Rigorous results for the free energy in the Hopfield model

We prove that the free energy of the Hopfield model with a finite number of patterns can be represented in terms of an asymptotic series expansion in inverse powers of the neurons number. The series is Borel summable for large temperatures. We also establish mathematically some other interesting properties, partly used before in a seminal paper by Amit, Gutfreund and Sompolinsky.     

The grounds for time dependent market potentials from dealers’ dynamics

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.     

An imperfect competition on scale-free networks

We study an imperfect quantity competition on networks that represent rivalry relationships among firms. We show that the more heterogeneous the underlying network is, the more the output and the price are. The output and the price on scale-free networks are counter-intuitively the same as those in the monopoly regardless of the number of rival firms. We also show that any inverse demand function represented by a network has the corresponding utility function, which justifies the inverse demand function.     

Corporate bond liquidity and matrix pricing

Matrix priced bond price data are investigated to model the liquidity of a corporate bond. Preliminary study shows that the yield spread is wide when a yield history records jumps. As well as respecting the way how matrix prices are generated, this finding leads us to a conjecture that time series of yield is represented by a jump-diffusion process. Then the kurtosis of a yield distribution can be regarded as a proxy variable for the liquidity. The conjecture is empirically validiated by regression analysis of yield spreads.     

Correlation correction to the free energy for the ising model of a binary alloy

We consider correlation corrections to the free energy of the Ising model of a binary solid solution. The correlation free energy is represented in the form of a high-temperature series, in which only the leading terms in the parameter 1/z are retained, where z is the number of lattice sites inside the effective interaction sphere of the interatomic potential. In some cases the series can be assumed and an explicit formula can be obtained for the correlation corrections. As one of the consequences of our results, we obtain a correction to the mean field theory expression for the order-disorder transition point.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 86–91, March, 1987.     

Visibility graph network analysis of gold price time series

Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L∼lnN$L\sim lnN$ into lnL∼lnN$lnL\sim lnN$ as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.     

Equivalence between supersymmetric self-dual and Maxwell–Chern–Simons models coupled to a matter spinor superfield

We study the duality of the supersymmetric self-dual and Maxwell–Chern–Simons theories coupled to a fermionic matter superfield, using a master action. This approach evades the difficulties inherent to the quartic couplings that appear when matter is represented by a scalar superfield. The price is that the spinorial matter superfield represents a unusual supersymmetric multiplet, whose main physical properties we also discuss.     

A Markov model of financial returns

We address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long-range correlated second moments. We show that a Markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations. We test the proposed model by analyzing index closing prices of the New York Stock Exchange and the DEM/USD tick-by-tick exchange rates obtained from Reuters EFX. We show that the model captures the characteristic features observed in actual financial time series, including volatility clustering, time scaling and fat tails in the probability density functions, power-law behavior of volatility correlations and, most importantly, the observed nonuniversal multifractal singularity spectrum. Motivated by our finding of strong agreement between the model and the data, we argue that at least two independent stochastic Gaussian variables are required to adequately model price fluctuations.     

Option pricing and perfect hedging on correlated stocks

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed and exact expression for the European call price which is always lower than Black-Scholes price. We obtain the same price and a modified delta hedging if we start from an effective one-dimensional market model. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation effects are also observed.     

Distributional Replication

A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.     

The oscillation of stock price by majority orienting traders with investment position

We consider an interacting particle system for the stock price fluctuation. The change of the stock price with a feedback by the price considering the herding behavior (majority orienting behavior) of traders, gives the van der Pol equation as a deterministic approximation. Considering the investment position of each trader, we introduce the delayed van der Pol equation. The history of investment positions, for example sell or buy, of each trader for a stock makes a memory effect, which is modeled by using the time retardation. The delayed van der Pol equation model seems to be natural and explains typical phenomena, for example triangle pattern, volatility jumps, price jumps and price trends, known for the time series of a stock price.     

关于软玻密子的结构

本文修改了Landshoff-Nachtmann的软玻密子(Pomeron P)场论模型.从强子组分夸克具有结构的观点出发,根据高能强作用软过程中的最大非微扰强作用反应假定,提出了有关软P新的结构图像.对撞强子中的一对组分夸克被分解为裸夸克和一系列非微扰胶子(和夸克对).与此相应,软P的结构是由胶子形成的一系列切割梯形图之和所代表.在系统能量s很大而动量转移|t|很小的多重雷吉(Regge)运动学区间,并在保留lns的领头阶近似下,计算了这组切割梯形图之和所对应的散射振幅和总截面.它们的表达式出现了对s的Regge型幂次因子,得出了软P轨迹的简洁表达式.简单说明了按本文提出的方案可以讨论那些相关的强作用过程.     

Characteristics of the volatility in the Korea composite stock price index

We empirically analyze the time series of the Korea Composite Stock Price Index (KOSPI) from March of 1992 to February of 2007 using methods from the hydrodynamic turbulence. To this end, we focus on characteristics of the return and volatility, which are respectively the price change and a measure of the financial market fluctuation over a time interval. With these, we show that the non-Gaussian probability distribution of the return can be modeled by the convolution of the conditional probability distribution of the return given the volatility and the distribution of the volatility per se. From this model, we suggest that the non-Gaussian characteristic of the return results from the fluctuation of the volatility. That is, a large return is partly, if not entirely, due to the market fluctuation in a long time scale influencing the fluctuation in a short time scale via net information flow. We further show that the volatility has a multi-fractal property, which resembles the multifractality of the energy dissipation in the turbulence.     

Compton profiles of electron momentum distribution inβ-Ga

We report for the first time the Compton profiles of electron momentum distribution inβ-gallium calculated along the crystallographic directions (100), (110) and (111). The conduction electron states for this purpose are determined in the energy band calculations using model potential. The core states, on the other hand, are represented each by a single tight-binding function. The results show that the Compton profiles are nearly isotropic with very little directional dependence, which is suggestive of a free-electron-like distribution of the conduction electrons in this system. The latter conclusion is in close confirmity with similar conclusions drawn in augmented plane wave (APW) calculation of energy bands and the derived Knight-shift results inβ-Ga.     

Entropic derivation of the spectral Eddington factors

In general, the closure of the finite system of moment equations by the corresponding maximum entropy distribution function results in the symmetric conservative system of first-order partial differential equations for the Lagrange multipliers of the constrained Boltzmann entropy maximization problem. Then the transformation of dependent variables yields the system of conservation equations for the moments which is consistent with the additional conservation equation identified with the balance of entropy. The objective of this paper is to employ these facts for the analysis of the spectral Eddington factors obtained from the maximum entropy distribution functions. The supposition that the spectral Eddington factors should depend on the energy density and the heat flux only through the single variable representing the heat flux normalized in some way by the energy density predominates in the literature on the subject. Here, it is demonstrated that this is true only for classical Maxwell-Boltzmann radiation and, in this case, the well-known results of Minerbo are recovered. A similar single-variable dependence postulated by Cernohorsky and Bludman for fermionic radiation cannot be justified since it leads to the contradiction with the consistency conditions between the moment evolution equations and the entropy balance. For Bose-Einstein radiation, we rederive and analyze the results given in the literature for low-energy and high-energy limits. We also show that, except for those limiting cases, the Eddington factor for bosonic radiation cannot be represented as a function of a single normalized variable. In the present approach, the entropy function plays a crucial role in determining the system of evolution equations for the energy density and the heat flux. In this system, the flux of the heat flux, and hence the Eddington factor, is determined by the additional scalar potential uniquely related to the entropy function for each type of statistics. Since the Eddington factor cannot be expressed in terms of elementary functions, we propose to use the polynomial approximation. Namely, for Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, we expand the entropy function in powers of the square of the heat flux and also calculate the corresponding power series expansion of the additional potential. By truncating the latter, we obtain the Eddington factor represented as the eighth-order polynomial in the heat flux with coefficients being the elementary functions of the energy density and the parameter which determines statistics. Finally, we analyze the behavior of the scalar Eddington factors in the limiting case when the normalized heat flux tends to one.     

Quantum Spin Transport in Rashba Spin-Orbit-Coupled Graphene Nanoflakes

We study the spin-resolved transport in a two-terminal graphene nanoflake device with a Rashba spinorbit coupling region in the center of the device. The Green's function method is applied to the system and the spin transmission probability and the spin polarization in x, y, and z directions are calculated. It is found that the components of the spin polarization are antisymmetric functions of Fermi energy, which oscillate and decay to the zero with increasing the energy for all values of the Rashba strength. It is shown that by tuning the Rashba strength via a gate voltage and/or changing the size of the system, it is possible to control the sign and magnitude of the spin polarization. The system represented here is a typical candidate for full electrical spintronic devices based on the carbon materials that are used for spin filtration.     

On the many-body Van der Waals binding energy of a dense fluid

We consider a dense system of neutral atoms. When the atoms are represented by isotropic oscillators (Drude-Lorentz model) interacting with nonretarded dipole-dipole forces, the binding energy of the system is given exactly by a well-known expression which is written as a sum of two-bond, three-bond, etc., Van der Waals interactions. For a Bravais lattice this expression for the binding energy can be computed numerically to arbitrary accuracy. This has been done for the f.c.c. lattices of the noble-gas solids by Lucas. For a fluid an exact evaluation would require the knowledge of higher-order molecular distribution functions. Various approximations are discussed for this case, the simplest of which is the so-called long-wavelength approximation due to Doniach. When this approximation is checked by comparison with the exact result for a lattice, it turns out that the two-bond contribution leads to a value which is more than twice too large. Some more refined approximations are considered which treat the two-bond contribution exactly. It is pointed out that the model is consistent only if the distance of closest approach between the atoms is not too small.     

Thermoelectric properties of a single quantum dot in mixed-valence regime

We study thermoelectric effects in correlated quantum dot coupled to ferromagnetic electrodes by calculating thermal conductance κ, thermopower S and Figure of merit ZT in the mixed-valence regime as function of on-dot energy level and temperature. The system is represented by the Anderson model and the results agree well with those recently experimental measured for a quantum dot coupled to two leads.