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We study Hadamard's variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for two-dimensional domain, which implies several new inequalities., Comment: submitted

Machine learning is widely utilized across various industries. Identifying the appropriate machine learning models and datasets for specific tasks is crucial for the effective industrial application of machine learning. However, this requires expertise in both machine learning and the relevant domain, leading to a high learning cost. Therefore, research focused on extracting combinations of tasks, machine learning models, and datasets from academic papers is critically important, as it can facilitate the automatic recommendation of suitable methods. Conventional information extraction methods from academic papers have been limited to identifying machine learning models and other entities as named entities. To address this issue, this study proposes a methodology extracting tasks, machine learning methods, and dataset names from scientific papers and analyzing the relationships between these information by using LLM, embedding model, and network clustering. The proposed method's expression extraction performance, when using Llama3, achieves an F-score exceeding 0.8 across various categories, confirming its practical utility. Benchmarking results on financial domain papers have demonstrated the effectiveness of this method, providing insights into the use of the latest datasets, including those related to ESG (Environmental, Social, and Governance) data., Comment: 10 pages, 8 figures

Strategies related to the blockchain concept of Extractable Value (MEV/BEV), such as arbitrage, front- or back-running create an economic incentive for network nodes to reduce latency, including minimizing transaction validation time -- a core feature to secure blockchain networks. A modified node, that neglects to filter invalid transactions in the Ethereum P2P network, introduces novel attack vectors. In this work, we formalize and evaluate a Blockchain Economic Denial of Sustainability (EDoS) attack, which can cause financial losses in traffic costs for operators of modified nodes. We 1) mathematically define the attack model, 2) identify thousands of empirical instances of this similar attack in the wild, 3) empirically measure the model parameters from our two monitoring nodes, and 4) conduct attack simulations on the local network to compare its performance with existing Denial-of-Service attacks. We show that an attacker can amplify network traffic at modified nodes by a factor of 3,600, and cause economic damages 13,800 times greater than the amount needed to carry out the attack. Despite these risks, aggressive latency reduction may still be profitable enough to justify the existence of modified nodes. To assess this trade-off, we 1) simulate the transaction validation process in the local network and 2) empirically measure the latency reduction by deploying our modified node in the Ethereum testnet. We conclude with a cost-benefit analysis of skipping validation and provide mitigation strategies against this attack.

In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability., Comment: 16 pages, 3 figures

The Leggett-Garg inequality (LGI) serves as a criterion to determine the adherence of macroscopic system dynamics to macrorealism, as postulated by Leggett and Garg. A violation of this inequality implies either the absence of a realistic description of the system or the impracticality of noninvasive measurements. In this work, we investigate the violation of the LGI for the system of bosons in a double-well potential. Specifically, we explore the violation of the LGI in the dynamics of bosons in a double-well potential in the Bose-Einstein-Condensation (BEC) regime, where the system can be considered as two weakly coupled Bose condensates, and in the single-particle regime to establish the conditions under which the violation of the LGI occurs. Our analysis reveals that the LGI is violated due to Josephson oscillations, while it remains unviolated in the strong coupling regime, attributed to the self-trapping phenomena. Notably, we observe that the violation of the LGI becomes increasingly significant as the particle number increases. These findings provide valuable insights into the macrorealistic behavior of Bose condensates and highlight the effect of measurements on the dynamics of a macroscopic system., Comment: 14 pages, 10 figures

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. Recently we performed complex Langevin simulations by adding a Lorentz invariant mass term as an IR regulator and found a (1+1)-dimensional expanding spacetime with a Lorentzian signature emerging dynamically at late times when the fermionic contribution is omitted. Here we find that this is merely an artifact of the Lorentz boosts by showing that the spontaneous breaking of rotational symmetry is eliminated if one chooses a Lorentz frame appropriately. On the other hand, when we include the fermionic contribution, we find some evidence suggesting the emergence of a smooth (3+1)-dimensional expanding Lorentzian spacetime., Comment: 12 pages, 9 figures, proceedings of Corfu Summer Institute 2023 "School and Workshops on Elementary Particle Physics and Gravity"

