Generalised Measures of Multivariate Information Content

The entropy of a pair of random variables is commonly depicted using a Venn diagram. This representation is potentially misleading, however, since the multivariate mutual information can be negative. This paper presents new measures of multivariate information content that can be accurately depicted using Venn diagrams for any number of random variables. These measures complement the existing measures of multivariate mutual information and are constructed by considering the algebraic structure of information sharing. It is shown that the distinct ways in which a set of marginal observers can share their information with a non-observing third party corresponds to the elements of a free distributive lattice. The redundancy lattice from partial information decomposition is then subsequently and independently derived by combining the algebraic structures of joint and shared information content.     

Neural Estimator of Information for Time-Series Data with Dependency

Novel approaches to estimate information measures using neural networks are well-celebrated in recent years both in the information theory and machine learning communities. These neural-based estimators are shown to converge to the true values when estimating mutual information and conditional mutual information using independent samples. However, if the samples in the dataset are not independent, the consistency of these estimators requires further investigation. This is of particular interest for a more complex measure such as the directed information, which is pivotal in characterizing causality and is meaningful over time-dependent variables. The extension of the convergence proof for such cases is not trivial and demands further assumptions on the data. In this paper, we show that our neural estimator for conditional mutual information is consistent when the dataset is generated with samples of a stationary and ergodic source. In other words, we show that our information estimator using neural networks converges asymptotically to the true value with probability one. Besides universal functional approximation of neural networks, a core lemma to show the convergence is Birkhoff’s ergodic theorem. Additionally, we use the technique to estimate directed information and demonstrate the effectiveness of our approach in simulations.     

Interaction of charged particle flows with plasmons in two-dimensional electron gas

The theory of interaction of charged particle beams with 2D electron gas, located in the field of the delta-like potential wallU(y) =U _o(y) has been developed. The kinetic equation for plasmons in 2D electron gas was obtained; the conditions of arising of their instability are given and the corresponding expressions for the increment of plasmons are found.     

X-ray diagnostics of semiconductor heterostructures: Some achievements and perspectives for development

Possibilities of new approaches for the interpretation of X-ray scattering data to characterize heterostructures with nanosized layers are demonstrated. These approaches are based on both simultaneous mathematical analysis of the experimental data of X-ray rocking curves from several crystallographic planes of the sample and joint processing of the experimental data of X-ray diffraction and reflectometry. Measurements are taken using the same device with the advanced technique of experiments. In the approaches proposed, the volume of the experimental information on one sought parameter increases significantly, which provides a greater reliability of reconstructing the structural parameters of the object under study. A mathematical apparatus is developed along with the software to solve the inverse problem with a large amount of input data and sought parameters. The proposed approaches are tested on nanosized Al_xGa_1-xAs/In_yGa_1-yAs and In_xAl_1-xAs/In_yGa_1-yAs heterostructures grown on GaAs and InP substrates, respectively. It is shown that the complex X-ray method allows a reliable determination of relationships between the real structure and electrophysical properties, and thus an improvement of the technology for producing these objects with predicted properties.     

Optical properties of GaN x As y P1?x?y semiconductor quaternary solid solutions

The photoluminescence method was used in the temperature range of 15?C300 K to study the optical properties of quantum-dimensional heterostructures based on GaN _x As _y P_(1?x?y) solid solutions, synthesized on the surface of a GaP (100) substrate. The calculations for the band-gap width of the GaN _x As _y P_(1?x?y) solid solution with the use of the band anticrossing model are shown to agree well with experimental data.     

3∶29型Gd3(Fe1-xCox)29-yCry化合物的成相与结构

通过X射线衍射分析和磁测量研究了Gd-Fe-Co-Cr四元系中对应于化学式Gd₃(Fe,Co,Cr)₂₉且Gd含量为一定值的截面内富Fe,Co区的相关系,重点探索了高Co含量3∶29型化合物合成的可能性,研究了3∶29型Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的结构与磁性.研究结果表明,获得3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的范围为:y=5,0≤x≤0.7;y=5.5,0.7≤x≤0.8和y=6,0.8≤x≤0.9.基于对Gd₃(Fe_1-xCo_x)_29-yCr_y化合物成相条件的研究,成功地合成了纯Co基Gd₃Co_29-yCr_y化合物,其固溶范围为6.5≤y≤7.3.3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的晶体结构都属于单斜晶系,Nd₃(Fe,Ti)₂₉型结构,空间群为A2m.得到3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的固溶极限即Co含量的极大值与稳定元素Cr含量有关.Co原子的含量越高,所需稳定元素Cr的含量越大.值得注意的是,用Co原子替代Fe原子会导致Gd₃(Fe_1-xCo_x)_29-yCr_y化合物磁晶各向异性的显著改变.当x≥0.4时,化合物的磁晶各向异性从易面型转变为易轴型 关键词： 3(Fe_1-xCo_x)_29-yCr_y化合物')" href="#">Gd₃(Fe_1-xCo_x)_29-yCr_y化合物 相关系和相结构 X射线衍射 磁晶各向异性     

