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This paper presents an accelerated spherical K-means clustering algorithm for large-scale and high-dimensional sparse document data sets. We design an algorithm working in an architecture-friendly manner (AFM), which is a procedure of suppressing performance-degradation factors such as the numbers of instructions, branch mispredictions, and cache misses in CPUs of a modern computer system. For the AFM operation, we leverage unique universal characteristics (UCs) of a data-object and a cluster's mean set, which are skewed distributions on data relationships such as Zipf's law and a feature-value concentration phenomenon. The UCs indicate that the most part of the number of multiplications for similarity calculations is executed regarding terms with high document frequencies (df) and the most part of a similarity between an object- and a mean-feature vector is obtained by the multiplications regarding a few high mean-feature values. Our proposed algorithm applies an inverted-index data structure to a mean set, extracts the specific region with high-df terms and high mean-feature values in the mean-inverted index by newly introduced two structural parameters, and exploits the index divided into three parts for efficient pruning. The algorithm determines the two structural parameters by minimizing the approximate number of multiplications related to that of instructions, reduces the branch mispredictions by sharing the index structure including the two parameters with all the objects, and suppressing the cache misses by keeping in the caches the frequently used data in the foregoing specific region, resulting in working in the AFM. We experimentally demonstrate that our algorithm efficiently achieves superior speed performance in large-scale documents compared with algorithms using the state-of-the-art techniques., Comment: 28 pages, 23 figures

We present a general theory of potentials that support bound states at positive energies (bound states in the continuum). On the theoretical side, we prove that, for systems described by nonlocal potentials of the form $V(r,r')$, bound states at positive energies are as common as those at negative energies. At the same time, we show that a local potential of the form $V(r)$ rarely supports a positive energy bound state. On the practical side, we show how to construct a (naturally nonlocal) potential which supports an arbitrary normalizable state at an arbitrary positive energy. We demonstrate our theory with numerical examples both in momentum and coordinate spaces with emphasis on the important role played by nonlocal potentials. Finally, we discuss how to observe bound states at positive energies, and where to search for nonlocal potentials which may support them., Comment: 32 pages, 22 figures

We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the magnetic helicity precisely equals the initial magnetic helicity added by a linear temporal growth and multiplied by an exponential temporal growth respectively in the additive and the linear multiplicative case. We employ the technique of convex integration to construct an analytically weak and probabilistically strong solution such that, with positive probability, all of the total energy, cross helicity, and magnetic helicity more than double from initial time. Second, we consider the three-dimensional magnetohydrodynamics system forced by additive noise and diffused up to the Lions' exponent and employ convex integration with temporal intermittency to prove non-uniqueness of solutions starting from prescribed initial data.

We present near-infrared high-dispersion spectroscopic observations of Europa using the Infrared Camera and Spectrograph (IRCS) onboard the Subaru Telescope, seeking direct evidence of water plumes on Europa and exploring spatial variations in plume activity. Using high spectral/spatial resolution and sensitivity of Subaru/IRCS, our observations have enabled a spatially resolved search for water plumes on Europa. Within our detection limits and time of observation, we found no evidence for the presence of water emission. For a rotation temperature of 50 K, we derived an upper limit on the H$_{2}$O abundance of 9.46$\times$10$^{19}$ - 5.92$\times$10$^{20}$ m$^{-2}$ in each divided slit area and 4.61$\times$10$^{19}$ m$^{-2}$ in the entire area covered by the slit. This upper limit lies below the inferred water abundance from previous UV observations by the Hubble Space Telescope (HST), while being less sensitive by a factor of three compared to the Keck telescope and by one order of magnitude or more than the James Webb Space Telescope (JWST) observations. Our results align with previous studies and demonstrate that using Subaru/IRCS is an effective strategy for searching for water plumes on Europa with high spatial resolution. Continued observations across different surface areas and orbital phases are essential to fully characterize Europa's plume activity and complement upcoming space missions., Comment: 8 pages, 7 figures. Accepted for publication in PASJ

We study chiral condensate in cold nuclear matter on the basis of holographic theory, which would be dual to a baryon system in quantum chromodynamics (QCD) in the confinement phase. Our model is a holographic model based on the D$3$/D$7$ branes. The magnitude of the chiral condensate obtained in our model is found to gradually increase with increasing baryon density $n$ within the range of the dilute nucleon gas, $n<1$, where our model is available. This is a result for the chiral condensate in the holographic model as a function of $n$, which can be compared to the chiral perturbation theory., Comment: 12 pages, 5 figures

Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based question-answering tools, issues of trustworthiness and explainability of generated answers motivate a greater role for visualization. In the context of graphs, we see the need for visualizations that can convince a critical audience that an assertion about the graph under analysis is valid. The requirements for such representations that convey precisely one specific graph property are quite different from standard network visualization criteria which optimize general aesthetics and readability. In this paper, we aim to provide a comprehensive introduction to visual proofs of graph properties and a foundation for further research in the area. We present a framework that defines what it means to visually prove a graph property. In the process, we introduce the notion of a visual certificate, that is, a specialized faithful graph visualization that leverages the viewer's perception, in particular, pre-attentive processing (e.g. via pop-out effects), to verify a given assertion about the represented graph. We also discuss the relationships between visual complexity, cognitive load and complexity theory, and propose a classification based on visual proof complexity. Finally, we provide examples of visual certificates for problems in different visual proof complexity classes., Comment: Appears in the Proceedings of the 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Utilizing four archival X-ray datasets taken with the Hard X-ray Detector onboard Suzaku, timing studies were performed on three magnetars, 1E 1841-045 (observed in 2006), SGR 0501+4516 (2008), and 1RXS J170849.0-400910 (2009 and 2010). Their pulsations were reconfirmed, typically in an energy range of 12-50 keV. The 11.783 s pulses of 1E 1841-045, and those of SGR 0501+4516 with 5.762 s were periodically phase modulated, with a long period of about 23.4 ks and about 16.4 ks, respectively. The pulse-phase modulation was also observed, at 46.5 ks, from two datasets of 1RXS J170849.0-400910. In all these cases, the modulation amplitude was 6 to 16 percent of the pulse cycle. Including previously confirmed four objects, this characteristic timing behavior is now detected from seven magnetars in total, and interpreted as a result of free precession of neutron stars that are deformed to an asphericity of ~10^{-4}. Assuming that the deformation is due to magnetic stress, these magnetars are inferred to harbor toroidal magnetic fields of Bt~10^{16} G. By comparing the estimated Bt of these objects with their poloidal dipole field Bd, the Bt/Bd ratio is found to increase with their characteristic age. Therefore, the toroidal fields of magnetars are likely to last longer than their dipole fields. This explains the presence of some classes of neutron stars that have relatively weak Bd but are suspected to hide strong Bt inside them., Comment: 16 pages, 15 figures; accepted for publication in MNRAS

We consider the momentum formulation of the two-dimensional surface quasi-geostrophic equations forced by random noise, of both additive and linear multiplicative types. For any prescribed deterministic function under some conditions, we construct solutions to each system whose energy is the fixed function. Consequently, we prove non-uniqueness of almost sure Markov selections of suitable class of weak solutions associated to the momentum surface quasi-geostrophic equations in both cases of noise.

The commonly used pseudo-C symmetry $(\nu_{L})^{c}=C\overline{\nu_{L}}^{T}$ is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions; the first is associated with the Dirac-type fermion with the conventional C and P symmetries, and the second is associated with the Weyl-type fermion defined by CP symmetry only and formally characterised by the pseudo-C symmetry. Taking the seesaw model as an example, it is shown that a generalized Pauli--G\"{u}rsey (or Bogoliubov-type) canonical transformation converts the neutrino defined by the Weyl-type fermion to the neutrino defined by the Dirac-type fermion and thus to the conventional Majorana fermion, while preserving the canonical anti-commutation relations. The mixing angles in the weak lepton sector are not modified by this generalized Pauli--G\"{u}rsey transformation., Comment: 12 pages. Minor typographical corrections together with two additional footnotes and an additional reference. This version is to be published in Phys. Lett. B

The oscillations of ultra-relativistic neutrinos are realized by the propagation of assumed zero-mass on-shell neutrinos with the speed of light in vacuum combined with the phase modulation by the small mass term $\exp[-i(m^{2}_{\nu_{k}}/2|\vec{p}|)\tau]$ with a time parameter $\tau$. This picture is realized in the first quantization by the mass expansion and in field theory by the use of $\delta(x^{0}-y^{0}-\tau) \langle 0|T^{\star}\nu_{L k}(x)\overline{\nu_{L k}(y)}|0\rangle$ with the neutrino mass eigenstates $\nu_{L k}$ and a finite positive $\tau$ after the contour integral of the propagating neutrino energies. By noting that the conventional detectors are insensitive to neutrino masses, the measured energy-momenta of the initial and final states with assumed zero-mass neutrinos are conserved. The propagating neutrinos preserve the three-momentum in this sense but the energies of the massive neutrinos are conserved up to uncertainty relations and thus leading to oscillations. Conceptual complications in the case of Majorana neutrinos due to the charge conjugation in $d=4$ are also discussed., Comment: 16 pages. Going to be published in EPJC

