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We study truthful mechanisms for approximating the Maximin-Share (MMS) allocation of agents with additive valuations for indivisible goods. Algorithmically, constant factor approximations exist for the problem for any number of agents. When adding incentives to the mix, a jarring result by Amanatidis, Birmpas, Christodoulou, and Markakis [EC 2017] shows that the best possible approximation for two agents and $m$ items is $\lfloor \frac{m}{2} \rfloor$. We adopt a learning-augmented framework to investigate what is possible when some prediction on the input is given. For two agents, we give a truthful mechanism that takes agents' ordering over items as prediction. When the prediction is accurate, we give a $2$-approximation to the MMS (consistency), and when the prediction is off, we still get an $\lceil \frac{m}{2} \rceil$-approximation to the MMS (robustness). We further show that the mechanism's performance degrades gracefully in the number of ``mistakes" in the prediction; i.e., we interpolate (up to constant factors) between the two extremes: when there are no mistakes, and when there is a maximum number of mistakes. We also show an impossibility result on the obtainable consistency for mechanisms with finite robustness. For the general case of $n\ge 2$ agents, we give a 2-approximation mechanism for accurate predictions, with relaxed fallback guarantees. Finally, we give experimental results which illustrate when different components of our framework, made to insure consistency and robustness, come into play.

The goal of this paper is twofold. Firstly, we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety, by developing the notion of algebraic dimensions of Bruhat intervals, strengthening a type $A$ result by Donten-Bury, Escobar and Portakal. In the process, we give an explicit description of the torus action on any Deodhar component as well as describe the root subgroups that comprise the component. Secondly, when a Levi subgroup in a reductive algebraic group acts on a Schubert variety, we exhibit a codimension preserving bijection between the Levi-Borel subgroup (a Borel subgroup in the Levi subgroup) orbits in the big open cell of that Schubert variety and torus orbits in the big open cell of a distinguished Schubert subvariety. This bijection has many applications including a type-uniform formula for the Levi-Borel complexity of the usual Levi-Borel subgroup action on a Schubert variety. We conclude by extending the Levi-Borel complexity results to a large class of Schubert varieties in the partial flag variety., Comment: 23 pages, corrections made to sections 4.1, 4.2

Quantum computing is currently hindered by hardware noise. We present a freestyle superconducting pulse optimization method, incorporating two-qubit channels, which enhances flexibility, execution speed, and noise resilience. A minimal 0.22 ns pulse is shown to determine the H2 groundstate to within chemical accuracy upon real-hardware, approaching the quantum speed limit. Similarly, a pulse significantly shorter than circuit-based counterparts is found for the LiH molecule, attaining state-of-the-art accuracy. The method is general and can potentially accelerate performance across various quantum computing components and hardware., Comment: 6 pages (main) + 6 pages (supplementary materials), 10 figures

Generalizing smooth volumetric growth to the singular case, using de Rham currents and flat chains, we demonstrate how regular boundaries of bodies may evolve to fractals.

It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through Homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional to N_e^2. This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation., Comment: 52 pages, 6 figures,Suppl. Mater. 25 pages, Suppl. Mater. 5 figures, 1 table

This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell's equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a $p$-form in an $n$-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an $(n-p-1)$-form, a generalization of the Maxwell $2$-form.

The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive property for which a smooth flux field exists, even if the property is not conserved. Singular flux fields are considered using the notion of a de Rham current. Writing a generalized balance law using the boundary of the current corresponding to a singular flux field, surface growth is unified with volumetric growth., Comment: 5 figures

The Electron-Ion Collider~(EIC), a forthcoming powerful high-luminosity facility, represents an exciting opportunity to explore new physics. In this article, we study the potential of the EIC to probe the coupling between axion-like particles~(ALPs) and photons in coherent scattering. The ALPs can be produced via photon fusion and decay back to two photons inside the EIC detector. In a prompt-decay search, we find that the EIC can set the most stringent bound for $m_a \lesssim 20\,\GeV$ and probe the effective scales $\Lambda \lesssim 10^{5}\,$GeV. In a displaced-vertex search, which requires adopting an EM calorimeter technology that provides directionality, the EIC could probe ALPs with $m_a \lesssim 1\,\GeV$ at effective scales $\Lambda \lesssim 10^{7}\,\GeV$. Combining the two search strategies, the EIC can probe a significant portion of unexplored parameter space in the $0.2 < m_a <20\,\GeV$ mass range., Comment: 23 pages, 9 figures

The need for reliable and low-cost infrastructure is crucial in today's world. However, achieving both at the same time is often challenging. Traditionally, infrastructure networks are designed with a radial topology lacking redundancy, which makes them vulnerable to disruptions. As a result, network topologies have evolved towards a ring topology with only one redundant edge and, from there, to more complex mesh networks. However, we prove that large rings are unreliable. Our research shows that a sparse mesh network with a small number of redundant edges that follow some design rules can significantly improve reliability while remaining cost-effective. Moreover, we have identified key areas where adding redundant edges can impact network reliability the most by using the SAIDI index, which measures the expected number of consumers disconnected from the source node. These findings offer network planners a valuable tool for quickly identifying and addressing reliability issues without the need for complex simulations. Properly planned sparse mesh networks can thus provide a reliable and a cost-effective solution to modern infrastructure challenges.

