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Based on ab initio calculations, we demonstrate that a Mott insulator LaTiO$_3$ (LTO), not inspected previously as an altermagnetic material, shows the characteristic features of altermagnets, i.e., (i) fully compensated antiferromagnetism and (ii) $\mathbf{k}$-dependent spin-split electron bands in the absence of spin-orbit coupling. The altermagnetic ground state of LTO is protected by the crystal symmetry and specifically ordered $d$-orbitals of Ti ions with the orbital momentum $l=2.$ The altermagnetism occurs when sites of Ti pair in the unit cell are occupied by single electrons with $m=-1,s_{z}=+1/2$ and $m=+1,s_{z}=-1/2$ per site, with $m$ and $s_{z}-$ being the $z-$ component of the orbital momentum and spin, respectively. By further simulating orbital disorder within the Green's function method, we disclose its damaging character on the spin splitting and the resulting altermagnetism. When the single-electron spin-polarized state at each Ti site is contributed almost equally by two or three $t_{2g}$ orbitals, LTO becomes antiferromagnetic. The effect of the spin-orbit coupling, which can cause orbital disorder and suppress altermagnetism, is discussed., Comment: 6 pages, 7 figures

Using the strong coupling diagram technique, we calculate the zero-temperature density of states $\rho$ of electrons on a square lattice immersed in a perpendicular uniform magnetic field. The electrons are described by Hubbard Hamiltonian. For moderate doping, Landau subbands are observed for small Hubbard repulsions $U$ only. For larger $U$, the subbands are blurred. Instead, small peaks varying with the field induction $B$ arise by opening the Mott gap in its vicinity. The related variation of $\rho$ with $1/B$ may be connected with the low-frequency quantum oscillations in lightly doped cuprates. For all considered repulsions, $\rho$ has gaps near transfer frequencies of the Hubbard atom, $-\mu$ and $U-\mu$, with $\mu$ the chemical potential. In the heavily underdoped case $\mu<0$, Landau subbands are grouped into the lower and upper Hubbard subbands for moderate and large repulsions. The intensity of the upper Hubbard subband decreases with approaching the Fermi level to the lower edge of the spectrum and finally vanishes., Comment: 17 pages, 8 figures

The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60 to 80 t capable of probing the remaining WIMP-nucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in $^{136}$Xe using a natural-abundance xenon target. XLZD can reach a 3$\sigma$ discovery potential half-life of 5.7$\times$10$^{27}$ yr (and a 90% CL exclusion of 1.3$\times$10$^{28}$ yr) with 10 years of data taking, corresponding to a Majorana mass range of 7.3-31.3 meV (4.8-20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community., Comment: 29 pages, 7 figures

This report describes the experimental strategy and technologies for a next-generation xenon observatory sensitive to dark matter and neutrino physics. The detector will have an active liquid xenon target mass of 60-80 tonnes and is proposed by the XENON-LUX-ZEPLIN-DARWIN (XLZD) collaboration. The design is based on the mature liquid xenon time projection chamber technology of the current-generation experiments, LZ and XENONnT. A baseline design and opportunities for further optimization of the individual detector components are discussed. The experiment envisaged here has the capability to explore parameter space for Weakly Interacting Massive Particle (WIMP) dark matter down to the neutrino fog, with a 3$\sigma$ evidence potential for the spin-independent WIMP-nucleon cross sections as low as $3\times10^{-49}\rm cm^2$ (at 40 GeV/c$^2$ WIMP mass). The observatory is also projected to have a 3$\sigma$ observation potential of neutrinoless double-beta decay of $^{136}$Xe at a half-life of up to $5.7\times 10^{27}$ years. Additionally, it is sensitive to astrophysical neutrinos from the atmosphere, sun, and galactic supernovae., Comment: 32 pages, 14 figures

We present MEGA-Bench, an evaluation suite that scales multimodal evaluation to over 500 real-world tasks, to address the highly heterogeneous daily use cases of end users. Our objective is to optimize for a set of high-quality data samples that cover a highly diverse and rich set of multimodal tasks, while enabling cost-effective and accurate model evaluation. In particular, we collected 505 realistic tasks encompassing over 8,000 samples from 16 expert annotators to extensively cover the multimodal task space. Instead of unifying these problems into standard multi-choice questions (like MMMU, MMBench, and MMT-Bench), we embrace a wide range of output formats like numbers, phrases, code, \LaTeX, coordinates, JSON, free-form, etc. To accommodate these formats, we developed over 40 metrics to evaluate these tasks. Unlike existing benchmarks, MEGA-Bench offers a fine-grained capability report across multiple dimensions (e.g., application, input type, output format, skill), allowing users to interact with and visualize model capabilities in depth. We evaluate a wide variety of frontier vision-language models on MEGA-Bench to understand their capabilities across these dimensions., Comment: Technical report. Project page: https://tiger-ai-lab.github.io/MEGA-Bench/. v2 includes more evaluated models and a single-image setting