Four X-ray data sets of the Soft Gamma Repeater SGR 1806-20, taken with the Gas Imaging Spectrometer (GIS) onboad ASCA, were analyzed. Three of them were acquired over 1993 October 9-20, whereas the last one in 1995 October. Epoch-folding analysis of the 2.8-12 keV signals confirmed the $\sim 7.6$ s pulses in these data, which Kouveliotou et al. (1998) reported as one of the earliest pulse detections from this object. In the 1995 observation, 3-12 keV pulses were phase modulated with a period of $T =16.4 \pm 0.4$ ks, and an amplitude of $\sim 1$ s. This makes a fourth example of the behavior observed from magnetars. Like in the previous three sources, the pulse-phase modulation of SGR 1806-20 disappeared at $\lesssim 2.5$ keV, where the soft X-ray component dominates. In the 1993 data sets, this periodic modulation was reconfirmed, and successfully phase-connected coherently across the 11 d interval. As a result, the modulation period was refined to $T =16.435 \pm 0.024$ ks. The implied high stability of the phenomenon strengthens its interpretation in terms of free precession of the neutron star, which is deformed to an asphericity of $\sim 10^{-4}$, presumably by the stress of toroidal magnetic fields reaching $\sim 10^{16}$ G. Toroidal fields of this level can be common among magnetars., Comment: accepted for publication in PASJ

A half-space problem of a linear kinetic equation for gas molecules physisorbed close to a solid surface, relevant to a kinetic model of gas-surface interactions and derived by Aoki et al. [K.~Aoki et al., in: Phys. Rev. E 106:035306, 2022], is considered. The equation contains a confinement potential in the vicinity of the solid surface and an interaction term between gas molecules and phonons. It is proved that a unique solution exists when the incoming molecular flux is specified at infinity. This validates the natural observation that the half-space problem serves as the boundary condition for the Boltzmann equation. It is also proved that the sequence of approximate solutions used for the existence proof converges exponentially fast. In addition, numerical results showing the details of the solution to the half-space problem are presented., Comment: 47 pages, 11 figures

Quantum algorithms are still challenging to solve linear systems of equations on real devices. This challenge arises from the need for deep circuits and numerous ancilla qubits. We introduce the quantum conjugate gradient (QCG) method using the quantum eigenvalue transformation (QET). The circuit depth of this algorithm depends on the square root of the coefficient matrix's condition number $\kappa$, representing a square root improvement compared to the previous quantum algorithms, while the total query complexity worsens. The number of ancilla qubits is constant, similar to other QET-based algorithms. Additionally, to implement the QCG method efficiently, we devise a QET-based technique that uses only the positive side of the polynomial (denoted by $P(x)$ for $x\in[0,1]$). We conduct numerical experiments by applying our algorithm to the one-dimensional Poisson equation and successfully solve it. Based on the numerical results, our algorithm significantly improves circuit depth, outperforming another QET-based algorithm by three to four orders of magnitude., Comment: 20 pages, 13 figures

This paper introduces the Passive Transformable Omni-Ball (PTOB), an advanced omnidirectional wheel engineered to enhance step-climbing performance, incorporate built-in actuators, diminish vibrations, and fortify structural integrity. By modifying the omni-ball's structure from two to three segments, we have achieved improved in-wheel actuation and a reduction in vibrational feedback. Additionally, we have implemented a sliding mechanism in the follower wheels to boost the wheel's step-climbing abilities. A prototype with a 127 mm diameter PTOB was constructed, which confirmed its functionality for omnidirectional movement and internal actuation. Compared to a traditional omni-wheel, the PTOB demonstrated a comparable level of vibration while offering superior capabilities. Extensive testing in varied settings showed that the PTOB can adeptly handle step obstacles up to 45 mm, equivalent to 35 $\%$ of the wheel's diameter, in both the forward and lateral directions. The PTOB showcased robust construction and proved to be versatile in navigating through environments with diverse obstacles., Comment: 8 pages, 17 figures