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In this article, the authors give the correct answer to the following problem, which is presented in the well-known problem book "CHALLENGING MATHEMATICAL PROBLEMS WITH ELEMENTARY SOLUTIONS"? by A. M. Yaglom and L. M. Yaglom. There are six long blades of grass with the ends protruding above and below, and you will tie together the six upper ends in pairs and then tie together the six lower ends in pairs. What is the probability that a ring will be formed when the blades of grass are tied at random in this fashion? The solution in the above book needs to be corrected, and we will present a correct answer in this article. Therefore, we are the first persons to present a correct?answer to a problem in a book published in the USSR? in 1954. By following the original idea of this problem book, we present the correct answer without using knowledge of higher knowledge, although we used a very basic knowledge of the Knot theory.

Rich spontaneous symmetry-breaking phenomena with nontrivial quantum geometric properties in metals represent central issues in condensed matter physics. The emergence of chiral loop-current order, accompanied by time-reversal symmetry (TRS) breaking in various kagome metals, has garnered significant attention as a novel quantum topological state. Particularly noteworthy is the giant electrical magnetochiral anisotropy (eMChA) in CsV3Sb5 [Guo et al, Nature 611, 461 (2022)], which provides compelling evidence of TRS and inversion-symmetry breaking. However, the underlying essence of this observation has remained obscured due to the lack of theoretical understanding. Here, we identify that the chiral loop-current induces substantial and switchable eMChA in kagome metals by taking account of the experimentally observed stripe charge-density-wave. The obtained eMChA coefficient is $\gamma_{eM}\propto M_{orb} \tau$, where $M_{orb}$ is the loop-current-induced orbital magnetization and $\tau$ is the lifetime of conduction electrons. Importantly, giant eMChA arises from the quantum metric (QM), which defines essential quantum phases of matter and their unique functionalities, including nonlinear effects. This effect is resonantly amplified in the loop-current phase, and the derived eMChA is switched by minute magnetic fields. This research elucidates the fundamental symmetry breaking in kagome metals and also sets the stage for investigating the QM-induced phenomena arising from electronic correlations., Comment: 21 pages, 10 figures

Over the years, numerous rank estimators for factor models have been proposed in the literature. This article focuses on information criterion-based rank estimators and investigates their consistency in rank selection. The gap conditions serve as necessary and sufficient conditions for rank estimators to achieve selection consistency under the general assumptions of random matrix theory. We establish a unified theorem on selection consistency, presenting the gap conditions for information criterion-based rank estimators with a unified formulation. To validate the theorem's assertion that rank selection consistency is solely determined by the gap conditions, we conduct extensive numerical simulations across various settings. Additionally, we undertake supplementary simulations to explore the strengths and limitations of information criterion-based estimators by comparing them with other types of rank estimators.

We study the bulk photovoltaic effect (BPVE) in Dirac and Weyl semimetals under two-frequency light irradiation. We show that the BPVE emerges for centrosymmetric Dirac and Weyl semimetals in the presence of light fields with frequencies $\Omega$ and $2\Omega$. The BPVE under the two frequency drive involves both shift current contribution independent of the carriers lifetime $\tau$ and the injection current contribution $\propto \tau$. Our calculations indicate that the photocurrent's direction, magnitude and type can be dynamically controlled by tuning parameters of the driving fields. Furthermore, we find that the tilt of the Dirac cone significantly affects the photocurrent, particularly in mirror symmetry-lacking Weyl semimetals, leading to an anisotropic optical response. These findings provide new insights into the dynamic control of photocurrents in topological semimetals, offering promising applications for optoelectronic devices., Comment: 11 pages, 5 figures

In this study, we propose the use of the phase-amplitude reduction method to construct an imitation learning framework. Imitating human movement trajectories is recognized as a promising strategy for generating a range of human-like robot movements. Unlike previous dynamical system-based imitation learning approaches, our proposed method allows the robot not only to imitate a limit cycle trajectory but also to replicate the transient movement from the initial or disturbed state to the limit cycle. Consequently, our method offers a safer imitation learning approach that avoids generating unpredictable motions immediately after disturbances or from a specified initial state. We first validated our proposed method by reconstructing a simple limit-cycle attractor. We then compared the proposed approach with a conventional method on a lemniscate trajectory tracking task with a simulated robot arm. Our findings confirm that our proposed method can more accurately generate transient movements to converge on a target periodic attractor compared to the previous standard approach. Subsequently, we applied our method to a real robot arm to imitate periodic human movements., Comment: 18 pages, 5 figures

This study proposes an approach to human-to-humanoid teleoperation using GAN-based online motion retargeting, which obviates the need for the construction of pairwise datasets to identify the relationship between the human and the humanoid kinematics. Consequently, it can be anticipated that our proposed teleoperation system will reduce the complexity and setup requirements typically associated with humanoid controllers, thereby facilitating the development of more accessible and intuitive teleoperation systems for users without robotics knowledge. The experiments demonstrated the efficacy of the proposed method in retargeting a range of upper-body human motions to humanoid, including a body jab motion and a basketball shoot motion. Moreover, the human-in-the-loop teleoperation performance was evaluated by measuring the end-effector position errors between the human and the retargeted humanoid motions. The results demonstrated that the error was comparable to those of conventional motion retargeting methods that require pairwise motion datasets. Finally, a box pick-and-place task was conducted to demonstrate the usability of the developed humanoid teleoperation system.

