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We investigate the geometrical structure of multiply enhanced codimension-two singularities in the $SU(5)$ model of six-dimensional F-theory, where the rank of the singularity increases by two or more. We perform blow-up processes for the enhancement $SU(5)\rightarrow G'$, where $G'=E_6$, $E_7$ or $E_8$, to examine whether a sufficient set of exceptional curves emerge that can explain the charged matter generation predicted from anomaly cancelation. We first apply one of the six Esole-Yau small resolutions to the multiply enhanced singularities, but it turns out that the proper transform of the threefold equation does not reflect changes in the singularity or how the generic codimension-two singularities gather there. We then use a(n) (apparently) different way of small resolutions than Esole-Yau to find that, except for the cases of $G'= E_6$ and special cases of $E_7$, either (1) the resolution only yields exceptional curves that are insufficient to cancel the anomaly, or (2) there arises a type of singularity that is neither a conifold nor a generalized conifold singularity. Finally, we revisit the Esole-Yau small resolution and show that the change of the way of small resolutions amounts to simply exchanging the proper transform and the constraint condition, and under this exchange the two ways of small resolutions are completely equivalent., Comment: 43 pages, 7 figures

Recent advances in deep learning have enabled the generation of realistic data by training generative models on large datasets of text, images, and audio. While these models have demonstrated exceptional performance in generating novel and plausible data, it remains an open question whether they can effectively accelerate scientific discovery through the data generation and drive significant advancements across various scientific fields. In particular, the discovery of new inorganic materials with promising properties poses a critical challenge, both scientifically and for industrial applications. However, unlike textual or image data, materials, or more specifically crystal structures, consist of multiple types of variables - including lattice vectors, atom positions, and atomic species. This complexity in data give rise to a variety of approaches for representing and generating such data. Consequently, the design choices of generative models for crystal structures remain an open question. In this study, we explore a new type of diffusion model for the generative inverse design of crystal structures, with a backbone based on a Transformer architecture. We demonstrate our models are superior to previous methods in their versatility for generating crystal structures with desired properties. Furthermore, our empirical results suggest that the optimal conditioning methods vary depending on the dataset.

We prove that two formulas of the orbital magnetic susceptibility, namely, Koshino-Ando's formula and G\'{o}mez-Santos and Stauber's formula, are equivalent for the tight-binding models. The difference between these two formulas can be written in a form containing the surface terms arising from the momentum-space integration, and we show that the surface terms are exactly vanishing although the primitive functions are seemingly non-periodic with respect to the translation by the reciprocal lattice vector., Comment: 2 pages

Nilpotent Lie groups with left-invariant metrics provide non-trivial examples of Ricci solitons. One typical example is given by the class of two-step nilpotent Lie algebras obtained from simple directed graphs. In this paper, however, we focus on the use of quivers to construct nilpotent Lie algebras. A quiver is a directed graph that allows loops and multiple arrows between two vertices. Utilizing the concept of paths within quivers, we introduce a method for constructing nilpotent Lie algebras from finite quivers without cycles. We prove that for all these Lie algebras, the corresponding simply-connected nilpotent Lie groups admit left-invariant Ricci solitons. The method we introduce constructs a broad family of Ricci soliton nilmanifolds with arbitrarily high degrees of nilpotency., Comment: 15pages, 9figures

Crystal Orbital Overlap Population (COOP) is one of the effective tools for chemical-bonding analysis, and thus it has been utilized in the materials development and characterization. In this study, we developed a code to perform the COOP-based chemical-bonding analysis based on the wavefunction obtained from a first principles all-electron calculation with numeric atom-centered orbitals. The chemical-bonding analysis using the developed code was demonstrated for F2 and Si. Furthermore, we applied the method to analyze the chemical-bonding changes associated with a Li intercalation in three representative layered materials: graphite, MoS2, and ZrNCl, because of their great industrial importance, particularly for the applications in battery and superconducting materials. The COOP analysis provided some insights for understanding the intercalation mechanism and the stability of the intercalated materials from a chemical-bonding viewpoint.

The L3 Collaboration reported data on 2-jet and 3-jet Bose-Einstein correlations (BECs) with the results obtained through the $\tau$-model in 2011. In this study, we analyze these correlations using the conventional formula with the Gaussian long-range correlation (${\rm CF\times LRC_{(Gauss)}}$). The estimated ranges of interactions for 2-jet and 3-jet, $R_{\rm 2-jet}$ and $R_{\rm 3-jet}$, have almost the same magnitude as those by $\tau$-model: $R_{\rm 2-jet}=0.83\pm 0.05$ fm and $R_{\rm 3-jet}=1.09\pm 0.04$ fm. The anticorrelation in BEC (less than 1.0) observed by the L3 Collaboration is related to the partially negative density profile ($\rho_{\rm \tau, BE}(\xi)$ in $\xi$ space) in the $\tau$-model and the ${\rm LRC_{(Gauss)}}=1/(1+\alpha e^{-\beta Q^2})$ in ${\rm CF_I\times LRC_{(Gauss)}}$, respectively. Remarkably, the probability $P_{\tau}(\xi)$ calculated from the Levy canonical form exhibits partially negative behavior.

