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We performed inelastic neutron scattering experiments on single-crystal samples of the honeycomb lattice magnet, ilmenite NiTiO3. Below the Neel temperature of 22 K, spin wave excitations with a band energy of 3.7 meV were observed. The neutron energy spectra were well-reproduced by modeling the system as a ferromagnetic honeycomb lattice with antiferromagnetic interlayer coupling, using linear spin wave theory. Similar to another ilmenite CoTiO3, a crossing structure was observed at the K point, suggesting the resence of Dirac magnons in NiTiO3. Further calculations suggested the formation of Dirac nodal line.

This paper presents a novel system for reconstructing high-resolution GPS trajectory data from truncated or synthetic low-resolution inputs, addressing the critical challenge of balancing data utility with privacy preservation in mobility applications. The system integrates transformer-based encoder-decoder models with graph convolutional networks (GCNs) to effectively capture both the temporal dependencies of trajectory data and the spatial relationships in road networks. By combining these techniques, the system is able to recover fine-grained trajectory details that are lost through data truncation or rounding, a common practice to protect user privacy. We evaluate the system on the Beijing trajectory dataset, demonstrating its superior performance over traditional map-matching algorithms and LSTM-based synthetic data generation methods. The proposed model achieves an average Fr\'echet distance of 0.198 km, significantly outperforming map-matching algorithms (0.632 km) and synthetic trajectory models (0.498 km). The results show that the system is not only capable of accurately reconstructing real-world trajectories but also generalizes effectively to synthetic data. These findings suggest that the system can be deployed in urban mobility applications, providing both high accuracy and robust privacy protection., Comment: Accepted paper for the 2nd ACM SIGSPATIAL International Workshop on Geo-Privacy and Data Utility for Smart Societies (GeoPrivacy 2024)

Altermagnetism is a newly discovered magnetic class named after the alternating spin polarizations in both real and reciprocal spaces. Like the spin-splitting of electronic bands, the magnon bands in altermagnets are predicted to exhibit alternating chiral splitting. In this work, by performing inelastic neutron scattering on $\alpha$-MnTe, we directly verified the chiral splitting in altermagnetic magnon dispersions. The lifted degeneracy of chirality is further explained by a symmetric-exchange origin. In addition, the $g$-wave magnetism was identified in MnTe., Comment: 6 pages, 3 figures. To appear in Phys. Rev. Lett. This is the initial manuscript that was submitted to Phys. Rev. Lett

Babai and Frankl posed the ``odd cover problem" of finding the minimum cardinality of a collection of complete bipartite graphs such that every edge of the complete graph of order $n$ is covered an odd number of times. In a previous paper with O'Neill, some of the authors proved that this value is always $\lceil n / 2 \rceil$ or $\lceil n / 2 \rceil + 1$ and that it is the former whenever $n$ is a multiple of $8$. In this paper, we determine this value to be $\lceil n / 2 \rceil$ whenever $n$ is odd or equivalent to $18$ modulo $24$. We also further the study of odd covers of graphs which are not complete, wherein edges are covered an odd number of times and nonedges an even number of times by the complete bipartite graphs in the collection. Among various results on disjoint unions, we find the minimum cardinality of an odd cover of a union of odd cliques and of a union of cycles., Comment: 19 pages, 6 figures

Accurate taxi-demand prediction is essential for optimizing taxi operations and enhancing urban transportation services. However, using customers' data in these systems raises significant privacy and security concerns. Traditional federated learning addresses some privacy issues by enabling model training without direct data exchange but often struggles with accuracy due to varying data distributions across different regions or service providers. In this paper, we propose CC-Net: a novel approach using collaborative learning enhanced with contrastive learning for taxi-demand prediction. Our method ensures high performance by enabling multiple parties to collaboratively train a demand-prediction model through hierarchical federated learning. In this approach, similar parties are clustered together, and federated learning is applied within each cluster. The similarity is defined without data exchange, ensuring privacy and security. We evaluated our approach using real-world data from five taxi service providers in Japan over fourteen months. The results demonstrate that CC-Net maintains the privacy of customers' data while improving prediction accuracy by at least 2.2% compared to existing techniques.

