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Matroids are often represented as oracles since there are no unified and compact representations for general matroids. This paper initiates the study of binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) as relatively compact data structures for representing matroids in a computer. This study particularly focuses on the sizes of BDDs and ZDDs representing matroids. First, we compare the sizes of different variations of BDDs and ZDDs for a matroid. These comparisons involve concise transformations between specific decision diagrams. Second, we provide upper bounds on the size of BDDs and ZDDs for several classes of matroids. These bounds are closely related to the number of minors of the matroid and depend only on the connectivity function or pathwidth of the matroid, which deeply relates to the classes of matroids called strongly pigeonhole classes. In essence, these results indicate upper bounds on the number of minors for specific classes of matroids and new strongly pigeonhole classes., Comment: 21 pages, 7 figures

Large Language Models(LLMs) have been attracting attention due to a ability called in-context learning(ICL). ICL, without updating the parameters of a LLM, it is possible to achieve highly accurate inference based on rules ``in the context'' by merely inputting a training data into the prompt. Although ICL is a developing field with many unanswered questions, LLMs themselves serves as a inference model, seemingly realizing inference without explicitly indicate ``inductive bias''. On the other hand, a code generation is also a highlighted application of LLMs. The accuracy of code generation has dramatically improved, enabling even non-engineers to generate code to perform the desired tasks by crafting appropriate prompts. In this paper, we propose a novel ``learning'' method called an ``Inductive-Bias Learning (IBL)'', which combines the techniques of ICL and code generation. An idea of IBL is straightforward. Like ICL, IBL inputs a training data into the prompt and outputs a code with a necessary structure for inference (we referred to as ``Code Model'') from a ``contextual understanding''. Despite being a seemingly simple approach, IBL encompasses both a ``property of inference without explicit inductive bias'' inherent in ICL and a ``readability and explainability'' of the code generation. Surprisingly, generated Code Models have been found to achieve predictive accuracy comparable to, and in some cases surpassing, ICL and representative machine learning models. Our IBL code is open source: https://github.com/fuyu-quant/IBLM, Comment: 17 pages, 8 figures

Energy losses in a magnetic nozzle radiofrequency plasma thruster are investigated to improve the thruster efficiency, which are calculated from particle energy losses in fully kinetic simulations. The simulations calculate particle energy fluxes with a vector resolution including the plasma energy lost to the dielectric wall, the plasma beam energy, and the divergent plasma energy in addition to collisional energy losses. As a result, distributions of energy losses in the thruster and the ratios of the energy losses to the input power are obtained. The simulation results show that the plasma energy lost to the dielectric is dramatically suppressed by increasing the magnetic field strength and the ion beam energy increases instead. In addition, the divergent ion energy and collisional energy losses account for approximately 4-12% and 30-40%, respectively, regardless of the magnetic field strength.

The fully kinetic simulations of magnetic nozzle acceleration are conducted to investigate the axial momentum gains of ions and electrons with the electrostatic and Lorentz forces. Axial momentum gains per ion and electron are directly calculated from the kinetics of charged particles, indicating that electrons in the magnetic nozzle obtain the net axial momentum by the Lorentz force even though they are decelerated by the electrostatic force. Whereas ions are also accelerated by the electrostatic force, the axial momentum gain of electrons increases significantly with increasing the magnetic field strength and becomes dominant in the magnetic nozzle. In addition, it is clearly shown that the axial momentum gain of electrons is due to the electron momentum conversion from the radial to axial direction, resulting in the significant increase in the thrust and the exhaust velocity.

Two-dimensional fully kinetic particle-in-cell simulations of an electrodeless plasma thruster, which uses a magnetic nozzle, were conducted to investigate the thrust generation induced by the internal plasma current. The results clearly show that the $\bf{E} \times \bf{B}$ and diamagnetic current densities are the major components of the internal plasma current. The simulated pressure structures reproduced the experimentally observed structures well. The results for various magnetic field strengths reveal that the $\bf{E} \times \bf{B}$ effect decreases and the diamagnetic effect becomes dominant with an increase in the magnetic field strength; this demonstrates the significant contribution of the diamagnetic effect in thrust generation., Comment: The following article has been accepted by Physics of Plasmas

The random access scheme is a fundamental scenario in which users transmit through a shared channel and cannot coordinate each other. In recent years, successive interference cancellation (SIC) was introduced into the random access scheme. It is possible to decode transmitted packets using collided packets by the SIC. The coded slotted ALOHA (CSA) is a random access scheme using the SIC. The CSA encodes each packet using a local code prior to transmission. It is known that the CSA achieves excellent throughput. On the other hand, it is reported that in the coding theory time shift improves the decoding performance for packet-oriented erasure correcting codes. In this paper, we propose a random access scheme which applies the time shift to the CSA in order to achieve better throughput. Numerical examples show that our proposed random access scheme achieves better throughput and packet loss rate than the CSA., Comment: 5 pages, 7 figures, submitted to ISITA 2018

