一种可用于资金分配的线性规划模型

本运用DEA方法,给出了一种能够用来进行资金分配决策的线性规划模型,并证明了其最优解的存在性。     

Characteristics analysis of acupuncture electroencephalograph based on mutual information Lempel-Ziv complexity

As a convenient approach to the characterization of cerebral cortex electrical information,electroencephalograph (EEG) has potential clinical application in monitoring the acupuncture effects.In this paper,a method composed of the mutual information method and Lempel-Ziv complexity method (MILZC) is proposed to investigate the effects of acupuncture on the complexity of information exchanges between different brain regions based on EEGs.In the experiments,eight subjects are manually acupunctured at ’Zusanli’ acupuncture point (ST-36) with different frequencies (i.e.,50,100,150,and 200 times/min) and the EEGs are recorded simultaneously.First,MILZC values are compared in general.Then average brain connections are used to quantify the effectiveness of acupuncture under the above four frequencies.Finally,significance index P values are used to study the spatiality of the acupuncture effect on the brain.Three main findings are obtained:(i) MILZC values increase during the acupuncture;(ii) manual acupunctures (MAs) with 100 times/min and 150 times/min are more effective than with 50 times/min and 200 times/min;(iii) contralateral hemisphere activation is more prominent than ipsilateral hemisphere’s.All these findings suggest that acupuncture contributes to the increase of brain information exchange complexity and the MILZC method can successfully describe these changes.     

Influences of preconditioning on the mutual coherence and the restricted isometry property of Gaussian/Bernoulli measurement matrices

This article discusses the influence of preconditioning on the mutual coherence and the restricted isometry property of Gaussian or Bernoulli measurement matrices. The mutual coherence can be reduced by preconditioning, although it is fairly small due to the probability estimate of the event that it is less than any given number in (0, 1). This can be extended to a set that contains either of the two types of matrices with a high probability but a subset with Lebesgue measure zero. The numerical results illustrate the reduction in the mutual coherence of Gaussian or Bernoulli measurement matrices. However, the first property can be true after preconditioning for a large type of measurement matrices having the property of s-order restricted isometry and being full row rank. This leads to a better estimate of the condition number of the corresponding submatrices and a more accurate error estimate of the conjugate gradient methods for the least squares problems typically used in greedy-like recovery algorithms.     

Mimicking Complexity of Structured Data Matrix’s Information Content: Categorical Exploratory Data Analysis

We develop Categorical Exploratory Data Analysis (CEDA) with mimicking to explore and exhibit the complexity of information content that is contained within any data matrix: categorical, discrete, or continuous. Such complexity is shown through visible and explainable serial multiscale structural dependency with heterogeneity. CEDA is developed upon all features’ categorical nature via histogram and it is guided by all features’ associative patterns (order-2 dependence) in a mutual conditional entropy matrix. Higher-order structural dependency of k(≥3) features is exhibited through block patterns within heatmaps that are constructed by permuting contingency-kD-lattices of counts. By growing k, the resultant heatmap series contains global and large scales of structural dependency that constitute the data matrix’s information content. When involving continuous features, the principal component analysis (PCA) extracts fine-scale information content from each block in the final heatmap. Our mimicking protocol coherently simulates this heatmap series by preserving global-to-fine scales structural dependency. Upon every step of mimicking process, each accepted simulated heatmap is subject to constraints with respect to all of the reliable observed categorical patterns. For reliability and robustness in sciences, CEDA with mimicking enhances data visualization by revealing deterministic and stochastic structures within each scale-specific structural dependency. For inferences in Machine Learning (ML) and Statistics, it clarifies, upon which scales, which covariate feature-groups have major-vs.-minor predictive powers on response features. For the social justice of Artificial Intelligence (AI) products, it checks whether a data matrix incompletely prescribes the targeted system.     

Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions

The previous attempts to launch liquid and standardized longevity derivatives in the market failed because banks do not seem to be ready to take longevity risk. Therefore, instead of trying to transfer longevity risk to investors, it could be interesting for financial institutions to propose interest rate hedges adapted to longevity portfolios, in the spirit of liability driven investments. In this paper, we introduce a new structured financial product: the so-called Longevity Nominal Chooser Swaption. Thanks to such a contract, insurers could keep pure longevity risk and transfer to financial markets a great part of interest rate risk underlying annuity portfolios.We use a population dynamics longevity model and a classical two-factor interest rate model to price this product. Numerical results show that the option offered to the insurer (in terms of choice of nominal) is not too expensive in many real-world cases. We also discuss the pros and the cons of the product and of our methodology.     

Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 88–95, November 2005.     

高斯谢尔光束通过湍流大气漫射目标的散射统计

基于广义惠更斯菲涅耳原理分析了高斯谢尔光束通过湍流大气漫射目标的散射统计特性。假定相位结构函数起主导作用,根据高斯谢尔光束的交叉密度函数,推导了散斑场的互相干函数表达式,进而得出接收面处的散斑尺寸大小和强湍流起伏的时延协方差函数表达式。数值分析了源相干长度、波长、湍流强度对互相干函数的影响。对理想漫射目标,接收面的散斑尺寸大小由束腰宽度、源相干长度和湍流强度确定,随着湍流强度的增加,散斑尺寸变小;在弱湍流区,散斑尺寸由源相干长度决定,当湍流增强时,散斑尺寸大小逐渐趋于一致。     

Critical Solution Temperatures for Two Phase Solvent Systems with Halide Salts,Carboxylic Acids,Surfactants, and Polynuclear Aromatic Compounds

Upper critical solution temperatures (UCST) of water‐phenol systems are reported with 0.1 mol kg^?1 halide salts, carboxylic acids, 1.0% PEG 200 in water, and 0.01 mol kg^?1 surfactants and polynuclear aromatic compounds namely benzene, naphthalene, anthracene, chrysene; and benzene derivatives solutions in phenol. The valence electrons and shell numbers, bascity, ‐CH₃ and ‐CH₂‐, hydrophilic, hydrophobic and π conjugated electrons of respective additives have been noted to affect the UCST values and mutual solubilities of the water and phenol. The surfactants decrease the UCST values with higher mutual solubilities due to effective hydrophilic as well as hydrophobic interactions with aqueous and organic phases, respectively. The stronger structure breaking action of the 3(‐OH) of the glycerol outweighs than those of the 3(‐COO^?) and 1(‐OH) of the citric acid and the urea does produce almost equal UCST values as compared to glycerol. A decrease in the UCST values is noted with number of conjugated π electrons of the benzene, naphthalene, anthracene, and chrysene. In general, the dTc/dx₂ values of salts for 0.20–0.16 mole fractions of phenol are found positive while for 0.055–0.052 mole fractions, the negative.     

Binary mutual diffusion coefficients of aqueous ammonium and potassium sulfates at 25°C

The diffusion coefficients of aqueous ammonium and potassium ions at infinite dilution differ by only 0.01% at 25°C, so, according to Nernst's law, the binary mutual diffusion coefficients D of pairs of dilute aqueous ammonium and potassium salts should be nearly identical. Yet precise optical interferometric data for ammonium and potassium sulfates contradict this rule: the value of D reported previously for 0.05 mol-L⁻¹ aqueous ammonium sulfate is 0.80×10⁻⁵ cm²-s⁻¹, while the corresponding value for potassium sulfate is 1.24×10⁻⁵ cm²-s⁻¹ about 50% higher. To confirm this surprising result, the diffusion coefficients of the two salts have been measured by the Taylor dispersion technique. The diffusion coefficients of the salts are indeed nearly identical, and the earlier ammonium sulfate data are found to be incorrect.