This paper explores the question of how accurately current large language models can perform logical reasoning in natural language, with an emphasis on whether these models exhibit reasoning biases similar to humans. Specifically, our study focuses on syllogistic reasoning, a form of deductive reasoning extensively studied in cognitive science as a natural form of human reasoning. We present a syllogism dataset called NeuBAROCO, which consists of syllogistic reasoning problems in English and Japanese. This dataset was originally designed for psychological experiments to assess human reasoning capabilities using various forms of syllogisms. Our experiments with leading large language models indicate that these models exhibit reasoning biases similar to humans, along with other error tendencies. Notably, there is significant room for improvement in reasoning problems where the relationship between premises and hypotheses is neither entailment nor contradiction. We also present experimental results and in-depth analysis using a new Chain-of-Thought prompting method, which asks LLMs to translate syllogisms into abstract logical expressions and then explain their reasoning process. Our analysis using this method suggests that the primary limitations of LLMs lie in the reasoning process itself rather than the interpretation of syllogisms., Comment: To appear in Findings of the Association for Computational Linguistics: ACL 2024

The nonequilibrium relaxation (NER) method, which has been used to investigate equilibrium systems via their nonequilibrium behavior, has been widely applied to various models to estimate critical temperatures and critical exponents. Although the estimation of critical temperatures has become more reliable and reproducible, that of critical exponents raises concerns about the method's reliability. Therefore, we propose a more reliable and reproducible approach using Gaussian process regression. In addition, the present approach introduces statistical errors through the bootstrap method by combining them using the extrapolation method. Our estimation for the two-dimensional Ising model yielded $\beta = 0.12504(6)$, $\gamma = 1.7505(10)$, and $\nu = 1.0003(6)$, consistent with the exact values. The value $z = 2.1669(9)$ is reliable because of the high accuracy of these exponents. We also obtained the critical exponents for the three-dimensional Ising model and found that they are close to those reported in a previous study. Thus, for systems undergoing second-order transitions, our approach improves the accuracy, reliability, and reproducibility of the NER analysis. Because the proposed approach requires the relaxation of some observables from Monte Carlo simulations, its simplicity imparts it with significant potential., Comment: 26 pages, 19 figures, LaTeX

Given integers $\Delta\ge 2$ and $t\ge 2\Delta$, suppose there is a graph of maximum degree $\Delta$ and a partition of its vertices into blocks of size at least $t$. By a seminal result of Haxell, there must be some independent set of the graph that is transversal to the blocks, a so-called independent transversal. We show that, if moreover $t\ge2\Delta+1$, then every independent transversal can be transformed within the space of independent transversals to any other through a sequence of one-vertex modifications, showing connectivity of the so-called reconfigurability graph of independent transversals. This is sharp in that for $t=2\Delta$ (and $\Delta\ge 2$) the connectivity conclusion can fail. In this case we show furthermore that in an essential sense it can only fail for the disjoint union of copies of the complete bipartite graph $K_{\Delta,\Delta}$. This constitutes a qualitative strengthening of Haxell's theorem.

