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An instrumentation problem with the signal acquisition at high frequencies was discovered and we no longer believe that the experimental data presented in the manuscript, showing a frequency enhancement of the elastoresistivity, are correct. After correcting the problem, the elastoresistivity data is frequency independent in the range investigated. Therefore, the authors have withdrawn this submission. We would like to thank Alex Hristov, Johanna Palmstrom, Josh Straquadine and Ian Fisher (Stanford) for the kind discussions and assistance we received which helped us identify these problems., Comment: This submission has been withdrawn by the authors, please see abstract for details

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work.

Human visual object recognition is typically rapid and seemingly effortless, as well as largely independent of viewpoint and object orientation. Until very recently, animate visual systems were the only ones capable of this remarkable computational feat. This has changed with the rise of a class of computer vision algorithms called deep neural networks (DNNs) that achieve human-level classification performance on object recognition tasks. Furthermore, a growing number of studies report similarities in the way DNNs and the human visual system process objects, suggesting that current DNNs may be good models of human visual object recognition. Yet there clearly exist important architectural and processing differences between state-of-the-art DNNs and the primate visual system. The potential behavioural consequences of these differences are not well understood. We aim to address this issue by comparing human and DNN generalisation abilities towards image degradations. We find the human visual system to be more robust to image manipulations like contrast reduction, additive noise or novel eidolon-distortions. In addition, we find progressively diverging classification error-patterns between humans and DNNs when the signal gets weaker, indicating that there may still be marked differences in the way humans and current DNNs perform visual object recognition. We envision that our findings as well as our carefully measured and freely available behavioural datasets provide a new useful benchmark for the computer vision community to improve the robustness of DNNs and a motivation for neuroscientists to search for mechanisms in the brain that could facilitate this robustness., Comment: updated article with reference to resulting publication (Geirhos et al, NeurIPS 2018)

We prove that there are no effective or anti-effective classes of square -1 or -2 arising from nodal curves on smooth algebraic surfaces by way of divisibility. This general fact has interesting applications to Enriques and K3 surfaces. The proof relies on specific properties of root lattices and their duals., Comment: 8 pages

Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed. If matrices are sparse, with application-specific sparsity patterns, the optimal implementation remains an open question. Here, we explore the performance of communication reducing 2.5D algorithms and one-sided MPI communication in the context of linear scaling electronic structure theory. In particular, we extend the DBCSR sparse matrix library, which is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. The library is specifically designed to efficiently perform block-sparse matrix-matrix multiplication of matrices with a relatively large occupation. Here, we compare the performance of the original implementation based on Cannon's algorithm and MPI point-to-point communication, with an implementation based on MPI one-sided communications (RMA), in both a 2D and a 2.5D approach. The 2.5D approach trades memory and auxiliary operations for reduced communication, which can lead to a speedup if communication is dominant. The 2.5D algorithm is somewhat easier to implement with one-sided communications. A detailed description of the implementation is provided, also for non ideal processor topologies, since this is important for actual applications. Given the importance of the precise sparsity pattern, and even the actual matrix data, which decides the effective fill-in upon multiplication, the tests are performed within the CP2K package with application benchmarks. Results show a substantial boost in performance for the RMA based 2.5D algorithm, up to 1.80x, which is observed to increase with the number of involved processes in the parallelization., Comment: In Proceedings of PASC '17, Lugano, Switzerland, June 26-28, 2017, 10 pages, 4 figures

DeConvNet, Guided BackProp, LRP, were invented to better understand deep neural networks. We show that these methods do not produce the theoretically correct explanation for a linear model. Yet they are used on multi-layer networks with millions of parameters. This is a cause for concern since linear models are simple neural networks. We argue that explanation methods for neural nets should work reliably in the limit of simplicity, the linear models. Based on our analysis of linear models we propose a generalization that yields two explanation techniques (PatternNet and PatternAttribution) that are theoretically sound for linear models and produce improved explanations for deep networks.

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but featuring novel aspects. Contracting the given rational curves, one can derive algebraic surfaces with isolated ADE-singularities and trivial canonical bundle whose Q_l-cohomology equals that of a projective plane. Similar existence results are developed for classical Enriques surfaces. We also work out an application to integral models of Enriques surfaces (and K3 surfaces)., Comment: 24 pages; v3: journal version, correcting 20 root types to 19 and ruling out the remaining type 4A_2+A_1 (in new section 11)

Ultrafast perturbations offer a unique tool to manipulate correlated systems due to their ability to promote transient behaviors with no equilibrium counterpart. A widely employed strategy is the excitation of coherent optical phonons, as they can cause significant changes in the electronic structure and interactions on short time scales. Here, we explore a promising alternative route: the non-equilibrium excitation of acoustic phonons. We demonstrate that it leads to the remarkable phenomenon of a momentum-dependent temperature, by which electronic states at different regions of the Fermi surface are subject to distinct local temperatures. Such an anisotropic electronic temperature can have a profound effect on the delicate balance between competing ordered states in unconventional superconductors, opening a novel avenue to control correlated phases., Comment: 9 pages, 3 figures + supplementary

Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dimensions. The compensated Hall effect in confined geometry is always accompanied by electron-hole recombination near the sample edges and at large-scale inhomogeneities. As the result, classical edge currents may dominate the resistance in the vicinity of charge compensation. The effect leads to linear magnetoresistance in two dimensions in a broad range of parameters. In three dimensions, the magnetoresistance is normally quadratic in the field, with the linear regime restricted to rectangular samples with magnetic field directed perpendicular to the sample surface. Finally, we discuss the effects of heat flow and temperature inhomogeneities on the magnetoresistance., Comment: 22 pages, 7 figures, published version

Understanding neural networks is becoming increasingly important. Over the last few years different types of visualisation and explanation methods have been proposed. However, none of them explicitly considered the behaviour in the presence of noise and distracting elements. In this work, we will show how noise and distracting dimensions can influence the result of an explanation model. This gives a new theoretical insights to aid selection of the most appropriate explanation model within the deep-Taylor decomposition framework., Comment: Presented at NIPS 2016 Workshop on Interpretable Machine Learning in Complex Systems

Using conservation of energy - a fundamental property of closed classical and quantum mechanical systems - we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal $\text{mol}^{-1}$ for energies and 1 kcal $\text{mol}^{-1}$ $\text{\AA}^{-1}$ for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.

We give a complete classification of Q_l-cohomology projective planes with isolated ADE-singularities and numerically trivial canonical bundle in odd characteristic. This leads to a beautiful relation with certain Enriques surfaces which parallels the situation in characteristic zero, yet displays intriguing subtleties., Comment: 27 pages; v3: small edits and additions, references updated

When watching the image of a natural scene on a computer screen, observers initially move their eyes towards the center of the image --- a reliable experimental finding termed central fixation bias. This systematic tendency in eye guidance likely masks attentional selection driven by image properties and top-down cognitive processes. Here we show that the central fixation bias can be reduced by delaying the initial saccade relative to image onset. In four scene-viewing experiments we manipulated observers' initial gaze position and delayed their first saccade by a specific time interval relative to the onset of an image. We analyzed the distance to image center over time and show that the central fixation bias of initial fixations was significantly reduced after delayed saccade onsets. We additionally show that selection of the initial saccade target strongly depended on the first saccade latency. Processes influencing the time course of the central fixation bias were investigated by comparing simulations of several dynamic and statistical models. Model comparisons suggest that the central fixation bias is generated by a default activation as a response to the sudden image onset and that this default activation pattern decreases over time. Our results suggest that it may often be preferable to use a modified version of the scene viewing paradigm that decouples image onset from the start signal for scene exploration and explicitly controls the central fixation bias. In general, the initial fixation location and the latency of the first saccade need to be taken into consideration when investigating eye movements during scene viewing.

Nematic order is ubiquitous in liquid crystals and is characterized by a rotational symmetry breaking in an otherwise uniform liquid. Recently a similar phenomenon has been observed in some electronic phases of quantum materials related to high temperature superconductivity, particularly in the Fe-based superconductors. While several experiments have probed nematic fluctuations, they have been primarily restricted to the uniform nematic susceptibility, i.e. q = 0 fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by measuring transverse acoustic phonon modes with wavelengths of up to 25 unit cells in the prototypical Fe-based compound Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. While the slope of the phonon dispersion gives information about the uniform nematic susceptibility, deviations from this linear behavior at finite but small wave-vectors are attributed to finite-momentum nematic fluctuations. Surprisingly, these non-zero q fluctuations lead to a softening of the phonon mode below the superconducting transition temperature, in contrast to the behavior of the phonon velocity at q = 0, which increases below $T_c$. Our work not only establishes a sound method to probe long wavelength nematic fluctuations, but also sheds light on the unique interplay between nematicity and superconductivity in Fe-based compounds.

Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text, and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding quantum many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into quantum-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep tensor neural networks (DTNN), which leads to size-extensive and uniformly accurate (1 kcal/mol) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the DTNN model reveals a classification of aromatic rings with respect to their stability -- a useful property that is not contained as such in the training dataset. Further applications of DTNN for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the high potential of machine learning for revealing novel insights into complex quantum-chemical systems.

In this work, we study the volume ratio of the projective tensor products $\ell^n_p\otimes_{\pi}\ell_q^n\otimes_{\pi}\ell_r^n$ with $1\leq p\leq q \leq r \leq \infty$. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence of our estimates, these spaces allow for a nearly Euclidean decomposition of Kashin type whenever $1\leq p \leq q\leq r \leq 2$ or $1\leq p \leq 2 \leq r \leq \infty$ and $q=2$. Also, from the Bourgain-Milman bound on the volume ratio of Banach spaces in terms of their cotype $2$ constant, we obtain information on the cotype of these $3$-fold projective tensor products. Our results naturally generalize to $k$-fold products $\ell_{p_1}^n\otimes_{\pi}\dots \otimes_{\pi}\ell_{p_k}^n$ with $k\in\mathbb N$ and $1\leq p_1 \leq \dots\leq p_k \leq \infty$., Comment: 21 pages

During scene perception our eyes generate complex sequences of fixations. Predictors of fixation locations are bottom-up factors like luminance contrast, top-down factors like viewing instruction, and systematic biases like the tendency to place fixations near the center of an image. However, comparatively little is known about the dynamics of scanpaths after experimental manipulation of specific fixation locations. Here we investigate the influence of initial fixation position on subsequent eye-movement behavior on an image. We presented 64 colored photographs to participants who started their scanpaths from one of two experimentally controlled positions in the right or left part of an image. Additionally, we computed the images' saliency maps and classified them as balanced images or images with high saliency values on either the left or right side of a picture. As a result of the starting point manipulation, we found long transients of mean fixation position and a tendency to overshoot to the image side opposite to the starting position. Possible mechanisms for the generation of this overshoot were investigated using numerical simulations of statistical and dynamical models. We conclude that inhibitory tagging is a viable mechanism for dynamical planning of scanpaths., Comment: 34 pages with 10 figures submitted to Vision Research. Reviews Received on June 8th, 2016 (Minor Revision). Updated Version will be uploaded within the year 2016

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential importance. Here we propose a maximum-likelihood approach for model analysis in a fully dynamical framework that includes time-ordered experimental data. Our methods can be applied to dynamical models for the prediction of discrete behavior (e.g., movement onsets), in particular, we use a dynamical model of saccade generation in scene viewing as a case study for our approach. For this model, the likelihood function can be computed directly by numerical simulation, which enables more efficient parameter estimation including Bayesian inference to obtain reliable estimates and corresponding credible intervals. Using hierarchical models inference is even possible for individual observers. Furthermore, our likelihood approach can be used to compare different models. In our example, the dynamical framework is shown to outperform non-dynamical statistical models. Additionally, the likelihood based evaluation differentiates model variants, which produced indistinguishable predictions on hitherto used statistics. Our results indicate that the likelihood approach is a promising framework for dynamical cognitive models., Comment: 29 pages, 10 figures, to appear in Psychological Review as a theoretical note

To shed light on the mechanism responsible for the in-plane resistivity anisotropy in the nematic phase of the iron-based superconductors, we investigate the impact of spin fluctuations on the anisotropic AC conductivity. On the one hand, the scattering of electrons off magnetic fluctuations causes an anisotropic scattering rate. On the other hand, the accompanying Fermi velocity renormalization contributes to both the plasma frequency and the scattering rate in antagonistic ways, giving rise to anisotropies in these quantities that exactly cancel each other in the DC limit. As a result, the effective scattering rate changes its sign as function of temperature, but the DC conductivity retains the same sign, in agreement with recent experiments., Comment: 6 pages, 5 pictures

Let K be a field of characteristic 2. We give a geometric proof that there are no smooth quartic surfaces in IP^3 with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic 2., Comment: 16 pages; v2: minor additions and edits, reference to 1604.05836 added

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the nematic/structural transition at $T_{s}\approx$90~K. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below $T_{s}$ and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy in FeSe is dominated by inelastic scattering by anisotropic spin fluctuations.

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices in the symmetric surface area deviation.

We present an effective hydrodynamic theory of electronic transport in graphene in the interaction-dominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account dissipation due to Coulomb interaction and find the viscosity of Dirac fermions in graphene for arbitrary densities. The viscous terms have a dramatic effect on transport coefficients in clean samples at high temperatures. Within linear response, we show that viscosity manifests itself in the nonlocal conductivity as well as dispersion of hydrodynamic plasmons. Beyond linear response, we apply the derived nonlinear hydrodynamics to the problem of hot spot relaxation in graphene., Comment: 17 pages, 5 figures

We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all moduli curves are rational and defined over Q, and we determine all families explicitly using extremal rational elliptic surfaces and Enriques involutions of base change type., Comment: 35 pages; v2: major revision streamlining and clarifying several arguments (esp. Lemma 3.1, Prop. 7.1); main results unchanged

For any odd characteristic p=2 mod 3, we exhibit an explicit automorphism on the supersingular K3 surface of Artin invariant one which does not lift to any characteristic zero model. Our construction builds on elliptic fibrations to produce a closed formula for the automorphism's characteristic polynomial on second cohomology, which turns out to be an irreducible Salem polynomial of degree 22 with coefficients varying with p., Comment: 12 pages, 3 figures; v2: main result improved to Salem degree 22

One of the prime manifestations of an anisotropic electronic state in underdoped cuprates is the in-plane resistivity anisotropy $\Delta\rho\equiv(\rho_{a}-\rho_{b})/\rho_{b}$. Here we use a Boltzmann-equation approach to compute the contribution to $\Delta\rho$ arising from scattering by anisotropic charge and spin fluctuations, which have been recently observed experimentally. While the anisotropy in the charge fluctuations is manifested in the correlation length, the anisotropy in the spin fluctuations emerges only in the structure factor. As a result, we find that spin fluctuations favor $\Delta\rho>0$, whereas charge fluctuations promote $\Delta\rho<0$, which are both consistent with the doping dependence of $\Delta\rho$ observed in YBa$_{2}$Cu$_{3}$O$_{7}$. We also discuss the role played by CuO chains in these materials, and propose transport experiments in strained HgBa$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$ to probe directly the different resistivity anisotropy regimes., Comment: 5 pages + Supplementary Material

We develop a hydrodynamic description of transport properties in graphene-based systems which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation we evaluate transport coeffcients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples the macroscopic currents are inhomogeneous which leads to linear magnetoresistance in classically strong fields. Applying our theory to double-layer graphene-based systems, we provide microscopic foundation for phenomenological description of giant magnetodrag at charge neutrality and find magnetodrag and Hall drag in doped graphene., Comment: 23 pages, 3 figures

Two-component systems with equal concentrations of electrons and holes exhibit non-saturating, linear magnetoresistance in classically strong magnetic fields. The effect is predicted to occur in finite-size samples at charge neutrality in both disorder- and interaction-dominated regimes. The phenomenon originates in the excess quasiparticle density developing near the edges of the sample due to the compensated Hall effect. The size of the boundary region is of the order of the electron-hole recombination length that is inversely proportional to the magnetic field. In narrow samples and at strong enough magnetic fields, the boundary region dominates over the bulk leading to linear magnetoresistance. Our results are relevant for semimetals and narrow-band semiconductors including most of the topological insulators., Comment: 11 pages, 3 figures

Over a field k of characteristic 3, we prove that there are no smooth quartic surfaces S in IP^3 with more than 112 lines. Moreover, the surface with 112 lines is projectively equivalent over k-bar to the Fermat quartic. As a key ingredient, we derive a characteristic free upper bound for the number of lines met by a quadric on a smooth quartic surface., Comment: 11 pages; v2: minor edits following referee's comments

We study Enriques surfaces with four A_2-configurations. In particular, we construct open Enriques surfaces with fundamental groups (Z/3Z)^2 x Z/2Z and Z/6Z, completing the picture of the A_2-case from previous work by Keum and Zhang. We also construct an explicit Gorenstein Q-homology projective plane of singularity type A3 + 3A2, supporting an open case from a paper by Hwang, Keum and Ohashi., Comment: 29 pages, 1 figure; v3: Lemma 2.1 added, proof of Lemma 2.3 reorganized and streamlined

In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities.