On Jones polynomials of alternating pretzel knots

We show that there are infinitely many pairs of alternating pretzel knots whose Jones polynomials are identical.Comment: 8 pages, 3 figure

Repeated Multimarket Contact with Private Monitoring: A Belief-Free Approach

This paper studies repeated games where two players play multiple duopolistic games simultaneously (multimarket contact). A key assumption is that each player receives a noisy and private signal about the other's actions (private monitoring or observation errors). There has been no game-theoretic support that multimarket contact facilitates collusion or not, in the sense that more collusive equilibria in terms of per-market profits exist than those under a benchmark case of one market. An equilibrium candidate under the benchmark case is belief-free strategies. We are the first to construct a non-trivial class of strategies that exhibits the effect of multimarket contact from the perspectives of simplicity and mild punishment. Strategies must be simple because firms in a cartel must coordinate each other with no communication. Punishment must be mild to an extent that it does not hurt even the minimum required profits in the cartel. We thus focus on two-state automaton strategies such that the players are cooperative in at least one market even when he or she punishes a traitor. Furthermore, we identify an additional condition (partial indifference), under which the collusive equilibrium yields the optimal payoff.Comment: Accepted for the 9th Intl. Symp. on Algorithmic Game Theory; An extended version was accepted at the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20

Numerical study on suppression of tsunami with under-sea breakwater

Large-scale tsunami occurs every 100 or 150 years statistically, and 95% of these tsunami lead to great disasters which kill over 1,000 people. In order to avoid, suppress or mitigate such damage, it is necessary to perform a risk management from the point of view of disaster prevention engineering. There are breakwaters as one of existing measures for tsunami, and the effectiveness of breakwaters has been demonstrated. However, a conventional breakwater can be disrupted by the impact of tsunami, and then it turns into debris that causes to expand the damage. There is also the problem of impairing the landscape by locating a large-scale breakwater along a sea shore. Construction of under-sea breakwaters is one possible way to coping with these problems. In this paper, tsunami behavior when the under-sea breakwater is located is numerically simulated using MPS method, which is one of the particle methods. And the effectiveness on suppression of tsunami with the under-sea breakwater is researched and verified. Through the present study, it was confirmed that the under-sea breakwater can suppress tsunami. The higher the under-sea breakwater is, the more it suppresses tsunami. However, if the height of the breakwater is too low, the effect on tsunami suppression is small. In addition, it was found that, by setting under-sea breakwater at a suitable position, arrival time of a tsunami can be delayed

Numerical simulation on deposition phenomena of Molten Droplet

Deposition is a phenomenon where melting particles passing through a combustion chamber are cooled and adhere to the surfaces of a turbine vane and endwalls. Though previous studies have investigated the effect on cooling efficiency after deposition, the deposition mechanism remains unclear. Since it is difficult to carry out the detailed measurement, numerical studies on the deposition mechanism are expected. In the present study, we consider the case where a high-temperature molten droplet impacts on a cold substrate. The temperature change and behavior of a droplet are reproduced, using a MPS-AS method[1]. Furthermore, the deposition phenomena in three cases with different impact speeds and four cases with different substrate temperatures are numerically investigated. We numerically investigate the deposition mechanism on the cooled substrate and describe in detail how the solidification process varies with the impact velocity and the temperature changes

A new determination method of interatomic potential for sodium silicate glass simulations

An interatomic potential for the classical molecular dynamics (MD) simulation of sodium silicate glasses was proposed. The ionic charges for this interatomic potential were determined by Mulliken population analysis via the density functional theory (DFT) calculation of alkali silicate crystals. The Si-O interatomic potential energy curve was determined by molecular orbital (MO) calculation of SiO2 +. The results of classical MD simulations using the new interatomic potential were consistent with the experimental trends in interatomic distance, thermal expansion coefficient, molar volume, Si-O-Si bond angle distribution, and Qn ratio with respect to the sodium composition of the silicate glass. The proposed interatomic potential improves the reproducibility of the ring size distribution in silicate glasses compared to conventional potentials

Skill of Eye-Hand Coordination in Calligraphy - Difference of Skill of Hand-Eye Coordination between Expert and Novice -

A system that can simultaneously measure the movement of a brush tip and the eye-gaze position during a calligraphy task has been developed. The system consisted of a device to measure the location of a brush tip and an eye tracker. Using this system, the skill of hand-eye coordination was measured for an expert and novices. It has been clarified that an expert of calligraphy distributes the eye-gaze over a wider area and gazes in advance a part that should be written next. In other words, an expert does not gaze at the brush tip but at the part that should be written at the next stage