As a highly sensitive vibrational imaging method, stimulated Raman scattering (SRS) microscopy is finding various applications, while its theoretical treatment seems still under development. Here we present a theoretical estimation of spontaneous Raman signal and SRS signal from Raman scattering cross section, irrespective of the numerical aperture of the objective lens. We confirm a reasonable agreement between our theory with a recently proposed treatment based on the stimulated Raman scattering cross section. Furthermore, we point out that the acceleration factor of SRS can be interpreted as the number of Stokes photons in the vibrational coherence time., Comment: 4 pages

The main result of this paper is an edge-coloured version of Tutte's $f$-factor theorem. We give a necessary and sufficient condition for an edge-coloured graph $G^c$ to have a properly coloured $f$-factor. We state and prove our result in terms of an auxiliary graph $G_f^c$ which has a 1-factor if and only if $G^c$ has a properly coloured $f$-factor; this is analogous to the "short proof" of the $f$-factor theorem given by Tutte in 1954. An alternative statement, analogous to the original $f$-factor theorem, is also given. We show that our theorem generalises the $f$-factor theorem; that is, the former implies the latter. We consider other properties of edge-coloured graphs, and show that similar results are unlikely for $f$-factors with rainbow components and distance-$d$-coloured $f$-factors, even when $d=2$ and the number of colours used is asymptotically minimal., Comment: 18 pages, 5 figures

The growing demand for ride-hailing services has led to an increasing need for accurate taxi demand prediction. Existing systems are limited to specific regions, lacking generalizability to unseen areas. This paper presents a novel taxi demand forecasting system that leverages a graph neural network to capture spatial dependencies and patterns in urban environments. Additionally, the proposed system employs a region-neutral approach, enabling it to train a model that can be applied to any region, including unseen regions. To achieve this, the framework incorporates the power of Variational Autoencoder to disentangle the input features into region-specific and region-neutral components. The region-neutral features facilitate cross-region taxi demand predictions, allowing the model to generalize well across different urban areas. Experimental results demonstrate the effectiveness of the proposed system in accurately forecasting taxi demand, even in previously unobserved regions, thus showcasing its potential for optimizing taxi services and improving transportation efficiency on a broader scale., Comment: Accepted to The 31st ACM International Conference on Advances in Geographic Information Systems(SIGSPATIAL '23) as a short paper in the Research, Systems and Industrial Experience Papers track

Programmable unitary converters are powerful tools for realizing unitary transformations, advancing fields of computing and communication. The accuracy of these unitary transformations is crucial for maintaining high fidelity in such applications. However, various physical artifacts can impair the accuracy of the synthesized transformations. A commonly employed approach uses the system's gradient to restore accuracy. Matrix norm is used to define error between matrices, and minimization of this norm using the gradient restores the accuracy. Although this gradient can indeed be physically measured using external equipment, it leads to a rather complex optical system. In this study, we propose a standalone method for measuring matrix norm gradients, where `standalone' means that no additional optical equipment is needed. This method is based on the mathematical fact that the central difference, which is generally used for the approximation of differentiation, can yield exact differentiation for any unitary converters. Furthermore, we introduce a new matrix distance that is suitable for optimizing unitary converters which use intensity detectors at the output. This distance also yields the exact differentiation with the central difference. Numerical analysis demonstrates that our method exhibits orders of magnitude higher tolerance to measurement noise than prior similar approaches., Comment: Submitted to Phys. Rev. Appl. (newer version)

Batch effects (BEs) refer to systematic technical differences in data collection unrelated to biological variations whose noise is shown to negatively impact machine learning (ML) model generalizability. Here we release CohortFinder, an open-source tool aimed at mitigating BEs via data-driven cohort partitioning. We demonstrate CohortFinder improves ML model performance in downstream medical image processing tasks. CohortFinder is freely available for download at cohortfinder.com., Comment: 26 pages, 9 figures, 4 tables. Abstract was accepted by European Society of Digital and Integrative Pathology (ESDIP), Germany, 2022

Let $K$ and $k$ be $p$-adic fields. Let $L$ be the composite field of $K$ and a certain Lubin-Tate extension over $k$ (including the case where $L=K(\mu_{p^{\infty}})$). In this paper, we show that there exists an explicitly described constant $C$, depending only on $K,k$ and an integer $g \ge 1$, which satisfies the following property: If $A_{/K}$ is a $g$-dimensional CM abelian variety, then the order of the $p$-torsion subgroup of $A(L)$ is bounded by $C$. We also give a similar bound in the case where $L=K(\sqrt[p^{\infty}]{K})$. Applying our results, we study bounds of orders of torsion subgroups of some CM abelian varieties over number fields with values in full cyclotomic fields., Comment: 21 pages, some minor modifications

Programmable unitary photonic devices are emerging as promising tools to implement unitary transformation for quantum information processing, machine learning, and optical communication. These devices typically use a rectangular mesh of Mach-Zehnder interferometers (MZIs), which has a clear mathematical structure and can be configured deterministically. However, this mesh architecture is sensitive to fabrication errors, and the correction techniques are still under investigation. In contrast, the multi-plane light conversion (MPLC) architecture is more robust against fabrication errors, but a deterministic method for configuring the converter has not yet been developed due to its complex mathematical structure. In this work, we propose a fast iterative configuration method for MPLC, following the mathematical review of the matrix distance and proposal of a new norm. We show through numerical simulations that adding a few redundant layers significantly improves the convergence of the MPLC architecture, making it a practical and attractive option. We also consider the effects of finite resolution and crosstalk in phase shifters in our simulations. In addition, we propose a phase-insensitive distance suited for applications using only intensity detections. Our method demonstrates orders of magnitude better accuracy and a 20-fold speed-up compared to previous approaches.

In 1973, Fisk proved that any $4$-coloring of a $3$-colorable triangulation of the $2$-sphere can be obtained from any $3$-coloring by a sequence of Kempe-changes. On the other hand, in the case where we are only allowed to recolor a single vertex in each step, which is a special case of a Kempe-change, there exists a $4$-coloring that cannot be obtained from any $3$-coloring. In this paper, we present a characterization of a $4$-coloring of a $3$-colorable triangulation of the $2$-sphere that can be obtained from a $3$-coloring by a sequence of recoloring operations at single vertices, and a criterion for a $3$-colorable triangulation of the $2$-sphere that all $4$-colorings can be obtained from a $3$-coloring by such a sequence. Moreover, our first result can be generalized to a high-dimensional case, in which ``$4$-coloring,'' ``$3$-colorable,'' and ``$2$-sphere'' above are replaced with ``$k$-coloring,'' ``$(k-1)$-colorable,'' and ``$(k-2)$-sphere'' for $k \geq 4$, respectively. In addition, we show that the problem of deciding whether, for given two $(k+1)$-colorings, one can be obtained from the other by such a sequence is PSPACE-complete for any fixed $k \geq 4$. Our results above can be rephrased as new results on the computational problems named {\sc $k$-Recoloring} and {\sc Connectedness of $k$-Coloring Reconfiguration Graph}, which are fundamental problems in the field of combinatorial reconfiguration., Comment: 35 pages

In this paper, we consider a transformation of $k$ disjoint paths in a graph. For a graph and a pair of $k$ disjoint paths $\mathcal{P}$ and $\mathcal{Q}$ connecting the same set of terminal pairs, we aim to determine whether $\mathcal{P}$ can be transformed to $\mathcal{Q}$ by repeatedly replacing one path with another path so that the intermediates are also $k$ disjoint paths. The problem is called Disjoint Paths Reconfiguration. We first show that Disjoint Paths Reconfiguration is PSPACE-complete even when $k=2$. On the other hand, we prove that, when the graph is embedded on a plane and all paths in $\mathcal{P}$ and $\mathcal{Q}$ connect the boundaries of two faces, Disjoint Paths Reconfiguration can be solved in polynomial time. The algorithm is based on a topological characterization for rerouting curves on a plane using the algebraic intersection number. We also consider a transformation of disjoint $s$-$t$ paths as a variant. We show that the disjoint $s$-$t$ paths reconfiguration problem in planar graphs can be determined in polynomial time, while the problem is PSPACE-complete in general.

