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Autonomous manipulation in everyday tasks requires flexible action generation to handle complex, diverse real-world environments, such as objects with varying hardness and softness. Imitation Learning (IL) enables robots to learn complex tasks from expert demonstrations. However, a lot of existing methods rely on position/unilateral control, leaving challenges in tasks that require force information/control, like carefully grasping fragile or varying-hardness objects. As the need for diverse controls increases, there are demand for low-cost bimanual robots that consider various motor inputs. To address these challenges, we introduce Bilateral Control-Based Imitation Learning via Action Chunking with Transformers(Bi-ACT) and"A" "L"ow-cost "P"hysical "Ha"rdware Considering Diverse Motor Control Modes for Research in Everyday Bimanual Robotic Manipulation (ALPHA-$\alpha$). Bi-ACT leverages bilateral control to utilize both position and force information, enhancing the robot's adaptability to object characteristics such as hardness, shape, and weight. The concept of ALPHA-$\alpha$ is affordability, ease of use, repairability, ease of assembly, and diverse control modes (position, velocity, torque), allowing researchers/developers to freely build control systems using ALPHA-$\alpha$. In our experiments, we conducted a detailed analysis of Bi-ACT in unimanual manipulation tasks, confirming its superior performance and adaptability compared to Bi-ACT without force control. Based on these results, we applied Bi-ACT to bimanual manipulation tasks. Experimental results demonstrated high success rates in coordinated bimanual operations across multiple tasks. The effectiveness of the Bi-ACT and ALPHA-$\alpha$ can be seen through comprehensive real-world experiments. Video available at: https://mertcookimg.github.io/alpha-biact/

Context. The supernova remnant (SNR) W44 and its surroundings are a prime target for studying the acceleration of cosmic rays (CRs). Several previous studies established an extended gamma-ray emission that is set apart from the radio shell of W44. This emission is thought to originate from escaped high-energy CRs that interact with a surrounding dense molecular cloud complex. Aims. We present a detailed analysis of Fermi-LAT data with an emphasis on the spatial and spectral properties of W44 and its surroundings. We also report the results of the observations performed with the MAGIC telescopes of the northwestern region of W44. Finally, we present an interpretation model to explain the gamma-ray emission of the SNR and its surroundings. Methods. We first performed a detailed spatial analysis of 12 years of Fermi-LAT data at energies above 1 GeV, in order to exploit the better angular resolution, while we set a threshold of 100MeV for the spectral analysis. We performed a likelihood analysis of 174 hours of MAGIC data above 130 GeV using the spatial information obtained with Fermi-LAT. Results. The combined spectra of Fermi-LAT and MAGIC, extending from 100MeV to several TeV, were used to derive constraints on the escape of CRs. Using a time-dependent model to describe the particle acceleration and escape from the SNR, we show that the maximum energy of the accelerated particles has to be ' 40 GeV. However, our gamma-ray data suggest that a small number of lower-energy particles also needs to escape. We propose a novel model, the broken-shock scenario, to account for this effect and explain the gamma-ray emission.

Microswimmers display an intriguing ability to navigate through fluids with spatially varying viscosity, a behavior known as viscotaxis, which plays a crucial role in guiding their motion. In this study, we reveal that the orientation dynamics of chiral squirmers in fluids with uniform viscosity gradients can be elegantly captured using the Landau-Lifshitz-Gilbert equations, originally developed for spin systems. Remarkably, we discover that chiral swimmers demonstrate negative viscotaxis, tracing spiral trajectories as they move. Specifically, a chiral squirmer with a misaligned source dipole and rotlet dipole exhibits a steady-state spiral motion-a stark contrast to the linear behavior observed when the dipoles are aligned. This work provides fresh insights into the intricate interplay between microswimmer dynamics and fluid properties., Comment: 6+3 pages, 4 figures

(2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$., Comment: 21 pages, 10 figures

Filamentary molecular clouds are an essential intermediate stage in the star formation process. To test whether these structures are universal throughout cosmic star formation history, it is crucial to study low-metallicity environments within the Local Group. We present an ALMA analysis of the ALMA archival data at the spatial resolution of $\sim$0.1 pc for 17 massive young stellar objects (YSOs) in the Small Magellanic Cloud (SMC; Z $\sim$0.2 $Z_{\odot}$). This sample represents approximately 30% of the YSOs confirmed by Spitzer spectroscopy. Early ALMA studies of the SMC have shown that the CO emission line traces an H$_2$ number density of $\gtrsim$10$^4$ cm$^{-3}$, an order of magnitude higher than in the typical Galactic environments. Using the CO($J$ = 3-2) data, we investigated the spatial and velocity distribution of molecular clouds. Our analysis shows that about 60% of the clouds have steep radial profiles from the spine of the elongated structures, while the remaining clouds have a smooth distribution and are characterized by lower brightness temperatures. We categorized the former as filaments and the latter as non-filaments. Some of the filamentary clouds are associated with YSOs with outflows and exhibit higher temperatures, likely reflecting their formation conditions, suggesting that these clouds are younger than non-filamentary ones. This indicates that even if filaments form during star formation, their steep structures may become less prominent and transit to a lower-temperature state. Such transitions in structure and temperature have not been reported in metal-rich regions, highlighting a key behavior for characterizing the evolution of the interstellar medium and star formation in low-metallicity environments., Comment: 22 pages, 10 figures, 2tables, Accepted for publication in ApJ

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of General Relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO--Virgo--KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering the single-harmonic and the dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is $6.4\!\times\!10^{-27}$ for the young energetic pulsar J0537-6910, while the lowest constraint on the ellipticity is $8.8\!\times\!10^{-9}$ for the bright nearby millisecond pulsar J0437-4715. Additionally, for a subset of 16 targets we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of non-standard polarizations as predicted by the Brans-Dicke theory., Comment: main paper: 12 pages, 6 figures, 4 tables