In this paper, we report on the investigation of (1) the transport properties of multi-carriers in semi-metal Bi and (2) the spin conversion physics in this semimetal system in a ferrimagnetic insulator, yttrium-iron-garnet. Hall measurements reveal that electrons and holes co-exist in the Bi, with electrons being the dominant carrier. The results of a spin conversion experiment corroborate the results of the Hall measurement; in addition, the inverse spin Hall effect governs the spin conversion in the semimetal/insulator system. This study provides further insights into spin conversion physics in semimetal systems., Comment: 16 pages, 4 Figures

Usually, General Relativity (GR) is known to be unrenormalizable perturbatively from the viewpoint of quantum field theory. But in the modern sense of renormalizability, there still remains the possibility to investigate whether GR is "nonpertubatively" renormalizable or not. Here I review the basics and results in this topic based on the "Effective Average Action" approach which was proposed by M.Reuter, and discuss its application to the balck hole geometry., Comment: 14, Plenary talk presented at Workshop on High Energy Physics&Field Theory (Protvino, Russia, 2005)

The possibility of asymptotic safety scenario (asymptotic freedom) for quantum gravity has been pointed out in many contexts recently. From this point of view, we discuss some applications of cutoff identification to the black hole. If we consider the condition that the Newton coupling becomes weaker as approaching the origin, the curvature singularity still remains., Comment: 18 pages; added references and typos

Strain at surfaces and interfaces play an important role in the optical and electronic properties of materials. MeV ion-induced strain determination in single crystal silicon substrates and in Ag (nanoisland)/Si(111) at surface and interfaces has been carried out using transmission electron microscopy (TEM) and surface-sensitive X-ray diffraction. Ag nanoislands are grown under various surface treatments using thermal evaporation in high vacuum conditions. Irradiation has been carried out with 1.5 MeV Au^{2+} ions at various fluences and impact angles. Selected area electron diffraction (SAED) and lattice imaging (using TEM) has been used to determine the strain at surface and interfaces. Preliminary results on the use of surface-sensitive asymmetric x-ray Bragg reflection method have been discussed. The TEM results directly indicate a contraction in the silicon lattice due to ion-induced effects. The nanoislands have shadowed the ion beam resulting in lesser strain beneath the island structures in silicon substrates. High-resolution lattice imaging has also been used to determine the strain in around amorphization zones caused by the ion irradiation., Comment: 11 papes, 4 figures, Submitted as contributary paper in INDO-GERMAN Workshop at NSC, New Delhi, India held from 20-24th Feb.,2005

In the SU(2)_L x U(1)_Y standard electroweak theory coupled with the Einstein gravity, new topological configurations naturally emerge, if the spatial section of the universe is globally a three-sphere (S^3) with a small radius. The SU(2)_L gauge fields wrap the space nontrivially, producing homogeneous but anisotropic space. As the universe expands, large electric and magnetic fields are produced. The electromagnetic field configuration is characterized by the Hopf map., Comment: 3 pages, 3 figures, for the proceeding for the ICHEP 2002, Amsterdam, 25 - 31 July, 2002

In the SU(2)_{L} x U(1)_{Y} standard electroweak theory coupled with the Einstein gravity, new topological configurations naturally emerge, if the spatial section of the universe is globally a three-sphere(S^3) with a small radius. The SU(2)_L gauge fields and Higgs fields wrap the space nontrivially, residing at or near a local minimum of the potential. As the universe expands, however, the shape of the potential rapidly changes and the local minimum eventually disappears. The fields then start to roll down towards the absolute minimum. In the absence of the U(1)_Y gauge interaction the resulting space is a homogeneous and isotropic S^3, but the U(1)_Y gauge interaction necessarily induces anisotropy while preserving the homogeneity of the space. Large magnetic fields are generically produced over a substantial period of the rolling-over transition. The magnetic field configuration is characterized by the Hopf map., Comment: 32 pages, 16 figures

The change of the thermal properties of semiconductor melts reflects the structural changes inside the melts, and a fundamental understanding of this structural transformation is essential for high quality semiconductor crystal growth process. This paper focused on the technical development and the measurement of thermal properties of III-VI semiconductor melts at high temperatures. Our previous work has improved the laser flash method for the specialized quartz sample cell. In this paper, we reported the results of our recent progress in further improvements of the measurement system by minimizing the free convection of the melt, adding a front IR detector, and placing the sample cell in a vacuum environment. The results for tellurium and selenium based compounds, some of which have never been reported in the literature, were obtained at different temperatures as a function of time. The data were compared with other measured thermophysical properties to shed light on the structural transformations of the melt.