We consider the problem of determining whether a target item assignment can be reached from an initial item assignment by a sequence of pairwise exchanges of items between agents. In particular, we consider the situation where each agent has a dichotomous preference over the items, that is, each agent evaluates each item as acceptable or unacceptable. Furthermore, we assume that communication between agents is limited, and the relationship is represented by an undirected graph. Then, a pair of agents can exchange their items only if they are connected by an edge and the involved items are acceptable. We prove that this problem is PSPACE-complete even when the communication graph is complete (that is, every pair of agents can exchange their items), and this problem can be solved in polynomial time if an input graph is a tree., Comment: PRIMA 2022

Let $p$ be a prime number and $M$ the extension field of a $p$-adic field $K$ obtained by adjoining all $p$-power roots of all elements of $K$. In this paper, we show that there exists a constant $C$, depending only on $K$ and an integer $g>0$, which satisfies the following property:If $A_{/K}$ is a $g$-dimensional CM abelian variety, then the order of the torsion subgroup of $A(M)$ is bounded by $C$., Comment: 9 pages, Proposition 7 is added

We consider the problem of reforming an envy-free matching when each agent is assigned a single item. Given an envy-free matching, we consider an operation to exchange the item of an agent with an unassigned item preferred by the agent that results in another envy-free matching. We repeat this operation as long as we can. We prove that the resulting envy-free matching is uniquely determined up to the choice of an initial envy-free matching, and can be found in polynomial time. We call the resulting matching a reformist envy-free matching, and then we study a shortest sequence to obtain the reformist envy-free matching from an initial envy-free matching. We prove that a shortest sequence is computationally hard to obtain even when each agent accepts at most four items and each item is accepted by at most three agents. On the other hand, we give polynomial-time algorithms when each agent accepts at most three items or each item is accepted by at most two agents. Inapproximability and fixed-parameter (in)tractability are also discussed., Comment: AAAI 2022

We prove the large deviation principle for the supports of Jacobi ensembles following Guionnet's method., Comment: 7 pages

In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched $\mathfrak{m}$-primary ideals with small first Hilbert coefficient in a Cohen-Macaulay local ring $(A,\mathfrak{m})$. In particular, we explore the structure of stretched $\mathfrak{m}$-primary ideals satisfying the equality $\mathrm{e}_1(I)=\mathrm{e}_0(I)-\ell_A(A/I)+4$ where $\mathrm{e}_0(I)$ and $\mathrm{e}_1(I)$ denote the multiplicity and the first Hilbert coefficient respectively., Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:2109.12918

We initiate the study of $k$-edge-connected orientations of undirected graphs through edge flips for $k \geq 2$. We prove that in every orientation of an undirected $2k$-edge-connected graph, there exists a sequence of edges such that flipping their directions one by one does not decrease the edge-connectivity, and the final orientation is $k$-edge-connected. This yields an ``edge-flip based'' new proof of Nash-Williams' theorem: an undirected graph $G$ has a $k$-edge-connected orientation if and only if $G$ is $2k$-edge-connected. As another consequence of the theorem, we prove that the edge-flip graph of $k$-edge-connected orientations of an undirected graph $G$ is connected if $G$ is $(2k+2)$-edge-connected. This has been known to be true only when $k=1$.

The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched $\mathfrak{m}$-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring $(A,\mathfrak{m})$. As an application, we present complete descriptions of the associated graded ring of stretched $\mathfrak{m}$-primary ideals with small reduction number., Comment: 22 pages

We show finiteness results on torsion points of commutative algebraic groups over a $p$-adic field $K$ with values in various algebraic extensions $L/K$ of infinite degree. We mainly study the following cases: (1) $L$ is an abelian extension which is a splitting field of a crystalline character (such as a Lubin-Tate extension). (2) $L$ is a certain iterate extension of $K$ associated with Lubin-Tate formal groups, which is familiar with Kummer theory., Comment: 21 pages