This paper investigates a novel nonlinear update rule based on temporal difference (TD) errors in reinforcement learning (RL). The update rule in the standard RL states that the TD error is linearly proportional to the degree of updates, treating all rewards equally without no bias. On the other hand, the recent biological studies revealed that there are nonlinearities in the TD error and the degree of updates, biasing policies optimistic or pessimistic. Such biases in learning due to nonlinearities are expected to be useful and intentionally leftover features in biological learning. Therefore, this research explores a theoretical framework that can leverage the nonlinearity between the degree of the update and TD errors. To this end, we focus on a control as inference framework, since it is known as a generalized formulation encompassing various RL and optimal control methods. In particular, we investigate the uncomputable nonlinear term needed to be approximately excluded in the derivation of the standard RL from control as inference. By analyzing it, Weber-Fechner law (WFL) is found, namely, perception (a.k.a. the degree of updates) in response to stimulus change (a.k.a. TD error) is attenuated by increase in the stimulus intensity (a.k.a. the value function). To numerically reveal the utilities of WFL on RL, we then propose a practical implementation using a reward-punishment framework and modifying the definition of optimality. Analysis of this implementation reveals that two utilities can be expected i) to increase rewards to a certain level early, and ii) to sufficiently suppress punishment. We finally investigate and discuss the expected utilities through simulations and robot experiments. As a result, the proposed RL algorithm with WFL shows the expected utilities that accelerate the reward-maximizing startup and continue to suppress punishments during learning., Comment: 36 pages 9 figures

This article is a record of the lecture at the centennial conference for Harish-Chandra. The admissibility theorem of Harish-Chandra concerns the restrictions of irreducible representations to maximal compact subgroups. In this article, we begin with a brief explanation of two directions for generalizing his pioneering work to {\it{non-compact}} reductive subgroups: one emphasizes discrete decomposability with the finite multiplicity property, while the other focuses on finite/uniformly bounded multiplicity properties. We discuss how the recent representation-theoretic developments in these directions collectively offer a powerful method for the new spectral analysis of standard locally symmetric spaces, extending beyond the classical Riemannian setting.

We study the moduli stabilization by the radiative corrections due to the moduli dependent vector-like masses invariant under the finite modular symmetry. The radiative stabilization mechanism can stabilize the modulus $\tau$ of the finite modular symmetry $\Gamma_N$ ($N \in \mathbb{N}$) at $\mathrm{Im}\,\tau \gg 1$, where the shift symmetry $\tau \to \tau+1$ remains unbroken approximately. The shift symmetry can be considered as the residual $\mathbb{Z}_N$ symmetry which realizes the Froggatt-Nielsen mechanism with the hierarchy parameter $e^{- 2\pi \mathrm{Im}\,\tau/N} \ll 1$. In this work, we study the stabilization of multiple moduli fields, so that various hierarchical values of the modular forms coexist in a model. For example, one modulus stabilized at $\mathrm{Im}\,\tau_1 \sim 3$ is responsible for the hierarchical structure of the quarks and leptons in the Standard Model, and another modulus stabilized at $\mathrm{Im}\,\tau_2 \sim 15$ can account for the flatness of the $\mathrm{Re}\,\tau_2$ direction which may be identified as the QCD axion., Comment: 12 pages, 3 figures

As part of the BISTRO survey, we present JCMT 850 $\mu$m polarimetric observations towards the Orion Integral-Shaped Filament (ISF) that covers three portions known as OMC-1, OMC-2, and OMC-3. The magnetic field threading the ISF seen in the JCMT POL-2 map appears as a tale of three: pinched for OMC-1, twisted for OMC-2, and nearly uniform for OMC-3. A multi-scale analysis shows that the magnetic field structure in OMC-3 is very consistent at all the scales, whereas the field structure in OMC-2 shows no correlation across different scales. In OMC-1, the field retains its mean orientation from large to small scales, but shows some deviations at small scales. Histograms of relative orientations between the magnetic field and filaments reveal a bimodal distribution for OMC-1, a relatively random distribution for OMC-2, and a distribution with a predominant peak at 90$^\circ$ for OMC-3. Furthermore, the magnetic fields in OMC-1 and OMC-3 both appear to be aligned perpendicular to the fibers, which are denser structures within the filament, but the field in OMC-2 is aligned along with the fibers. All these suggest that gravity, turbulence, and magnetic field are each playing a leading role in OMC-1, 2, and 3, respectively. While OMC-2 and 3 have almost the same gas mass, density, and non-thermal velocity dispersion, there are on average younger and fewer young stellar objects in OMC-3, providing evidence that a stronger magnetic field will induce slower and less efficient star formation in molecular clouds., Comment: published in the ApJ Letters

A tree is said to be even if for every pair of distinct leaves, the length of the unique path between them is even. In this paper we discuss the problem of determining whether an input graph has a spanning even tree. Hofmann and Walsh [Australas. J Comb. 35, 2006] proved that this problem can be solved in polynomial time on bipartite graphs. In contrast to this, we show that this problem is NP-complete even on planar graphs. We also give polynomial-time algorithms for several restricted classes of graphs, such as split graphs, cographs, cobipartite graphs, unit interval graphs, and block graphs., Comment: 12 pages

Elucidating the rationale behind neural models' outputs has been challenging in the machine learning field, which is indeed applicable in this age of large language models (LLMs) and in-context learning (ICL). When it comes to estimating input attributions (IA), ICL poses a new issue of interpreting which example in the prompt, consisting of a set of examples, contributed to identifying the task/rule to be solved. To this end, in this paper, we introduce synthetic diagnostic tasks inspired by the poverty of the stimulus design in inductive reasoning; here, most in-context examples are ambiguous w.r.t. their underlying rule, and one critical example disambiguates the task demonstrated. The question is whether conventional IA methods can identify such an example in interpreting the inductive reasoning process in ICL. Our experiments provide several practical findings; for example, a certain simple IA method works the best, and the larger the model, the generally harder it is to interpret the ICL with gradient-based IA methods., Comment: Preprint