We investigate the effect of the spin-orbit (SO) and Rabi couplings on the localization of the spin-1/2 condensate trapped in a one-dimensional random potential. Our studies reveal that the spin-dependent couplings create distinct localization regimes, resulting in various relations between localization and spin-related properties. First, we examine the localization in the linear condensate and find that the SO coupling can lead to a transition of the localized state from the "basin-like" to the "void" region of the potential. For a weak random potential upon an increase in the SO coupling, we find a re-entrant transition from a broad to narrow localized state and back at a higher SO coupling. Further, we analyze the competing role of inter-species and intra-species interactions on the localization of the condensate. We find the appearance of spin-dependent localization as the interactions increase beyond threshold values for a sufficiently strong disorder. Our findings on controlling spin-dependent localization may be useful for future ultracold atomic experiments and corresponding spin-related quantum technologies., Comment: 18pages, 21figures

We present the discovery of Aquarius III, an ultra-faint Milky Way satellite galaxy identified in the second data release of the DECam Local Volume Exploration (DELVE) survey. Based on deeper follow-up imaging with DECam, we find that Aquarius III is a low-luminosity ($M_V = -2.5^{+0.3}_{-0.5}$; $L_V = 850^{+380}_{-260} \ L_{\odot}$), extended ($r_{1/2} = 41^{+9}_{-8}$ pc) stellar system located in the outer halo ($D_{\odot} = 85 \pm 4$ kpc). From medium-resolution Keck/DEIMOS spectroscopy, we identify 11 member stars and measure a mean heliocentric radial velocity of $v_{\rm sys} = -13.1^{+1.0}_{-0.9} \ \rm km \ s^{-1}$ for the system and place an upper limit of $\sigma_v < 3.5 \rm \ km \ s^{-1}$ ($\sigma_v < 1.6 \rm \ km \ s^{-1}$) on its velocity dispersion at the 95% (68%) credible level. Based on Calcium-Triplet-based metallicities of the six brightest red giant members, we find that Aquarius III is very metal-poor ([Fe/H]$ = -2.61 \pm 0.21$) with a statistically-significant metallicity spread ($\sigma_{\rm [Fe/H]} = 0.46^{+0.26}_{-0.14}$ dex). We interpret this metallicity spread as strong evidence that the system is a dwarf galaxy as opposed to a star cluster. Combining our velocity measurement with $Gaia$ proper motions, we find that Aquarius III is currently situated near its orbital pericenter in the outer halo ($r_{\rm peri} = 78 \pm 7$ kpc) and that it is plausibly on first infall onto the Milky Way. This orbital history likely precludes significant tidal disruption from the Galactic disk, notably unlike other satellites with comparably low velocity dispersion limits in the literature. Thus, if further velocity measurements confirm that its velocity dispersion is truly below $\sigma_v \lesssim 2 \rm \ km \ s^{-1}$, Aquarius III may serve as a useful laboratory for probing galaxy formation physics in low-mass halos., Comment: 25 pages, 7 figures. Submitted to AAS Journals

The capture of photoexcited hot electrons in semiconductors before they lose their excess energy to cooling is a long-standing goal in photon energy conversion. Semiconductor nanocrystals have large electron energy spacings that are expected to slow down electron relaxation by phonon emission, but hot electrons in photoexcited nanocrystals nevertheless cool rapidly by energy transfer to holes. This makes the intrinsic phonon-bottleneck limited electron lifetime in nanocrystals elusive. We used a combination of theory and experiments to probe the hot electron dynamics of negatively charged Cadmium Sulfide (CdS) colloidal quantum dots (QDs) in the absence of holes. Experiments found that these hot electrons cooled on a 100 ps timescale. Theoretical simulations predicted that pure phonon-bottleneck limited electron cooling occurs on a similar timescale. This similarity suggests that the experimental measurements reflect the upper limit on hot electron lifetimes in these CdS QDs and the lower limit on the rates of processes that can harvest those hot electrons.

Low Probability of Detection (LPD) communication aims to obscure the presence of radio frequency (RF) signals to evade surveillance. In the context of mobile surveillance utilizing unmanned aerial vehicles (UAVs), achieving LPD communication presents significant challenges due to the UAVs' rapid and continuous movements, which are characterized by unknown nonlinear dynamics. Therefore, accurately predicting future locations of UAVs is essential for enabling real-time LPD communication. In this paper, we introduce a novel framework termed predictive covert communication, aimed at minimizing detectability in terrestrial ad-hoc networks under multi-UAV surveillance. Our data-driven method synergistically integrates graph neural networks (GNN) with Koopman theory to model the complex interactions within a multi-UAV network and facilitating long-term predictions by linearizing the dynamics, even with limited historical data. Extensive simulation results substantiate that the predicted trajectories using our method result in at least 63%-75% lower probability of detection when compared to well-known state-of-the-art baseline approaches, showing promise in enabling low-latency covert operations in practical scenarios.

Fast Radio Bursts (FRBs) are millisecond-duration events detected from beyond the Milky Way. FRB emission characteristics favor highly magnetized neutron stars, or magnetars, as the sources, as evidenced by FRB-like bursts from a galactic magnetar, and the star-forming nature of FRB host galaxies. However, the processes that produce FRB sources remain unknown. Although galactic magnetars are often linked to core-collapse supernovae (CCSNe), it's uncertain what determines which supernovae result in magnetars. The galactic environments of FRB sources can be harnessed to probe their progenitors. Here, we present the stellar population properties of 30 FRB host galaxies discovered by the Deep Synoptic Array. Our analysis shows a significant deficit of low-mass FRB hosts compared to the occurrence of star-formation in the universe, implying that FRBs are a biased tracer of star-formation, preferentially selecting massive star-forming galaxies. This bias may be driven by galaxy metallicity, which is positively correlated with stellar mass. Metal-rich environments may favor the formation of magnetar progenitors through stellar mergers, as higher metallicity stars are less compact and more likely to fill their Roche lobes, leading to unstable mass transfer. Although massive stars do not have convective interiors to generate strong magnetic fields by dynamo, merger remnants are thought to have the requisite internal magnetic-field strengths to result in magnetars. The preferential occurrence of FRBs in massive star-forming galaxies suggests that CCSN of merger remnants preferentially forms magnetars., Comment: Accepted for publication in Nature. The final version will be published by the journal

Approximately half of the Universe's dark matter resides in collapsed halos; significantly less than half of the baryonic matter (protons and neutrons) remains confined to halos. A small fraction of baryons are in stars and the interstellar medium within galaxies. The lion's share are diffuse (less than $10^{-3}$ cm$^{-3}$) and ionized (neutral fraction less than $10^{-4}$), located in the intergalactic medium (IGM) and in the halos of galaxy clusters, groups, and galaxies. The quantity and spatial distribution of this diffuse ionized gas is notoriously difficult to measure, but has wide implications for galaxy formation, astrophysical feedback, and precision cosmology. Recently, the dispersion of extragalactic Fast Radio Bursts (FRBs) has been used to measure the total content of cosmic baryons. However, past efforts had modest samples and methods that cannot discriminate between IGM and halo gas, which is critical for studying feedback and for observational cosmology. Here, we present a large cosmological sample of FRB sources localized to their host galaxies. We have robustly partitioned the missing baryons into the IGM, galaxy clusters, and galaxies, providing a late-Universe measurement of the total baryon density of $\Omega_b h_{70}$=0.049$\pm$0.003. Our results indicate efficient feedback processes that can expel gas from galaxy halos and into the intergalactic medium, agreeing with the enriched cosmic web scenario seen in cosmological simulations. The large diffuse baryon fraction that we have measured disfavours bottom-heavy stellar initial mass functions, which predict a large total stellar density, $\Omega_*$.