A Model capable of handling various elemental species and substances is essential for discovering new materials in the vast phase and compound space. Message-passing neural networks (MPNNs) are promising as such models, in which various vector operations model the atomic interaction with its neighbors. However, conventional MPNNs tend to overlook the importance of physicochemical information for each node atom, relying solely on the geometric features of the material graph. We propose the new three-body MPNN architecture with a message-passing layer that utilizes optimized basis functions based on the electronic structure of the node elemental species. This enables conveying the message that includes physical information and better represents the interaction for each elemental species. Inspired by the LCAO (linear combination of atomic orbitals) method, a classical method for calculating the orbital interactions, the linear combination of atomic basis constructed based on the wave function of hydrogen-like atoms is used for the present message-passing. Our model achieved higher prediction accuracy with smaller parameters than the state-of-the-art models on the challenging crystalline dataset containing many elemental species, including heavy elements. Ablation studies have also shown that the proposed method is effective in improving accuracy. Our implementation is available online., Comment: 11 pages, 2 figures

To understand physical properties of the interstellar medium (ISM) on various scales, we investigate it at parsec resolution on the kiloparsec scale. Here, we report on the sub-kpc scale Gas Density Histogram (GDH) of the Milky Way. The GDH is a density probability distribution function (PDF) of the gas volume density. Using this method, we are free from an identification of individual molecular clouds and their spatial structures. We use survey data of $^{12}$CO and $^{13}$CO ($J$=1-0) emission in the Galactic plane ($l = 10^{\circ}$-$50^{\circ}$) obtained as a part of the FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45m telescope (FUGIN). We make a GDH for every channel map of $2^{\circ} \times 2^{\circ}$ area, including the blank sky component, and without setting cloud boundaries. This is a different approach from previous works for molecular clouds. The GDH fits well to a single or double log-normal distribution, which we name the low-density log-normal (L-LN) and high-density log-normal (H-LN) components, respectively. The multi-log-normal components suggest that the L-LN and H-LN components originate from two different stages of structure formation in the ISM. Moreover, we find that both the volume ratios of H-LN components to total ($f_{\mathrm{H}}$) and the width of the L-LN along the gas density axis ($\sigma_{\rm{L}}$) show coherent structure in the Galactic-plane longitude-velocity diagram. It is possible that these GDH parameters are related to strong galactic shocks and other weak shocks in the Milky Way.

Rydberg atoms in optical lattices and tweezers is now a well established platform for simulating quantum spin systems. However, the role of the atoms' spatial wavefunction has not been examined in detail experimentally. Here, we show a strong spin-motion coupling emerging from the large variation of the interaction potential over the wavefunction spread. We observe its clear signature on the ultrafast many-body nanosecond-dynamics of atoms excited to a Rydberg $S$ state, using picosecond pulses, from an unity-filling atomic Mott-insulator. We also propose a novel approach to tune arbitrarily the strength of the spin-motion coupling relative to the motional energy scale set by trapping potentials. Our work provides a new direction for exploring the dynamics of strongly-correlated quantum systems by adding the motional degree of freedom to the Rydberg simulation toolbox., Comment: v2: revised version accepted in PRL

This paper describes an overview of the techniques of Hibikino-Musashi@Home, which intends to participate in the domestic standard platform league. The team has developed a dataset generator for the training of a robot vision system and an open-source development environment running on a human support robot simulator. The robot system comprises self-developed libraries including those for motion synthesis and open-source software works on the robot operating system. The team aims to realize a home service robot that assists humans in a home, and continuously attend the competition to evaluate the developed system. The brain-inspired artificial intelligence system is also proposed for service robots which are expected to work in a real home environment.

Spatial non-uniformity in tight-binding models serves as a source of rich phenomena. In this paper, we study a diamond-chain tight-binding model with a spatially-modulated magnetic flux at each plaquette. In the numerical studies with various combinations of the minimum and maximum flux values, we find the characteristic dynamics of a particle, namely, a particle slows down when approaching the plaquette with $\pi$-flux. This originates from the fact that the sharply localized eigenstates exist around the $\pi$-flux plaquette. These localized modes can be understood from a squared model of the original one. This characteristic blocked dynamics will be observed in photonic waveguides or cold atoms., Comment: 12 pages, 13 figures

Given the time and expense associated with bringing a drug to market, numerous studies have been conducted to predict the properties of compounds based on their structure using machine learning. Federated learning has been applied to compound datasets to increase their prediction accuracy while safeguarding potentially proprietary information. However, federated learning is encumbered by low accuracy in not identically and independently distributed (non-IID) settings, i.e., data partitioning has a large label bias, and is considered unsuitable for compound datasets, which tend to have large label bias. To address this limitation, we utilized an alternative method of distributed machine learning to chemical compound data from open sources, called data collaboration analysis (DC). We also proposed data collaboration analysis using projection data (DCPd), which is an improved method that utilizes auxiliary PubChem data. This improves the quality of individual user-side data transformations for the projection data for the creation of intermediate representations. The classification accuracy, i.e., area under the curve in the receiver operating characteristic curve (ROC-AUC) and AUC in the precision-recall curve (PR-AUC), of federated averaging (FedAvg), DC, and DCPd was compared for five compound datasets. We determined that the machine learning performance for non-IID settings was in the order of DCPd, DC, and FedAvg, although they were almost the same in identically and independently distributed (IID) settings. Moreover, the results showed that compared to other methods, DCPd exhibited a negligible decline in classification accuracy in experiments with different degrees of label bias. Thus, DCPd can address the low performance in non-IID settings, which is one of the challenges of federated learning.

From the standpoint of applied ontology, the problem of understanding and modeling causation has been recently challenged on the premise that causation is real. As a consequence, the following three results were obtained: (1) causation can be understood via the notion of systemic function; (2) any cause can be decomposed using only four subfunctions, namely Achieves, Prevents, Allows, and Disallows; and (3) the last three subfunctions can be defined in terms of Achieves alone. It follows that the essence of causation lies in a single function, namely Achieves. It remains to elucidate the nature of the Achieves function, which has been elaborated only partially in the previous work. In this paper, we first discuss a couple of underlying policies in the above-mentioned causal theory since these are useful in the discussion, then summarize the results obtained in the former paper, and finally reveal the nature of Achieves giving a complete solution to the problem of what causation is., Comment: 13 pages, 3 figures