Equilibrium Points of an AND-OR Tree: under Constraints on Probability

We study a probability distribution d on the truth assignments to a uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium among independent distributions (ID) then d is an independent identical distribution (IID). We show a stronger form of the above result. Given a real number r such that 0 < r < 1, we consider a constraint that the probability of the root node having the value 0 is r. Our main result is the following: When we restrict ourselves to IDs satisfying this constraint, the above result of Liu and Tanaka still holds. The proof employs clever tricks of induction. In particular, we show two fundamental relationships between expected cost and probability in an IID on an OR-AND tree: (1) The ratio of the cost to the probability (of the root having the value 0) is a decreasing function of the probability x of the leaf. (2) The ratio of derivative of the cost to the derivative of the probability is a decreasing function of x, too.Comment: 13 pages, 3 figure

Interest Rate Risk of Banking Accounts: Measurement Using the VaR Framework

In order to measure the interest rate risk of banking accounts such as deposits and loans, this paper extends the value at risk (hereafter, VaR) analysis framework, which is useful for the risk evaluation of trading accounts. In order to apply the VaR concept derived from trading accounts to banking accounts, we should take into account the following issues: (1) the longer risk evaluation period because of the inflexibility of adjustability of banking account positions; (2) the evaluation of risk included in the administered rates (the long-term prime rate and the short-term prime rate); and (3) the prepayment risk (associated with housing loans, etc.). Therefore, in this paper we first construct a VaR model including a term-structure model to express the stochastic process of market rate, the administered rate model, and the prepayment function model. Then, we perform a simulation using an imaginary portfolio to analyze the factors determining interest rate risk. In conclusion, it has been proved that the factor of administered rates increases interest rate risk both in single products and in a portfolio. Taking into account the behavior of customers who want better interest rate conditions, the factor of prepayment decreases the present value, which is itself the basis of calculating risk. Finally, we perform a sensitivity analysis of model parameters to show the magnitude of model risk.

A New Description of Nuclear Rotational Motion in terms of Intrinsic Pair Mode

A new method describing nuclear rotational motion microscopically is proposed. We extract the rotational Hamiltonian by introducing the intrinsic pair modes which commute with the rotational mode. Thereby the rotational mode is not treated as zero energy mode in contrast with the conventional RPA formalism so that we circumvent the difficulty related with infrared divergence. The wave function is constructed by angular momentum projection on each intrinsic state. Without numerical integration for projection we calculate the matrix elements analytically under a certain approximation. The numerical calculations are carried out to illustrate the applicability of our method and they show that our method works well.Comment: 14pages,1figur

Single-Flux-Quantum Bipolar Digital-to-Analog Converter Comprising Polarity-Switchable Double-Flux-Quantum Amplifier

We present a single-flux-quantum (SFQ)-based digital-to-analog converter (DAC) generating bipolar output voltages, in which the key component is a polarity-switchable double-flux-quantum amplifier (PS-DFQA). The DAC comprised a dc/SFQ converter, an 8-bit variable pulse-number-multiplier (PNM), and a 8-fold PS-DFQA integrated on a single chip. SFQ pulse-frequency modulation was employed to realize variable output voltage amplitude, for which the multiplication factor of the variable-PNM was controlled by a commercial data generator situated at room temperature. The variable-PNM realized 8-bit resolution with a multiplication factor between 0 and 255. Bias currents fed to the 8-fold PS-DFQA were polarity-switched in synchronization with the digital code for the variable-PNM. The whole circuits including I/O elements were designed using SFQ cell libraries, and fabricated using a niobium integration process. Sinusoidal bipolar voltage waveform of 0.38 mVpp was demonstrated using a reference signal source of 43.94 MHz

Numerical Simulation of Single-Electron Tunneling in Random Arrays of Small Tunnel Junctions Formed by Percolation of Conductive Nanoparticles

We numerically simulated electrical properties, i.e., the resistance and Coulomb blockade threshold, of randomly-placed conductive nanoparticles. In simulation, tunnel junctions were assumed to be formed between neighboring particle-particle and particle-electrode connections. On a plane of triangle 100×100 grids, three electrodes, the drain, source, and gate, were defined. After random placements of conductive particles, the connection between the drain and source electrodes were evaluated with keeping the gate electrode disconnected. The resistance was obtained by use of a SPICE-like simulator, whereas the Coulomb blockade threshold was determined from the current-voltage characteristics simulated using a Monte-Carlo simulator. Strong linear correlation between the resistance and threshold voltage was confirmed, which agreed with results for uniform one-dimensional arrays