Search

We discuss the locomotion of a thermally driven elastic two-sphere microswimmer with internal feedback control that is realized by the position-dependent friction coefficients. In our model, the two spheres are in equilibrium with independent heat baths having different temperatures, causing a heat flow between the two spheres. We generally show that the average velocity of the microswimmer is nonzero when the friction coefficients are position-dependent. Using the method of stochastic thermodynamics, we obtain the entropy production rate and discuss the efficiency of the two-sphere microswimmer. The proposed self-propulsion mechanism highlights the importance of information in active matter and can be a fundamental process in various biological systems.

We report improved absolute frequency measurement of the $^{1}$S$_{0}-^{3}$P$_{0}$ transition of $^{171}$Yb at National Metrology Institute of Japan (NMIJ) by comparing the $^{171}$Yb optical lattice clock NMIJ-Yb1 with 13 Cs primary frequency standards via International Atomic Time from August 2021 to May 2023. The measured absolute frequency is 518 295 836 590 863.62(10) Hz with a fractional uncertainty of $1.9\times10^{-16}$, in good agreement with the recommended frequency of $^{171}$Yb as a secondary representation of the second. This uncertainty is 2.6 times lower than our previous measurement uncertainty, and slightly lower than any uncertainties of the absolute frequency measurements of $^{171}$Yb that have so far been reported by other institutes. We also estimate correlation coefficients between our present and previous measurements, which is important for updating the recommended frequency.

This is a sequel to a paper by the authors. We formulate a prototype of a Batyrev-Manin type conjecture for DM stacks in positive characteristic with emphasis on the wild case. The key to doing so is the notion of sectoroids, which plays a role similar to the role played by sectors in characteristic zero. We also check some compatibilities of the proposed prototype and see how it reduces to special cases. In the course of formulating the prototype, we introduce a new type of height functions, which is more general and flexible than the one we considered in the preceding paper. Examples of this new height function include discriminants of torsors, minimal discriminants and conductors of elliptic curves in characteristic three. In appendices, we generalize construction of a moduli stack by Tonini-Yasuda and construct a morphism between stacks of twisted arcs. These results are closely related to the main text, but also of independent interest., Comment: 66 pages

Recently, a concept known as $\mu$TRISTAN, which involves the acceleration of $\mu^+$, has been proposed. This initiative has led to considerations of a new design for a neutrino factory. Additionally, leveraging the polarization of $\mu^+$, measurements of T violation in neutrino oscillations are also being explored. In this paper, we present analytical expressions for T violation in neutrino oscillations within the framework of standard three flavor neutrino oscillations, a scenario involving nonstandard interactions, and a case of unitarity violation. We point out that examining the energy spectrum of T violation may be useful for probing new physics effects., Comment: 15 pages. Contribution to a Festscrift for the 80th birthday of Paul Frampton

A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge compilation map, all representation classes are subsets of the negation normal form (NNF). However, Boolean functions may be better expressed by a representation that is different from that of the NNF subsets. In this study, we treat tensor trains as Boolean function representations and analyze their succinctness and tractability. Our study is the first to evaluate the expressiveness of a tensor decomposition method using criteria from knowledge compilation literature. Our main results demonstrate that tensor trains are more succinct than ordered binary decision diagrams (OBDDs) and support the same polytime operations as OBDDs. Our study broadens their application by providing a theoretical link between tensor decomposition and existing NNF subsets.

The drying rate profile of granular beds can be divided into the constant rate period (CRP), which is characterized by a nearly constant drying rate, and the falling rate period (FRP), in which the drying rate rapidly decays. In order to explain this behavior quantitatively, we proposed a simple one-dimensional power law model in which the product of the water permeability and the pressure gradient is assumed to be proportional to the cube of the saturation. To test this model, we measured the drying rates of glass beads and hierarchical granular materials produced by sintering and breaking glass beads. Our results and those of previous experiments showed consistency with the power law. The obtained proportional constant of the experimental power law also shows a rough agreement with that estimated from previous studies on water permeability and capillary pressure. Drying behavior in FRP also agrees with our model in some points. The remnant deviation of the model from experimental results may be attributed to the inhomogeneity of granular media, which was qualitatively verified., Comment: 23 pages, 18 figures, to be published in Physical Review Fluids

In this work we investigate the two-neutron decay of 13Li and of the excited states of 11Li populated via one-proton removal from 14Be and 12Be, respectively. A phenomenological model is used to describe the decay of 11Li and 13Li. While the first one displays important sequential components, the second one appears dominated by the direct two-neutron decay. A microscopic three-body model is used to extract information on the spatial configuration of the emitted neutrons before the decay and shows that the average distance between the neutrons increases going from 11Li to 13Li.

Despite the extensive use of electrochemiluminescence in sensing applications, its potential in lighting and display technology has been constrained by the low luminance and short operational lifetime of electrochemiluminescence devices (ECLDs). Here, we demonstrate a substantial enhancement in the luminance, efficiency, and operational longevity of ECLDs by introducing electrochemically induced hyperfluorescence (ECiHF) via electrogeneration of charge-transfer (CT) excimers and subsequent energy transfer to fluorescent acceptors. By assuming a double-decker arrangement of the electron donor and acceptor groups, the molecule TpAT-tFFO supports solution-state thermally activated delayed fluorescence from a CT excimer state and efficient energy transfer to the rubrene dye TBRb. Optimized ECLDs based on this material combination achieve an unprecedented luminance of 6,220 cd/m2 and their operational lifetime (LT50) at an initial luminance of 100 cd/m2 exceeds 20 minutes, more than 10-fold longer than other ECLDs with meaningful efficiency or brightness. We identify energy level alignment between the excimer and the emitter as a crucial factor for efficient ECiHF. In mixtures with energy gaps > 0.5 eV, electron transfer results in reduced performance and renders the operation strongly dependent on applied voltage and frequency. By contrast, spectroelectrochemical analysis reveals that devices with favorable energy level alignment operate on a pure excimer mechanism across a wide range of frequencies. These findings highlight the innovative potential of ECiHF in improving the performance of ECLD, which can be widely applied in future commercial lighting solutions., Comment: 21 pages, 4 figures, 1 table

We give a faster algorithm for computing an approximate John ellipsoid around $n$ points in $d$ dimensions. The best known prior algorithms are based on repeatedly computing the leverage scores of the points and reweighting them by these scores [CCLY19]. We show that this algorithm can be substantially sped up by delaying the computation of high accuracy leverage scores by using sampling, and then later computing multiple batches of high accuracy leverage scores via fast rectangular matrix multiplication. We also give low-space streaming algorithms for John ellipsoids using similar ideas., Comment: NeurIPS 2024

We investigate the driving mechanism of Alfv\'en wave-driven stellar winds from red giant stars, Arcturus ($\alpha$ Boo; K1.5 III) and Aldebaran ($\alpha$ Tau; K5 III), with nonideal MHD simulations. Since the atmosphere is not fully ionized, upward propagating Alfv\'enic waves excited by surface convection are affected by ambipolar diffusion. Our fiducial run with the nonideal MHD effect for $\alpha$ Boo gives time-averaged mass-loss rate, $\dot{M}=3.3\times 10^{-11}M_{\odot}/$yr, which is more than one order of magnitude reduced from the result in the ideal MHD run and nicely explains the observational value. Magnetized hot bubbles with $T\gtrsim 10^6$K are occasionally present simultaneously with cool gas with $T\sim$ a few thousands K in the atmosphere because of the thermal instability triggered by radiative cooling; there coexist fully ionized plasma emitting soft X-rays and molecules absorbing/emitting infrared radiations. The inhomogeneity in the atmosphere also causes large temporal variations in the mass-loss rate within an individual magnetic flux tube. We also study the effect of magnetic field strength and metallicity, and find that the wind density, and accordingly the mass-loss rate, positively and sensitively depends on both of them through the ambipolar diffusion of Alfv\'enic waves.The nonideal MHD simulation for $\alpha$ Tau, which is slightly more evolved than $\alpha$ Boo and has weaker magnetic field, results in weaker wind with $\dot{M}=1.5\times 10^{-12}M_{\odot}/$yr with the atmospheric temperature $\lesssim 10^5$K throughout the simulation time. However, given the observations implying the presence of locally strong magnetic fields on the surface of $\alpha$~Tau, we also conduct a simulation with a field strength twice as strong. This results in $\dot{M}=2.0\times 10^{-11}M_{\odot}/$yr -- comparable to the observed value -- with transient magnetized hot bubbles., Comment: 15 pages, 10 figures, submitted to PASJ, comments welcome

