arXiv subjects

Jun-ichi Inoue

Publications and source records attributed to Jun-ichi Inoue.

At least 55 records · Page 3Linked to original sources

arXiv2007

Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem

We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming that stochastic processes of the market price changes could be regarded as a renewal process, we use the theorem to calculate the average waiting time of the process. In the conventional derivation of the theorem, it is apparently hard to evaluate the higher order moments of the waiting time. To overcome this type of difficulties, we attempt to derive the waiting time distribution Omega(s) directly for arbitrary time interval distribution (first passage time distribution) of the stochastic process P_{W}(tau) and observation time distribution P_{O}(t) of customers. Our analysis enables us to evaluate not only the first moment (the average waiting time) but also any order of the higher moments of the waiting time. Moreover, in our formalism, it is possible to model the observation of the price on the internet by the customers in terms of the observation time distribution P_{O}(t). We apply our analysis to the stochastic process of the on-line foreign exchange rate for individual customers from the Sony bank and compare the moments with the empirical data analysis.

physics.data-an↗

arXiv2006

Fluctuations in time intervals of financial data from the view point of the Gini index

We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the Gini index gives a very close value with that of empirical data analysis.

physics.data-an↗

arXiv2006

Analysis of the long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions with random fields on each site, following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many-valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.

cond-mat.dis-nn↗

arXiv2005

A solvable quantum antiferromagnet model

We introduce a quantum antiferromagnet model, having exactly soluble thermodynamic properties. It is an infinite range antiferromagnetic Ising model put in a transverse field. The free energy gives the ground state energy in the zero temperature limit and it also gives the low temperature behaviour of the specific heat, the exponential variation of which gives the precise gap magnitude in the excitation spectrum of the system. The detailed behaviour of the (random sublattice) staggard magnetisation and susceptibilities are obtained and studied near the Néel temperature and the zero temperature quantum critical point.

cond-mat.stat-mech↗

arXiv2004

Competition between ferro-retrieval and anti-ferro orders in a Hopfield-like network model for plant intelligence

We introduce a simple cellular-network model to explain the capacity of the plants as memory devices. Following earlier observations (Bose \cite{Bose} and others), we regard the plant as a network in which each of the elements (plant cells) are connected via negative (inhibitory) interactions. To investigate the performance of the network, we construct a model following that of Hopfield, whose energy function possesses both Hebbian spin glass and anti-ferromagnetic terms. With the assistance of the replica method, we find that the memory state of the network decreases enormously due to the effect of the anti-ferromagnetic order induced by the inhibitory connections. We conclude that the ability of the plant as a memory device is rather weak.

cond-mat.dis-nn↗

arXiv2001

Dynamics of the maximum marginal likelihood hyper-parameter estimation in image restoration : gradient descent vs. EM algorithm

Dynamical properties of image restoration and hyper-parameter estimation are investigated by means of statistical mechanics. We introduce an exactly solvable model for image restoration and derive differential equations with respect to macroscopic quantities. From these equations, we evaluate relaxation processes of the system to the equilibrium state. Our statistical mechanical approach also enable us to investigate the hyper-parameter estimation by means of maximization of marginal likelihood by using gradient decent and EM algorithm from dynamical point of view.

cond-mat.dis-nn↗

arXiv2001

Multi-State Image Restoration by Transmission of Bit-Decomposed Data

We report on the restoration of gray-scale image when it is decomposed into a binary form before transmission. We assume that a gray-scale image expressed by a set of Q-Ising spins is first decomposed into an expression using Ising (binary) spins by means of the threshold division, namely, we produce (Q-1) binary Ising spins from a Q-Ising spin by the function F(σ_i - m) = 1 if the input data σ_i \in {0,.....,Q-1} is σ_i \geq m and 0 otherwise, where m \in {1,....,Q-1} is the threshold value. The effects of noise are different from the case where the raw Q-Ising values are sent. We investigate which is more effective to use the binary data for transmission or to send the raw Q-Ising values. By using the mean-field model, we first analyze the performance of our method quantitatively. Then we obtain the static and dynamical properties of restoration using the bit-decomposed data. In order to investigate what kind of original picture is efficiently restored by our method, the standard image in two dimensions is simulated by the mean-field annealing, and we compare the performance of our method with that using the Q-Ising form. We show that our method is more efficient than the one using the Q-Ising form when the original picture has large parts in which the nearest neighboring pixels take close values.