We study the effect of the magnon-magnon interaction on the nonlinear magnon transport. The magnon-magnon interaction induces nonreciprocal magnon decay when the time-reversal symmetry is broken, and leads to nonlinear thermal responses of magnons. We construct a theoretical framework to study the nonlinear thermal responses due to the nonreciprocal magnon decay by using the imaginary Dyson equation and quantum kinetic theory, which is then applied to a model of honeycomb ferromagnets with Dzyaloshinskii-Moriya interactions. An order estimate shows that the nonlinear thermal response from the present mechanism is feasible for experimental measurement., Comment: 7 pages, 5 figures

Aspect-based sentiment analysis aims to predict sentiment polarity with fine granularity. While Graph Convolutional Networks (GCNs) are widely utilized for sentimental feature extraction, their naive application for syntactic feature extraction can compromise information preservation. This study introduces an innovative edge-enhanced GCN, named SentiSys, to navigate the syntactic graph while preserving intact feature information, leading to enhanced performance. Specifically,we first integrate a bidirectional long short-term memory (Bi-LSTM) network and a self-attention-based transformer. This combination facilitates effective text encoding, preventing the loss of information and predicting long dependency text. A bidirectional GCN (Bi-GCN) with message passing is then employed to encode relationships between entities. Additionally, unnecessary information is filtered out using an aspect-specific masking technique. To validate the effectiveness of our proposed model, we conduct extensive evaluation experiments and ablation studies on four benchmark datasets. The results consistently demonstrate improved performance in aspect-based sentiment analysis when employing SentiSys. This approach successfully addresses the challenges associated with syntactic feature extraction, highlighting its potential for advancing sentiment analysis methodologies.

The computation of the skyline provides a mechanism for utilizing multiple location-based criteria to identify optimal data points. However, the efficiency of these computations diminishes and becomes more challenging as the input data expands. This study presents a novel algorithm aimed at mitigating this challenge by harnessing the capabilities of Apache Spark, a distributed processing platform, for conducting area skyline computations. The proposed algorithm enhances processing speed and scalability. In particular, our algorithm encompasses three key phases: the computation of distances between data points, the generation of distance tuples, and the execution of the skyline operators. Notably, the second phase employs a local partial skyline extraction technique to minimize the volume of data transmitted from each executor (a parallel processing procedure) to the driver (a central processing procedure). Afterwards, the driver processes the received data to determine the final skyline and creates filters to exclude irrelevant points. Extensive experimentation on eight datasets reveals that our algorithm significantly reduces both data size and computation time required for area skyline computation.

Deep generative models, such as generative adversarial networks (GANs), have been employed for $de~novo$ molecular generation in drug discovery. Most prior studies have utilized reinforcement learning (RL) algorithms, particularly Monte Carlo tree search (MCTS), to handle the discrete nature of molecular representations in GANs. However, due to the inherent instability in training GANs and RL models, along with the high computational cost associated with MCTS sampling, MCTS RL-based GANs struggle to scale to large chemical databases. To tackle these challenges, this study introduces a novel GAN based on actor-critic RL with instant and global rewards, called InstGAN, to generate molecules at the token-level with multi-property optimization. Furthermore, maximized information entropy is leveraged to alleviate the mode collapse. The experimental results demonstrate that InstGAN outperforms other baselines, achieves comparable performance to state-of-the-art models, and efficiently generates molecules with multi-property optimization. The source code will be released upon acceptance of the paper.

Lapid and Mao conjectured Ichino-Ikeda type formula of Whittaker periods for any quasi-split reductive groups and metaplectic groups. In this paper, we prove this formula for any irreducible cuspidal globally generic automorphic representation of quasi-split unitary groups., Comment: 54 pages

In this paper, we newly formulate and solve the optimal density control problem with Gromov-Wasserstein (GW) terminal cost in discrete-time linear Gaussian systems. Differently from the Wasserstein or Kullback-Leibler distances employed in the existing works, the GW distance quantifies the difference in shapes of the distribution, which is invariant under translation and rotation. Consequently, our formulation allows us to find small energy inputs that achieve the desired shape of the terminal distribution, which has practical applications, e.g., robotic swarms. We demonstrate that the problem can be reduced to a Difference of Convex (DC) programming, which is efficiently solvable through the DC algorithm. Through numerical experiments, we confirm that the state distribution reaches the terminal distribution that can be realized with the minimum control energy among those having the specified shape., Comment: 7 pages

