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We investigate the asymptotic behavior of the $\mathrm{SU}(2)$-Yang-Mills-Higgs energy $E(\Phi,A)=\int_M|d_A\Phi|^2+|F_A|^2$ in the large mass limit, proving convergence to the codimension-three area functional in the sense of De Giorgi's $\Gamma$-convergence. More precisely, for a compact manifold with boundary $M$ and any family of pairs $\Phi_m\in\Omega^0(M;\mathfrak{su}(2))$ and $A_m\in \Omega^1(M;\mathfrak{su}(2))$ indexed by a mass parameter $m\to\infty$, satisfying $$E(\Phi_m,A_m)\leq Cm\quad\text{and}\quad\lim_{m\to\infty}\frac{1}{m}\int_M(m-|\Phi_m|)^2=0,$$ we prove that the $(n-3)$-currents dual to $\frac{1}{2\pi m}\mathrm{tr}(d_{A_m}\Phi_m\wedge F_{A_m})$ converge subsequentially to a relative integral $(n-3)$-cycle $T$ of mass \begin{equation} \mathbb{M}(T)\leq \liminf_{m\to\infty}\frac{1}{4\pi m}E(\Phi_m,A_m), \end{equation} and show conversely that any integral $(n-3)$-current $T$ with $[T]=0\in H_{n-3}(M,\partial M;\mathbb{Z})$ admits such an approximation, with equality in the above inequality. In the special case of pairs $(\Phi_m,A_m)$ satisfying the generalized monopole equation $*d_{A_m}\Phi_m=F_{A_m}\wedge \Theta$ for a calibration form $\Theta\in \Omega^{n-3}(M)$, we deduce that the limit $\nu=\lim_{m\to\infty}\frac{1}{2\pi m}|d_{A_m}\Phi_m|^2$ of the Dirichlet energy measures satisfies $\nu\leq |T|$, with equality if and only if $T$ is calibrated by $\Theta$, giving evidence for predictions of Donaldson-Segal in the settings of $G_2$-manifolds and Calabi-Yau $3$-folds., Comment: 37 pages

As part of the PIP-II project at Fermilab, a pre-production cryomodule featuring 325 MHz Single Spoke Resonator type 2 (SSR2) superconducting RF cavities is under construction. These SSR2 cavities are fabricated by industry partners and undergo initial cold testing at our collaborating institution, IJCLab in France, utilizing low-power coupler. Subsequently, the cavities are subjected to final qualification at Fermilab, complete with tuner and high-power coupler assemblies. This paper provides an overview of the ongoing efforts dedicated to high-power testing of jacketed SSR2 cavities in the Spoke Test Cryostat (STC) at Fermilab. Performance parameters obtained from these tests are presented, offering valuable insights into the cavities operational characteristics and readiness for integration into the PIP-II cryomodule., Comment: 32nd Linear Accelerator Conference (LINAC 2024)

We establish a direct log-epiperimetric inequality for Yang$-$Mills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singularity for energy minimizing Yang$-$Mills fields and $\omega$-ASD connections (where $\omega$ is not necessarily closed) satisfying some suitable regularity assumptions. En route to this we establish a Luckhaus type lemma for Yang$-$Mills connections to exclude curvature concentration along blow-up sequences., Comment: Any comments are welcome

Dielectric capillaries are widely used to generate plasmas for plasma wakefield acceleration. When a relativistic drive bunch travels through a capillary with misaligned trajectory with respect to the capillary axis, it is deflected by the effect of the dielectric transverse wakefields it drives. We experimentally show that the deflection effect increases along the bunch and with larger misalignment, and we investigate the decay of dielectric wakefields by measuring the effect on the front of a trailing bunch. We discuss the implications for the design of a plasma wakefield accelerator based on dielectric capillaries., Comment: Proceedings of the 2024 Advanced Accelerator Concepts Workshop