The utilization of excited charge carriers in semiconductor nanocrystals (NCs) for optoelectronic technologies has been a long-standing goal in the field of nanoscience. Experimental efforts to extend the lifetime of excited carriers have therefore been a principal focus. To understand the limits of these lifetimes, in this work, we theoretically study the timescales of pure electron relaxation in negatively charged NCs composed of two prototypical materials: CdSe and CdS. We find that hot electrons in CdSe have lifetimes that are five to six orders of magnitude longer than in CdS when the relaxation is governed only by the intrinsic properties of the materials. Although these two materials are known to have somewhat different electronic structure, we elucidate how this enormous difference in lifetimes arises from relatively small quantitative differences in electronic energy gaps, phonon frequencies, and their couplings. We also highlight that the effect of the phonons on electron relaxation is dominated by a Fr\"ohlich-type mechanism in these charged systems with no holes., Comment: main text (11 pages, 5 figures) + supplementary information (11 pages, 1 figure)

The set of perfect matchings of a connected bipartite plane graph $G$ has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the height of a matching. In this article, our focus is the dimer face polynomial of $G$, which is the height generating function of all perfect matchings of $G$. We connect the dimer face polynomial on the one hand to knot theory, and on the other to cluster algebras. We show that certain dimer face polynomials are multivariate generalizations of Alexander polynomials of links, highlighting another combinatorial view of the Alexander polynomial. We also show that an arbitrary dimer face polynomial is an $F$-polynomial in the cluster algebra whose initial quiver is dual to the graph $G$. As a result, we recover a recent representation theoretic result of Bazier-Matte and Schiffler that connects $F$-polynomials and Alexander polynomials, albeit from a very different, dimer-based perspective. As another application of our results, we also show that all nonvanishing Pl\"ucker coordinates on open positroid varieties are cluster monomials.

We study elastic electron scattering and localization by ubiquitous isotopic disorder in one-dimensional systems appearing due to interaction with phonon modes localized at isotope impurities. By using a tight-binding model with intersite hopping matrix element dependent on the interatomic distance, we find mass-dependent backscattering probability by single and pairs of isotopic impurities. For the pairs, in addition to the mass, the distance between the isotopes plays the critical role. Single impurities effectively attract electrons and can produce localized weakly bound electron states. In the presence of disorder, the electron free path at positive energies becomes finite and the corresponding Anderson localization at the spatial scale greatly exceeding the distance between the impurities becomes possible., Comment: 11 figues

relentless is an open-source Python package that enables the optimization of objective functions computed using molecular dynamics simulations. It has a high-level, extensible interface for model parametrization; setting up, running, and analyzing simulations natively in established software packages; and gradient-based optimization. We describe the design and implementation of relentless in the context of relative entropy minimization, and we demonstrate its abilities to design pairwise interactions between particles that form targeted structures. relentless aims to streamline the development of computational materials design methodologies and promote the transparency and reproducibility of complex workflows integrating molecular dynamics simulations., Comment: 13 pages, 6 figures

This systematic review explores the viability of virtual reality (VR) technologies for enhancing learning outcomes and operational efficiency within the construction industry. This study evaluates the current integration of VR in construction education and practice. Employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines, this review analyzed 36 peer-reviewed journal articles from databases such as the Web of Science, ERIC, and Scopus. The methodology focused on identifying, appraising, and synthesizing all relevant studies to assess the effectiveness of VR applications in construction-related fields. This review highlights that VR significantly enhances learning by providing immersive interactive simulations that improve the understanding of every complex construction process, such as structural elements or tunnel-boring machine operations. This review contributes by systematically compiling and evaluating evidence on using VR in construction, which has seen a limited comprehensive analysis. It provides practical examples of how VR can revolutionize education and work., Comment: 34 pages, 5 figures, 2 tables

As TESLA-enabled GNSS for authenticated positioning reaches ubiquity, receivers must use an onboard, GNSS-independent clock and carefully constructed time synchronization algorithms to assert the authenticity afforded. This work provides the necessary checks and synchronization protocols needed in the broadcast-only GNSS context. We provide proof of security for each of our algorithms under a delay-capable adversary. The algorithms included herein enable a GNSS receiver to use its onboard, GNSS-independent clock to determine whether a message arrived at the correct time, to determine whether its onboard, GNSS-independent clock is safe to use and when the clock will no longer be safe in the future due to predicted clock drift, and to resynchronize its onboard, GNSS-independent clock. Each algorithm is safe to use even when an adversary induces delays within the protocol. Moreover, we discuss the implications of GNSS authentication schemes that use two simultaneous TESLA instances of different authentication cadences. To a receiver implementer or standards author, this work provides the necessary implementation algorithms to assert security and provides a comprehensive guide on why these methods are required., Comment: 16 pages, 15 figures

The recent years have witnessed great advances in video generation. However, the development of automatic video metrics is lagging significantly behind. None of the existing metric is able to provide reliable scores over generated videos. The main barrier is the lack of large-scale human-annotated dataset. In this paper, we release VideoFeedback, the first large-scale dataset containing human-provided multi-aspect score over 37.6K synthesized videos from 11 existing video generative models. We train VideoScore (initialized from Mantis) based on VideoFeedback to enable automatic video quality assessment. Experiments show that the Spearman correlation between VideoScore and humans can reach 77.1 on VideoFeedback-test, beating the prior best metrics by about 50 points. Further result on other held-out EvalCrafter, GenAI-Bench, and VBench show that VideoScore has consistently much higher correlation with human judges than other metrics. Due to these results, we believe VideoScore can serve as a great proxy for human raters to (1) rate different video models to track progress (2) simulate fine-grained human feedback in Reinforcement Learning with Human Feedback (RLHF) to improve current video generation models.

Large language models (LLMs) are increasingly being used in human-centered social scientific tasks, such as data annotation, synthetic data creation, and engaging in dialog. However, these tasks are highly subjective and dependent on human factors, such as one's environment, attitudes, beliefs, and lived experiences. Thus, it may be the case that employing LLMs (which do not have such human factors) in these tasks results in a lack of variation in data, failing to reflect the diversity of human experiences. In this paper, we examine the role of prompting LLMs with human-like personas and asking the models to answer as if they were a specific human. This is done explicitly, with exact demographics, political beliefs, and lived experiences, or implicitly via names prevalent in specific populations. The LLM personas are then evaluated via (1) subjective annotation task (e.g., detecting toxicity) and (2) a belief generation task, where both tasks are known to vary across human factors. We examine the impact of explicit vs. implicit personas and investigate which human factors LLMs recognize and respond to. Results show that explicit LLM personas show mixed results when reproducing known human biases, but generally fail to demonstrate implicit biases. We conclude that LLMs may capture the statistical patterns of how people speak, but are generally unable to model the complex interactions and subtleties of human perceptions, potentially limiting their effectiveness in social science applications., Comment: Accepted at Findings of EMNLP 2024

Using the strong coupling diagram technique, we find three phases of the half-filled isotropic Hubbard model on a triangular lattice at finite temperatures. The weak-interaction ($U\lesssim5t$) and strong-interaction ($U\gtrsim9t$) phases are similar to those obtained by zero-temperature methods -- the former is a metal without perceptible spin excitations; the latter is a Mott insulator with the 120$^\circ$ short-range spin ordering. Zero-temperature approaches predict a nonmagnetic insulating spin-liquid phase sandwiched between these two regions. In our finite-temperature calculations, the Mott gap in the intermediate phase is filled by the Fermi-level peak, which is a manifestation of the bound states of electrons with pronounced spin excitations. We relate the appearance of these excitations at finite temperatures to the Pomeranchuk effect., Comment: 15 pages, 5 figures

We present a multi-wavelength study of the apparently non-repeating, heavily scattered fast radio burst, FRB 20221219A, detected by the Deep Synoptic Array 110 (DSA-110). The burst exhibits a moderate dispersion measure (DM) of $706.7^{+0.6}_{-0.6}$ $\mathrm{pc}~\mathrm{cm}^{-3}$ and an unusually high scattering timescale of $\tau_{\mathrm{obs}} = 19.2_{-2.7}^{+2.7}$ ms at 1.4 GHz. We associate the FRB with a Milky Way-like host galaxy at $z_{\mathrm{host}} = 0.554$ of stellar mass $\mathrm{log}_{10}(M_{\star, \mathrm{host}}) = 10.20^{+0.04}_{-0.03} ~M_\odot$. We identify two intervening galaxy halos at redshifts $z_{\mathrm{igh1}} = 0.492$ and $z_{\mathrm{igh2}} = 0.438$, with low impact parameters, $b_{\mathrm{igh1}} = 43.0_{-11.3}^{+11.3}$ kpc and $b_{\mathrm{igh2}} = 36.1_{-11.3}^{+11.3}$ kpc, and intermediate stellar masses, $\mathrm{log}_{10}(M_{\star, \mathrm{igh1}}) = 10.01^{+0.02}_{-0.02} ~M_\odot$ and $\mathrm{log}_{10}(M_{\star, \mathrm{igh2}}) = 10.60^{+0.02}_{-0.02} ~M_\odot$. The presence of two such galaxies suggests that the sightline is significantly overcrowded compared to the median sightline to this redshift, as inferred from the halo mass function. We perform a detailed analysis of the sightline toward FRB 20221219A, constructing both DM and scattering budgets. Our results suggest that, unlike most well-localized sources, the host galaxy does not dominate the observed scattering. Instead, we posit that an intersection with a single partially ionized cloudlet in the circumgalactic medium of an intervening galaxy could account for the substantial scattering in FRB 20221219A and remain in agreement with typical electron densities inferred for extra-planar dense cloud-like structures in the Galactic and extragalactic halos (e.g., high-velocity clouds)., Comment: 18 pages, 6 figures, submitted to ApJ, comments appreciated

