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We obtain restrictions on units of even order in the integral group ring $\mathbb{Z}G$ of a finite group $G$ by studying their actions on the reductions modulo $4$ of lattices over the $2$-adic group ring $\mathbb{Z}_2G$. This improves the "lattice method" which considers reductions modulo primes $p$, but is of limited use for $p=2$ essentially due to the fact that $1\equiv -1 \ (\textrm{mod }2)$. Our methods yield results in cases where $\mathbb Z_2 G$ has blocks whose defect groups are Klein four groups or dihedral groups of order $8$. This allows us to disprove the existence of units of order $2p$ for almost simple groups with socle $\operatorname{PSL}(2,p^f)$ where $p^f\equiv \pm 3 \ (\textrm{mod } 8)$ and to answer the Prime Graph Question affirmatively for many such groups., Comment: 17 pages, comments welcome

Together with EuGa4 and EuAl4, EuAl2Ga2 belongs to the BaAl4 structure type with space group symmetry I4/mmm. EuAl2Ga2 develops an incommensurate charge density wave (CDW) at temperatures below TCDW = 51 K. On the basis of temperature dependent single-crystal X-ray diffraction (SXRD) data, the incommensurately modulated CDW crystal structure of EuAl2Ga2 is determined to possess orthorhombic superspace symmetry Immm(00g)s00. This symmetry is different from the orthorhombic Fmmm based symmetry of the CDW state of EuAl4. Nevertheless, both symmetries Immm(00g)s00 and Fmmm(00g)s00 lead to the same conclusion, that the CDW is supported by the layers of Al1 type atoms, while the Eu and Al2 or Ga atoms are not directly involved in CDW formation. The different symmetries of the CDW states of EuAl4 and EuAl2Ga2, as well as the observation of negative thermal expansion in the CDW state of EuAl2Ga2 might be explained by the effects of Ga substitution in the latter compound., Comment: 24 pages, 6 figures

The manifestation of surface spots on magnetic chemically peculiar (mCP) stars is most commonly explained by the atomic diffusion theory, which requires a calm stellar atmosphere and only moderate rotation. While very successful and well described, this theory still needs to be revised and fine-tuned to the observations. Our study aims to enlarge the sample of known photometrically variable mCP stars (ACV variables) to pave the way for more robust and significant statistical studies. We derive accurate physical parameters for these objects and discuss our results in the framework of the atomic diffusion theory. We studied 1314 candidate ACV variables that were selected from the Zwicky Transient Factory catalogue of periodic variables based on light curve characteristics. We investigated these objects using photometric criteria, a colour-magnitude diagram, and spectroscopic data from the LAMOST and Gaia missions to confirm their status as ACV variables. We present a sample of 1232 new ACV variables, including information on distance from the Sun, mass, fractional age on the main sequence, fraction of the radius between the zero-age and terminal-age main sequence, and the equatorial velocity and its ratio to the critical velocity. Our results confirm that the employed selection process is highly effcient for detecting ACV variables. We have identified 38 stars with v(equ) in excess of 150 km/s (with extreme values up to 260 km/s). This challenges current theories that cannot explain the occurrence of such fast-rotating mCP stars., Comment: 11 pages, 4 figures, accepted for Astronomy & Astrophysics

Dyna-style model-based reinforcement learning (MBRL) combines model-free agents with predictive transition models through model-based rollouts. This combination raises a critical question: 'When to trust your model?'; i.e., which rollout length results in the model providing useful data? Janner et al. (2019) address this question by gradually increasing rollout lengths throughout the training. While theoretically tempting, uniform model accuracy is a fallacy that collapses at the latest when extrapolating. Instead, we propose asking the question 'Where to trust your model?'. Using inherent model uncertainty to consider local accuracy, we obtain the Model-Based Actor-Critic with Uncertainty-Aware Rollout Adaption (MACURA) algorithm. We propose an easy-to-tune rollout mechanism and demonstrate substantial improvements in data efficiency and performance compared to state-of-the-art deep MBRL methods on the MuJoCo benchmark.