Context. IRAS 16293E is a rare case of a prestellar core being subjected to the effects of at least one outflow.Aims. We want to disentangle the actual structure of the core from the outflow impact and evaluate the evolutionary stage of the core. Methods. Prestellar cores being cold and depleted, the best tracers of their central regions are the two isotopologues of trihydrogren cation which are observable from the ground, ortho-H$_2$D and para-D$_2$H . We used the Atacama Pathfinder EXperiment (APEX) telescope to map the para-D$_2$H$^+$ emission in IRAS 16293E and collected James Clerk Maxwell Telescope (JCMT) archival data of ortho-H$_2$D$^+$ . We compare their emission to that of other tracers, including dust emission, and analyse their abundance with the help of a 1D radiative transfer tool. The ratio of the abundances of ortho-H$_2$D$^+$ and para-D$_2$H$^+$ can be used to estimate the stage of the chemical evolution of the core.Results. We have obtained the first complete map of para-D$_2$H$^+$ emission in a prestellar core. We compare it to a map of ortho-H$_2$D$^+$ and show their partial anti-correlation. This reveals a strongly evolved core with a para-D$_2$H$^+$/ortho-H$_2$D$^+$ abundance ratio towards the centre for which we obtain a conservative lower limit from 3.9 (at 12 K) up to 8.3 (at 8 K) while the high extinction of the core is indicative of a central temperature below 10 K. This ratio is higher than predicted by the known chemical models found in the literature. Para-D$_2$H$^+$ (and indirectly ortho-H$_2$D$^+$) is the only species that reveals the true centre of this core, while the emission of other molecular tracers and dust are biased by the temperature structure that results from the impact of the outflow.Conclusions. This study invites to reconsider the analysis of previous observations of this source and possibly questions the validity of the deuteration chemical models or of the reaction and inelastic collisional rate coefficients of the H$^{+3}$ isotopologue family. This could impact the deuteration clock predictions for all sources.

We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, \kappa_0}$ $m$-form $\omega$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at $\mathcal{H}^{m - 2}$-a.e. point in the interior singular set of $T$. Our proof adapts techniques that were recently developed in [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting., Comment: References updated

We investigate a traffic assignment problem on a transportation network, considering both the demands of individual drivers and of a large fleet controlled by a central operator (minimizing the fleet's average travel time). We formulate this problem as a two-player convex game and we study how the size of the coordinated fleet, measured in terms of share of the total demand, influences the Price of Anarchy (PoA). We show that, for two-terminal networks, there are cases in which the fleet must reach a minimum share before actually affecting the PoA, which otherwise remains unchanged. Moreover, for parallel networks, we prove that the PoA is monotonically non-increasing in the fleet share.

In this paper, we present a framework for multi-agent learning in a nonstationary dynamic network environment. More specifically, we examine projected gradient play in smooth monotone repeated network games in which the agents' participation and connectivity vary over time. We model this changing system with a stochastic network which takes a new independent realization at each repetition. We show that the strategy profile learned by the agents through projected gradient dynamics over the sequence of network realizations converges to a Nash equilibrium of the game in which players minimize their expected cost, almost surely and in the mean-square sense. We then show that the learned strategy profile is an almost Nash equilibrium of the game played by the agents at each stage of the repeated game with high probability. Using these two results, we derive non-asymptotic bounds on the regret incurred by the agents., Comment: 10 pages

We study a family of random graph models - termed subgraph generated models (SUGMs) - initially developed by Chandrasekhar and Jackson in which higher-order structures are explicitly included in the network formation process. We use matrix concentration inequalities to show convergence of the adjacency matrix of networks realized from such SUGMs to the expected adjacency matrix as a function of the network size. We apply this result to study concentration of centrality measures (such as degree, eigenvector, and Katz centrality) in sampled networks to the corresponding centralities in the expected network, thus proving that node importance can be predicted from knowledge of the random graph model without the need of exact network data.