Follow-the-Regularized-Leader (FTRL) is a powerful framework for various online learning problems. By designing its regularizer and learning rate to be adaptive to past observations, FTRL is known to work adaptively to various properties of an underlying environment. However, most existing adaptive learning rates are for online learning problems with a minimax regret of $\Theta(\sqrt{T})$ for the number of rounds $T$, and there are only a few studies on adaptive learning rates for problems with a minimax regret of $\Theta(T^{2/3})$, which include several important problems dealing with indirect feedback. To address this limitation, we establish a new adaptive learning rate framework for problems with a minimax regret of $\Theta(T^{2/3})$. Our learning rate is designed by matching the stability, penalty, and bias terms that naturally appear in regret upper bounds for problems with a minimax regret of $\Theta(T^{2/3})$. As applications of this framework, we consider two major problems dealing with indirect feedback: partial monitoring and graph bandits. We show that FTRL with our learning rate and the Tsallis entropy regularizer improves existing Best-of-Both-Worlds (BOBW) regret upper bounds, which achieve simultaneous optimality in the stochastic and adversarial regimes. The resulting learning rate is surprisingly simple compared to the existing learning rates for BOBW algorithms for problems with a minimax regret of $\Theta(T^{2/3})$., Comment: 31 pages

From 1998 to 2017, neutron monitors located at an altitude of 4300 m on the Tibetan plateau detected 127 long-duration bursts of high-energy radiation in association with thunderclouds. These bursts typically lasted for 10 to 40 minutes, and 89\% of them occurred between 10:00 and 24:00 local time. They were also found to be more likely to occur at night, especially during 18:00$-$06:00 local time period. The observed diurnal and seasonal variations in burst frequency were consistent with the frequencies of lightning and precipitation on the Tibetan plateau. Based on 19 years of data, the present study suggests that an annual variation in burst frequency has a periodicity of $\sim$16 years and a lag of $\sim$3 years relative to solar activity., Comment: 28 pages, accepted for publication in Progress in Earth and Planetary Science

Grain alignment is a key factor that determines the performance of a superconducting bulk. In this study, the spark plasma texturing (SPT) technique was used to fabricate a CaKFe$_4$As$_4$ superconducting bulk. X-ray diffraction and electron backscatter diffraction revealed that the $c$-axes of the CaKFe$_4$As$_4$ grains in the SPT bulk are aligned, demonstrating that the SPT technique is effective in achieving $c$-axis texture. In addition, chemical composition analysis showed that oxide impurities, which affect the grain boundary characteristics that determine the inter-grain critical current density ($J_c$), are randomly distributed in the SPT bulk. Magnetization measurements showed high $J_c$ values of the SPT bulk, reaching 127 kA cm$^{-2}$ and 26 kA cm$^{-2}$ at 4.2 K under a self-field and magnetic field of 5 T, respectively. These results suggest that the SPT technique is a promising approach for obtaining a high-performance superconducting bulk material for high-field applications.

A high density CaKFe$_4$As$_4$ bulk sample was successfully synthesized using a spark plasma sintering (SPS) technique. The density of the synthesized sample was 5.02 g cm$^{-3}$, corresponding to 96.2% of the theoretical density of CaKFe$_4$As$_4$. Moreover, a reasonably high Vickers hardness of 1 GPa was measured. The electrical resistivity of the SPS bulk sample was as low as approximately 600 $\mu\Omega$ cm at 300 K, which is smaller than that of the ordinary sintered polycrystalline sample by nearly one order of magnitude, and exhibited a sharp superconducting transition, with the transition width $\Delta\textit{T}_c$ less than 2 K, indicating an improved grain connectivity. The critical current density of the SPS bulk sample, as calculated from the magnetization hysteresis loops (magnetic $\textit{J}_c$), reached 18 kA cm$^{-2}$ at 4.2 K under 5 T, which is the highest among the iron-based superconductor polycrystalline samples reported thus far., Comment: 13 pages, 6 figures, 1 table

Since the Voyager mission flybys in 1979, we have known the moon Io to be extremely volcanically active as well as to be the main source of plasma in the vast magnetosphere of Jupiter. Material lost from Io forms neutral clouds, the Io plasma torus and ultimately the extended plasma sheet. This material is supplied from the upper atmosphere and atmospheric loss is likely driven by plasma-interaction effects with possible contributions from thermal escape and photochemistry-driven escape. Direct volcanic escape is negligible. The supply of material to maintain the plasma torus was estimated from various methods at roughly one ton per second. Most of the time the magnetospheric plasma environment of Io is stable on timescales from days to months. Similarly, Io's atmosphere was found to have a stable average density on the dayside, although it exhibits lateral, diurnal and seasonal variations. There is a potential positive feedback in the Io torus supply: collisions of torus plasma with atmospheric neutrals likely are a significant loss process, which increases with torus density. The stability of the torus environment might be maintained by limiting mechanisms of either torus supply from Io or the loss from the torus by centrifugal interchange in the middle magnetosphere. Various observations suggest that occasionally the plasma torus undergoes major transient changes over a period of several weeks, apparently overcoming possible stabilizing mechanisms. Such events (and more frequent minor changes) are commonly explained by some kind of change in volcanic activity that triggers a chain of reactions which modify the plasma torus state via a net increase in supply of new mass. However, it remains unknown what kind of volcanic event can trigger torus events, whether Io's atmosphere undergoes a change before or during such magnetospheric events, and what processes could enable such a change.

