We show, on the basis of our recently introduced stochastic model, that triangular arbitrage makes the auto-correlation function of foreign exchange rates negative in a short time scale.

We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen–dollar rate, the dollar–euro rate and the yen–euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model...

We first review our previous work, showing what is the triangular arbitrage transaction and how to quantify the triangular arbitrage opportunity. Next we explain that the correlation of the foreign exchange rates can appear without actual triangular arbitrage transaction.

Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high...

We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of...

A recent development in studies of random non-Hermitian quantum systems is reviewed. Delocalization was found to occur under a sufficiently large constant imaginary vector potential even in one and two dimensions. The phenomenon has a physical realization as flux-line depinning in type-II...

We explain a possible mechanism of an information spreading on a network which spreads extremely far from a seed node, namely the viral spreading. On the basis of a model of the information spreading in an online social network, in which the dynamics is expressed as a random multiplicative...

Relaxation from a metastable state is studied in a spin-boson model. We observe a large oscillation due to the interaction between a spin and bosons. The interaction dependence of the temporal behavior of the magnetization is also studied.

Non-adiabatic transitions are studied in a spin-boson model with multiple scattering points. In order to generalize the Landau–Zener formula, which describes the case of a single scattering point, we define an “effective gap” for a set of scattering points. The generalized formula agrees...

A type of non-Hermitian generalization of quantum mechanics is discussed. We introduce an imaginary vector potential to the Hamiltonian of systems such as Anderson-localization systems and mesoscopic systems. In these systems the imaginary part of the wave number of the eigenfunction asymptote...