The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method. Gonz\'alez-Acu\~na and Kamada independently extended this characterization to the knot groups of orientable surface-links. Kamada applied the closed 2-dimensional braid method to show this result. In this paper, we generalize these results to characterize the knot groups of surface-links, including non-orientable ones. We use a plat presentation for surface-links to prove it. Furthermore, we show a similar characterization for the knot symmetric quandles of surface-links. As an application, we show that every dihedral quandle with an arbitrarily good involution can be realized as the knot symmetric quandle of a surface-link., Comment: 12 pages, 1 figure, Comments welcome

A knitted surface is a surface with boundary properly embedded in $D^2 \times B^2$, which is a generalization of a braided surface. A knitted surface is called a 2-dimensional knit if its boundary is the closure of a trivial braid. From a 2-dimensional knit $S$, we obtain a surface-link in $\mathbb{R}^4$ by taking the closure of $S$. We show that any surface-link is ambiently isotopic to the closure of some 2-dimensional knit. Further, we consider another type of the closure of a knitted surface, called the plat closure. It is known that any trivial surface-knot is ambiently isotopic to the plat closure of a knitted surface of degree 2. We show that the plat closure of any knitted surface of degree 2 is a trivial surface-link, and any trivial surface-link is ambiently isotopic to the plat closure of a knitted surface of degree $2$. We also show the same result for the closure of 2-dimensional knits of degree 2., Comment: 20 pages, 17 figures

Using an underdamped active Ornstein-Uhlenbeck particle, we propose two information swimmer models having either external or internal feedback control and perform their numerical simulations. Depending on the velocity that is measured after every fixed time interval (measurement time), the friction coefficient is modified in the externally controlled model, whereas the persistence time for the activity is changed in the internally controlled one. In the steady state, both of these information swimmers acquire finite average velocities in the noisy environment, and the efficiency can be maximized by tuning the measurement time. The internally controlled swimmer is more relevant to biological systems and can generally achieve larger average velocity and efficiency than the externally controlled model.

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.

Photoelectron diffraction (PED) is a powerful spectroscopic technique that combines elemental resolution with a high sensitivity to the local atomic arrangement at crystal surfaces, thus providing unique fingerprints of selected atomic sites in matter. Stimulated by the rapid innovation in the development of various analysis methods for probing the atomic and electronic structures of van der Waals (vdW) heterostructures of two-dimensional materials, we present a theoretical assessment of the capacity of PED for extracting structural properties such as stacking, twist angles and interlayer distances. We provide a complete description of PED for the benchmark vdW heterostructure bilayer graphene (BLG), by calculating and analyzing the PED of BLG in Bernal and AA-stacking as well as twisted BLG for a wide range of the twist angle., Comment: 10 pages, 7 figures

Although conceptual assessment tests are frequently administered in a pre/post-semester fashion, there are inherent issues with this paradigm. Specifically, education researchers and instructors have limited ability to observe the progression of student conceptual understanding throughout the course. Furthermore, instructors are limited in the usefulness of the feedback they can give to the students involved. To address these issues, we propose the use of computerized adaptive testing (CAT) and increasing the frequency of CAT-based assessments during the course, while reducing the test length per administration, thus keeping or decreasing the total number of test items administered throughout the course. The feasibility of this idea depends on how far the test length per administration can be reduced without compromising the test accuracy and precision. Specifically, the overall test length is desired to be shorter than when the full assessment is administered as a pretest and subsequent post-test. To achieve this goal, we developed a CAT algorithm that we call Chain-CAT. This algorithm sequentially links the results of each CAT administration using collateral information. We developed the Chain-CAT algorithm using the items of the Force Concept Inventory (FCI) and analyzed the efficiency by numerical simulations. We found that collateral information significantly improved the test efficiency, and the overall test length could be shorter than the pre-post method. Without constraints for item balancing and exposure control, simulation results indicated that the efficiency of Chain-CAT is comparable to that of the pre-post method even if the length of each CAT administration is only 5 items and the CAT is administered 9 times throughout the semester. (To continue, see text.)

