Decision Maker using Coupled Incompressible-Fluid Cylinders

The multi-armed bandit problem (MBP) is the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards by referring to past experiences. Inspired by fluctuated movements of a rigid body in a tug-of-war game, we formulated a unique search algorithm that we call the `tug-of-war (TOW) dynamics' for solving the MBP efficiently. The cognitive medium access, which refers to multi-user channel allocations in cognitive radio, can be interpreted as the competitive multi-armed bandit problem (CMBP); the problem is to determine the optimal strategy for allocating channels to users which yields maximum total rewards gained by all users. Here we show that it is possible to construct a physical device for solving the CMBP, which we call the `TOW Bombe', by exploiting the TOW dynamics existed in coupled incompressible-fluid cylinders. This analog computing device achieves the `socially-maximum' resource allocation that maximizes the total rewards in cognitive medium access without paying a huge computational cost that grows exponentially as a function of the problem size.Comment: 5 pages, 5 figures, Waseda AICS Symposium and the 14th Slovenia-Japan Seminar, Waseda University, Tokyo, 24-26 October 2014. in Special Issue of ASTE: Advances in Science, Technology and Environmentology (2015

Randomness Evaluation and Hardware Implementation of Nonadditive CA-Based Stream Cipher

We shall review the cellular automaton(CA)-based pseudorandom-number generators (PRNGs), and show that one of these PRNGs can generate high-quality random numbers which can pass all of the statistical tests provided by the National Institute of Standards and Technology (NIST). A CA is suitable for hardware implementation. We demonstrate that the CA-based stream cipher, which is implemented in the field-programmable gate arrays (FPGA), has a high encryption speed in a real-time video encryption and decryption system.Comment: to be published in Journal of Signal Processin

The Painlev\'e Test of Higher Dimensional KdV Equation

We argue the integrability of the generalized KdV(GKdV) equation using the Painlev\'e test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlev\'e test but does not for $d \geq 3$ dimensional space. We also apply the Ablowitz-Ramani-Segur's conjecture to the GKdV equation in order to complement the Painlev\'e test.Comment: 7 pages, LaTe

Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.Comment: 28 page

Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations

We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.Comment: 18pages, submitted. arXiv admin note: substantial text overlap with arXiv:1111.292

Self-sustaining oscillations of a falling sphere through Johnson-Segalman fluids

We confirm numerically that the Johnson-Segalman model is able to reproduce the continual oscillations of the falling sphere observed in some viscoelastic models. The empirical choice of parameters used in the Johnson-Segalman model is from the ones that show the non-monotone stress-strain relation of the steady shear flows of the model. The carefully chosen parameters yield continual, self-sustaining, (ir)regular and periodic oscillations of the speed for the falling sphere through the Johnson-Segalman fluids. In particular, our simulations reproduce the phenomena: the falling sphere settles slower and slower until a certain point at which the sphere suddenly accelerates and this pattern is repeated continually

Controlling decoherence speed limit of a single impurity atom in a Bose-Einstein-condensate reservoir

We study the decoherence speed limit (DSL) of a single impurity atom immersed in a Bose-Einsteincondensed (BEC) reservoir when the impurity atom is in a double-well potential. We demonstrate how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. We show that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double-well potential imposed on the impurity. We uncover the physical mechanisms of controlling the DSL at root of the spectral density of the BEC reservoir.Comment: 8 pages, 8 figure

Hierarchy of Higher Dimensional Integrable System

Integrable equations in ($1 + 1$) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in ($2 + 1$) dimensions have also the analogous hierarchies to those in ($1 + 1$) dimensions. Explicitly is discussed the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an ambiguity in the Painlev\'e test. Nevertheless, it may be concluded that the BS hierarchy is integrable.Comment: 10 pages, uses ioplppt.st

Efficient Decision-Making by Volume-Conserving Physical Object

We demonstrate that any physical object, as long as its volume is conserved when coupled with suitable operations, provides a sophisticated decision-making capability. We consider the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. These decisions are made as dictated by a physical object, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war game. Our analytical calculations validate statistical reasons why our method exhibits higher efficiency than conventional algorithms.Comment: 5 pages, 3 figure

Harnessing Natural Fluctuations: Analogue Computer for Efficient Socially Maximal Decision Making

Each individual handles many tasks of finding the most profitable option from a set of options that stochastically provide rewards. Our society comprises a collection of such individuals, and the society is expected to maximise the total rewards, while the individuals compete for common rewards. Such collective decision making is formulated as the `competitive multi-armed bandit problem (CBP)', requiring a huge computational cost. Herein, we demonstrate a prototype of an analog computer that efficiently solves CBPs by exploiting the physical dynamics of numerous fluids in coupled cylinders. This device enables the maximisation of the total rewards for the society without paying the conventionally required computational cost; this is because the fluids estimate the reward probabilities of the options for the exploitation of past knowledge and generate random fluctuations for the exploration of new knowledge. Our results suggest that to optimise the social rewards, the utilisation of fluid-derived natural fluctuations is more advantageous than applying artificial external fluctuations. Our analog computing scheme is expected to trigger further studies for harnessing the huge computational power of natural phenomena for resolving a wide variety of complex problems in modern information society.Comment: 30 pages, 3 figure