From a spectroscopic survey of candidate H II regions in the Andromeda galaxy (M31) with MMT/Hectospec, we have identified 294 H II regions using emission line ratios and calculated elemental abundances from strong-line diagnostics (values ranging from sub-solar to super-solar) producing both Oxygen and Nitrogen radial abundance gradients. The Oxygen gradient is relatively flat, while the Nitrogen gradient is significantly steeper, indicating a higher N/O ratio in M31's inner regions, consistent with recent simulations of galaxy chemical evolution. No strong evidence was found of systematic galaxy-scale trends beyond the radial gradient. After subtracting the radial gradient from abundance values, we find an apparently stochastic and statistically significant scatter of standard deviation 0.06 dex, which exceeds measurement uncertainties. One explanation includes a possible collision with M32 200 - 800 Myrs ago. Using the two-point correlation function of the Oxygen abundance, we find that, similar to other spiral galaxies, M31 is well-mixed on sub-kpc scales but less so on larger (kpc) scales, which could be a result of an exponential decrease in mixing speed with spatial scale, and the aforementioned recent merger. Finally, the MMT spectroscopy is complemented by a dust continuum and CO survey of individual Giant Molecular Clouds, conducted with the Submillimeter Array. By combining the MMT and SMA observations, we obtain a unique direct test of the Oxygen abundance dependence of the $\alpha^{\prime}(^{12}\mathrm{CO})$ factor which is crucial to convert CO emission to dust mass. Our results suggest that within our sample there is no trend of the $\alpha^{\prime}(^{12}\mathrm{CO})$ with Oxygen abundance., Comment: MNRAS, in press

The BL Lacertae object VER J0521+211 underwent a notable flaring episode in February 2020. A short-term monitoring campaign, led by the MAGIC (Major Atmospheric Gamma Imaging Cherenkov) collaboration, covering a wide energy range from radio to very-high-energy (VHE, 100 GeV < E < 100 TeV) gamma rays was organised to study its evolution. These observations resulted in a consistent detection of the source over six consecutive nights in the VHE gamma-ray domain. Combining these nightly observations with an extensive set of multiwavelength data made modelling of the blazar's spectral energy distribution (SED) possible during the flare. This modelling was performed with a focus on two plausible emission mechanisms: i) a leptonic two-zone synchrotron-self-Compton scenario, and ii) a lepto-hadronic one-zone scenario. Both models effectively replicated the observed SED from radio to the VHE gamma-ray band. Furthermore, by introducing a set of evolving parameters, both models were successful in reproducing the evolution of the fluxes measured in different bands throughout the observing campaign. Notably, the lepto-hadronic model predicts enhanced photon and neutrino fluxes at ultra-high energies (E > 100 TeV). While the photon component, generated via decay of neutral pions, is not directly observable as it is subject to intense pair production (and therefore extinction) through interactions with the cosmic microwave background photons, neutrino detectors (e.g. IceCube) can probe the predicted neutrino component. Finally, the analysis of the gamma-ray spectra, as observed by MAGIC and the Fermi-LAT telescopes, yielded a conservative 95\% confidence upper limit of z \leq 0.244 for the redshift of this blazar., Comment: Accepted for publication in A&A

Processing large amounts of data fast, in constant and small space is the point of stream processing and the reason for its increasing use. Alas, the most performant, imperative processing code tends to be almost impossible to read, let alone modify, reuse -- or write correctly. We present both a stream compilation theory and its implementation as a portable stream processing library Strymonas that lets us assemble complex stream pipelines just by plugging in simple combinators, and yet attain the performance of hand-written imperative loops and state machines. The library supports finite and infinite streams and offers a rich set of combinators: from map, filter, take(while) to flat-map (nesting), zip, map-accumulate and sliding windowing. The combinators may be freely composed, and yet the resulting convoluted imperative code contains no traces of combinator abstractions: no closures, intermediate objects or tuples. The high-performance is portable and statically guaranteed, without relying on compiler or black-box optimizations. We greatly exceed in performance the available stream processing libraries in OCaml. The library exists in two versions, OCaml and Scala 3, and supports pluggable backends for code generation (currently: C, OCaml and Scala). Strymonas has been developed in tandem with the equational theory of stateful streams. Our theoretical model can represent all desired pipelines and also guarantees the existence of unique normal forms, which are mappable to (fused) state machines. We describe the normalization algorithm, as a form of normalization-by-evaluation. Stream pipeline compilation and optimization are represented as normalization, and are hence deterministic and terminating, with the guaranteed outcome. The equational theory lets us state and prove the correctness of the complete fusion optimization.

We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning tree of the graph that specifies the routing of power from the root to each vertex so that all the demands are satisfied and the energy loss is minimized. This problem is known to be NP-hard in general. When restricted to grids with uniform resistance and the root located at a corner, Gupta, Khodabaksh, Mortagy and Nikolova [Mathematical Programming 2022] invented the so-called Min-Min algorithm whose approximation factor is theoretically guaranteed. Our contributions are twofold. First, we prove that the problem is NP-hard even for grids; this resolves the open problem posed by Gupta et al. Second, we give a refined analysis of the Min-Min algorithm and improve its approximation factor under the same setup. In the analysis, we formulate the problem of giving an upper bound for the approximation factor as a non-linear optimization problem that maximizes a convex function over a polytope, which is less commonly employed in the analysis of approximation algorithms than linear optimization problems.

We derive an analytical form of the joint prior of effective spin parameters, $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$, assuming an isotropic and uniform-in-magnitude spin distribution. This is a vital factor in performing hierarchical Bayesian inference for studying the population properties of merging compact binaries observed with gravitational waves. In previous analyses, this was evaluated numerically using kernel density estimation (KDE). However, we find that this numerical approach is inaccurate in certain parameter regions, where both $|\chi_\mathrm{eff}|$ and $\chi_\mathrm{p}$ are small. Our analytical approach provides accurate computations of the joint prior across the entire parameter space and enables more reliable population inference. Employing our analytic prior, we reanalyze binary black holes in the Gravitational-Wave Transient Catalog 3 (GWTC-3) by the LIGO-Virgo-KAGRA collaboration. While the results are largely unchanged, log-likelihood errors due to the use of the inaccurate prior evaluations are $\mathcal{O}(1)$. Since these errors accumulate with the increasing number of events, our analytical prior will be crucial in the future analyses., Comment: 6 figures

Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a quantum circuit. In real devices, however, the noise profile is much more complex and contains non-trivial spatiotemporal correlations, such as cross-talk, non-Markovianity, and their mixtures. Here, we examine the performance of two paradigmatic QEC codes in the presence of complex noise by using process tensors to represent spatiotemporal correlations beyond iid errors. This integration is an instance of the recently proposed \textit{strategic code}, which combines QEC with process tensors. In particular, we construct the maximum likelihood (ML) decoder for a quantum error correction code with a process tensor. To understand the computational overhead and implications of this approach, we implement our framework numerically for small code instances and evaluate its performance. We also propose a method to evaluate the performance of strategic codes and construct the ML decoder with an efficient tensor network approximation. Our results highlight the possible detrimental effects of correlated noise and potential pathways for designing decoders that account for such effects., Comment: 27 pages, 12 figures, 2 tables