Batched sparse (BATS) code is a network coding solution for multi-hop wireless networks with packet loss. Achieving a close-to-optimal rate relies on an optimal degree distribution. Technical challenges arise from the sensitivity of this distribution to the often empirically obtained rank distribution at the destination node. Specifically, if the empirical distribution overestimates the channel, BATS codes experience a significant rate degradation, leading to unstable rates across different runs and hence unpredictable transmission costs. Confronting this unresolved obstacle, we introduce a formulation for distributionally robust optimization in degree optimization. Deploying the resulting degree distribution resolves the instability of empirical rank distributions, ensuring a close-to-optimal rate, and unleashing the potential of applying BATS codes in real-world scenarios., Comment: 8 pages, accepted by 2024 IEEE International Symposium on Information Theory

This paper explores the value of archival theory as a means of grappling with bias in algorithmic design. Rather than seek to mitigate biases perpetuated by datasets and algorithmic systems, archival theory offers a reframing of bias itself. Drawing on a range of archival theory from the fields of history, literary and cultural studies, Black studies, and feminist STS, we propose absence-as power, presence, and productive-as a concept that might more securely anchor investigations into the causes of algorithmic bias, and that can prompt more capacious, creative, and joyful future work. This essay, in turn, can intervene into the technical as well as the social, historical, and political structures that serve as sources of bias., Comment: 16 pages, to be published in the 2024 ACM Conference on Designing Interactive Systems (DIS '24)

In recent years, reinforcement learning (RL) has emerged as a valuable tool in drug design, offering the potential to propose and optimize molecules with desired properties. However, striking a balance between capabilities, flexibility, reliability, and efficiency remains challenging due to the complexity of advanced RL algorithms and the significant reliance on specialized code. In this work, we introduce ACEGEN, a comprehensive and streamlined toolkit tailored for generative drug design, built using TorchRL, a modern RL library that offers thoroughly tested reusable components. We validate ACEGEN by benchmarking against other published generative modeling algorithms and show comparable or improved performance. We also show examples of ACEGEN applied in multiple drug discovery case studies. ACEGEN is accessible at \url{https://github.com/acellera/acegen-open} and available for use under the MIT license.

We present \texttt{muRelBench}, a suite of synthetic benchmarks for weakly-relational abstract domains and their operations. For example, the benchmarks can support experimental evaluations of proposed algorithms such as domain closure., Comment: NEAT paper for SAS 2024

We introduce Sylow subgroups and $0$-groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and $p$-groups in the theory of finite groups. We prove that Sylow subgroups are always $0$-groups, and show that they are unique up to conjugacy. Further, we give an explicit classification of $0$-groups which will be very useful for future applications. Finally, we prove an analogue of Sylow's third theorem on the number of Sylow subgroups of a supergroup., Comment: 33 pages; comments welcome!

Core-collapse Supernovae (CCSNe) are considered the primary magnetar formation channel, with 15 magnetars associated with supernova remnants (SNRs). A large fraction of these should occur in massive stellar binaries that are disrupted by the explosion, meaning that $\sim45\%$ of magnetars should be nearby high-velocity stars. Here we conduct a multi-wavelength search for unbound stars, magnetar binaries, and SNR shells using public optical ($uvgrizy-$bands), infrared ($J-$, $H-$, $K-$, and $K_s-$bands), and radio ($888$ MHz, $1.4$ GHz, and $3$ GHz) catalogs. We use Monte Carlo analyses of candidates to estimate the probability of association with a given magnetar based on their proximity, distance, proper motion, and magnitude. In addition to recovering a proposed magnetar binary, a proposed unbound binary, and 13 of 15 magnetar SNRs, we identify two new candidate unbound systems: an OB star from the Gaia catalog we associate with SGR J1822.3-1606, and an X-ray pulsar we associate with 3XMM J185246.6+003317. Using a Markov-Chain Monte Carlo simulation that assumes all magnetars descend from CCSNe, we constrain the fraction of magnetars with unbound companions to $5\lesssim f_u \lesssim 24\%$, which disagrees with neutron star population synthesis results. Alternate formation channels are unlikely to wholly account for the lack of unbound binaries as this would require $31\lesssim f_{nc} \lesssim 66\%$ of magnetars to descend from such channels. Our results support a high fraction ($48\lesssim f_m \lesssim 86\%$) of pre-CCSN mergers, which can amplify fossil magnetic fields to preferentially form magnetars., Comment: 35 pages, 8 figures, 5 tables, minor errata accepted to MNRAS (10.1093/mnras/stae2124) correcting the position errors for 1E1547, AXJ1818, AXJ1845 and truncated UKIDSS query; no changes to conclusions

The amplituhedron $A_{n,k,m}$ is a geometric object introduced in the context of scattering amplitudes in $N=4$ super Yang Mills. It generalizes the positive Grassmannian (when $n=k+m$), cyclic polytopes (when $k=1$), and the bounded complex of the cyclic hyperplane arrangement (when $m=1$). Of substantial interest are the tilings of the amplituhedron, which are analogous to triangulations of a polytope. Karp, Williams and Zhang (2020) observed that the known tilings of $A_{n,k,2}$ have cardinality ${n-2 \choose k}$ and the known tilings of $A_{n,k,4}$ have cardinality the Narayana number $\frac{1}{n-3}{n-3 \choose k+1}{n-3 \choose k}$; generalizing these observations, they conjectured that for even $m$ the tilings of $A_{n, k,m}$ have cardinality the MacMahon number, the number of plane partitions which fit inside a $k \times (n-k-m) \times \frac{m}{2}$ box. We refer to this prediction as the `Magic Number Conjecture'. In this paper we prove the Magic Number Conjecture for the $m=2$ amplituhedron: that is, we show that each tiling of $A_{n,k,2}$ has cardinality ${n-2 \choose k}$. We prove this by showing that all positroid tilings of the hypersimplex $\Delta_{k+1,n}$ have cardinality ${n-2 \choose k}$, then applying T-duality. In addition, we give combinatorial necessary conditions for tiles to form a tiling of $A_{n,k,2}$; we give volume formulas for Parke-Taylor polytopes and certain positroid polytopes in terms of circular extensions of cyclic partial orders; and we prove new variants of the classical Parke-Taylor identities., Comment: 44 pages, 14 figures. v2: minor changes

Let $(\mathfrak{g},\mathfrak{k})$ be a supersymmetric pair arising from a finite-dimensional, symmetrizable Kac-Moody superalgebra $\mathfrak{g}$. An important branching problem is to determine the finite-dimensional highest-weight $\mathfrak{g}$-modules which admit a $\mathfrak{k}$-coinvariant, and thus appear as functions in a corresponding supersymmetric space $\mathcal{G}/\mathcal{K}$. This is the super-analogue of the Cartan-Helgason theorem. We solve this problem via a rank one reduction and an understanding of reflections in singular roots, which generalize odd reflections in the theory of Kac-Moody superalgebras. An explicit presentation of spherical weights is provided for every pair when $\mathfrak{g}$ is indecomposable., Comment: 21 pages; comments welcome!

As Multi-Robot Systems (MRS) become more affordable and computing capabilities grow, they provide significant advantages for complex applications such as environmental monitoring, underwater inspections, or space exploration. However, accounting for potential communication loss or the unavailability of communication infrastructures in these application domains remains an open problem. Much of the applicable MRS research assumes that the system can sustain communication through proximity regulations and formation control or by devising a framework for separating and adhering to a predetermined plan for extended periods of disconnection. The latter technique enables an MRS to be more efficient, but breakdowns and environmental uncertainties can have a domino effect throughout the system, particularly when the mission goal is intricate or time-sensitive. To deal with this problem, our proposed framework has two main phases: i) a centralized planner to allocate mission tasks by rewarding intermittent rendezvous between robots to mitigate the effects of the unforeseen events during mission execution, and ii) a decentralized replanning scheme leveraging epistemic planning to formalize belief propagation and a Monte Carlo tree search for policy optimization given distributed rational belief updates. The proposed framework outperforms a baseline heuristic and is validated using simulations and experiments with aerial vehicles.