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We establish a family of inequalities that hold true on any $6$ points in any $\mathrm{CAT}(0)$ space. We prove that the validity of these inequalities does not follow from any properties of $5$-point subsets of $\mathrm{CAT}(0)$ spaces. In particular, the validity of these inequalities does not follow from the $\mathrm{CAT}(0)$ $4$-point condition., Comment: 10 pages

We systematically investigate local phonon hopping in the radial direction of a linear trapped-ion string. We measure the decay of hopping as a function of key trap parameters and analyze the results in terms of the decay time and the number of oscillations. We attribute the loss of coherence to nonlinear coupling between different modes. Despite quantitative differences, the overall trends in our numerical simulations are similar to those of the experimental results. This work establishes a method for evaluating phonon hopping coherence and provides insight into the underlying decoherence mechanisms.

Traditional blockchain systems, such as Ethereum, typically rely on a \emph{single volatile cryptocurrency for transaction fees}. This leads to fluctuating transaction fee prices and limits the flexibility of users' payment options. To address these issues, we propose MStableChain, which leverage multiple stablecoins as native tokens for transaction fee settlements, thus ensuring stable transaction fees and flexible payment options. To address the challenges of mass adoption and practicality, we propose several core designs. To maintain compatibility with the Ethereum Virtual Machine (EVM) for mass adoption while supporting multiple native stablecoins, MStableChain employs a multi-currency units, multi-type RPCs mechanism. This mechanism enables the system to handle multiple stablecoins without altering the EVM or requiring changes to user applications. Furthermore, an oracle-based gas fee adjustment mechanism is proposed to manage exchange rates between different stablecoins, ensuring equitable transaction costs across various currencies. The system also introduces a secure, on-chain voting-based management protocol for the administrative functions related to these stablecoins. Experimental results from a prototype implementation demonstrate that MStableChain provides stable transaction fee prices, high effectiveness, and good usability., Comment: In submission to IEEE TSC

We study chiral condensate in cold nuclear matter on the basis of holographic theory, which would be dual to a baryon system in quantum chromodynamics (QCD) in the confinement phase. Our model is a holographic model based on the D$3$/D$7$ branes. The magnitude of the chiral condensate obtained in our model is found to gradually increase with increasing baryon density $n$ within the range of the dilute nucleon gas, $n<1$, where our model is available. This is a result for the chiral condensate in the holographic model as a function of $n$, which can be compared to the chiral perturbation theory., Comment: 12 pages, 5 figures

A compact energy-recovery linac (cERL) has been un-der construction at KEK since 2009 to develop key technologies for the energy-recovery linac. The cERL began operating in 2013 to create a high-current beam with a low-emittance beam with stable continuous wave (CW) superconducting cavities. Owing to the development of critical components, such as the DC gun, superconducting cavities, and the design of ideal beam transport optics, we have successfully established approximately 1 mA stable CW operation with a small beam emittance and extremely small beam loss. This study presents the details of our key technologies and experimental results for achieving 100% energy recovery operation with extremely small beam loss during a stable, approximately 1 mA CW beam operation., Comment: 11 pages, 16 figures

We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection, and call a collection of such edges a network. Our objective is thus rephrased as uncovering the network by selecting relevant edges, referred to as the network exploration. Our methodology is based on multiple testing for the presence or absence of each edge, designed to ensure statistical reproducibility via controlling the false discovery rate (FDR). In particular, we carefully construct $p$-variables, and apply the Benjamini-Hochberg (BH) procedure. We show that the BH with our $p$-variables controls the FDR under arbitrary dependence structure with any sample size and dimension, and has asymptotic power one under mild conditions. The validity is also confirmed by simulations and a real data example.

Blockchain technology and Artificial Intelligence (AI) have emerged as transformative forces in their respective domains. This paper explores synergies and challenges between these two technologies. Our research analyses the biggest projects combining blockchain and AI, based on market capitalization, and derives a novel framework to categorize contemporary and future use cases. Despite the theoretical compatibility, current real-world applications combining blockchain and AI remain in their infancy.

Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. As stated in their paper, this family seems to include all previously used quadratic metric inequalities that hold true in every $\mathrm{CAT}(0)$ space. We prove that there exists a metric space that satisfies all inequalities in this family but does not admit an isometric embedding into any $\mathrm{CAT}(0)$ space. More precisely, we prove that the $6$-point metric space constructed by Nina Lebedeva, which does not admit an isometric embedding into any $\mathrm{CAT}(0)$ space, satisfy all inequalities in this family., Comment: 14 pages

This paper presents an Euler--Lagrange system for a continuous-time model of the accelerated gradient methods in smooth convex optimization and proposes an associated Lyapunov-function-based convergence analysis framework. Recently, ordinary differential equations (ODEs) with dumping terms have been developed to intuitively interpret the accelerated gradient methods, and the design of unified model describing the various individual ODE models have been examined. In existing reports, the Lagrangian, which results in the Euler-Lagrange equation, and the Lyapunov function for the convergence analysis have been separately proposed for each ODE. This paper proposes a unified Euler--Lagrange system and its Lyapunov function to cover the existing various models. In the convergence analysis using the Lyapunov function, a condition that parameters in the Lagrangian and Lyapunov function must satisfy is derived, and a parameter design for improving the convergence rate naturally results in the mysterious dumping coefficients. Especially, a symmetric Bregman divergence can lead to a relaxed condition of the parameters and a resulting improved convergence rate. As an application of this study, a slight modification in the Lyapunov function establishes the similar convergence proof for ODEs with smooth approximation in nondifferentiable objective function minimization.

We conducted measurements of $K^- + {^3{\rm He}} \to \pi \!Y \!N + N'$ reactions using a $1~{\rm GeV}/c$ $K^-$-beam, with the objective of understanding the broad decay width of $\bar{K} \!N \!N$ (approximately twice as broad as that of $\Lambda(1405)$ considered to be the $\bar{K} \!N$ quasi-bound state). We successfully reproduced distributions of the $\pi \! Y \! N$ invariant mass and momentum transfer for $\pi \! Y \! N$ using model fitting functions for $\bar{K} \!N \!N$ formation and quasi-free $\bar{K}$ absorption (${\rm QF}_{\bar{K}-{\rm abs}}$) processes. The model can describe the experimental data quite well, and four $\bar{K} \! N \! N \to \pi \! Y \! N $ cross-sections were obtained. The results indicate that mesonic decay is the dominant decay branch of $\bar{K} \! N \! N$. The results also suggest that $\Gamma_{\pi \Lambda N} \sim \Gamma_{\pi \Sigma N}$, which indicates that the $I_{\bar{K} \! N}=1$ absorption channel, in addition to the $I_{\bar{K} \! N}=0$ absorption channel, substantially contribute to the $\bar{K} \! N \! N$ decay, making the $\bar{K} \! N \! N$ state approximately twice as unstable as $\Lambda$(1405).

The Texas Higher Education Coordinating Board (THECB) seeks to improve student outcomes by promoting a variety of student success efforts. These efforts include direct programs with well-defined target populations and program participants, offering specific student support services following a program model, and indirect programs aimed at providing faculty and staff members professional development or at improving campus facilities. MDRC led an implementation study of student success programs across the state that were funded by a grant from the U.S. Department of Education, Education Stabilization Fund Program Governor's Emergency Education Relief (GEER II) Fund. This fund was a COVID-19 recovery initiative, allowing recipients great flexibility in the use of grants, evident in the findings below. A total of nearly $12 million in grants was disbursed to 59 institutions of higher education in Texas. This report presents: (1) implementation research findings from the 59 institutions; (2) highlights research findings from previously conducted, rigorous evaluations of student support programs; and (3) offers recommendations for future research and practice.

A common narrative about women students of color in postsecondary education centers on the fact that they typically outperform men of color on measures such as college access, retention, and persistence. As a result, decision-makers might conclude that women of color do not need additional supports from institutions of higher education. Although they do earn associate's and bachelor's degrees at higher rates than men of color, equity gaps remain between women of color and their White female peers. In addition to barriers related to race, women of color also face barriers related to gender. These intersecting factors contribute to economic, social, and health disparities and challenges that women of color may carry over into their lives as students. In early 2023, MDRC convened a virtual gathering, "Resisting Erasure: Women of Color College Success Research and Practice Roundtable," to address this void. It brought together 24 students, higher education administrators, faculty scholars, and funders from across the country who were interested in advancing knowledge and best practices in postsecondary education regarding the needs of women of color. The goals of the roundtable were to understand more deeply, and hear firsthand about, the disparities, needs, and knowledge gaps regarding women of color; to synthesize knowledge on targeted supports; and to develop recommendations and a research agenda that could help improve postsecondary education and career outcomes. This brief highlights some of the insights distilled from that roundtable, including themes and issues at both the student and institutional levels, recommendations for how to address those issues, and considerations for future action.

Increasingly, obtaining a job that pays family-sustaining wages means getting a college degree or other postsecondary credential. However, according to the 2021 U.S. Census, only 31.5 percent of Texans ages 25 and older have a bachelor's degree or higher. The Texas Higher Education Coordinating Board (THECB)--the highest authority in the state regarding public higher education--has therefore set out a strategic plan to increase that percentage. Specifically, the plan calls for 60 percent of Texans ages 25 to 64 to have a postsecondary credential "of value" by 2030. THECB seeks to improve student outcomes by promoting a variety of student success interventions, particularly corequisite models. To meet this goal, THECB is giving grants to colleges across the state to fund student success programs: programs designed to help more students stay in college and earn degrees, particularly students of color, students from lower-income backgrounds, and students who need additional assistance to make satisfactory academic progress (that is, to earn enough credits to keep their federal financial aid). This brief summarizes some of the information THECB and its partners will use in that effort. It describes best practices and programs with proven effectiveness--the information that policymakers and practitioners need to consider in designing and promoting student success programs. The findings are based on MDRC's 20-year history conducting rigorous evaluations in postsecondary education as well as research and evaluations by other researchers. [This brief was funded by a grant from the U.S. Department of Education, Education Stabilization Fund Program Governor's Emergency Education Relief Fund, as part of the THECB Student Success Acceleration Program Implementation Grants.]

Open-domain dialogue systems have started to engage in continuous conversations with humans. Those dialogue systems are required to be adjusted to the human interlocutor and evaluated in terms of their perspective. However, it is questionable whether the current automatic evaluation methods can approximate the interlocutor's judgments. In this study, we analyzed and examined what features are needed in an automatic response evaluator from the interlocutor's perspective. The first experiment on the Hazumi dataset revealed that interlocutor awareness plays a critical role in making automatic response evaluation correlate with the interlocutor's judgments. The second experiment using massive conversations on X (formerly Twitter) confirmed that dialogue continuity prediction can train an interlocutor-aware response evaluator without human feedback while revealing the difficulty in evaluating generated responses compared to human responses., Comment: 9 pages, 3 figures, 5 tables, Accepted by IJCNLP-AACL 2023 SRW

This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and presents convergence analysis framework. Similar to the gradient method, the gradient flow is inapplicable to the non-differentiable function minimization; therefore, this paper addresses the smoothing gradient method, which exploits a decreasing smoothing parameter sequence in the smooth approximation. The convergence analysis is presented using conventional Lyapunov-function-based techniques, and a Lyapunov function applicable to both strongly convex and non-strongly convex objective functions is provided by taking into consideration the effect of the smooth approximation. Based on the equivalence of the stepsize in the smoothing gradient method and the discretization step in the forward Euler scheme for the numerical integration of the smoothing gradient flow, the sample values of the exact solution of the smoothing gradient flow are compared with the state variable of the smoothing gradient method, and the equivalence of the convergence rates is shown.

We study properties and algorithms of a minimization problem of the maximum generalized eigenvalue of symmetric-matrix-valued affine functions, which is nonsmooth and quasiconvex, and has application to eigenfrequency optimization of truss structures. We derive an explicit formula of the Clarke subdifferential of the maximum generalized eigenvalue and prove the maximum generalized eigenvalue is a pseudoconvex function, which is a subclass of a quasiconvex function, under suitable assumptions. Then, we consider smoothing methods to solve the problem. We introduce a smooth approximation of the maximum generalized eigenvalue and prove the convergence rate of the smoothing projected gradient method to a global optimal solution in the considered problem. Also, some heuristic techniques to reduce the computational costs, acceleration and inexact smoothing, are proposed and evaluated by numerical experiments., Comment: 33 pages, 16 figures

The MEG II experiment, based at the Paul Scherrer Institut in Switzerland, reports the result of a search for the decay $\mu^+\to e^+\gamma$ from data taken in the first physics run in 2021. No excess of events over the expected background is observed, yielding an upper limit on the branching ratio of B($\mu^+\to e^+\gamma$) < $7.5 \times 10^{-13}$ (90% C.L.). The combination of this result and the limit obtained by MEG gives B($\mu^+\to e^+\gamma$) < $3.1 \times 10^{-13}$ (90% C.L.), which is the most stringent limit to date. A ten-fold larger sample of data is being collected during the years 2022-2023, and data-taking will continue in the coming years., Comment: 10 pages, 6 figures. To be published in EPJC

The MEG II experiment, located at the Paul Scherrer Institut (PSI) in Switzerland, is the successor to the MEG experiment, which completed data taking in 2013. MEG II started fully operational data taking in 2021, with the goal of improving the sensitivity of the mu+ -> e+ gamma decay down to 6e-14 almost an order of magnitude better than the current limit. In this paper, we describe the operation and performance of the experiment and give a new estimate of its sensitivity versus data acquisition time., Comment: 42 pages, 55 figures. Submitted to EPJC