On metrics matched to the discrete memoryless channel

A sequence of metrics {D_N} is said to be additive and matched to a discrete memoryless channel (DMC) if D_N is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum D_N-distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 (2).     

Fixed point properties of the binomial function

Fixed point properties of the binomial function

are developed. It is shown that for any 1 < L < N, T^L_Nhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability p_FAand an initial detection probability p_D, then T^L_N(p_FA) < p_FAand T^L_N(p_D) > p_Dif, and only if, p_FA < p? < p_D. When this condition is satisfied, as N → ∞, T^L_N(p_FA) → 0 and T^L_N(p_D → 1.     

Towards the minimum-cost control of target nodes in directed networks with linear dynamics

Determining an input matrix, i.e., locating predefined number of nodes (named “key nodes”) connected to external control sources that provide control signals, so as to minimize the cost of controlling a preselected subset of nodes (named “target nodes”) in directed networks is an outstanding issue. This problem arises especially in large natural and technological networks. To address this issue, we focus on directed networks with linear dynamics and propose an iterative method, termed as “L₀-norm constraint based projected gradient method” (LPGM) in which the input matrix B is involved as a matrix variable. By introducing a chain rule for matrix differentiation, the gradient of the cost function with respect to B can be derived. This allows us to search B by applying probabilistic projection operator between two spaces, i.e., a real valued matrix space R^N?×?M and a L₀ norm matrix space $R_{L_0}^{N\times M}$ by restricting the L₀ norm of B as a fixed value of M. Then, the nodes that correspond to the M nonzero elements of the obtained input matrix (denoted as $B^{L_0}$) are selected as M key nodes, and each external control source is connected to a single key node. Simulation examples in real-life networks are presented to verify the potential of the proposed method. An interesting phenomenon we uncovered is that generally the control cost of scale free (SF) networks is higher than Erdos-Renyi (ER) networks using the same number of external control sources to control the same size of target nodes of networks with the same network size and mean degree. This work will deepen the understanding of optimal target control problems and provide new insights to locate key nodes for achieving minimum-cost control of target nodes in directed networks.     

基于国产GF-1遥感影像的山区细小水体提取方法研究

以国产"高分一号"16m遥感图像为数据源,在特克斯县选取两个研究区域,针对山区细小线状河流提取难度较大的问题,使用基于规则的面向对象的方法实现了对山区细小水体的精确化提取。首先,在总结前人选择最优分割尺度的基础上,考虑了各层权重信息,针对某一特定地物,提出了指示最优分割尺度的指标——改进的与邻域绝对均值差分方差比(MRMAS),并由此获取了影像上细小水体的最优分割尺度。其次,为区分水体和山体阴影,构建阴影水体指数SWI=B1+B2-B4,成功剔除了绝大部分阴影信息。最后,利用形态学膨胀滤波及Pavlidis异步细化算法对提取的细小水体进行后处理,最终得到细小河流的矢量化水系图。实验结果表明,该方法可以完整、快速地提取出山区细小线状河流信息,总体精度在90%以上,Kappa系数在85%以上,有效排除阴影等暗色地物的干扰,基本消除椒盐噪声。该研究成果或对国产高分影像处理系统的研发与应用提供一定的科学参考。     

In vitro study of vitamin B6 status in cancer breast patients

There is ample evidence that vitamin status of an individual can have a profound influence on the resistance of Cancer. Pyridoxine is one of the water soluble vitamins playing an important role in various metabolic reactions. Aspartate aminotransferase and Alanine aminotransferase are pyridoxal phosphate requiring enzymes and their activities in erythrocytes have been used to assess the state of vitamin B₆ nutrition in man. We report here the erythrocyte transaminase levels in controls and patients with early and advanced cancer of breast. Thein vitro study of vitamin B₆ shows a marked difference in the per cent stimulation in patients as compared to the controls on addition of pyridoxal phosphate. The difference indicates a subclinical deficiency of vitamin B₆. The possibility exists that the rapid progression of the disease could be due to lack of host resistance caused by the deficiency of vitamin B₆. The possibility of an effective treatment response after enhancing the vitamin B₆ status is being looked into.     

On convergence criteria for jarratt's method

Let f(χ) together with its first two derivatives be continuous in the domain D and additionally let χ_M?D be an extremum (or turning point) of this function. Also, let χ_n+1 = T (χ_n,χ_n-1,χ_n-2) be Jarratt's Method for computing the extremum (or turning point) of a function. Criteria are demonstrated which insure that, for any triple of initial assumptions (χ₁,χ₀,χ_-1)?D, Jarratt's Method, converges to the extremum of f(χ), and that from and after some n = N₀, the rate of convergence of this method increases steadily, finally becoming unbounded when the solution χ_M is attained.     

基于国产GF-1遥感影像的水体提取方法

山区水资源信息高精度提取是西北干旱区水文水循环及水资源利用等研究领域的核心热点问题,但山区由于各种限制因素,如阴影、积雪和山体裸地等,使得高分辨率遥感监测效果不佳。本文基于高分一号遥感影像,利用单波段阈值法、NDWI与多波段法进行特克斯河流域水体信息提取,通过分析3种水体提取方法的利弊,提出单波段阈值法与构建的阴影水体指数SWI=B₁+B₂-B₄相结合的决策树水体信息提取方法,用结合实地采样得到的混淆矩阵对水体区域的整体提取结果进行精度验证对比分析。实验结果表明,单波段阈值法易受山体阴影的影响,但受积雪与裸地的影响较小;NDWI法易受山区小面积阴影影响;多波段法提取水体信息较好,但受部分阴影与薄雪影响。决策树法能有效地消除积雪和裸地等气候环境的干扰,完整地提取水体信息,总体精度为92.34%以上,Kappa系数在0.82以上。     

Vitamin B<Subscript>12</Subscript> Immunoassay on Roche Elecsys 2010: Effects of High Excess Concentration of Serum Vitamin B<Subscript>12</Subscript> in CKD Patients on Parenteral Administration

Vitamin B₁₂ being water soluble is excreted in the urine when administered in excess. The probability of finding an abnormally excess serum concentration would be almost surreal. We report a peculiar clinical situation that may impact the vitamin B₁₂ immunoassay on the Roche Elecsys 2010 due to excess analyte concentration. In separate episodes (Feb and June 2010), the Biochemistry laboratory of a tertiary-care hospital, Kolkata, India, encountered two critically ill patients with background chronic kidney disease (CKD), low urine output, and on cyanocoabalamin supplementation, who had serum vitamin B₁₂ concentrations far exceeding expected values; even post dialysis. The B₁₂ assays (pmol/l) were performed using electrochemiluminiscence immunoassay on Roche Elecsys 2010, the assay validity confirmed by concomitant quality control runs. The immunoassays failed to deliver results, flagged with “signal level below limit”. Biotin therapy was ruled out as a possible interferent. In the first episode, re-assay of a repeat draw yielded same outcome; outsourcing on Immulite provided concentration of >738 pmol/l. Serial dilution gave result of >29520 pmol/l on Elecsys 2010. In the second, we gained from past experience. Vitamin B₁₂ concentration >59040 pmol/l was conveyed to the treating nephrologist the very day. The B₁₂ immunoassay on the Elecsys 2010 employs sequential incubation steps for competitive binding that is compromised in the event of abnormally excess B₁₂ concentration in patient sera akin to the prozone effect. This knowledge may be beneficial while assaying sera of CKD patients to avoid financial loss due unnecessary repeats and delay in turnaround time.     

Numerical modeling of MHD stability in a cylindrical configuration

A numerical modeling of natural convection under the influence of either axial (B_z) or radial (B_r) magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conducting fluid, is studied. The finite volume method is used to discretize the equations of continuity, Navier Stokes and energy. A computer program based on the SIMPLER algorithm is developed. The flow and temperature fields are presented by stream function and isotherms, respectively. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Grashof number, Gr_cr with the increase of the Hartmann number, Ha. The strongest stabilization of the convective flows occurs when the magnetic field is applied in the radial direction. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a radial magnetic field.     

A useful identity in circuit theory

A useful identity expressing the derivative of an unknown variable x_k of X with respect to an entry in the coefficient matrix of a linear system AX = B is presented. If the derivatives of x_k with respect to each entry of A or their combinations are required, then the identity avoids the repeated solution of the linear equations, and may result in a symbolic solution provided A^-1 is known. A method to measure the sensitivity in an n-port linear system is proposed, and its relationships to Kron's method of tearing and Branin's formulae are also discussed.     

Stable denominators for the simplification of z-Transfer Functions

A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m₁ and m₂ = m−m₁ zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m₁=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method.     

1, 25-Dihydroxycholecalciferol (1,25-(OH)<Subscript>2</Subscript> D<Subscript>3</Subscript>) levels in osteoporosis

In the present study primary involution osteoporosis and vitamin D levels were studied in 60 subjects including thirty controls. The biochemical analysis of serum calcium, phosphorus, ALP, albumin and vitamin D₃ (1,25-(OH)₂ D₃) levels were significantly decreased in osteoporotic patients when compared to non-osteoporotic control group. There was a significant correlation of magnitude of sun exposure with 1,25-(OH)₂ D₃ levels. Similarly, vitamin D intake in the diet has a significant correlation with 1,25-(OH)₂ D₃ concentration. However, no correlation could be obtained between vitamin D₃ levels with increasing age. Among the biochemical markers serum calcium, phosphorus, ALP and albumin could not be correlated with 1,25-(OH)₂ D₃ levels.     

On recursive averaging processes and Hilbert space extensions of the contraction mapping principle

If T maps a convex domain D_T into itself, and if {ω_n} is a real sequence with range in (0, 1] then the recursive averaging process,

$\text{X}{}_{\mathrm{n+1}}\text{=(1?omega;}{}_{\mathrm{n}}\text{)}\text{X}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{+ω}{}_{\mathrm{n}}\text{T}\text{x}{}_{\mathrm{n}}\text{,}\text{x}{}_0\text{=ξ?D}{}_{\mathrm{T}}$

generates a sequence {x?_n}; with range in D_T. Under suitable conditions on D_T, T and {ω_n} the sequence {x?_n} will converge in some sense to a fixed point of T. We prove that if D_T is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ω_n} satisfies the conditions,

$\text{ω}{}_{\mathrm{n}}\text{→ 0}$

and

$\text{∑}\text{n=0}\text{∞}\text{ω}{}_{\mathrm{n}}\text{=∞}$

then, for arbitrary ξ ? D_T, {x?_n} converges strongly to (the unique) fixed point of T. We also prove that if D_T and {ω_n} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? D_T, {x?_n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series.     

A modified PID controller (PIIσβD)

The purpose of this study is to modify the traditional PID controller in order to improve its performance (stability and tracking) by changing the length of integration interval. The performance of the traditional PID controller was improved by changing the length of integration interval to make the most of the returns of the PID and PI_σD controllers. The asymptotic stability domain, in terms of the feedback gains, is derived for systems of second order using the modified controller which will be identified as PII_σ^βD. Comparing this controller with the traditional PID controller and PI_σD controller proposed in [1], it proves that it is more accurate and more stable. For illustration and comparison, two examples have been simulated to evaluate the performance of the modified controller. All simulation results indicate that the modified controller is better than the traditional PID controller and the PI_σD controller from the accuracy and stability point of view.     

基于MODIS数据的泰国林地资源提取

遥感技术的发展为我们对世界资源的研究提供了新的手段,克服了世界资源研究过程中数据缺乏的困难。泰国曾经是林地资源丰富的国家,尤其是热带林地资源,但是近几十年来林地面积在不断减少,带来了一系列生态问题。选用MOD09Q1的1、2波段,MOD09A1的第6波段以及MOD11A2数据产品提取了泰国林地分布情况。由于泰国地处热带地区云雾噪音为林地的提取造成了很大的不确定性,为了有效去除云雾噪音影响,结合NDVI、NDSI、LST多参数在林地提取中的优势对泰国林地进行提取。采用泰国2003年统计年鉴提供的分省林地面积以及2003年p131r47和p131r48共2景ETM影像进行了精度验证。结果表明,利用多参数综合分类方法对林地提取精度较高,通过与2003年统计年鉴数据进行回归分析发现二者存在明显的线性关系,决定系数达到0.9264。     

Study on stability and stabilizability of discrete-time mean-field stochastic systems

This paper is to study the mean square stabilizability and regional stability of discrete-time mean-field stochastic systems. Firstly, a necessary and sufficient condition is presented via the spectrum of linear operator to illustrate the stabilizability of discrete-time mean-field stochastic systems. B(0, γ)-stabilizability is introduced and transformed into solving linear matrix inequalities (LMIs). Secondly, B_M-stability is characterized, especially, the stabilities of circular region, sector region and annulus regions are discussed extensively. Finally, as applications, it is shown that B(0, γ₁; γ₂)-stability has close relationship with the decay rate of the system state response and the Lyapunov exponent.     

Irradiation swelling,creep and thermal fatigue behaviors of LMFBR pressure vessels

The behaviors of irradiation swelling, irradiation creep and thermal-cycling fatigue induced by fast neutron fluence and developed in the LMFBR pressure vessels are analyzed on the basis of experimental data. From the interactions of the irradiation swelling, irradiation creep and thermal-cycling fatigue, the failure criterion for the design and safety surveillance of the pressure vessels can be expressed as a(frbuilt|t/t_c)^u+b(frbuilt|N/N_f)^v+c(?/?_s)^w=1, where t is time, t_c is creep rupture time, N is number of cycles, N_f is number of cycles to failure, ? is strain, ?_s is swelling strain to failure, and a, b, c, u, v and w are parameters or constants. The tangential tensile strain produced by the irradiation creep, thermal-cycling fatigue and hydrostatic pressure of the liquid sodium coolant may be combined together with the irradiation swelling strain ? as a whole. The inter-relationships between the behaviors of irradiation swelling, irradiation creep and thermal-cycling fatigue developed in the LMFBR pressure vessels are discussed.     

Plasma Homocysteine,Folate and Vitamin B<Subscript>12</Subscript> levels in senile cataract

Elevated plasma Homocysteine level is an independent risk factor for age related (senile) cataract. Certain nutritional deficiencies, in particular Folate, Vitamin B₁₂, Vitamin B₆ relate inversely with Homocysteine level. This study was undertaken to evaluate the plasma level of Vitamin B₁₂, Folate, and Homocysteine of cataract patients and to study the interplay between them. Serum Homocysteine level is significantly increased in cataract patients when compared with control (p< 0.001). There was a significant decrease in the level of Folate as compared with control (p<0.001). There was a negative correlation between Homocysteine vs. Vitamin B₁₂ (p<0.01) and Folate (p<0.01) in the Cataract patients. Our findings suggest that increased plasma Homocysteine level is associated with decreased plasma levels of Folate and VitaminB₁₂ in Cataract patients, which might have a possible role in the root cause of cataract pathogenesis.