We study how light scalar fields can change the stellar landscape by triggering a new phase of nuclear matter. Scalars coupled to nucleons can develop a non-trivial expectation value at finite baryon density. This sourcing of a scalar reduces the nucleon mass and provides an additional energy density and pressure source. Under generic conditions, a new ground state of nuclear matter emerges, with striking implications for the configuration of stellar remnants. Notably, neutron stars in the new ground state can be significantly heavier than QCD equations of state currently predict. We also find hybrid stellar compositions and stable self-bound objects with sizes as small as the Compton wavelength of the scalar. We discuss several specific realizations of this scenario: the QCD axion and lighter generalizations thereof and linearly or quadratically coupled scalar fields effectively equivalent to a class of scalar-tensor modification of gravity. Lastly, we explore phenomenological signatures relevant to electromagnetic and gravitational wave observations of neutron stars, such as atypical compactness and instability gaps in radii., Comment: 56 pages, 11 figures

Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of fundamental problems such as the Santa Claus problem (maximizing minimum utility), Nash welfare maximization (maximizing geometric mean of utilities), makespan minimization (minimizing maximum cost), minimization of $\ell_p$-norms, and so on. We focus on divisible items (i.e., fractional allocations) in this paper. Even for divisible items, these problems are characterized by strong super-constant lower bounds in the classical worst-case online model. In this paper, we study online allocations in the {\em learning-augmented} setting, i.e., where the algorithm has access to some additional (machine-learned) information about the problem instance. We introduce a {\em general} algorithmic framework for learning-augmented online allocation that produces nearly optimal solutions for this broad range of maximization and minimization objectives using only a single learned parameter for every agent. As corollaries of our general framework, we improve prior results of Lattanzi et al. (SODA 2020) and Li and Xian (ICML 2021) for learning-augmented makespan minimization, and obtain the first learning-augmented nearly-optimal algorithms for the other objectives such as Santa Claus, Nash welfare, $\ell_p$-minimization, etc. We also give tight bounds on the resilience of our algorithms to errors in the learned parameters, and study the learnability of these parameters.

Only two types of Standard Model particles are able to propagate the $480\,$meters separating the ATLAS interaction point and FASER: neutrinos and muons. Furthermore, muons are copiously produced in proton collisions. We propose to use FASER$\nu$ as a muon fixed target experiment in order to search for new bosonic degrees of freedom coupled predominantly to muons. These muon force carriers are particularly interesting in light of the recent measurement of the muon anomalous magnetic moment. Using a novel analysis technique, we show that even in the current LHC run, FASER$\nu$ could potentially probe previously unexplored parts of the parameter space. In the high-luminosity phase of the LHC, we find that the improved sensitivity of FASER$\nu2$ will probe unexplored parameter space and may be competitive with dedicated search proposals., Comment: 13 pages + appendices, 11 figures

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety $G/B$ of finite Lie type. We apply this to the study of multiplicity-free decompositions of a Demazure module into irreducible representations of a Levi subgroup., Comment: 11 pages. Minor corrections made in v2. To appear in Advances in Mathematics

Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points, changes. The setting we propose may be relevant to phenomena such as plasticity, fracture, discontinuities, and non-injectivity of the deformations. In this framework, we construct an unambiguous decomposition into incompatible and compatible factors which includes the standard elastic-plastic decomposition in plasticity.

We study the effects of exceptionally light QCD axions on the stellar configuration of white dwarfs. At finite baryon density, the non-derivative coupling of the axion to nucleons displaces the axion from its in-vacuum minimum which implies a reduction of the nucleon mass. This dramatically alters the composition of stellar remnants. In particular, the modifications of the mass-radius relationship of white dwarfs allow us to probe large regions of unexplored parameter space without requiring that axions are dark matter., Comment: 13 pages, 12 figures, added appendices, published version

We study the problem of real-time scheduling in a multi-hop millimeter-wave (mmWave) mesh. We develop a model-free deep reinforcement learning algorithm called Adaptive Activator RL (AARL), which determines the subset of mmWave links that should be activated during each time slot and the power level for each link. The most important property of AARL is its ability to make scheduling decisions within the strict time slot constraints of typical 5G mmWave networks. AARL can handle a variety of network topologies, network loads, and interference models, it can also adapt to different workloads. We demonstrate the operation of AARL on several topologies: a small topology with 10 links, a moderately-sized mesh with 48 links, and a large topology with 96 links. We show that for each topology, we compare the throughput obtained by AARL to that of a benchmark algorithm called RPMA (Residual Profit Maximizer Algorithm). The most important advantage of AARL compared to RPMA is that it is much faster and can make the necessary scheduling decisions very rapidly during every time slot, while RPMA cannot. In addition, the quality of the scheduling decisions made by AARL outperforms those made by RPMA.

We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states. It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles. Phenomenological indications that these portraits are rich and rather unusual are provided., Comment: 6 pages, 4 figures