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A (multi)set of literals, called a clause, is strongly satisfied by an assignment if no literal evaluates to false. Finding an assignment that maximises the number of strongly satisfied clauses is NP-hard. We present a simple algorithm that finds, given a set of clauses that admits an assignment that strongly satisfies a $\rho$-fraction of the clauses, an assignment in which at least a $\rho$-fraction of the clauses is weakly satisfied, in the sense that an even number of literals evaluates to false. In particular, this implies an efficient algorithm for finding an undirected cut of value $\rho$ in a graph given that a directed cut of value $\rho$ in the graph is promised to exist., Comment: subsumes arXiv:2402.07863

Flexoelectricity refers to a linear coupling between the electric polarization and the strain gradient, such as bending or asymmetric compression. This effect is enhanced in nano-scale structures, where grain boundaries or dislocation cores induce the strain gradient. In this study, we theoretically investigate the flexoelectric polarization induced by misfit dislocations in a thin film. A nano-scale dislocation structure is modeled in a periodic SrTiO$_3$ supercell, and then the structure is optimized by using neural-network-potential and first-principles approaches. We point out that a pyramidal TiO$_5$ coordination forms near the dislocation cores, which in turn dominantly causes the sizable flexoelectric polarization., Comment: 5 pages, 4 figures, submitted for publication

Global optimization of crystal compositions is a significant yet computationally intensive method to identify stable structures within chemical space. The specific physical properties linked to a three-dimensional atomic arrangement make this an essential task in the development of new materials. We present a method that efficiently uses active learning of neural network force fields for structure relaxation, minimizing the required number of steps in the process. This is achieved by neural network force fields equipped with uncertainty estimation, which iteratively guide a pool of randomly generated candidates towards their respective local minima. Using this approach, we are able to effectively identify the most promising candidates for further evaluation using density functional theory (DFT). Our method not only reliably reduces computational costs by up to two orders of magnitude across the benchmark systems Si16 , Na8Cl8 , Ga8As8 and Al4O6 , but also excels in finding the most stable minimum for the unseen, more complex systems Si46 and Al16O24 . Moreover, we demonstrate at the example of Si16 that our method can find multiple relevant local minima while only adding minor computational effort.

We present an analysis of a stellar occultation event caused by a near-Earth asteroid (98943) 2001 CC21, an upcoming flyby target in the Hayabusa2 extended mission, on March 5, 2023. To accurately determine the asteroid's shape from diffraction-affected light curves, we developed a novel data reduction technique named the Diffracted Occultation's United Simulator for Highly Informative Transient Explorations (DOUSHITE). Using DOUSHITE-generated synthetic models, we derived constraints on (98943) 2001 CC21's shadow shape from the single-chord occultation data. Our results suggest a significant elongation of the shadow with an axis ratio of $b/a = 0.37\pm0.09$. This shape can be crucial for planning Hayabusa2's high-speed flyby to optimise the limited imaging opportunities., Comment: 10 pages, 9 figures, PASJ accepted

We introduce a versatile machine-learning scheme for predicting dipole moments of molecular liquids to study dielectric properties. We attribute the center of mass of Wannier functions, called Wannier centers, to each chemical bond and create neural network models that predict the Wannier centers for each chemical bond. Application to liquid methanol and ethanol shows that our neural network models successfully predict the dipole moment of various liquid configurations in close agreement with DFT calculations. We show that the dipole moment and dielectric constant in the liquids are greatly enhanced by the polarization of Wannier centers due to local intermolecular interactions. The calculated dielectric spectra agree well with experiments quantitatively over terahertz (THz) to infrared regions. Furthermore, we investigate the physical origin of THz absorption spectra of methanol, confirming the importance of translational and librational motions. Our method is applicable to other molecular liquids and can be widely used to study their dielectric properties.

Given a (multi)graph $G$ which contains a bipartite subgraph with $\rho$ edges, what is the largest triangle-free subgraph of $G$ that can be found efficiently? We present an SDP-based algorithm that finds one with at least $0.8823 \rho$ edges, thus improving on the subgraph with $0.878 \rho$ edges obtained by the classic Max-Cut algorithm of Goemans and Williamson. On the other hand, by a reduction from Hastad's 3-bit PCP we show that it is NP-hard to find a triangle-free subgraph with $(25 / 26 + \epsilon) \rho \approx (0.961 + \epsilon) \rho$ edges. As an application, we classify the Maximum Promise Constraint Satisfaction Problem MaxPCSP($G$,$H$) for all bipartite $G$: Given an input (multi)graph $X$ which admits a $G$-colouring satisfying $\rho$ edges, find an $H$-colouring of $X$ that satisfies $\rho$ edges. This problem is solvable in polynomial time, apart from trivial cases, if $H$ contains a triangle, and is NP-hard otherwise., Comment: Subsumes a part of arXiv:2311.00440

Antiferromagnetic topological insulators (AF TIs) are predicted to exhibit exotic physical properties such as gigantic optical and topological magnetoelectric responses. While a key to achieving such phenomena relies on how to break the symmetry protecting the Dirac-cone surface state (SS) and acquire the mass of Dirac fermions, the mechanism has yet to be clarified. To address this issue, we carried out micro-focused angle-resolved photoemission spectroscopy for GdBi hosting the type-II AF order, and uncovered the stripe-type 2$\times$1 reconstruction of the Fermi surface associated with the AF band folding. Intriguingly, in contrast to NdBi with the type-I AF order displaying the surface-selective Dirac-fermion mass, GdBi shows massless behavior irrespective of AF domains due to the robust topological protection. These results strongly suggest a crucial role of the ThetaTD (time-reversal and translational) symmetry to create the Dirac-fermion mass in AF TIs., Comment: 21 pages, 6 figures

A linearly ordered (LO) $k$-colouring of a hypergraph assigns to each vertex a colour from the set $\{0,1,\ldots,k-1\}$ in such a way that each hyperedge has a unique maximum element. Barto, Batistelli, and Berg conjectured that it is NP-hard to find an LO $k$-colouring of an LO 2-colourable 3-uniform hypergraph for any constant $k\geq 2$ [STACS'21] but even the case $k=3$ is still open. Nakajima and \v{Z}ivn\'{y} gave polynomial-time algorithms for finding, given an LO 2-colourable 3-uniform hypergraph, an LO colouring with $O^*(\sqrt{n})$ colours [ICALP'22] and an LO colouring with $O^*(\sqrt[3]{n})$ colours [ACM ToCT'23]. Very recently, Louis, Newman, and Ray gave an SDP-based algorithm with $O^*(\sqrt[5]{n})$ colours. We present two simple polynomial-time algorithms that find an LO colouring with $O(\log_2(n))$ colours, which is an exponential improvement., Comment: This paper is a merger of independent work by H{\aa}stad and Martinsson, and by Nakajima and \v{Z}ivn\'y respectively. A full, slightly improved version of an APPROX'24 paper. A discussion of related work on unique-maximum colourings and other similar notions

Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming Khot's Unique Games Conjecture [SICOMP'07]. In the problem of maximum cuts in directed graphs (Max-DiCut), in which we seek as many edges going from one particular side of the cut to the other, the situation is more complicated but the recent work of Brakensiek, Huang, Potechin, and Zwick showed that their 0.874-approximation algorithm is tight under the Unique Games Conjecture (up to a small delta)[FOCS'23]. We consider a promise version of the problem and design an SDP-based algorithm which, if given a directed graph G that has a directed cut of value rho, finds an undirected cut in G (ignoring edge directions) with value at least \rho., Comment: Subsumed by arXiv:2409.07837

A linearly ordered (LO) $k$-colouring of a hypergraph is a colouring of its vertices with colours $1, \dots, k$ such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO $k$-colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the `linearly ordered chromatic number' of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO $3$-colourable, and the case that it is not even LO $4$-colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opr\v{s}al, Wrochna, and \v{Z}ivn\'y (2023)., Comment: full version of a paper accepted to STACS 2024 (Track A)

We present polynomial-time SDP-based algorithms for the following problem: For fixed $k \leq \ell$, given a real number $\epsilon>0$ and a graph $G$ that admits a $k$-colouring with a $\rho$-fraction of the edges coloured properly, it returns an $\ell$-colouring of $G$ with an $(\alpha \rho - \epsilon)$-fraction of the edges coloured properly in polynomial time in $G$ and $1 / \epsilon$. Our algorithms are based on the algorithms of Frieze and Jerrum [Algorithmica'97] and of Karger, Motwani and Sudan [JACM'98]. When $k$ is fixed and $\ell$ grows large, our algorithm achieves an approximation ratio of $\alpha = 1 - o(1 / \ell)$. When $k, \ell$ are both large, our algorithm achieves an approximation ratio of $\alpha = 1 - 1 / \ell + 2 \ln \ell / k \ell - o(\ln \ell / k \ell) - O(1 / k^2)$; if we fix $d = \ell - k$ and allow $k, \ell$ to grow large, this is $\alpha = 1 - 1 / \ell + 2 \ln \ell / k \ell - o(\ln \ell / k \ell)$. By extending the results of Khot, Kindler, Mossel and O'Donnell [SICOMP'07] to the promise setting, we show that for large $k$ and $\ell$, assuming Khot's Unique Games Conjecture (\UGC), it is \NP-hard to achieve an approximation ratio $\alpha$ greater than $1 - 1 / \ell + 2 \ln \ell / k \ell + o(\ln \ell / k \ell)$, provided that $\ell$ is bounded by a function that is $o(\exp(\sqrt[3]{k}))$. For the case where $d = \ell - k$ is fixed, this bound matches the performance of our algorithm up to $o(\ln \ell / k \ell)$. Furthermore, by extending the results of Guruswami and Sinop [ToC'13] to the promise setting, we prove that it is \NP-hard to achieve an approximation ratio greater than $1 - 1 / \ell + 8 \ln \ell / k \ell + o(\ln \ell / k \ell)$, provided again that $\ell$ is bounded as before (but this time without assuming the \UGC).

Quantum oscillations in magnetic torque and electrical resistivity were measured to investigate the electronic structure of \b{eta}-ReO2, a candidate hourglass nodal chain metal (Dirac loop chain metal). All the de Haas-van Alphen oscillation branches measured at 30 mK in magnetic fields of up to 17.5 T were consistent with first-principles calculations predicting four Fermi surfaces (FSs). The small-electron FS of the four FSs exhibited a very small cyclotron mass, 0.059 times that of the free electrons, which is likely to be related to the linear dispersion of the energy band. The consistency between the quantum oscillation results and band calculations indicates the presence of the hourglass nodal chain predicted for \b{eta}-ReO2 in the vicinity of the Fermi energy., Comment: 11 pages, 8 figures, 2 tables

Solid-state methods for cooling and heating promise a more sustainable alternative to current compression cycles of greenhouse gases and inefficient fuel-burning heaters. Barocaloric effects (BCE) driven by hydrostatic pressure ($p$) are especially encouraging in terms of large adiabatic temperature changes ($|\Delta T| \sim 10$ K) and colossal isothermal entropy changes ($|\Delta S| \sim 100$ JK$^{-1}$kg$^{-1}$). However, BCE typically require large pressure shifts due to irreversibility issues, and sizeable $|\Delta T|$ and $|\Delta S|$ seldom are realized in a same material. Here, we demonstrate the existence of colossal and reversible BCE in LiCB$_{11}$H$_{12}$, a well-known solid electrolyte, near its order-disorder phase transition at $\approx 380$ K. Specifically, for $\Delta p \approx 0.23$ $(0.10)$ GPa we measured $|\Delta S_{\rm rev}| = 280$ $(200)$ JK$^{-1}$kg$^{-1}$ and $|\Delta T_{\rm rev}| = 32$ $(10)$ K, which individually rival with state-of-the-art barocaloric shifts obtained under similar pressure conditions. Furthermore, over a wide temperature range, pressure shifts of the order of $0.1$ GPa yield huge reversible barocaloric strengths of $\approx 2$ JK$^{-1}$kg$^{-1}$MPa$^{-1}$. Molecular dynamics simulations were carried out to quantify the role of lattice vibrations, molecular reorientations and ion diffusion on the disclosed colossal BCE. Interestingly, lattice vibrations were found to contribute the most to $|\Delta S|$ while the diffusion of lithium ions, despite adding up only slightly to the accompanying entropy change, was crucial in enabling the molecular order-disorder phase transition. Our work expands the knowledge on plastic crystals and should motivate the investigation of BCE in a variety of solid electrolytes displaying ion diffusion and concomitant molecular orientational disorder., Comment: 13 pages, 7 figures

The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we investigate this constraint satisfaction problem in a regime where the promise is weakened from either side by a rainbow-free structure, and establish a complexity dichotomy for the resulting class of computational problems., Comment: Full version of a LICS 2024 paper; v2 has a different title, abstract, and introduction

We calculate the lattice dielectric function of strongly anharmonic rutile $\mathrm{TiO}_2$ from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the $\Gamma$ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the $\Gamma$ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as much as the third-order anharmonic term to phonon linewidths. Furthermore, incorporating the frequency dependence of phonon linewidth reveals that experimentally known but unidentified peaks of the dielectric function are due to two-phonon process. This work emphasizes the importance of a self-consistent approach in predicting the optical properties of highly anharmonic materials., Comment: 12 pages, 10 figures

The complexity of the promise constraint satisfaction problem $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ is largely unknown, even for symmetric $\mathbf{A}$ and $\mathbf{B}$, except for the case when $\mathbf{A}$ and $\mathbf{B}$ are Boolean. First, we establish a dichotomy for $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ where $\mathbf{A}, \mathbf{B}$ are symmetric, $\mathbf{B}$ is functional (i.e. any $r-1$ elements of an $r$-ary tuple uniquely determines the last one), and $(\mathbf{A},\mathbf{B})$ satisfies technical conditions we introduce called dependency and additivity. This result implies a dichotomy for $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ with $\mathbf{A},\mathbf{B}$ symmetric and $\mathbf{B}$ functional if (i) $\mathbf{A}$ is Boolean, or (ii) $\mathbf{A}$ is a hypergraph of a small uniformity, or (iii) $\mathbf{A}$ has a relation $R^{\mathbf{A}}$ of arity at least 3 such that the hypergraph diameter of $(A, R^{\mathbf{A}})$ is at most 1. Second, we show that for $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$, where $\mathbf{A}$ and $\mathbf{B}$ contain a single relation, $\mathbf{A}$ satisfies a technical condition called balancedness, and $\mathbf{B}$ is arbitrary, the combined basic linear programming relaxation (BLP) and the affine integer programming relaxation (AIP) is no more powerful than the (in general strictly weaker) AIP relaxation. Balanced $\mathbf{A}$ include symmetric $\mathbf{A}$ or, more generally, $\mathbf{A}$ preserved by a transitive permutation group., Comment: Full version (with stronger results) of a LICS'23 paper

The origin of the phase stability of 18$R$ Mg-Zn-Y alloys with a long-period stacking order (LPSO) is studied using first-principles calculations. We calculate the heat of formation as a function of the number of Zn vacancies to discuss the role of Zn atoms. The calculated convex hull indicates that the Zn atoms in the LPSO alloys are stable even if they number about half of the Y atoms. The bonding state with Zn $p$ orbitals leads to the stability of the LPSO structure because the partial density of states of Mg nearest to the solute cluster forms a valley structure.

NaAlSi and NaAlGe are isostructural and isoelectronic semimetals with topological nodal lines close to the Fermi level. Despite having virtually identical electronic structures, NaAlSi exhibits superconductivity below Tc = 6.8 K, whereas NaAlGe does not. We investigate NaAlGe by measuring its electrical resistivity, Hall effect, magnetic susceptibility, and heat capacity using single crystals. It is revealed that NaAlGe is not a simple semimetal but rather has an unusual ground state with a small pseudogap of approximately 100 K close to the Fermi level. We argue that the formation of the pseudogap in NaAlGe is due to an unexpected Fermi surface instability, such as an excitonic instability, as opposed to the electron-phonon instability that leads to the formation of the superconducting gap in NaAlSi., Comment: 6 pages, 5 figures

A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ldots, k \}$ to every vertex so that, in every edge, the (multi)set of colours has a unique maximum. Equivalently, for $r=3$, if two vertices in an edge are assigned the same colour, then the third vertex is assigned a larger colour (as opposed to a different colour, as in classic non-monochromatic colouring). Barto, Battistelli, and Berg [STACS'21] studied LO colourings on $3$-uniform hypergraphs in the context of promise constraint satisfaction problems (PCSPs). We show two results. First, given a 3-uniform hypergraph that admits an LO $2$-colouring, one can find in polynomial time an LO $k$-colouring with $k=O(\sqrt[3]{n \log \log n / \log n})$. Second, given an $r$-uniform hypergraph that admits an LO $2$-colouring, we establish NP-hardness of finding an LO $k$-colouring for every constant uniformity $r\geq k+2$. In fact, we determine relationships between polymorphism minions for all uniformities $r\geq 3$, which reveals a key difference between $r

The cathode properties of Na2MTiO4 (M: transition-metal element) are investigated by means of density-functional-theory calculations. The stability between the layered structure and the disordered structure are focused in comparison with the Li2MTiO4 prototypical case. It is found that the layered structure is more stable than the disordered structure in Na2MTiO4 while those structure shows the similar stability in Li2MTiO4. In layered-structure Na2MTiO4, the formation enthalpies at the intermediate compounds during charge/discharge reactions are significantly low, leading to the unstable voltage-capacity profiles. A machine-learning analysis reveals that the total-energy difference between these structures can be described by a simple function of ionic radii., Comment: 5 pages, 7 figures, submitted for publication

It is well known that the temperature dependence of the effective magnetocrystalline anisotropy energy obeys the $l(l+1)/2$ power law of magnetization in the Callen-Callen theory. Therefore, according to the Callen-Callen theory, the magnetocrystalline anisotropy energy is assumed to be zero at the critical temperature where the magnetization is approximately zero. This study estimates the temperature dependence of the magnetocrystalline anisotropy energy by integrating the magnetization versus magnetic field ($M$--$H$) curves, and found that the magnetocrystalline anisotropy is still finite even above the Curie temperature in the uniaxial anisotropy, whereas this does not appear in the cubic anisotropy case. The origin is the fast reduction of the anisotropy field, which is the magnetic field required to saturate the magnetization along the hard axis, in the case of cubic anisotropy. Therefore, the magnetization anisotropy and anisotropic magnetic susceptibility, those are the key factors of magnetic anisotropy, could not be established in the case of cubic anisotropy. In addition, the effect of magnetocrystalline anisotropy on magnetocaloric properties, as the difference between the entropy change curves of AlFe$_{2}$B$_{2}$ appears above the Curie temperature, which is in good agreement with a previous experimental study. This is proof of magnetic anisotropy at slightly above Curie temperature.

CrI$_{3}$ is considered to be a promising candidate for spintronic devices and data storage. We derived the Heisenberg Hamiltonian for CrI$_{3}$ from density functional calculations using the Liechtenstein formula. Moreover, the Monte--Carlo simulations with the Sucksmith--Thompson method were performed to analyze the effect of magnetic anisotropy energy on the thermodynamic properties. Our method successfully reproduced the negative sign of isothermal magnetic entropy changes when a magnetic field was applied along the hard plane. We found that the temperature dependence of the magnetocrystalline anisotropy energy is not negligible at temperatures slightly above the Curie temperature. We clarified that the origin of this phenomenon is attributed to anisotropic magnetic susceptibility and magnetization anisotropy. The difference between the entropy change of the easy axis and the hard plane is proportional to the temperature dependence of the magnetic anisotropy energy, implying that the anisotropic entropy term is the main source of the temperature dependence of the free energy difference when magnetizing in a specific direction other than the easy axis. We also investigated the magnetic susceptibility that can be used for the characterization of the negative sign of the entropy change in the case of a hard plane. The competition of magnetocrystalline anisotropy energy and external magnetic field at low temperature and low magnetic field region causes a high magnetic susceptibility as the fluctuation of magnetization. Meanwhile, the anisotropy energy is suppressed at a sufficient magnetic field applied along the hard axis, the magnetization is fully rotated to the direction of the external magnetic field.

Honeycomb layered oxides constitute an emerging class of materials that show interesting physicochemical and electrochemical properties. However, the development of these materials is still limited. Here, we report the combined use of alkali atoms ($\rm Na$ and $\rm K$) to produce a mixed alkali honeycomb layered oxide material, namely, $\rm NaKNi_2TeO_6$. Via transmission electron microscopy measurements, we reveal the local atomic structural disorders characterised by aperiodic stacking and incoherency in the alternating arrangement of $\rm Na$ and $\rm K$ atoms. We also investigate the possibility of mixed electrochemical transport and storage of $\rm Na$ and $\rm K$ ions in $\rm NaKNi_2TeO_6$. In particular, we report an average discharge cell voltage of about $4\, \rm V$ and a specific capacity of around $80\, \rm mAh\, g^{-1}$ at low specific currents (i.e., $< 10\, \rm mA\, g^{-1}$) when a $\rm NaKNi_2TeO_6$-based positive electrode is combined with a room-temperature $\rm NaK$ liquid alloy negative electrode using an ionic liquid-based electrolyte solution. These results represent a step towards the use of tailored cathode active materials for dendrite-free electrochemical energy storage systems exploiting room-temperature liquid alkali metal alloy materials., Comment: 39 Pages, 7 Figures, 1 Cover Art