The New York City P-TECH 9-14 schools are an educational model that ties together the secondary, higher education, and workforce systems to improve outcomes across domains. The distinguishing feature of the model is a partnership among a high school, a community college, and one or more employer partners that focuses on preparing students for both college and careers within six years. P-TECH 9-14 schools collaborate with local colleges to provide students with an opportunity to earn a high school diploma within four years, followed by a cost-free, industry-recognized associate's degree. During the six-year program, employer partners provide students with work-based learning experiences such as internships, mentoring, and job shadowing. This study provides impact, implementation, and cost study findings from the first rigorous evaluation of the model, examining the first seven P-TECH 9-14 schools that opened in New York City. The study follows entering classes of students for seven years after they begin ninth grade, which would carry them through the end of their expected high school graduations and through three years of postsecondary education. The study takes advantage of the random lottery process created by the New York City high school admissions system to identify the model's effects: It compares students who won lotteries to attend P-TECH 9-14 schools (the P-TECH 9-14 group) with students who applied but did not win (the comparison group). It also includes an in-depth implementation study that assesses how schools carried out the model, and a cost-effectiveness study that examines costs per college degree earned for P-TECH 9-14 schools compared with other schools. [For the full report, see ED632477.]

Beamline components, such as superconducting radio frequency cavities and focusing lenses, need to be assembled together in a string while in a cleanroom environment. The present contribution identifies and characterizes materials for additive manufacturing that can be used in a cleanroom. The well known advantages of additive manufacturing processes would highly benefit the design and development of tooling needed for the mechanical support and alignment of string components. Cleanliness, mechanical properties, and leak tightness of the chosen materials are the main focus of this contribution, which also paves the way for the integration of such materials in cryomodule assemblies. Results reported here were obtained in the framework of the PIP-II project at Fermilab., Comment: 21st International Conference on Radio-Frequency Superconductivity (SRF 2023)

The space-charge field of a relativistic charged bunch propagating in plasma is screened due to the presence of mobile charge carriers. We experimentally investigate such screening by measuring the effect of dielectric wakefields driven by the bunch in a uncoated dielectric capillary where the plasma is confined. We show that the plasma screens the space-charge field and therefore suppresses the dielectric wakefields when the distance between the bunch and the dielectric surface is much larger than the plasma skin depth. Before full screening is reached, the effects of dielectric and plasma wakefields are present simultaneously.

We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manifold, a function that nearly saturates a critical Sobolev inequality is quantitatively $W^{1,2}$-close to a non-empty set of extremal functions, provided that the corresponding optimal Sobolev constant satisfies a suitable strict bound. The case of sub-critical Sobolev inequalities is also covered. Finally, we discuss degenerate phenomena in our quantitative controls., Comment: Comments welcome!

We investigate the dynamics of plasma-based acceleration processes with collisionless particle dynamics and non negligible thermal effects. We aim at assessing the applicability of fluid-like models, obtained by suitable closure assumptions applied to the relativistic kinetic equations, thus not suffering of statistical noise, even in presence of a finite temperature. The work here presented focuses on the characterization of pressure anisotropies, which crucially depend on the adopted closure scheme, and hence are useful to discern the appropriate thermal fluid model. To this aim, simulation results of spatially resolved fluid models with different thermal closure assumptions are compared with the results of particle-in-cell (PIC) simulations at changing temperature and amplitude of plasma oscillations., Comment: The following article has been submitted to Physics of Plasma

Networks of coupled nonlinear oscillators have been used to model circadian rhythms, flashing fireflies, Josephson junction arrays, high-voltage electric grids, and many other kinds of self-organizing systems. Recently, several authors have sought to understand how coupled oscillators behave when they interact according to a random graph. Here we consider interaction networks generated by a graphon model known as a $W$-random network, and examine the dynamics of an infinite number of identical phase oscillators, following an approach pioneered by Medvedev. We show that with sufficient regularity on $W$, the solution to the dynamical system over a $W$-random network of size $n$ converges in the $L^{\infty}$ norm to the solution of the continuous graphon system, with high probability as $n\rightarrow\infty$. This result suggests a framework for studying synchronization properties in large but finite random networks. In this paper, we leverage our convergence result in the $L^{\infty}$ norm to prove synchronization results for two classes of identical phase oscillators on Erd\H{o}s-R\'enyi random graphs. First, we show that the Kuramoto model on the Erd\H{o}s-R\'enyi graph $G(n, \alpha_n)$ achieves phase synchronization with high probability as $n$ goes to infinity, if the edge probability $\alpha_n$ exceeds $(\log n)/n$, the connectivity threshold of an Erd\H{o}s-R\'enyi random graph. Then we show that the Sakaguchi-Kuramoto model on the Erd\H{o}s-R\'enyi graph $G(n, p)$ achieves frequency synchronization with high probability as $n$ goes to infinity, assuming a fixed edge probability $p\in(0,1]$ and a certain regime for the model's phase shift parameter. A notable feature of the latter result is that it holds for an oscillator model whose dynamics are not simply given by a gradient flow., Comment: 29 pages, 3 figures

A prototype cryomodule containing eight Single Spoke Resonators type-1 (SSR1) operating at 325 MHz and four superconducting focusing lenses was successfully assembled, cold tested, and accelerated beam in the framework of the PIP-II project at Fermilab. The impact of induced residual magnetic fields from the solenoids on performance of cavities is presented in this contribution. In addition, design optimizations for the production cryomodules as a result of this impact are highlighted., Comment: SRF2023 Conference

When students drop out of high school there are substantial social and economic consequences that can persist throughout their lives. They are more likely to be unemployed, to become teenage parents, to become involved in the criminal justice system, and to suffer a lifetime of low wages. Dropout rates soared during the COVID-19 pandemic as schools struggled to adapt and keep students engaged. During the 2021-2022 school year, Communities In Schools® (CIS®) introduced the Reengagement Coordinator (RC) Initiative, with the goal of reengaging high school students (particularly eleventh and twelfth grade students) who did not reenroll in school or were chronically absent. CIS partnered with MDRC in 2021 to conduct a qualitative evaluation of the implementation of the RC Initiative. The evaluation set out to answer key questions related to the reasons for students' disengagement, how RCs identified students, which strategies were most effective, and the potential pathways for reengagement. This brief summarizes the main findings and shares takeaways and considerations for practitioners in schools and other organizations who are looking to work with and reengage disengaged students or create a dedicated position to reengage students. [This research project received funding from Blue Meridian Partners.]

We study the boundary behavior of any limit-interface arising from a sequence of general critical points of the Allen-Cahn energy functionals on a smooth bounded domain. Given any such sequence with uniform energy bounds, we prove that the limit-interface is a free boundary varifold which is integer rectifiable up to the boundary. This extends earlier work of Hutchinson and Tonegawa on the interior regularity of such limit-interface. A key novelty in our result is that no convexity assumption of the boundary is required and it is valid even when the limit-interface clusters near the boundary. Moreover, our arguments are local and thus works in the Riemannian setting. This work provides the first step towards the regularity theory for the Allen-Cahn min-max theory for free boundary minimal hypersurfaces, which was developed in the Almgren-Pitts setting by the first-named author and Zhou., Comment: 37 pages, no figure; all comments are welcome

This contribution reports the design of the production Single Spoke Resonator Type 1 Cryomodule (SSR1 CM) for the PIP-II project at Fermilab. The innovative design is based on a structure, the strongback, which supports the coldmass from the bottom, stays at room temperature during operations, and can slide longitudinally with respect to the vacuum vessel. The Fermilab style cryomodule developed for the prototype Single Spoke Resonator Type 1 (pSSR1), the prototype High Beta 650 MHz (pHB650), and preproduction Single Spoke Resonator Type 2 (ppSSR2) cryomodules is the baseline of the present design. The focus of this contribution is on the results of calculations and finite element analyses performed to optimize the critical components of the cryomodule: vacuum vessel, strongback, thermal shield, and magnetic shield., Comment: 21st Intl Conf Radio Frequency Superconductivity (SRF 2023). arXiv admin note: substantial text overlap with arXiv:2209.01282