This paper proposes a new design method for a stochastic control policy using a normalizing flow (NF). In reinforcement learning (RL), the policy is usually modeled as a distribution model with trainable parameters. When this parameterization has less expressiveness, it would fail to acquiring the optimal policy. A mixture model has capability of a universal approximation, but it with too much redundancy increases the computational cost, which can become a bottleneck when considering the use of real-time robot control. As another approach, NF, which is with additional parameters for invertible transformation from a simple stochastic model as a base, is expected to exert high expressiveness and lower computational cost. However, NF cannot compute its mean analytically due to complexity of the invertible transformation, and it lacks reliability because it retains stochastic behaviors after deployment for robot controller. This paper therefore designs a restricted NF (RNF) that achieves an analytic mean by appropriately restricting the invertible transformation. In addition, the expressiveness impaired by this restriction is regained using bimodal student-t distribution as its base, so-called Bit-RNF. In RL benchmarks, Bit-RNF policy outperformed the previous models. Finally, a real robot experiment demonstrated the applicability of Bit-RNF policy to real world. The attached video is uploaded on youtube: https://youtu.be/R_GJVZDW9bk, Comment: 27 pages, 13 figures

We discuss selection rules of chiral matters in type IIA intersecting and IIB magnetized D-brane models on toroidal orbifolds. Since the chiral matters on toroidal orbifolds are labeled by a certain conjugacy class of the gauged orbifold group, the selection rules involve non-trivial fusion rules. We find that the representation of the chiral matters is described by a $D_4$ flavor symmetry for an even number of magnetic fluxes or winding numbers at tree level. Furthermore, the $D_4$ symmetry still remains even when we take into account loop effects. We also study non-perturbative effects such as D-brane instantons., Comment: 30 pages, 2 figures

Understanding the high-temperature properties of materials with (anti-)fluorite structures is crucial for their application in nuclear reactors. In this study, we employ machine learning molecular dynamics (MLMD) simulations to investigate the high-temperature thermal properties of thorium dioxide, which has a fluorite structure, and lithium oxide, which has an anti-fluorite structure. Our results show that MLMD simulations effectively reproduce the reported thermal properties of these materials. A central focus of this work is the analysis of specific heat anomalies in these materials at high temperatures, commonly referred to as Bredig, pre-melting, or $\lambda$-transitions. We demonstrate that a local order parameter, analogous to those used to describe liquid-liquid transitions in supercooled water and liquid silica, can effectively characterize these specific heat anomalies. The local order parameter identifies two distinct types of defective structures: lattice defect-like and liquid-like local structures. Above the transition temperature, liquid-like local structures predominate, and the sub-lattice character of mobile atoms disappears.

In this note we discuss Gauss maps for M\"obius surfaces in the $n$-sphere, and their applications in the study of Willmore surfaces. One such ``Gauss map'', naturally associated to a Willmore surface that has a dual Willmore surface, is the Lorentzian $2$-plane bundle given by a lift of the suface and its dual. More generally, we define the concept of a Lorentzian $2$-plane lift for an arbitrary M\"obius surface, and show that the conformal harmonicity of this lift is equivalent to the Willmore condition for the surface. This clarifies some previous work of F. H\'elein, Q. Xia-Y Shen, X. Ma and others, and, for instance, allows for the treatment of the Bj\"orling problem for Willmore surfaces in the presence of umbilics., Comment: 13 pages

We present a spectroscopic analysis of two star-forming galaxies at z~5 observed with JWST/NIRSpec as part of the Early eXtragalactic Continuum and Emission Line Science (EXCELS) survey. The detection of the C III]$\lambda\lambda$1906,09, [O II]$\lambda\lambda$3726,29, [O III]$\lambda\lambda$4363,5007, and [N II]$\lambda$6584 nebular emission lines enables investigation of the C/O, N/O, and C/N abundance ratios using the temperature-sensitive method. The two galaxies have stellar masses of log($M_{\star}$/M$_{\odot}$ ) = 8.13$\pm$0.09 and log($M_{\star}$/M$_{\odot}$ )=8.52$\pm$0.13 and corresponding metallicities of Z~0.2Z$_{\odot}$ and Z~0.3Z$_{\odot}$. These metallicities are somewhat higher than is typical for other z>5 galaxies with similar stellar mass and are in fact comparable to high-redshift analogue galaxies at z~0. Both galaxies display evidence for N/O enhancement with respect to the z~0 sample, with log(N/O)=-1.07$\pm$0.17 and log(N/O)=-0.86$\pm$0.15 respectively. In contrast, we find low C abundances, with log(C/O)=-0.82$\pm$0.22 and log(C/O)=-1.02$\pm$0.22, consistent with the predicted yields of core-collapse supernovae. Following the trend observed in other high-redshift sources, we find that the C/N ratios are lower at fixed O/H compared to the majority of local galaxies. In contrast to the top-heavy IMF invoked in some studies to explain low C/N ratios in metal-poor galaxies, we find, via comparison to chemical evolution models, that a standard or bottom-heavy IMF better explains the observed abundance ratios in more enriched systems due to an increase in N-enrichment from intermediate mass (4-7M$_{\odot}$) stars. Our results demonstrate that robust measurements of CNO abundances with JWST can reveal unique enrichment pathways in galaxies as a function of both metallicity and redshift., Comment: 17 pages, 8 Figures, and 3 Tables. Submitted to MNRAS. Comments Welcome

This study presents a comprehensive mathematical model for Volterra defects and explores their relations using differential geometry on Riemann--Cartan manifolds. Following the standard Volterra process, we derived the Cartan moving frame, a geometric representation of plastic fields, and the associated Riemannian metric using exterior algebra. Although the analysis naturally defines the geometry of three types of dislocations and the wedge disclination, it fails to classify twist disclinations owing to the persistent torsion component, suggesting the need for modifications to the Volterra process. By leveraging the interchangeability of the Weitzenb\"ock and Levi-Civita connections and applying an analytical solution for plasticity derived from the Biot--Savart law, we provide a rigorous mathematical proof of the long-standing phenomenological relationship between edge dislocations and wedge disclinations. Additionally, we showcase the effectiveness of novel mathematical tools, including Riemannian holonomy for analysing the Frank vector and complex potentials that encapsulate the topological properties of wedge disclinations as jump discontinuities. Furthermore, we derive analytical expressions for the linearized stress fields of wedge disclinations and confirm their consistency with existing results. These findings demonstrate that the present geometrical framework extends and generalizes the classical theory of Volterra defects.

