DM interaction contribution originating from the spin current model. By exploring then magnon dispersion in the full Brillouin Zone, we show that the exchange is isotropic, but the DM interaction and anisotropy prefer any propagation and any magnetization direction within the full (111) plane. Our work emphasizes the significance of the asymmetric potential induced by the spin current over the structural asymmetry induced by the anionic octahedron in multiferroics such as BiFeO3.

Count data with excessive zeros are often encountered when modelling infectious disease occurrence. The degree of zero inflation can vary over time due to non-epidemic periods as well as by age group or region. The existing endemic-epidemic modelling framework (aka HHH) lacks a proper treatment for surveillance data with excessive zeros as it is limited to Poisson and negative binomial distributions. In this paper, we propose a multivariate zero-inflated endemic-epidemic model with random effects to extend HHH. Parameters of the new zero-inflation and the HHH part of the model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. A simulation study confirms proper convergence and coverage probabilities of confidence intervals. Applying the model to measles counts in the 16 German states, 2005--2018, shows that the added zero-inflation improves probabilistic forecasts.

IEA's International Computer and Information Literacy Study (ICILS) 2018 is designed to assess how well students are prepared for study, work, and life in a digital world. The study measures international differences in students' computer and information literacy (CIL): their ability to use computers to investigate, create, participate, and communicate at home, at school, in the workplace, and in the community. Participating countries also have an option for their students to complete an assessment of computational thinking (CT). The ICILS 2018 user guide describes the content and format of the data in the ICILS 2018 international database. It introduces the use of weighting and variance estimation variables for analyzing the ICILS 2018 data, and provides a comprehensive overview of how to work with IEA's International Database (IDB) Analyzer software. The ICILS 2018 user guide is accompanied by three appendices: the international versions of all questionnaires; an overview of national adaptations to the national versions of the ICILS 2018 international questionnaires; and a comprehensive catalogue of the derived variables used in the ICILS 2018 international report. [This guide was written with contributions from: Sabine Tieck, Sabine Meinck, Oriana Mora, and Wolfram Schulz.]

We use first-principles calculations based on density functional theory to study how the magnetic properties of an Fe monolayer on a W(001) surface -- exhibiting a $c(2 \times 2)$ antiferromagnetic ground state -- can be modified by an additional 4d transition-metal overlayer. To obtain an overview of how the 4d-band filling influences the exchange interactions in the Fe layer we have calculated the energy dispersion of spin spirals for 4d/Fe/2W unsupported quadlayers, in which the W(001)substrate is represented by only two atomic layers. Hybridization with the overlayer leads to a reduced ferromagnetic nearest-neighbor exchange interaction and the next-nearest neighbor exchange gains in strength. Surprisingly, we find that the $c(2 \times 2)$ antiferromagnetic state is unfavorable for all systems with a 4d overlayer. For 4d overlayers from the beginning (Nb) or end (Pd) of the series we find a ferromagnetic ground state. As one moves to the center of the series there is a transition via a spin spiral (Mo, Rh) to a $p (2 \times 1)$ antiferromagnetic ground state (Tc, Ru). We have studied the Mo, Ru, and Pd overlayer on Fe/W(001) representing the surface by a sufficiently large number of W layers to obtain bulk like properties in its center. The energy dispersion of spin spirals show qualitatively the same results as those from the 4\textit{d}/Fe/2W quadlayers. The Dzyaloshinskii-Moriya interaction calculated upon including spin-orbit coupling shows significant strength and considerable frustration effects. The calculated magnetocrystalline anisotropy energy is large as well. All 4d/Fe/W(001) films are potential candidates for complex non-collinear spin structures.

We demonstrate that topological-chiral magnetic interactions can play a key role for magnetic ground states in ultrathin films at surfaces. Based on density functional theory we show that significant chiral-chiral interactions occur in hexagonal Mn monolayers due to large topological orbital moments which interact with the emergent magnetic field. Due to the competition with higher-order exchange interactions superposition states of spin spirals such as the 2Q state or a distorted 3Q state arise. Simulations of spin-polarized scanning tunneling microscopy images suggest that the distorted 3Q state could be the magnetic ground state of a Mn monolayer on Re(0001).

We present a systematic study of higher-order exchange interactions beyond the pair-wise Heisenberg exchange in transition-metal trilayers based on density functional theory calculations. We show that these terms can play an important role in magnetic trilayers composed of a single hexagonal Fe or Co atomic layer sandwiched between $4d$ and $5d$ transition-metal layers. We study the dependence of the biquadratic and the three-site and four-site four spin interaction on the band filling of the $4d$ and $5d$ layers as well as the stacking sequence, i.e. fcc vs. hcp stacking. Our calculations reveal relatively small higher-order interactions for Co based trilayers. For Fe based trilayers with a Rh or Ir layer the higher-order terms can be on the same order of magnitude as pair-wise Heisenberg exchange. The trends obtained for freestanding trilayers are used to understand the higher-order interactions in ultrathin film systems on surfaces that are experimentally accessible. It is shown that hcp Rh/Fe/Ir(111) and hcp-Rh/Fe/Rh(111) exhibit the largest values for the biquadratic and the three-site four spin interaction of all systems under study. We further demonstrate that the three-site four spin interaction is responsible for the experimentally observed change of the magnetic ground state of Rh/Fe/Ir(111) from a spin spiral (single-Q) for fcc-Rh to a 2Q state for hcp-Rh. We find similar trends for Rh/Fe/Rh(111), i.e. replacing the Ir surface by the isoelectronic Rh surface. For Rh/Co/Ir(111), we obtain a negative value for the four-site four spin interaction which will lead to a reduced stability of magnetic skyrmions which are metastable in this film at zero magnetic field. In contrast, for Pd/Fe/Ir(111), the four-site four spin interaction is positive which leads to an enhanced stability of skyrmions.

Metasurfaces allow for the spatiotemporal variation of amplitude, phase, and polarization of optical wavefronts. Implementation of active tunability of metasurfaces promises compact flat optics capable of reconfigurable wavefront shaping. Phase-change materials (PCMs), such as germanium telluride or germanium antimony telluride, are a prominent material class enabling reconfigurable metasurfaces due to their large refractive index change upon structural transition. However, commonly employed laser-induced switching of PCMs limits the achievable feature sizes and thus, restricts device miniaturization. Here, we propose thermal scanning-probe-induced local switching of germanium telluride to realize near-infrared metasurfaces with feature sizes far below what is achievable with diffraction-limited optical switching. Our design is based on a planar multilayer stack and does not require fabrication of protruding dielectric or metallic resonators as commonly applied in the literature. Instead, we numerically demonstrate that a broad-band tuning of perfect absorption could be realized by the localized and controlled tip-induced crystallization of the PCM layer. The spectral response of the metasurface is explained using simple resonance mode analysis and numerical simulations. To facilitate experimental realization, we provide a detailed theoretical description of the tip-induced crystallization employing multiphysics simulations to demonstrate the great potential for fabricating compact reconfigurable metasurfaces. Our concept allows for tunable perfect absorption and can be applied not only for thermal imaging or sensing, but also for spatial frequency filtering., Comment: 7 pages, 4 figures

We experimentally verify the existence of two model-type magnetic ground states which were previously predicted but so far unobserved. We find them in Mn monolayers on the Re(0001) surface using spin-polarized scanning tunneling microscopy. For fcc stacking of Mn the collinear row-wise antiferromagnetic state occurs, whereas for hcp Mn a three-dimensional spin structure appears, which is a superposition of three row-wise antiferromagnetic states and is known as triple-Q state. Density functional theory calculations elucidate the subtle interplay of different magnetic interactions to form these spin structures and provide insight into the role played by relativistic effects., Comment: 5 pages, 4 figures

Superparamagnetic iron oxide nanoparticles (SPIONs) have recently been introduced as information carriers in a testbed for molecular communication (MC) in duct flow. Here, a new receiver for this testbed is presented, based on the concept of a bridge circuit. The capability for a reliable transmission using the testbed and detection of the proposed receiver was evaluated by sending a text message and a 80 bit random sequence at a bit rate of 1/s, which resulted in a bit error rate of 0 %. Furthermore, the sensitivity of the device was assessed by a dilution series, which gave a limit for the detectability of peaks between 0.1 to 0.5 mg/mL. Compared to the commercial susceptometer that was previously used as receiver, the new detector provides an increased sampling rate of 100 samples/s and flexibility in the dimensions of the propagation channel. Furthermore, it allows to implement both single-ended and differential signaling in SPION-bases MC testbeds., Comment: ACM NanoCom 2019