In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and agents may not be present at each iteration. To get tractability, we assume that at each iteration, the network of interactions is sampled from an underlying random network model and agents participate at random with a given probability. Under these assumptions, we consider a gradient-based learning algorithm and establish almost sure convergence of the agents' strategies to the Nash equilibrium of the game played over the expected network. Additionally, we prove, in the large population regime, that the learned strategy is an $\epsilon$-Nash equilibrium for each stage game with high probability. We validate our results over an online market application., Comment: 8 pages, 2 figures, Extended version of the original paper to appear in the proceedings of the 2023 IEEE Conference on Decision and Control (CDC). Updated numerical example

A comprehensive characterization of lattice Boltzmann (LB) schemes to perform warm fluid numerical simulations of particle wakefield acceleration (PWFA) processes is discussed in this paper. The LB schemes we develop hinge on the moment matching procedure, allowing the fluid description of a warm relativistic plasma wake generated by a driver pulse propagating in a neutral plasma. We focus on fluid models equations resulting from two popular closure assumptions of the relativistic kinetic equations, i.e., the local equilibrium and the warm plasma closure assumptions. The developed LB schemes can thus be used to disclose insights on the quantitative differences between the two closure approaches in the dynamics of PWFA processes. Comparisons between the proposed schemes and available analytical results are extensively addressed., Comment: Published on Physics of Plasmas

We develop the asymptotic analysis as $\epsilon\to 0$ for the natural gradient flow of the self-dual $U(1)$-Higgs energies $$E_{\epsilon}(u,\nabla)=\int_M\left(|\nabla u|^2+\epsilon^2|F_{\nabla}|^2+\frac{(1-|u|^2)^2}{4\epsilon^2}\right)$$ on Hermitian line bundles over closed manifolds $(M^n,g)$ of dimension $n\ge 3$, showing that solutions converge in a measure-theoretic sense to codimension-two mean curvature flows -- i.e., integral $(n-2)$-Brakke flows -- generalizing results of the last two authors from the stationary case. Given any integral $(n-2)$-cycle $\Gamma_0$ in $M$, these results can be used together with the convergence theory developed in previous work of the authors to produce nontrivial integral Brakke flows starting at $\Gamma_0$ with additional structure, similar to those produced via Ilmanen's elliptic regularization., Comment: Comments welcome

The Proton Improvement Plan-II (PIP-II [1]) linac will include 35 Single Spoke Resonators type 2 (SSR2). A preproduction SSR2 cryomodule will contain 5 jacketed cavities. Several units are already manufactured and prepared for cold testing. In this work, data collected from the fabrication, processing and preparation of the cavities will be presented and the improvements implemented after the completion of the first unit will be highlighted.

It is known that there exist functions in certain de Branges--Rovnyak spaces whose Taylor series diverge in norm, even though polynomials are dense in the space. This is often proved by showing that the sequence of Taylor partial sums is unbounded in norm. In this note we show that it can even happen that the Taylor partial sums tend to infinity in norm. We also establish similar results for lower-triangular summability methods such as the Ces\`aro means.

We consider network games where a large number of agents interact according to a network sampled from a random network model, represented by a graphon. By exploiting previous results on convergence of such large network games to graphon games, we examine a procedure for estimating unknown payoff parameters, from observations of equilibrium actions, without the need for exact network information. We prove smoothness and local convexity of the optimization problem involved in computing the proposed estimator. Additionally, under a notion of graphon parameter identifiability, we show that the optimal estimator is globally unique. We present several examples of identifiable homogeneous and heterogeneous parameters in different classes of linear quadratic network games with numerical simulations to validate the proposed estimator., Comment: The extended arXiv version of the original paper accepted for publication in the 2023 American Control Conference, 9 pages, 1 figure

We introduce kernel-summability methods in Banach spaces using the vector-valued integrals and prove an analogue of the Silverman-Toeplitz Theorem for regular kernel-summability methods. We also show that if $X$ is a Banach space and one kernel-summability method is included in another kernel-summability method for scalar-valued functions, then the first method is included in the second method, for $X$-valued functions. This extends a previous result from Javad Mashreghi, Thomas Ransford and the author. We then apply these abstract results to the summability of Taylor series of functions in a Banach space of holomorphic functions on the unit disk.