Experimental modeling of physical laws

A physical law is represented by the probability distribution of a measured variable. The probability density is described by measured data using an estimator whose kernel is the instrument scattering function. The experimental information and data redundancy are defined in terms of information entropy. The model cost function, comprised of data redundancy and estimation error, is minimized by the creation-annihilation process. Received 24 February 2000 and Received in final form 21 February 2001     

双合成反铁磁结构及其对自旋阀巨磁电阻效应的影响

用直流磁控溅射方法制备了双合成反铁磁结构Co₉₀Fe₁₀(5 nm)/Ru(x nm)/Co₉₀Fe₁₀(3 nm)/Ru(y nm)/Co₉₀Fe₁₀(5 nm)(x=0.45,0.45,1.00; y=0.45,1.00,1.00)的系列样品,并对样品的性能及其作为钉扎层对自旋阀巨磁电阻(GMR)效应的影响进行了研究 关键词： 双合成反铁磁 自旋阀 巨磁电阻     

Semiinclusive two-particle correlations and independent cluster emission at ISR energies

Semiinclusive two-particle correlations are calculated in the independent cluster emission model. The resulting semi-inclusive correlation functions ?₂ⁿ(y₁ = y₂ = 0) agree rather than well experimental data, esp. with respect to the multiplicity dependence. The average number of charged particles per cluster found from comparison with semiinclusive data is 2.5 charged particles per cluster, a value found earlier also from analysis of inclusive correlations.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Determination of random variations in ionosphere height from phase fluctuations of VLF signals

Conclusions A feature of our problem of restoration of fluctuations in ionosphere height is that the experimental data(t, _k) obtained at a fixed reception point are functions of time, whereas the function ₁(u, y₂) to be restored is a function of the coordinates. If we use the assumption that the irregularities migrate transversely, coordinate y₂ can be exchanged for time t. Restoration with respect to the second coordinate u=x_i–x₀/2 is in effect obtained by using data(t, _k) on some set of carrier frequencies.The resultant solution of the restoration problem is in the form of an expansion of ₁(u, y₂) in known functions determined from the observed data(t, _k). We have evaluated the solution accuracy, which depends on the overall power signal-to-noise ratio at all frequencies used. We have demonstrated that the restoration algorithm contains an optimum number (with respect to accuracy) of coefficients to be evaluated.Khar'kov Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 20, No. 8, pp. 1138–1145, August, 1977.     

Using dithering for implementing geometric moment function estimation in a correlation retina

Correlation retinas measure the correlation product of an image projected on a sensor by optical means and a function f(x, y) stored in the retina. This optical correlation is well suited for the measurement of geometric moments, and this is why one can find in the literature several correlation retina circuits dedicated to it. Unfortunately, these architectures are not programmable and are dedicated to specific applications. Moment functions are of great interest in pattern recognition. This application needs to compute, for example, geometric moments whose order can depend on the application. Thus, the implementation of this function in a correlation retina requires a flexible architecture where the function f(x, y) can be modified to allow the measurement of the product of the image under analysis and f(x, y). The most robust solution is to memorize f(x, y) in memory devices distributed in the array of pixels constituting the retina. But, for technological problems, it is necessary to limit the number of bits used to store f(x, y) in the sensor. In this article, we propose to use dithering algorithms to code f(x, y) on only one bit. We present herein the architecture of the retina circuit on which we are currently working and show that it is possible to obtain approximate geometric moment values with it. The text was submitted by the authors in English.     

