Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

Simplest optimal cutting patterns for equal rectangles

This paper presents branch-and-bound algorithms that can guarantee the simplest optimal cutting patterns of equal rectangles. An existing linear algorithm determines the global upper bound exactly. The branching process ends when a branch of a lower bound equal to the global upper bound is found.     

Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

基于Copula的金融资产相关结构建模

分析了几种相关结构函数(Copula)表示的相关结构模型,给出了用相关结构函数对金融资产间的相关结构进行建模的方法.结果表明混合Gumbel(M-Gumbel)相关结构函数能较全面地描述上海深圳两证券指数的相关结构,模拟计算VaR的结果支持了实证分析的结论.     

A two-echelon base-stock inventory model with Poisson demand and the sequential processing of orders at the upper echelon

We consider a two-echelon inventory system with a number of non-identical, independent ‘retailers’ at the lower echelon and a single ‘supplier’ at the upper echelon. Each retailer experiences Poisson demand and operates a base stock policy with backorders. The supplier manufactures to order and holds no stock. Orders are produced, in first-come first-served sequence, with a fixed production time. The supplier therefore functions as an M/D/1 queue. We are interested in the performance characteristics (average inventory, average backorder level) at each retailer. By finding the distribution of order lead time and hence the distribution of demand during order lead time, we find the steady state inventory and backorder levels based on the assumption that order lead times are independent of demand during order lead time at a retailer. We also propose two alternative approximation procedures based on assumed forms for the order lead time distribution. Finally we provide a derivation of the steady state inventory and backorder levels which will be exact as long as there is no transportation time on orders between the supplier and retailers. A numerical comparison is made between the exact and approximate measures. We conclude by recommending an approach which is intuitive and computationally straightforward.     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

To take into account the temporal dimension of uncertainty in stock markets, this paper introduces a cross-sectional estimation of stock market volatility based on the intrinsic entropy model. The proposed cross-sectional intrinsic entropy (CSIE) is defined and computed as a daily volatility estimate for the entire market, grounded on the daily traded prices—open, high, low, and close prices (OHLC)—along with the daily traded volume for all symbols listed on The New York Stock Exchange (NYSE) and The National Association of Securities Dealers Automated Quotations (NASDAQ). We perform a comparative analysis between the time series obtained from the CSIE and the historical volatility as provided by the estimators: close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, Yang–Zhang, and intrinsic entropy (IE), defined and computed from historical OHLC daily prices of the Standard & Poor’s 500 index (S&P500), Dow Jones Industrial Average (DJIA), and the NASDAQ Composite index, respectively, for various time intervals. Our study uses an approximate 6000-day reference point, starting 1 January 2001, until 23 January 2022, for both the NYSE and the NASDAQ. We found that the CSIE market volatility estimator is consistently at least 10 times more sensitive to market changes, compared to the volatility estimate captured through the market indices. Furthermore, beta values confirm a consistently lower volatility risk for market indices overall, between 50% and 90% lower, compared to the volatility risk of the entire market in various time intervals and rolling windows.     

Neural Networks for Financial Time Series Forecasting

Financial and economic time series forecasting has never been an easy task due to its sensibility to political, economic and social factors. For this reason, people who invest in financial markets and currency exchange are usually looking for robust models that can ensure them to maximize their profile and minimize their losses as much as possible. Fortunately, recently, various studies have speculated that a special type of Artificial Neural Networks (ANNs) called Recurrent Neural Networks (RNNs) could improve the predictive accuracy of the behavior of the financial data over time. This paper aims to forecast: (i) the closing price of eight stock market indexes; and (ii) the closing price of six currency exchange rates related to the USD, using the RNNs model and its variants: the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The results show that the GRU gives the overall best results, especially for the univariate out-of-sample forecasting for the currency exchange rates and multivariate out-of-sample forecasting for the stock market indexes.     

Effects of SiNx on two-dimensional electron gas and current collapse of AlGaN/GaN high electron mobility transistors

SiN_x is commonly used as a passivation material for AlGaN/GaN high electron mobility transistors (HEMTs). In this paper, the effects of SiN_x passivation film on both two-dimensional electron gas characteristics and current collapse of AlGaN/GaN HEMTs are investigated. The SiN_x films are deposited by high- and low-frequency plasma-enhanced chemical vapour deposition, and they display different strains on the AlGaN/GaN heterostructure, which can explain the experiment results.     

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.