Characterizing low-energy (O(1keV)) nuclear recoils near the detector threshold is one of the major challenges for large direct dark matter detectors. To that end, we have successfully used a Yttrium-Beryllium photoneutron source that emits 152 keV neutrons for the calibration of the light and charge yields of the XENONnT experiment for the first time. After data selection, we accumulated 474 events from 183 hours of exposure with this source. The expected background was $55 \pm 12$ accidental coincidence events, estimated using a dedicated 152 hour background calibration run with a Yttrium-PVC gamma-only source and data-driven modeling. From these calibrations, we extracted the light yield and charge yield for liquid xenon at our field strength of 23 V/cm between 0.5 keV$_{\rm NR}$ and 5.0 keV$_{\rm NR}$ (nuclear recoil energy in keV). This calibration is crucial for accurately measuring the solar $^8$B neutrino coherent elastic neutrino-nucleus scattering and searching for light dark matter particles with masses below 12 GeV/c$^2$.

The origin of PeV cosmic rays is a long-standing mystery, and ultrahigh-energy gamma-ray observations would play a crucial role in identifying it. Recently, LHAASO reported the discovery of ``dark'' gamma-ray sources that were detected above 100 TeV without any GeV--TeV gamma-ray counterparts. The origins of these dark gamma-ray sources are unknown. We propose isolated black holes (IBHs) wandering in molecular clouds as the origins of PeV cosmic rays and LHAASO dark sources. An IBH accretes surrounding dense gas, which forms a magnetically arrested disk (MAD) around the IBH. Magnetic reconnection in the MAD can accelerate cosmic-ray protons up to PeV energies. Cosmic-ray protons of GeV-TeV energies fall to the IBH, whereas cosmic-ray protons at sub-PeV energies can escape from the MAD, providing PeV CRs into the interstellar medium. The sub-PeV cosmic-ray protons interact with the surrounding molecular clouds, producing TeV-PeV gamma rays without emitting GeV-TeV gamma rays. This scenario can explain the dark sources detected by LHAASO. Taking into account the IBH and molecular cloud distributions in our Galaxy, we demonstrate that IBHs can provide a significant contribution to the PeV cosmic rays observed on Earth. Future gamma-ray detectors in the southern sky and neutrino detectors would provide a concrete test to our scenario., Comment: 9 pages, 4 figures, 1 table

Recent advancements in text-to-image diffusion models have brought them to the public spotlight, becoming widely accessible and embraced by everyday users. However, these models have been shown to generate harmful content such as not-safe-for-work (NSFW) images. While approaches have been proposed to erase such abstract concepts from the models, jail-breaking techniques have succeeded in bypassing such safety measures. In this paper, we propose TraSCE, an approach to guide the diffusion trajectory away from generating harmful content. Our approach is based on negative prompting, but as we show in this paper, conventional negative prompting is not a complete solution and can easily be bypassed in some corner cases. To address this issue, we first propose a modification of conventional negative prompting. Furthermore, we introduce a localized loss-based guidance that enhances the modified negative prompting technique by steering the diffusion trajectory. We demonstrate that our proposed method achieves state-of-the-art results on various benchmarks in removing harmful content including ones proposed by red teams; and erasing artistic styles and objects. Our proposed approach does not require any training, weight modifications, or training data (both image or prompt), making it easier for model owners to erase new concepts.

A recent report on the detection of very-high-energy gamma rays from V4641 Sagittarii (V4641 Sgr) up to ~0.8 peta-electronvolt has made it the second confirmed "PeVatron" microquasar. Here we report on the observation of V4641 Sgr with X-Ray Imaging and Spectroscopy Mission (XRISM) in September 2024. Thanks to the large field of view and low background, the CCD imager Xtend successfully detected for the first time X-ray extended emission around V4641 Sgr with a significance of > 4.5 sigma and > 10 sigma based on our imaging and spectral analysis, respectively. The spatial extent is estimated to have a radius of $7 \pm 3$ arcmin ($13 \pm 5$ pc at a distance of 6.2 kpc) assuming a Gaussian-like radial distribution, which suggests that the particle acceleration site is within ~10 pc of the microquasar. If the X-ray morphology traces the diffusion of accelerated electrons, this spatial extent can be explained by either an enhanced magnetic field (~80 uG) or a suppressed diffusion coefficient (~$10^{27}$ cm$^2$ s$^{-1}$ at 100 TeV). The integrated X-ray flux, (4-6)$\times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ (2-10 keV), would require a magnetic field strength higher than the galactic mean (> 8 uG) if the diffuse X-ray emission originates from synchrotron radiation and the gamma-ray emission is predominantly hadronic. If the X-rays are of thermal origin, the measured extension, temperature, and plasma density can be explained by a jet with a luminosity of ~$2\times 10^{39}$ erg s$^{-1}$, which is comparable to the Eddington luminosity of this system., Comment: 9 pages, 5 figures, accepted for publication in ApJL

Radiogenic neutrons emitted by detector materials are one of the most challenging backgrounds for the direct search of dark matter in the form of weakly interacting massive particles (WIMPs). To mitigate this background, the XENONnT experiment is equipped with a novel gadolinium-doped water Cherenkov detector, which encloses the xenon dual-phase time projection chamber (TPC). The neutron veto (NV) tags neutrons via their capture on gadolinium or hydrogen, which release $\gamma$-rays that are subsequently detected as Cherenkov light. In this work, we present the key features and the first results of the XENONnT NV when operated with demineralized water in the initial phase of the experiment. Its efficiency for detecting neutrons is $(82\pm 1)\,\%$, the highest neutron detection efficiency achieved in a water Cherenkov detector. This enables a high efficiency of $(53\pm 3)\,\%$ for the tagging of WIMP-like neutron signals, inside a tagging time window of $250\,\mathrm{\mu s}$ between TPC and NV, leading to a livetime loss of $1.6\,\%$ during the first science run of XENONnT.