Recent high-cadence transient surveys have discovered rapid transients whose light curve timescales are shorter than those of typical supernovae. In this paper, we present a systematic search for rapid transients at medium-high redshifts among 3381 supernova candidates obtained from the Subaru HSC-SSP transient survey. We developed a machine learning classifier to classify the supernova candidates into four types (Type Ia, Ibc, II supernovae, and rapid transients) based on the features derived from the light curves. By applying this classifier to the 3381 supernova candidates and by further applying the quality cut, we selected 14 rapid transient samples. They are located at a wide range of redshifts ($0.34 \leq z \leq 1.85$) and show a wide range of the peak absolute magnitude ($-17 \geq M \geq -22$). The event rate of the rapid transients is estimated to be $\sim 6\times10^3~\rm{events~yr^{-1}~Gpc^{-3}}$ at $z \sim 0.74$, which corresponds to about $2$ $\%$ of the event rate of normal core-collapse supernovae at the similar redshift. Based on the luminosity and color evolution, we selected two candidates of Type Ibn supernovae at $z\sim0.75$. The event rate of Type Ibn SN candidates is more than 1 $\%$ of Type Ib SN rate at the same redshift, suggesting that this fraction of massive stars at this redshift range eruptively ejects their He-rich envelope just before the explosions. Also, two objects at $z=1.37$ and 1.85 show high luminosities comparable to superluminous supernovae. Their event rate is about 10-25 $\%$ of superluminous supernovae at $z\sim 2$., Comment: 17 pages, 13 figures, accepted for publication in ApJ

Diffusion models have made substantial progress in facilitating image generation and editing. As the technology matures, we see its potential in the context of driving simulations to enhance the simulated experience. In this paper, we explore this potential through the introduction of a novel system designed to boost visual fidelity. Our system, DRIVE (Diffusion-based Realism Improvement for Virtual Environments), leverages a diffusion model pipeline to give a simulated environment a photorealistic view, with the flexibility to be adapted for other applications. We conducted a preliminary user study to assess the system's effectiveness in rendering realistic visuals and supporting participants in performing driving tasks. Our work not only lays the groundwork for future research on the integration of diffusion models in driving simulations but also provides practical guidelines and best practices for their application in this context.

Learning motor skills for sports or performance driving is often done with professional instruction from expert human teachers, whose availability is limited. Our goal is to enable automated teaching via a learned model that interacts with the student similar to a human teacher. However, training such automated teaching systems is limited by the availability of high-quality annotated datasets of expert teacher and student interactions that are difficult to collect at scale. To address this data scarcity problem, we propose an approach for training a coaching system for complex motor tasks such as high performance driving via a Multi-Task Imitation Learning (MTIL) paradigm. MTIL allows our model to learn robust representations by utilizing self-supervised training signals from more readily available non-interactive datasets of humans performing the task of interest. We validate our approach with (1) a semi-synthetic dataset created from real human driving trajectories, (2) a professional track driving instruction dataset, (3) a track-racing driving simulator human-subject study, and (4) a system demonstration on an instrumented car at a race track. Our experiments show that the right set of auxiliary machine learning tasks improves performance in predicting teaching instructions. Moreover, in the human subjects study, students exposed to the instructions from our teaching system improve their ability to stay within track limits, and show favorable perception of the model's interaction with them, in terms of usefulness and satisfaction., Comment: 12 pages, 3 figures, 3 tables

In feed-forward neural networks, dataset-free weight-initialization methods such as LeCun, Xavier (or Glorot), and He initializations have been developed. These methods randomly determine the initial values of weight parameters based on specific distributions (e.g., Gaussian or uniform distributions) without using training datasets. To the best of the authors' knowledge, such a dataset-free weight-initialization method is yet to be developed for restricted Boltzmann machines (RBMs), which are probabilistic neural networks consisting of two layers. In this study, we derive a dataset-free weight-initialization method for Bernoulli--Bernoulli RBMs based on statistical mechanical analysis. In the proposed weight-initialization method, the weight parameters are drawn from a Gaussian distribution with zero mean. The standard deviation of the Gaussian distribution is optimized based on our hypothesis that a standard deviation providing a larger layer correlation (LC) between the two layers improves the learning efficiency. The expression of the LC is derived based on a statistical mechanical analysis. The optimal value of the standard deviation corresponds to the maximum point of the LC. The proposed weight-initialization method is identical to Xavier initialization in a specific case (i.e., when the sizes of the two layers are the same, the random variables of the layers are $\{-1,1\}$-binary, and all bias parameters are zero). The validity of the proposed weight-initialization method is demonstrated in numerical experiments using a toy and real-world datasets.