Strongly correlated electron systems with a kagome lattice can host abundant exotic quantum states such as superconductivity and spin/charge density waves (CDW) due to the complicated interactions between different degrees of freedoms in the framework of a unique two-dimensional geometrically frustrated lattice structure. Recently, successive orders of A-type antiferromagnetism (AFM), $2\times2\times2$ CDW and canted double-cone AFM have been manifested upon cooling in magnetic kagome FeGe. However, the mechanism of the CDW order and its interaction with magnetism are presently enigmatic at best. Here we investigate the evolution of CDW order with temperature across the spin canting transition in FeGe by single-crystal x-ray diffraction. Refinements of its modulated structure are presented using the superspace approach. Interestingly, the superlattice reflections originating from CDW-induced long-range structural modulation become extremely weak after the system enters the canted AFM while a $2\times2$ CDW in the $ab$ plane persists as a long-range order demonstrated by strong electronic modulation in the d$I$/d$V$ map of scanning tunneling spectroscopy. We discovered a novel CDW order without long-range structural modulation in FeGe probably because of the competition between CDW and canted AFM in determining the underlying crystal structure. In addition, occupational modulations of Ge1 atoms located in the kagome plane and displacive modulations of all the atoms were extracted from the refinements, confirming the existence of Ge atom dimerization along the $c$ axis as the major distortion and indicating a dynamic transformation between different CDW domains., Comment: 22 pages, 6 figures. Comments on the manuscript are welcome

Charge density wave (CDW) systems are proposed to exhibit application potential for electronic and optoelectronic devices. Therefore, identifying new materials that exhibit a CDW state at room temperature is crucial for the development of CDW-based devices. Here, we present a non-layered tetragonal polymorph of Gd2Os3Si5, which exhibits a CDW state at room temperature. Gd2Os3Si5 crystallizes in the U2Mn3Si5-type tetragonal crystal structure with the space group P4/mnc. Single-crystal x-ray diffraction (SXRD) analysis shows that Gd2Os3Si5 possesses an incommensurately modulated structure with modulation wave vector q = (0.53, 0, 0), while the modulation reduces the symmetry to orthorhombic Cccm({\sigma}00)0s0. This differs in contrast to isostructural Sm2Ru3Ge5, where the modulated phase has been reported to possess the superspace symmetry Pm({\alpha} 0 {\gamma})0. However, reinvestigation of Sm2Ru3Ge5 suggests that its modulated crystal structure can alternatively be described by Cccm({\sigma}00)0s0, with modulations similar to Gd2Os3Si5. The magnetic susceptibility, \c{hi}(T), exhibits a maximum at low temperatures that indicates an antiferromagnetic transition at TN = 5.5 K. The \c{hi}(T) furthermore shows an anomaly at around 345 K, suggesting a CDW transition at TCDW = 345 K, that corroborates the result from high-temperature SXRD measurements. Interestingly, R2T3X5 compounds are known to crystallize either in the tetragonal Sc2Fe3Si5 type structure or in the orthorhombic U2Co3Si5 structure type. Not all of the compounds in the R2T3X5 series undergo CDW phase transitions. We find that R2T3X5 compounds will exhibit a CDW transition, if the condition : 0.526 < c/sqrt(ab) < 0.543 is satisfied. We suggest the wave vector-dependent electron-phonon coupling to be the dominant mechanism of CDW formation in the tetragonal polymorph of Gd2Os3Si5.

Testing with randomly generated inputs (fuzzing) has gained significant traction due to its capacity to expose program vulnerabilities automatically. Fuzz testing campaigns generate large amounts of data, making them ideal for the application of machine learning (ML). Neural program smoothing (NPS), a specific family of ML-guided fuzzers, aims to use a neural network as a smooth approximation of the program target for new test case generation. In this paper, we conduct the most extensive evaluation of NPS fuzzers against standard gray-box fuzzers (>11 CPU years and >5.5 GPU years), and make the following contributions: (1) We find that the original performance claims for NPS fuzzers do not hold; a gap we relate to fundamental, implementation, and experimental limitations of prior works. (2) We contribute the first in-depth analysis of the contribution of machine learning and gradient-based mutations in NPS. (3) We implement Neuzz++, which shows that addressing the practical limitations of NPS fuzzers improves performance, but that standard gray-box fuzzers almost always surpass NPS-based fuzzers. (4) As a consequence, we propose new guidelines targeted at benchmarking fuzzing based on machine learning, and present MLFuzz, a platform with GPU access for easy and reproducible evaluation of ML-based fuzzers. Neuzz++, MLFuzz, and all our data are public., Comment: Accepted as conference paper at ESEC/FSE 2023

At ambient conditions SrAl4 adopts the BaAl4 structure type with space group I4/mmm. It undergoes a charge-density-wave (CDW) transition at TCDW = 243 K, followed by a structural transition at TS = 87 K. Temperature-dependent single-crystal X-ray diffraction (SXRD) leads to the observation of incommensurate superlattice reflections at q = \sigma c* with \sigma = 0.1116 at 200 K. The CDW has orthorhombic symmetry with the acentric superspace group F222(00sigma)00s, where F222 is a subgroup of Fmmm as well as of I4/mmm. Atomic displacements mainly represent a transverse wave, with displacements that are 90 deg out of phase between the two diagonal directions of the I-centered unit cell, resulting in a helical wave. Small longitudinal displacements are provided by the second harmonic modulation. The orthorhombic phase realized in SrAl4 is similar to that found in EuAl4. Electronic structure calculations and phonon calculations by density functional theory (DFT) have failed to reveal the mechanism of CDW formation. However, DFT reveals that Al atoms dominate the density of states near the Fermi level, thus, corroborating the SXRD measurements. SrAl4 remains incommensurately modulated at the structural transition, where the symmetry lowers from orthorhombic to b-unique monoclinic. We have identified a simple criterion, that correlates the presence of a phase transition with the interatomic distances. Only those compounds XAl4-xGax(X = Ba, Eu, Sr, Ca; 0 < x <4) undergo phase transitions, for which the ratio c/a falls within the narrow range 2.51 < c/a < 2.54.

Charge density wave (CDW) in kagome materials with the geometric frustration is able to carry unconventional characteristics. Recently, a CDW has been observed below the antiferromagnetic order in kagome FeGe, in which magnetism and CDW are intertwined to form an emergent quantum ground state. However, the CDW is only short-ranged and the structural modulation originating from it has yet to be determined experimentally. Here we realize a long-range CDW order by post-annealing process, and resolve the structure model through single crystal x-ray diffraction. Occupational disorder of Ge resulting from short-range CDW correlations above $T_\mathrm{CDW}$ is identified from structure refinements. The partial dimerization of Ge along the $c$ axis is unveiled to be the dominant distortion for the CDW. Occupational disorder of Ge is also proved to exist in the CDW phase due to the random selection of partially dimerized Ge sites. Our work provides useful insights for understanding the unconventional nature of the CDW in FeGe., Comment: 4 figures and 1 table in the main text. Supplementary materials included. To be published in SCIENCE CHINA Physics, Mechanics & Astronomy (SCPMA)

We show that there are finite monoids $M$ such that the Cartan matrix of the monoid algebra $\mathbb C M$ is non-singular, whilst the Cartan matrix of $kM$ is singular for some field $k$ of positive characteristic, disproving a recent conjecture of Steinberg.

Building on previous work by Caicedo and the second author, we develop a method that decides the existence of units of finite order in blocks of $\mathbb{Z}_p G$ of defect 1. This allows us to prove that if $p$ is a prime and $G$ is a finite group whose Sylow $p$-subgroup has order $p$, then any unit $u\in \mathbb{Z} G$ of order $p$ is conjugate to an element of $\pm G$. This is a special case of the Zassenhaus conjecture. We also prove some new results on units of finite order in $\mathbb{Z} \mathrm{PSL}(2,q)$ for certain $q$, and construct a unit of order $15$ in $V(\mathbb{Z}_{(3,5)}\mathrm{PSL}(2,16))$ which is a $3$- and $5$-local counterexample to the Zassenhaus conjecture, raising the hope that our methods may lead to a global counterexample amongst simple groups., Comment: 29 pages