We analyzed the 7.92$\times 10^{11}$ cosmic-ray-induced muon events collected by the IceCube Neutrino Observatory from May 13, 2011, when the fully constructed experiment started to take data, to May 12, 2023. This dataset provides an up-to-date cosmic-ray arrival direction distribution in the Southern Hemisphere with unprecedented statistical accuracy covering more than a full period length of a solar cycle. Improvements in Monte Carlo event simulation and better handling of year-to-year differences in data processing significantly reduce systematic uncertainties below the level of statistical fluctuations compared to the previously published results. We confirm the observation of a change in the angular structure of the cosmic-ray anisotropy between 10 TeV and 1 PeV, more specifically in the 100-300 TeV energy range.

Although recent quantized Large Language Models (LLMs), such as BitNet, have paved the way for significant reduction in memory usage during deployment with binary or ternary weights, training these models still demands substantial memory footprints. This is partly because high-precision (i.e., unquantized) weight matrices required for straight-through estimation must be maintained throughout the whole training process. To address this, we explore the potential of directly updating the quantized low-precision weight matrices without relying on the straight-through estimator during backpropagation, thereby saving memory usage during training. Specifically, we employ a stochastic rounding technique to minimize information loss caused by the use of low-bit weights throughout training. Experimental results on our LLaMA-structured models indicate that (1) training with only low-precision weights is feasible even when they are constrained to ternary values, (2) extending the bit width to 8 bits results in only a 5% loss degradation compared to BitNet b1.58 while offering the potential for reduced memory usage during training, and (3) our models can also perform inference using ternary weights, showcasing their flexibility in deployment., Comment: work in progress

The crossing number of a graph is the least number of crossings over all drawings of the graph in the plane. Computing the crossing number of a given graph is NP-hard, but fixed-parameter tractable (FPT) with respect to the natural parameter. Two well-known variants of the problem are 2-layer crossing minimization and circular crossing minimization, where every vertex must lie on one of two layers, namely two parallel lines, or a circle, respectively. Both variants are NP-hard, but FPT with respect to the natural parameter. Recently, a local version of the crossing number has also received considerable attention. A graph is $k$-planar if it admits a drawing with at most $k$ crossings per edge. In contrast to the crossing number, recognizing $k$-planar graphs is NP-hard even if $k=1$. In this paper, we consider the two above variants in the local setting. The $k$-planar graphs that admit a straight-line drawing with vertices on two layers or on a circle are called 2-layer $k$-planar and outer $k$-planar graphs, respectively. We study the parameterized complexity of the two recognition problems with respect to $k$. For $k=0$, both problems can easily be solved in linear time. Two groups independently showed that outer 1-planar graphs can also be recognized in linear time [Algorithmica 2015/2016]. One group asked whether outer 2-planar graphs can be recognized in polynomial time. Our main contribution consists of XP-algorithms for recognizing 2-layer $k$-planar graphs and outer $k$-planar graphs. We complement these results by showing that both recognition problems are XNLP-hard. This implies that both problems are W$[t]$-hard for every $t$ and that it is unlikely that they admit FPT-algorithms. On the other hand, we present an FPT-algorithm for recognizing 2-layer $k$-planar graphs where the order of the vertices on one layer is specified., Comment: 23 pages, 6 figures

In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of \emph{diverse} solutions plays an indispensable role in enhancing human decision-making. In this paper, we investigate the problem of finding diverse solutions of Satisfiability from the perspective of parameterized complexity with a particular focus on \emph{tractable} Boolean formulas. We present several parameterized tractable and intractable results for finding a diverse pair of satisfying assignments of a Boolean formula. In particular, we design an FPT algorithm for finding an ``almost disjoint'' pair of satisfying assignments of a $2$CNF formula., Comment: 14 pages, 1 figure

Single crystals of (Ca$_{1-x}$La$_x$)KFe$_4$As$_4$ (0 <= x <=0.16) have been grown by using the self-flux method, and the evolution of physical properties including the critical current density (Jc) with La-doping has been investigated. Tc decreases monotonically with increasing x, while Jc at the same temperature and magnetic field increases initially and reach its maximum at x = 0.082. The increase in Jc is more obvious at low temperatures and high fields. At T = 5 K and H = 40 kOe, Jc reaches 0.34 MA/cm$^2$, which is ~4 times larger than that for pure crystals. It is also found that anomalous temperature dependence of Jc in CaKFe$_4$As$_4$ is wiped away as the La content is increased. However, Jc shows non-monotonic field dependence (peak effect) at high fields in crystals with large x. In addition, we found that despite weak anisotropy of H$_{c2}$, there is extremely large anisotropy of Jc up to ~15, which is most likely caused by novel planar defects in the crystal, similar to CaKFe$_4$As$_4$. Jc characteristics in (Ca$_{1-x}$La$_x$)KFe$_4$As$_4$ with disorder outside FeAs planes is compared with that in CaK(Fe$_{1-x}$Co$_x$)$_4$As$_4$ with disorder within FeAs planes., Comment: 12 pages, 8 figures, 1 table

The first spectroscopy of $^{52}$K was investigated via in-beam $\gamma$-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory after one-proton and one-neutron knockout from $^{53}$Ca and $^{53}$K beams impinging on a 15-cm liquid hydrogen target at $\approx$ 230~MeV/nucleon. The energy level scheme of $^{52}$K was built using single $\gamma$ and $\gamma$-$\gamma$ coincidence spectra. The spins and parities of the excited states were established based on momentum distributions of the fragment after the knockout reaction and based on exclusive cross sections. The results were compared to state-of-the-art shell model calculations with the SDPF-Umod interaction and ab initio IMSRG calculations with chiral effective field theory nucleon-nucleon and three-nucleon forces.

Heterotic string theory has nonsupersymmetric branes whose existence is suggested by the cobordism conjecture. We numerically construct static, spherically symmetric, and asymptotically flat black brane solutions in ten-dimensional heterotic superstring theories for 0- and 4-branes. These branes carry charges that are measured by Chern classes on the sphere surrounding the branes. For the extremal case, the solutions have a throat region with a linear dilaton profile as expected from the corresponding world-sheet theory. We also construct non-extremal solutions by compactifying the time direction. To verify the reliability of our numerical calculations, we confirm that they reproduce the known analytical solutions for the 6-brane. Our black brane solutions provide evidence supporting the existence of such branes in heterotic string theory., Comment: 28 pages, 24 figures

We demonstrate the feasibility of the radar-based measurement of body movements in scenarios involving multiple students using a pair of 79-GHz millimeter-wave radar systems with array antennas. We quantify the body motion using the Doppler frequency calculated from radar echoes. The measurement accuracy is evaluated for two experimental scenarios, namely university students in an office and elementary school students in a classroom. The body movements measured using the two radar systems are compared to evaluate the repeatability and angle dependency of the measurement. Moreover, in the first scenario, we compare the radar-estimated body movement with subjective evaluation scores provided by two evaluators. In the first scenario, the coefficient of correlation between the radar-estimated body movement and the subjective evaluation score is 0.73 on average, with a maximum value of 0.97; in the second scenario, the average correlation coefficient of body movements measured using two radar systems is as high as 0.78. These results indicate that the proposed approach can be used to monitor the body movements of multiple students in realistic scenarios., Comment: 10 pages, 8 figures, 7 tables. This work is going to be submitted to the IEEE for possible publication

Statistics of excitations play an essential role in understanding phases of matter. In this paper, we introduce a universal method for studying the generalized statistics of Abelian particles and extended excitations in lattices of any dimension. We compute the statistics using the Berry phase of a sequence of unitary operators that transports the excitations while canceling local ambiguities at each step. The sequence is derived from locality, using the Smith normal form. We show that the statistics are quantized invariants. Our method unifies the statistics for the braiding and fusion of particles and loops, and leads to the discovery of novel statistics for membrane excitations. The statistics can be interpreted as the quantum anomaly of a generalized global symmetry, which manifests as an obstruction to gauging the symmetry on lattices. Furthermore, we show that non-trivial statistics forbid short-range entangled states, establishing the dynamical consequence of anomalies in microscopic lattice models., Comment: 39 pages, 11 figures. added refs, minor edits

Real-time monitoring of critical parameters is essential for energy systems' safe and efficient operation. However, traditional sensors often fail and degrade in harsh environments where physical sensors cannot be placed (inaccessible locations). In addition, there are important parameters that cannot be directly measured by sensors. We need machine learning (ML)-based real-time monitoring in those remote locations to ensure system operations. However, traditional ML models struggle to process continuous sensor profile data to fit model requirements, leading to the loss of spatial relationships. Another challenge for real-time monitoring is ``dataset shift" and the need for frequent retraining under varying conditions, where extensive retraining prohibits real-time inference. To resolve these challenges, this study addressed the limitations of real-time monitoring methods by enabling monitoring in locations where physical sensors are impractical to deploy. Our proposed approach, utilizing Multi-Input Operator Network virtual sensors, leverages deep learning to seamlessly integrate diverse data sources and accurately predict key parameters in real-time without the need for additional physical sensors. The approach's effectiveness is demonstrated through thermal-hydraulic monitoring in a nuclear reactor subchannel, achieving remarkable accuracy., Comment: 17 pages, 7 figures

Imaging spin-wave propagation in magnetic materials in a wide frequency range is crucial for understanding and applying spin-wave dynamics. Recently, nitrogen-vacancy (NV) centers in diamond have attracted attention as sensors capable of quantitatively measuring the amplitude and phase of coherent spin waves. However, the conventional sensing protocol has been limited to detecting spin waves whose frequencies match the resonance frequency of the NV spins. We demonstrate that by utilizing the AC Zeeman effect, it is possible to image spin waves propagating in a yttrium iron garnet (YIG) thin film over a wide frequency range up to a maximum detuning of 567 MHz without changing the external magnetic field. Our results expand the applicability of NV centers for spin-wave sensing and pave the way for quantitative investigations of the dynamics in various magnetic materials, such as metallic ferromagnets and van der Waals magnets., Comment: 19 pages, 17 figures

An electron confined by a semiconductor quantum dot (QD) can be displaced by changes in electron occupations of surrounding QDs owing to the Coulomb interaction. For a single-spin qubit in an inhomogeneous magnetic field, such a displacement of the host electron results in a qubit energy shift which must be handled carefully for high-fidelity operations. Here we spectroscopically investigate the qubit energy shift induced by changes in charge occupations of nearby QDs for a silicon single-spin qubit in a magnetic-field gradient. Between two different charge configurations of an adjacent double QD, a spin qubit shows an energy shift of about 4 MHz, which necessitates strict management of electron positions over a QD array. We confirm a correlation between the qubit frequency and the charge configuration by using a postselection analysis., Comment: 15 pages, 4 figures

We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by symmetry-protected topological responses, which correspond to generators of group cohomology and can be expressed explicitly on the lattice using cohomology operations including cup product, Steenrod squares and new combinations of higher cup products called higher Pontryagin powers. Our study covers most types of the cohomology operations in the literature. This hence gives rise to several new classes of diagonal and non-diagonal logical gates in increasing Clifford hierarchies beyond the usual color code paradigm corresponding to an $n$-fold cup product, including the logical $R_k$ and multi-controlled $C^m R_k$ gates for codes defined in projective spaces. Implementing these gates could make it more efficient to compile specific types of quantum algorithms such as Shor's algorithm. We further extend the construction to quantum codes with boundaries, which generalizes the folding approach in color codes. We also present a formalism for addressable and parallelizable logical gates in LDPC codes via higher-form symmetries and apply it to construct addressable logical Clifford gates in expander-based codes including the asymptotically good LDPC codes and hypergraph-product codes. As a byproduct, we find new topological responses of finite higher-form symmetries using higher Pontryagin powers., Comment: 31 pages, 7 figures, 2 tables. added refs, minor edits

Diffusion models are prone to exactly reproduce images from the training data. This exact reproduction of the training data is concerning as it can lead to copyright infringement and/or leakage of privacy-sensitive information. In this paper, we present a novel way to understand the memorization phenomenon, and propose a simple yet effective approach to mitigate it. We argue that memorization occurs because of an attraction basin in the denoising process which steers the diffusion trajectory towards a memorized image. However, this can be mitigated by guiding the diffusion trajectory away from the attraction basin by not applying classifier-free guidance until an ideal transition point occurs from which classifier-free guidance is applied. This leads to the generation of non-memorized images that are high in image quality and well-aligned with the conditioning mechanism. To further improve on this, we present a new guidance technique, \emph{opposite guidance}, that escapes the attraction basin sooner in the denoising process. We demonstrate the existence of attraction basins in various scenarios in which memorization occurs, and we show that our proposed approach successfully mitigates memorization.

We report on a blinded search for dark matter with single- and few-electron signals in the first science run of XENONnT relying on a novel detector response framework that is physics-model-dependent. We derive 90\% confidence upper limits for dark matter-electron interactions. Heavy and light mediator cases are considered for the standard halo model and dark matter up-scattered in the Sun. We set stringent new limits on dark matter-electron scattering via a heavy mediator with a mass within 10-20\,MeV/$c^2$ and electron absorption of axion-like particles and dark photons for $m_\chi$ below 0.186\,keV/$c^2$., Comment: 9 pages, 5 figures

Understanding mass, size, and surface mass density of giant molecular clouds (GMCs) in galaxies is key to insights into star formation processes. We analyze these in M33 using Herschel dust and archival IRAM 30m telescope data, compared to Milky Way CO data. A Dendrogram algorithm on a 2D dust map and a Xco factor map are used for M33 instead of a constant value. Dust and CO-derived values are similar, with mean radii of $\sim\,$$58\,$pc for the dust and $\sim\,$$68\,$pc for CO. Largest GMAs are about $150\,$pc in radius, similar to the Milky Way, suggesting a size-limiting process. M33 contains less massive, lower-density GMCs compared to the Milky Way. The highest mass GMCs observed in the Milky Way are mostly absent in M33. M33's mean surface mass density is much lower, due to the Milky Way's higher column densities despite similar GMC areas. No systematic gradients in M33's physical properties were found with galactocentric radius, but higher densities and masses near the center suggest increased star formation. In both galaxies, 30% of molecular mass is central. The GMC mass power-law spectrum index is $\alpha=2.3\pm0.1$ and $\alpha=1.9\pm0.1$ for dust and CO in M33, respectively. We conclude that M33 and Milky Way GMCs are mostly similar, though M33 lacks high-mass GMCs, with no clear explanation. GMC properties weakly depend on galactic environment, with stellar feedback as a factor needing further study.

We study the three-body Fermi liquid effects in the SU($N$) Anderson impurity model in the strong interaction limit where the occupation number $N_d^{}$ of the impurity levels varies over the range of $0

The nanosized boron vacancy ($V_\mathrm{B}^-$) defect spot in hexagonal boron nitride ($h$-BN) is promising for a local magnetic field quantum sensor. One of its advantages is that a helium-ion microscope can make a spot at any location in an $h$-BN flake with nanometer accuracy. In this study, we investigate the properties of the created nanosized $V_\mathrm{B}^-$ defect spots by systematically varying three conditions: the helium-ion dose, the thickness of the $h$-BN flakes, and the substrate on which the $h$-BN flakes are attached. The physical background of the results obtained is successfully interpreted using Monte Carlo calculations. From the findings obtained here, a guideline for their optimal creation conditions is obtained to maximize its performance as a quantum sensor concerning sensitivity and localization., Comment: 12 pages, 7 figures

Important advances have recently been made in the search for materials with complex multi-phase landscapes that host photoinduced metastable collective states with exotic functionalities. In almost all cases so far, the desired phases are accessed by exploiting light-matter interactions via the imaginary part of the dielectric function through above-bandgap or resonant mode excitation. Nonresonant Raman excitation of coherent modes has been experimentally observed and proposed for dynamic material control, but the resulting atomic excursion has been limited to perturbative levels. Here, we demonstrate that it is possible to overcome this challenge by employing nonresonant ultrashort pulses with low photon energies well below the bandgap. Using mid-infrared pulses, we induce ferroelectric reversal in lithium niobate and phase switching in tin selenide and characterize the large-amplitude mode displacements through femtosecond Raman scattering, second harmonic generation, and x-ray diffraction. This approach, validated by first-principle calculations, defines a novel method for synthesizing hidden phases with unique functional properties and manipulating complex energy landscapes at reduced energy consumption and ultrafast speeds., Comment: 5 figures

The introduction of machine learned potentials (MLPs) has greatly expanded the space available for studying Nuclear Quantum Effects computationally with ab initio path integral (PI) accuracy, with the MLPs' promise of an accuracy comparable to that of ab initio at a fraction of the cost. One of the challenges in development of MLPs is the need for a large and diverse training set calculated by ab initio methods. This data set should ideally cover the entire phase space, while not searching this space using ab initio methods, as this would be counterproductive and generally intractable with respect to computational time.In this paper, we present the self-learning PI hybrid Monte Carlo Method using a mixed ab initio and ML potential (SL-PIHMC-MIX), where the mixed potential allows for the study of larger systems and the extension of the original SL-HMC method [Nagai et al., Phys. Rev. B 102, 041124 (2020)] to PI methods and larger systems. While the MLPs generated by this method can be directly applied to run long-time ML-PIMD simulations, we demonstrate that using PIHMC-MIX with the trained MLPs allows for an exact reproduction of the structure obtained from ab initio PIMD. Specifically, we find that the PIHMC-MIX simulations require only 5,000 evaluations of the 32-bead structure, compared to the 100,000 evaluations needed for the ab initio PIMD result., Comment: 44 pages, 9 figures and 25 pages supplemental materials, accepted in J. Chem. Phys

Topological superconductors and Majorana edge modes at their boundaries have been theoretically predicted. However, their experimental observation remains controversial. Recent theoretical studies suggest that chiral Majorana edge modes exhibit distinct spatially-resolved optical conductivity compared to chiral Dirac edge modes. In this work, we investigate the optical conductivity and spatially-resolved optical conductivity induced by Majorana edge modes and Dirac edge modes under time-reversal symmetry and crystalline symmetry. We conduct numerical calculations and analytical calculations with edge effective theory for two-dimensional ${\mathbb Z}_2$ topological insulators, strong topological superconductors, and topological crystalline superconductors. Our results show that even under time-reversal symmetry and crystalline symmetry, Majorana edge modes and Dirac edge modes exhibit different optical responses., Comment: 17 pages + 12 pages