The quotient variety associated to a permutation representation of a finite group has only canonical singularities in arbitrary characteristic. Moreover, the log pair associated to such a representation is Kawamata log terminal except in characteristic two, and log canonical in arbitrary characteristic., Comment: 17 pages; v2. minor revision

We prove motivic versions of mass formulas by Krasner, Serre and Bhargava concerning (weighted) counts of extensions of local fields., Comment: 31 pages

This paper introduces a novel method for finding integer sets that satisfy the Pythagorean theorem by leveraging the Higher-Order Binary Optimization (HOBO) formulation. Unlike the Quadratic Unconstrained Binary Optimization (QUBO) formulation, which struggles to express complex mathematical equations, HOBO's ability to model higher-order interactions between binary variables makes it well-suited for addressing more complex and expressive problem settings.

It is the theoretical structure of electromagnetism that led Einstein to special relativity. To foster an intuitive understanding of relativity's core idea, it is valuable to create a fully special relativistic computer simulation incorporating electromagnetic dynamics. In this paper, we provide a basic formulation for such an implementation. Specifically, the player observes the world via their past light cone and experiences the Lorentz force generated by the electromagnetic field at their spacetime location. The electromagnetic field at any given spacetime point is determined by the sublight-speed motion of individual point charges on the past light cone of that spacetime point., Comment: 35 pages, 5 figures, minor modification (v2)

This study has applied information thermodynamics to a bivariate linear stochastic differential equation (SDE) that describes a synchronization phenomenon of sea surface temperatures (SSTs) between the Gulf Stream and the Kuroshio Current, which is referred to as the boundary current synchronization (BCS). Information thermodynamics divides the entire system fluctuating with stochastic noise into subsystems and describes the interactions between these subsystems from the perspective of information transfer. The SDE coefficients have been estimated through regression analysis using observational and numerical simulation data. In the absence of stochastic noise, the solution of the estimated SDE shows that the SSTs relax toward zero without oscillation. The estimated SDE can be interpreted as a Maxwell's demon system, with the Gulf Stream playing the role of the "Particle" and the Kuroshio Current playing the role of the "Demon." The Gulf Stream forces the SST of the Kuroshio Current to be in phase. By contrast, the Kuroshio Current maintains the phase by interfering with the relaxation of the Gulf Stream SST. In the framework of Maxwell's demon, the Gulf Stream is measured by the Kuroshio Current, whereas the Kuroshio Current performs feedback control on the Gulf Stream. When the Gulf Stream and the Kuroshio Current are coupled in an appropriate parameter regime, synchronization is realized with atmospheric and oceanic fluctuations as the driving source. This new mechanism, "stochastic synchronization," suggests that such fluctuations can be converted into directional variations in a subsystem of the climate system through synchronization by utilizing information (i.e., information-to-energy conversion).

In this study, we introduce HOBOTAN, a new solver designed for Higher Order Binary Optimization (HOBO). HOBOTAN supports both CPU and GPU, with the GPU version developed based on PyTorch, offering a fast and scalable system. This solver utilizes tensor networks to solve combinatorial optimization problems, employing a HOBO tensor that maps the problem and performs tensor contractions as needed. Additionally, by combining techniques such as batch processing for tensor optimization and binary-based integer encoding, we significantly enhance the efficiency of combinatorial optimization. In the future, the utilization of increased GPU numbers is expected to harness greater computational power, enabling efficient collaboration between multiple GPUs for high scalability. Moreover, HOBOTAN is designed within the framework of quantum computing, thus providing insights for future quantum computer applications. This paper details the design, implementation, performance evaluation, and scalability of HOBOTAN, demonstrating its effectiveness.