We present an effective method for transmitting electromagnetic waves as surface waves with a tape-based metasurface design. This design incorporates silver square patches periodically patterned on an adhesive tape substrate. Specifically, our study proposes a strategy to enhance the efficiency of power transfer in high-frequency bands by guiding signals as surface waves rather than free-space waves. Both the numerical and experimental results validate the markedly enhanced efficiency in power transfer of high-frequency signals compared to that achieved with conventional methods, such as wireless power transfer and microstrips. Importantly, our metasurface design can be readily manufactured and tailored for various environments. Thus, our study contributes to designing power-efficient next-generation communication systems such as 6G and 7G, which leverage high-frequency signals in the millimeter-wave and THz bands.

Follow-The-Regularized-Leader (FTRL) is known as an effective and versatile approach in online learning, where appropriate choice of the learning rate is crucial for smaller regret. To this end, we formulate the problem of adjusting FTRL's learning rate as a sequential decision-making problem and introduce the framework of competitive analysis. We establish a lower bound for the competitive ratio and propose update rules for learning rate that achieves an upper bound within a constant factor of this lower bound. Specifically, we illustrate that the optimal competitive ratio is characterized by the (approximate) monotonicity of components of the penalty term, showing that a constant competitive ratio is achievable if the components of the penalty term form a monotonically non-increasing sequence, and derive a tight competitive ratio when penalty terms are $\xi$-approximately monotone non-increasing. Our proposed update rule, referred to as \textit{stability-penalty matching}, also facilitates constructing the Best-Of-Both-Worlds (BOBW) algorithms for stochastic and adversarial environments. In these environments our result contributes to achieve tighter regret bound and broaden the applicability of algorithms for various settings such as multi-armed bandits, graph bandits, linear bandits, and contextual bandits.

In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result., Comment: to appear in Applications of Mathematics

In this paper, we explore online convex optimization (OCO) and introduce a new analysis that provides fast rates by exploiting the curvature of feasible sets. In online linear optimization, it is known that if the average gradient of loss functions is larger than a certain value, the curvature of feasible sets can be exploited by the follow-the-leader (FTL) algorithm to achieve a logarithmic regret. This paper reveals that algorithms adaptive to the curvature of loss functions can also leverage the curvature of feasible sets. We first prove that if an optimal decision is on the boundary of a feasible set and the gradient of an underlying loss function is non-zero, then the algorithm achieves a regret upper bound of $O(\rho \log T)$ in stochastic environments. Here, $\rho > 0$ is the radius of the smallest sphere that includes the optimal decision and encloses the feasible set. Our approach, unlike existing ones, can work directly with convex loss functions, exploiting the curvature of loss functions simultaneously, and can achieve the logarithmic regret only with a local property of feasible sets. Additionally, it achieves an $O(\sqrt{T})$ regret even in adversarial environments where FTL suffers an $\Omega(T)$ regret, and attains an $O(\rho \log T + \sqrt{C \rho \log T})$ regret bound in corrupted stochastic environments with corruption level $C$. Furthermore, by extending our analysis, we establish a regret upper bound of $O\Big(T^{\frac{q-2}{2(q-1)}} (\log T)^{\frac{q}{2(q-1)}}\Big)$ for $q$-uniformly convex feasible sets, where uniformly convex sets include strongly convex sets and $\ell_p$-balls for $p \in [1,\infty)$. This bound bridges the gap between the $O(\log T)$ regret bound for strongly convex sets ($q=2$) and the $O(\sqrt{T})$ regret bound for non-curved sets ($q\to\infty$)., Comment: 17 pages