R3(Fe1-xCox)29-yCry(R=Gd,Sm)化合物相稳定性研究

在制备出Gd₃(Fe_1-xCo_x)_29-yCr_{y化合物基础上，成功制备出Sm3(Fe1-xCox)29 -yCry化合物，通过x射线衍射和热磁分析对R3(Fe1-x< /sub>Co x)29-yCry 关键词： 3(Fe1-xCox)29-yCry化合物')" href="#">R3(Fe1-xCox)29-yCry化合物 相结构 单轴磁晶各向异性}     

两不同奇相干态组成的第Ⅲ种四态叠加多模叠加态光场的等阶N次方H压缩

本文构造了由两不同奇相干态组成的第种四态叠加多模叠加态光场|ψ_o⁽⁴⁾,Ⅲ〉_q.利用新近建立的多模压缩态理论,详细研究了态|ψ_o⁽⁴⁾,Ⅲ〉_q的广义非线性等阶N次方H压缩特性,结果发现由多模奇相干态|ψ,_o〉_q和多模虚奇相干态|ψ_i⁽²⁾,_o〉_q这两者线性叠加所组成的新量子光场态、|ψ_o⁽⁴⁾,Ⅲ〉_q是一种典型的非经典光场.1)当腔模总数q与压缩阶数N的乘积q·N为偶数、且qN=4m(m=1,2,3,…,…)时,态|ψ_o⁽⁴⁾,Ⅲ〉_q恒处于等阶N-H最小测不准态,与其它参量的取值无关;2)当qN为偶数、且qN=4m-2(m=1,2,3,…,…)时,(i)态|ψ_o⁽⁴⁾,Ⅲ〉_q可呈现等阶N次方H压缩效应,其两正交分量的压缩特性呈现周期性变化的、互补对称关系;(ii)态|ψ_o⁽⁴⁾,Ⅲ〉_q可呈现“半相干态”效应.3)当qN为奇数时,态|ψ_o⁽⁴⁾,Ⅲ〉_q始终不呈现等阶N次方H压缩效应,也不处于等阶N-H最小测不准态,但在一定条件下可呈现“半相干态”效应.     

Investigation of refractive index modifications in CW CO2 laser written planar optical waveguides

This paper presents the measurement of the refractive index profile of buried channel waveguides fabricated by a CW CO₂ direct writing technique. A reflectance method is used to assess the refractive index distribution n(x,y) in these structures as it is a key parameter determining the propagation properties of guided wave devices. Beam propagation method (BMP) is used with experimentally determined cross-sectional data and refractive index profile to model the waveguides. The spatial resolution is 1.3 μm and, 5.10⁻⁴ for the refractive index.     

Polynomial chaos representation of spatio-temporal random fields from experimental measurements

Two numerical techniques are proposed to construct a polynomial chaos (PC) representation of an arbitrary second-order random vector. In the first approach, a PC representation is constructed by matching a target joint probability density function (pdf) based on sequential conditioning (a sequence of conditional probability relations) in conjunction with the Rosenblatt transformation. In the second approach, the PC representation is obtained by having recourse to the Rosenblatt transformation and simultaneously matching a set of target marginal pdfs and target Spearman’s rank correlation coefficient (SRCC) matrix. Both techniques are applied to model an experimental spatio-temporal data set, exhibiting strong non-stationary and non-Gaussian features. The data consists of a set of oceanographic temperature records obtained from a shallow-water acoustics transmission experiment [1]. The measurement data, observed over a finite denumerable subset of the indexing set of the random process, is treated as a collection of observed samples of a second-order random vector that can be treated as a finite-dimensional approximation of the original random field. A set of properly ordered conditional pdfs, that uniquely characterizes the target joint pdf, in the first approach and a set of target marginal pdfs and a target SRCC matrix, in the second approach, are estimated from available experimental data. Digital realizations sampled from the constructed PC representations based on both schemes capture the observed statistical characteristics of the experimental data with sufficient accuracy. The relative advantages and disadvantages of the two proposed techniques are also highlighted.     

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Radiative corrections to positronium decay

In this work a method for calculating radiative corrections to positronium decay is presented that is direct, and allows for a systematic extension applicable to the calculation of corrections beyond the first [o(α)] correction. An expression for the decay amplitude in terms of the Bethe-Salpeter wavefunction is employed. The Bethe-Salpeter wavefunction is evaluated perturbatively in a scheme having a lowest-order bound state equation that is exactly soluble. The decay amplitude is evaluated in Coulomb gauge, without the introduction of a photon mass. One-loop renormalization in Coulomb gauge is shown to be consistent. Using this method the known analytic result for the o(α) correction to the parapositronium decay rate is obtained. The same method is applied to orthopositronium, and the existing theoretical discrepancy in the value of the o(α) correction to the decay rate is resolved. This o(α) correction is obtained with an error which corresponds to an uncertainty in the total rate much smaller than α²Γ_LO (where Γ_LO is the lowest-order rate). Also, the o(α) correction to the differential decay rate is computed for the first time.     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .