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Ferroelectricity can exist in elemental phases as a result of charge transfers between atoms occupying inequivalent Wyckoff positions. We investigate the emergence of ferroelectricity in two-dimensional elemental materials with buckled honeycomb lattices. Various multi-bilayer structures hosting ferroelectricity are designed by stacking-engineering. Ferroelectric materials candidates formed by group IV and V elements are predicted theoretically. Ultrathin Bi films show layer-stacking-dependent physical properties of ferroelectricity, topology, and metallicity. The two-bilayer Bi film with a polar stacking sequence is found to be an elemental topological ferroelectric material. Three and four bilayers Bi films with polar structures are ferroelectric-like elemental polar metals with topological nontrivial edge states. For Ge and Sn, trivial elemental polar metals are predicted. Our work reveals the possibility of design two-dimensional elemental topological ferroelectrics and polar metals by stacking-engineering., Comment: 18 pages, 6 figures

Multiferroics are materials with a coexistence of magnetic and ferroelectric order allowing the manipulation of magnetism by applications of an electric field through magnetoelectric coupling effects. Here we propose an idea to design a class of multiferroics with a $d^9$ configuration using the magnetic order in copper-oxygen layers appearing in copper oxide high-temperature superconductors by inducing ferroelectricity. Copper-based charge transfer multiferroics SnCuO2 and PbCuO2 having the inversion symmetry breaking $P4mm$ polar space group are predicted to be such materials. The active inner s electrons in Sn and Pb hybridize with O $2p$ states leading the buckling in copper-oxygen layers and thus induces ferroelectricity, which is known as the lone pair mechanism. As a result of the $d^9$ configuration, SnCuO2 and PbCuO2 are charge transfer insulators with the antiferromagnetic ground state of the moment on Cu retaining some strongly correlated physical properties of parent compounds of copper oxide high-temperature superconductors. Our work reveals the possibility of designing multiferroics based on copper oxide high-temperature superconductors., Comment: 18 pages, 5 figures, 1 table

Motivated by the recently discovered superconductivity in Sr-doped nickelate oxides NdNiO$_2$, we predict a material BiNiO$_2$ that provides an opportunity to study the intertwined ferroelectricity, metallicity, and magnetism in a crystal with very simple atomic structures. There is a ferroelectric structural transition from the nonpolar phase with the P4/mmm space group to the polar phase with the P4mm space group, which is driven by the lone pair on Bi. Calculations based on the Heyd-Scuseria-Ernzerhof hybrid density functional reveal that both the nonmagnetic and ferromagnetic states are metallic for nonpolar and polar phases, while the lowest energy ground-state for polar BiNiO$_2$ is a Hubbard Mott insulator with the G-type antiferromagnetic spin configurations. As a ferroelectric material with an electric polarization of 0.49 C/m2, it may be possible to control the magnetic order in BiNiO$_2$ by an applied electric field. The replacement of Nd by Bi serves as a connecting link between a high-temperature superconductor and a Mott multiferroic. Our work supports a route towards strongly correlated ferroelectrics., Comment: 20 pages, 9 figures, 3 tables

Despite the huge advancement in knowledge discovery and data mining techniques, the X-ray diffraction (XRD) analysis process has mostly remained untouched and still involves manual investigation, comparison, and verification. Due to the large volume of XRD samples from high-throughput XRD experiments, it has become impossible for domain scientists to process them manually. Recently, they have started leveraging standard clustering techniques, to reduce the XRD pattern representations requiring manual efforts for labeling and verification. Nevertheless, these standard clustering techniques do not handle problem-specific aspects such as peak shifting, adjacent peaks, background noise, and mixed phases; hence, resulting in incorrect composition-phase diagrams that complicate further steps. Here, we leverage data mining techniques along with domain expertise to handle these issues. In this paper, we introduce an incremental phase mapping approach based on binary peak representations using a new threshold based fuzzy dissimilarity measure. The proposed approach first applies an incremental phase computation algorithm on discrete binary peak representation of XRD samples, followed by hierarchical clustering or manual merging of similar pure phases to obtain the final composition-phase diagram. We evaluate our method on the composition space of two ternary alloy systems- Co-Ni-Ta and Co-Ti-Ta. Our results are verified by domain scientists and closely resembles the manually computed ground-truth composition-phase diagrams. The proposed approach takes us closer towards achieving the goal of complete end-to-end automated XRD analysis., Comment: Accepted and presented at the International Workshop on Domain-Driven Data Mining (DDDM) as a part of the SIAM International Conference on Data Mining (SDM 2021). Contains 11 pages and 5 figures

In this paper, we studied the metric mean dimension in Feldman-Katok(FK for short) metric. We introduced the notions of FK-Bowen metric mean dimension and FK-Packing metric mean dimension on subset. And we established two variational principles.

Pedestrian dead reckoning is a challenging task due to the low-cost inertial sensor error accumulation. Recent research has shown that deep learning methods can achieve impressive performance in handling this issue. In this letter, we propose inertial odometry using a deep learning-based velocity estimation method. The deep neural network based on Res2Net modules and two convolutional block attention modules is leveraged to restore the potential connection between the horizontal velocity vector and raw inertial data from a smartphone. Our network is trained using only fifty percent of the public inertial odometry dataset (RoNIN) data. Then, it is validated on the RoNIN testing dataset and another public inertial odometry dataset (OXIOD). Compared with the traditional step-length and heading system-based algorithm, our approach decreases the absolute translation error (ATE) by 76%-86%. In addition, compared with the state-of-the-art deep learning method (RoNIN), our method improves its ATE by 6%-31.4%.

Let $(X, T)$ be a weakly mixing minimal system, $p_1, \cdots, p_d$ be integer-valued generalized polynomials and $(p_1,p_2,\cdots,p_d)$ be non-degenerate. Then there exists a residual subset $X_0$ of $X$ such that for all $x\in X_0$ $$\{ (T^{p_1(n)}x, \cdots, T^{p_d(n)}x): n\in \mathbb{Z}\}$$ is dense in $X^d$., Comment: 27 pages

In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dynamical system, we define measure-theoretical restricted asymptotic rate with respect to sensitivity, and obtain that it equal to the reciprocal of the Brin-Katok local entropy for almost every point. For topological version we have similar definitions and conclusions.