This paper investigates the problem of controlling a linear system under possibly unbounded and degenerate noise with unknown cost functions, known as an online control problem. In contrast to the existing work, which assumes the boundedness of noise, we reveal that for convex costs, an $ \widetilde{O}(\sqrt{T}) $ regret bound can be achieved even for unbounded noise, where $ T $ denotes the time horizon. Moreover, when the costs are strongly convex, we establish an $ O({\rm poly} (\log T)) $ regret bound without the assumption that noise covariance is non-degenerate, which has been required in the literature. The key ingredient in removing the rank assumption on noise is a system transformation associated with the noise covariance. This simultaneously enables the parameter reduction of an online control algorithm., Comment: 26 pages

Partial monitoring is a generic framework of online decision-making problems with limited observations. To make decisions from such limited observations, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, exploration by optimization (ExO), was proposed, which achieves the optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this problem in locally observable games, we first establish a novel framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve the existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / \Delta_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $\Delta_a$ is the suboptimality gap for action $a$. This bound is roughly $\Theta(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound., Comment: 30 pages

This paper studies online structured prediction with full-information feedback. For online multiclass classification, Van der Hoeven (2020) established \emph{finite} surrogate regret bounds, which are independent of the time horizon, by introducing an elegant \emph{exploit-the-surrogate-gap} framework. However, this framework has been limited to multiclass classification primarily because it relies on a classification-specific procedure for converting estimated scores to outputs. We extend the exploit-the-surrogate-gap framework to online structured prediction with \emph{Fenchel--Young losses}, a large family of surrogate losses that includes the logistic loss for multiclass classification as a special case, obtaining finite surrogate regret bounds in various structured prediction problems. To this end, we propose and analyze \emph{randomized decoding}, which converts estimated scores to general structured outputs. Moreover, by applying our decoding to online multiclass classification with the logistic loss, we obtain a surrogate regret bound of $O(\| \mathbf{U} \|_\mathrm{F}^2)$, where $\mathbf{U}$ is the best offline linear estimator and $\| \cdot \|_\mathrm{F}$ denotes the Frobenius norm. This bound is tight up to logarithmic factors and improves the previous bound of $O(d\| \mathbf{U} \|_\mathrm{F}^2)$ due to Van der Hoeven (2020) by a factor of $d$, the number of classes.

We demonstrate that quantum error correction is realized by the renormalization group in scalar field theories. We construct $q$-level states by using coherent states in the IR region. By acting on them the inverse of the unitary operator $U$ that describes the renormalization group flow of the ground state, we encode them into states in the UV region. We find the situations in which the Knill-Laflamme condition is satisfied for operators that create coherent states. We verify this to the first order in the perturbation theory. This result suggests a general relationship between the renormalization group and quantum error correction and should give insights into understanding the role played by them in the gauge/gravity correspondence., Comment: 21 pages, typos corrected, a more detailed analysis of the results added, abstract changed, published version

Kempe equivalence is a classical and important notion on vertex coloring in graph theory. In the present paper, we introduce several ideals associated with graphs and provide a method to determine whether two $k$-colorings are Kempe equivalent via commutative algebra. Moreover, we give a way to compute all $k$-colorings of a graph up to Kempe equivalence by virtue of the algebraic technique on Gr\"{o}bner bases. As a consequence, the number of $k$-Kempe classes can be computed by using Hilbert functions. Finally, we introduce several algebraic algorithms related to Kempe equivalence., Comment: 18 pages, 3 figures

Monolayers of $AB$Te$_4$ ($A$/$B$ = Ti, Zr, Hf) were theoretically predicted to be two-dimensional topological insulators, but little has been known about the physical properties of these compounds. Here, we report on the single crystal growth, bulk transport properties, and band structure calculations of these compounds. The magnetotransport properties indicate that all three compounds are multi-carrier systems. The experimental results of ZrTiTe$_4$ and HfTiTe$_4$ can be well fitted by the multi-carrier formula assuming two types of carriers, while three carrier components were necessary for HfZrTe$_4$. Interestingly, one of the carrier mobilities of HfZrTe$_4$ exceeded 1000 cm$^2$V$^{-1}$s$^{-1}$, which was nearly one order in magnitude larger than the carrier mobilities of ZrTiTe$_4$ and HfTiTe$_4$. Our band structure calculations showed that all three compounds are semimetals consistent with the magnetotransport properties. The band structure around the $\Gamma$-point of HfZrTe$_4$ exhibits features that are distinct from the other two compounds, which is likely the reason of the different carrier properties.