cond-mat.dis-nn↗

arXiv2001

Dynamics of on-line Hebbian learning with structurally unrealizable restricted training sets

We present an exact solution for the dynamics of on-line Hebbian learning in neural networks, with restricted and unrealizable training sets. In contrast to other studies on learning with restricted training sets, unrealizability is here caused by structural mismatch, rather than data noise: the teacher machine is a perceptron with a reversed wedge-type transfer function, while the student machine is a perceptron with a sigmoidal transfer function. We calculate the glassy dynamics of the macroscopic performance measures, training error and generalization error, and the (non-Gaussian) student field distribution. Our results, which find excellent confirmation in numerical simulations, provide a new benchmark test for general formalisms with which to study unrealizable learning processes with restricted training sets.

cond-mat.dis-nn↗

arXiv2001

Image restoration using the Q-Ising spin glass

We investigate static and dynamic properties of gray-scale image restoration (GSIR) by making use of the Q-Ising spin glass model, whose ladder symmetry allows to take in account the distance between two spins. We thus give an explicit expression of the Hamming distance between the original and restored images as a function of the hyper-parameters in the mean field limit. Finally, numerical simulations for real-world pictures are carried out to prove the efficiency of our model.

cond-mat.dis-nn↗

arXiv2000

Application of the quantum spin glass theory to image restoration

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based MPM estimate.

cond-mat.dis-nn↗

arXiv1999

Strong Enhancement of Superconducting Correlation in a Two-Component Fermion Gas

We study high-density electron-hole (e-h) systems with the electron density slightly larger than the hole density. We find a new superconducting phase, in which the excess electrons form Cooper pairs moving in an e-h BCS phase. The coexistence of the e-h and e-e orders is possible because e and h have opposite charges, whereas analogous phases are impossible in the case of two fermion species that have the same charge or are neutral. Most strikingly, the e-h order enhances the superconducting e-h order parameter by more than one order of magnitude as compared with that given by the BCS formula, for the same value of the effective e-e attractive potential λ^{ee}. This new phase should be observable in an e-h system created by photoexcitation in doped semiconductors at low temperatures.

cond-mat.supr-con↗

arXiv1999

Time evolution of condensed state of interacting bosons with reduced number fluctuation in a leaky box

We study the time evolution of the Bose-Einstein condensate of interacting bosons confined in a leaky box, when its number fluctuation is initially (t=0) suppressed. We take account of quantum fluctuations of all modes, including k = 0. We identify a ``natural coordinate'' b_0 of the interacting bosons, by which many physical properties can be simply described. Using b_0, we successfully define the cosine and sine operators for interacting many bosons. The wavefunction, which we call the ``number state of interacting bosons'' (NSIB), of the ground state that has a definite number N of interacting bosons can be represented simply as a number state of b_0. We evaluate the time evolution of the reduced density operator ρ(t) of the bosons in the box with a finite leakage flux J, in the early time stage for which Jt << N. It is shown that ρ(t) evolves from a single NSIB at t = 0, into a classical mixture of NSIBs of various values of N at t > 0. We define a new state called the ``number-phase squeezed state of interacting bosons'' (NPIB). It is shown that ρ(t) for t>0 can be rewritten as the phase-randomized mixture (PRM) of NPIBs. It is also shown that the off-diagonal long-range order (ODLRO) and the order parameter defined by it do not distinguish the NSIB and NPIB. On the other hand, the other order parameter Ψ, defined as the expectation value of the boson operator, has different values among these states. For each element of the PRM of NPIBs, we show that Ψevolves from zero to a finite value very quickly. Namely, after the leakage of only two or three bosons, each element acquires a full, stable and definite (non-fluctuating) value of Ψ.

quant-ph↗

arXiv1999

Pump Built-in Hamiltonian Method for Pump-Probe Spectroscopy

We propose a new method of calculating nonlinear optical responses of interacting electronic systems. In this method, the total Hamiltonian (system + system-pump interaction) is transformed into a different form that (apparently) does not have a system-pump interaction. The transformed Hamiltonian, which we call the pump built-in Hamiltonian, has parameters that depend on the strength of the pump beam. Using the pump built-in Hamiltonian, we can calculate nonlinear responses (responses to probe beams as a function of the pump beam) by applying the {\em linear} response theory. We demonstrate the basic idea of this new method by applying it to a one-dimensional, two-band model, in the case the pump excitation is virtual (coherent excitation). We find that the exponent of the Fermi edge singularity varies with the pump intensity.

cond-mat.mtrl-sci↗

arXiv1999

Renormalized Bosonic Interaction of Excitons

An effective bosonic Hamiltonian of $1s$ excitons with ``spin'' degrees of freedom in two dimension is obtained through a projection procedure, starting from a conventional electron-hole Hamiltonian ${\cal H}_{eh}$. We first demonstrate that a straightforward transformation of ${\cal H}_{eh}$ into a Hamiltonian of bosonic excitons does not give the two-body interaction between an ``up-spin'' exciton and a ``down-spin'' exciton, which are created by the left- and right-circularly polarized light beams, respectively. We then show that this interaction is generated through a projection procedure onto the subspace spanned by $1s$ excitons, as a renormalization effect coming from higher exciton states. The projection also renormalizes the interaction between $1s$ excitons with the same spins by a large amount. These renormalization effects are crucial for the polarization dependence of the optical responses from semiconductors. The present theory gives the microscopic foundation of the phenomenology that was successfully applied to the analysis of four-wave mixing experiments in GaAs quantum wells strongly coupled to the radiation field in a high-Q micro cavity.

cond-mat.mtrl-sci↗

arXiv1999

Image restoration using the chiral Potts spin-glass

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which can not be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three gray-scale level case. In order to check our analytical result and the efficiency of our model, 2D Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.

cond-mat.dis-nn↗

arXiv1998

Effective Hamiltonian for Excitons with Spin Degrees of Freedom

Starting from the conventional electron-hole Hamiltonian ${\cal H}_{eh}$, we derive an effective Hamiltonian $\tilde{\cal H}_{1s}$ for $1s$ excitons with spin degrees of freedom. The Hamiltonian describes optical processes close to the exciton resonance for the case of weak excitation. We show that straightforward bosonization of ${\cal H}_{eh}$ does not give the correct form of $\tilde{\cal H}_{1s}$, which we obtain by a projection onto the subspace spanned by the $1s$ excitons. The resulting relaxation and renormalization terms generate an interaction between excitons with opposite spin. Moreover, exciton-exciton repulsive interaction is greatly reduced by the renormalization. The agreement of the present theory with the experiment supports the validity of the description of a fermionic system by bosonic fields in two dimensions.

cond-mat.mtrl-sci↗

arXiv1998

Noise reduction in signal processing using binary couplings

We report a simple extension of a model for noise reduction in signal processing, already introduced by Mourik et al., in the presence of binary coupling vectors, which turns to be more useful for practical and engineering implementations. We also compute annealed approximation which gives an upper bound of the correct critical number of noise-sources. Finally, we also find that the full RSB Parisi solution just above the AT line is an universal function for any symmetric distribution of the coupling vectors.

cond-mat.dis-nn↗

arXiv1998

Generalization ability of a perceptron with non-monotonic transfer function

We investigate the generalization ability of a perceptron with non-monotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning algorithms. By the perceptron algorithm the generalization error is shown to decrease by the $α^{-1/3}$-law similarly to the case of a simple perceptron in a restricted range of the parameter $a$ characterizing the non-monotonic transfer function. For other values of $a$, the perceptron algorithm leads to the state where the weight vector of the student is just opposite to that of the teacher. The Hebbian learning algorithm has a similar property; it works only in a limited range of the parameter. The conventional AdaTron algorithm does not give a vanishing generalization error for any values of $a$.We thus introduce a modified AdaTron algorithm which yields a good performance for all values of $a$. We also investigate the effects of optimization of the learning rate as well as of the learning algorithm. Both methods give excellent learning curves proportional to $α^{-1}$. The latter optimization is related to the Bayes statistics and is shown to yield useful hints to extract maximum amount of information necessary to accelerate learning processes.

cond-mat.dis-nn↗