We study direct current (DC) generation induced by microwave irradiation to ferroelectric materials. The DC generation originates from microwave absorption called dielectric loss due to the delay of dielectric response. Such current generation can be formulated as the low-frequency limit of the phonon shift current which arises from an increase of electric polarization accompanying photoexcitation of phonons due to the electron-phonon coupling. To study the DC generation by the dielectric loss, we apply the diagrammatic treatment of nonlinear optical responses to photoexcitations of phonons and derive the general formula for phonon shift current. We then study the DC generation in the low-frequency region and find that the current scales as $\propto \omega^2$ for the linearly polarized light and time reversal symmetric systems. We estimate the order of magnitude of the DC generation by dielectric loss, indicating its feasibility for experimental detection in the GHz region., Comment: 9 pages, 3 figures

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1-fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams., Comment: 30 pages, 8 figures

Motivated by the recent study of the non-Hermitian matrix-valued Brownian motion, we propose two kinds of dynamical processes of $n \times n$ matrices generated by nonnormal Toeplitz matrices. As a perturbation $\delta J$ is added at time $m \leq n$, where $\delta \in {\mathbb{C}}$ and $J$ is the all-one matrix. First we report the complicated motions of the ``eigenvalues'' which are numerically calculated. Then we derive the equations which determine the exact-eigenvalue processes. Comparison between the numerical results and the solutions of the equations, coexistence of exact eigenvalues and pseudospectra in the numerical results is clarified. The Catalan numbers play an important role to describe the specified exact eigenvalues. We tried to characterize the numerical results using the symbol curves of the corresponding nonnormal Toeplitz operators without perturbation. Then we report a new phenomenon in our second model such that at each time the outermost closed simple curve cut out from the symbol curve is realized as exact eigenvalues, but the inner part of symbol curve composed of several closed simple curves osculating each other is reduced in size and embedded as a complicated structure in the pseudospectrum. The asymptotics of the processes in the infinite-matrix limit $n \to \infty$ are also discussed., Comment: v2: LaTeX, 33 pages, 11 figures

We construct an efficient momentum space approach to the superconductivity in quasiperiodic multilayer systems. To this end, we extend the Brillouin zone (BZ) folding method to the superconducting (SC) phases by formulating the gap equation in the momentum space representation with the BZ folding. In this picture, we find that the SC order parameters generally exhibit finite momenta, which corresponds to the spatial fluctuation of the SC order in quasiperiodic multilayers. We apply the BZ folding method to a one dimensional model of quasiperiodic superconductors and demonstrate its numerical efficiency compared to the conventional method based on the real space representation with a large system size., Comment: 11 pages, 8 figures

In this paper, we introduce the quantum adaptive distribution search (QuADS), a quantum continuous optimization algorithm that integrates Grover adaptive search (GAS) with the covariance matrix adaptation - evolution strategy (CMA-ES), a classical technique for continuous optimization. QuADS utilizes the quantum-based search capabilities of GAS and enhances them with the principles of CMA-ES for more efficient optimization. It employs a multivariate normal distribution for the initial state of the quantum search and repeatedly updates it throughout the optimization process. Our numerical experiments show that QuADS outperforms both GAS and CMA-ES. This is achieved through adaptive refinement of the initial state distribution rather than consistently using a uniform state, resulting in fewer oracle calls. This study presents an important step toward exploiting the potential of quantum computing for continuous optimization.

Recent advances in electron microscopy trigger the question whether attosecond electron diffraction can resolve atomic-scale electron dynamics in crystalline materials in space and time. Here we explore the physics of the relevant electron-lattice scattering process in the time domain. We drive a single-crystalline silicon membrane with the optical cycles of near-infrared laser light and use attosecond electron pulses to produce electron diffraction patterns as a function of delay. For all Bragg spots, we observe time-dependent intensity changes and position shifts that are correlated with a time delay of 0.5-1.2 fs. For single-cycle excitation pulses with strong peak intensity, the correlations become nonlinear. Origin of these effects are local and integrated beam deflections by the optical electric and magnetic fields at the crystal membrane that modify the diffraction intensities in addition to the atomic structure factor dynamics by time-dependent rocking-curve effects. However, the measured time delays and symmetries allow to disentangle both effects. Future attosecond electron diffraction and microscopy experiments need to be based on these results., Comment: 14 pages, 3 figures

Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at a given transition rate. This paper explores how such stochastic processes involving multiple particles can model group behaviors of ants. Recent experimental research by the last author's group has investigated how ants switch between two types of primarily relied cues to select foraging paths based on the current situation. Here, we propose a discrete-time interacting random walk model on a square lattice, incorporating two types of hopping rules. Numerical simulation results demonstrate global changes in selected homing paths, transitioning from trailing paths of the `pheromone road' to nearly optimal paths depending on the switching parameters. By introducing two types of order parameters characterizing the dependence of homing duration distributions on switching parameters, we discuss these global changes as phase transitions in ant path selections. We also study critical phenomena associated with continuous phase transitions., Comment: v3: LaTeX, 22 pages, 7 figures

In this paper, generalizing the techniques of Bour's theorem, we prove that every generic cuspidal edge, more generally, generic $n$-type edge, which is invariant under a helicoidal motion in Euclidean $3$-space admits non-trivial isometric deformations. As a corollary, several geometric invariants, such as the limiting normal curvature, the cusp-directional torsion, the higher order cuspidal curvature and the bias, are proved to be extrinsic invariants., Comment: 21 pages, 9 figures