The neutron-rich unbound fluorine isotope $^{30}$F$_{21}$ has been observed for the first time by measuring its neutron decay at the SAMURAI spectrometer (RIBF, RIKEN) in the quasi-free proton knockout reaction of $^{31}$Ne nuclei at 235 MeV/nucleon. The mass and thus one-neutron-separation energy of $^{30}$F has been determined to be $S_n = -472\pm 58 \mathrm{(stat.)} \pm 33 \mathrm{(sys.)}$ keV from the measurement of its invariant-mass spectrum. The absence of a sharp drop in $S_n$($^{30}$F) shows that the ``magic'' $N=20$ shell gap is not restored close to $^{28}$O, which is in agreement with our shell-model calculations that predict a near degeneracy between the neutron $d$ and $fp$ orbitals, with the $1p_{3/2}$ and $1p_{1/2}$ orbitals becoming more bound than the $0f_{7/2}$ one. This degeneracy and reordering of orbitals has two potential consequences: $^{28}$O behaves like a strongly superfluid nucleus with neutron pairs scattering across shells, and both $^{29,31}$F appear to be good two-neutron halo-nucleus candidates., Comment: 9 pages, 2 figures, accepted for publication in Physical Review Letters

The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in $^{53}$Ca and $^{55}$Ca, populated from \ts{54,56}Ca($p,pn$) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum $l$ assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)\,keV in $^{53}$Ca and 6000(250)\,keV in $^{55}$Ca indicate a significant $l$\, =\,3 component, providing the first experimental evidence for the $\nu 0f_{7/2}$ single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the $\nu 0f_{7/2}$ orbital in $^{55}$Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and \textit{ab initio} calculations and diverge markedly from the experimental distributions in the nickel isotones at $Z=28$., Comment: 13 pages, 7 figures

The $\ell_p$ subspace approximation problem is an NP-hard low rank approximation problem that generalizes the median hyperplane problem ($p = 1$), principal component analysis ($p = 2$), and the center hyperplane problem ($p = \infty$). A popular approach to cope with the NP-hardness of this problem is to compute a strong coreset, which is a small weighted subset of the input points which simultaneously approximates the cost of every $k$-dimensional subspace, typically to $(1+\varepsilon)$ relative error for a small constant $\varepsilon$. We obtain the first algorithm for constructing a strong coreset for $\ell_p$ subspace approximation with a nearly optimal dependence on the rank parameter $k$, obtaining a nearly linear bound of $\tilde O(k)\mathrm{poly}(\varepsilon^{-1})$ for $p<2$ and $\tilde O(k^{p/2})\mathrm{poly}(\varepsilon^{-1})$ for $p>2$. Prior constructions either achieved a similar size bound but produced a coreset with a modification of the original points [SW18, FKW21], or produced a coreset of the original points but lost $\mathrm{poly}(k)$ factors in the coreset size [HV20, WY23]. Our techniques also lead to the first nearly optimal online strong coresets for $\ell_p$ subspace approximation with similar bounds as the offline setting, resolving a problem of [WY23]. All prior approaches lose $\mathrm{poly}(k)$ factors in this setting, even when allowed to modify the original points.

In this study, we theoretically investigated x-ray spectra from the radiative decay of muonic deuterium molecules in resonance states dd$\mu^\ast$, which plays an important role in a new kinetic model of muon catalyzed fusion ($\mu$CF). The resonance states are Feshbach resonances located below the d$\mu$($n=2$) + d threshold energy and radiatively decay into the continuum or bound states. The x-ray spectra having characteristic shapes according to the radial distribution of the two nuclei are obtained using precise three-body wave functions. We carefully examined the convergence of the x-ray spectra and achieved agreements between the length- and velocity-gauge calculations. We revealed a non-adiabatic kinetic energy distribution of the decay fragments, indicating that the radiative decay becomes a heating source of muonic atoms. We also investigated the decay branch that directly results in bound-state muonic molecules. Some resonance states dd$\mu^\ast$ and dt$\mu^\ast$ are found to have high branching ratios to the bound state where intramolecular nuclear fusion occurs. The formation of the muonic molecules in the bound states from metastable muonic atoms can be a fast track in the $\mu$CF cycle which skips a slow path to form the bound state from the ground-state muonic atoms and increases the $\mu$CF cycle rate. Although the spectra from the radiative decays are located in the energy range of $1.5$--$1.997$ keV, which is close to the K$\alpha$ x-ray of 1.997 keV from muonic deuterium atoms, state-of-the-art microcalorimeters can distinguish them., Comment: 19 pages, 16 figures, 4 tables