Due to their exceptional topological and dynamical properties magnetic skyrmions - localized stable spin structures on the nanometre scale - show great promise for future spintronic applications. To become technologically competitive, isolated skyrmions with diameters below 10 nm that are stable at zero magnetic field and room temperature are desired. Despite finding skyrmions in a wide spectrum of materials, the quest for a material with these envisioned properties is still ongoing. Here we report zero field isolated skyrmions with diameters smaller than 5 nm coexisting with 1 nm thin domain walls in Rh/Co atomic bilayers on the Ir(111) surface. These spin structures are characterized by spin-polarized scanning tunnelling microscopy and can also be detected using non-spin-polarized tips due to a large non-collinear magnetoresistance. We demonstrate that sub-10 nm skyrmions are stabilised in these ferromagnetic Co films at zero field due to strong frustration of exchange interaction, together with Dzyaloshinskii-Moriya interaction and a large magnetocrystalline anisotropy.

Forecasting the future course of epidemics has always been one of the main goals of epidemic modelling. This chapter reviews statistical methods to quantify the accuracy of epidemic forecasts. We distinguish point and probabilistic forecasts and describe different methods to evaluate and compare the predictive performance across models. Two case studies demonstrate how to apply the different techniques to uni- and multivariate forecasts. We focus on forecasting count time series from routine public health surveillance: weekly counts of influenza-like illness in Switzerland, and age-stratified counts of norovirus gastroenteritis in Berlin, Germany. Data and code for all analyses are available in a supplementary R package., Comment: This is an author-created preprint of a book chapter to appear in the Handbook of Infectious Disease Data Analysis edited by Leonhard Held, Niel Hens, Philip D O'Neill and Jacco Wallinga, Chapman and Hall/CRC, 2019. 19 pages, including 9 figures and 4 tables; supplementary R package 'HIDDA.forecasting' available https://HIDDA.github.io/forecasting/

We show that stable skyrmions with diameters of a few nanometers can emerge in atomic Pd/Fe bilayers on the Rh(111) surface. Based on density functional theory we calculate the exchange and the Dzyaloshinskii-Moriya interaction as well as the magnetocrystalline anisotropy energy. The later two terms are driven by spin-orbit coupling and significantly reduced compared to Pd/Fe bilayers on Ir(111) as expected since Rh and Ir are isoelectronic $4d$ and $5d$ transition-metals. However, there is still a spin spiral ground state at zero magnetic field. Atomistic spin dynamics simulations show that a skyrmion phase occurs at small magnetic fields of $\sim$ 1 T. Skyrmion diameters amount to 2 to 8 nm and skyrmion lifetimes are up to 1 hour at temperatures of 25 to 45 K.

This is a comment on Reinhart's "Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications" (arXiv:1708.02647v1). I contribute some experiences from modelling the spread of infectious diseases. Furthermore, I try to complement the review with regard to the availability of software for the described models, which I think is essential in "paving the way for new uses"., Comment: comment on arXiv:1708.02647v1, submitted to Statistical Science, 4 pages

We use spin-polarized scanning tunneling microscopy and density functional theory (DFT) to study domain walls (DWs) and the Dzyaloshinskii-Moriya interaction (DMI) in epitaxial films of Co/Ir(111) and Pt/Co/Ir(111). Our measurements reveal DWs with fixed rotational sense on one monolayer of Co on Ir, with a wall width around 2.7 nm. With Pt islands on top, we observe that the DWs occur mostly in the uncovered Co/Ir areas, suggesting that the wall energy density is higher in the Pt/Co/Ir(111). From DFT we find an interfacial DMI that stabilizes N\'{e}el-type DWs with clockwise rotational sense. The calculated DW widths are in good agreement with the experimental observations. The total DMI nearly doubles from Co/Ir(111) to Pt/Co/Ir(111), however, in the latter case the DMI is almost entirely due to the Pt with only a minor Ir contribution. Therefore a simple additive effect, where both interfaces contribute significantly to the total DMI, is not observed for one atomic Co layer., Comment: 5 pages, 4 figures, 1 table