Properties and Applications of Preimage Distributions of Perfect Nonlinear Functions

The preimage distributions of perfect nonlinear functions from an Abelian group of order $n$ to an Abelian group of order $3$ or $4$, respectively, are studied. Based on the properties of the preimage distributions of perfect nonlinear functions from an Abelian group of order $3^{r}$ to an Abelian group of order $3$, the weight distributions of the ternary linear codes $C_{Pi}$ from the perfect nonlinear functions $Pi (x)$ from $F_{3^{r}}$ to itself are determined. These results suggest that two open problems, proposed by Carlet, Ding, and Yuan in 2005 and 2006, respectively, are answered.      

关于完全非线性函数的非线性度的界

非线性函数在编码和密码领域中扮演着非常重要的角色,衡量函数的非线性性质很重要。非线性度和差分概率是衡量函数非线性性质的重要指标,差分概率均匀的函数称为具有完全非线性的函数。文中改进了Carlet和Ding所给出的完全非线性函数的非线性度的上界和下界,提出了更好的界的优化问题模型。     

Programmable Hash Functions and Their Applications

We introduce a new combinatorial primitive called programmable hash functions (PHFs). PHFs can be used to program the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard model realizations of PHFs (with different parameters).     

On Almost Perfect Nonlinear Functions Over$mmb F_2^n$

We investigate some open problems on almost perfect nonlinear (APN) functions over a finite field of characteristic 2. We provide new characterizations of APN functions and of APN permutations by means of their component functions. We generalize some results of Nyberg (1994) and strengthen a conjecture on the upper bound of nonlinearity of APN functions. We also focus on the case of quadratic functions. We contribute to the current works on APN quadratic functions by proving that a large class of quadratic functions cannot be APN     

Reconstructing Extended Perfect Binary One-Error-Correcting Codes From Their Minimum Distance Graphs

The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect binary one-error-correcting code from its minimum distance graph is presented. Consequently, inequivalent such codes have nonisomorphic minimum distance graphs. Moreover, it is shown that the automorphism group of a minimum distance graph is isomorphic to that of the corresponding code.      

两类Plateaued函数的Walsh谱值分布

Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr(R(x)) with n=3r or 4r variables, where r > 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.     

光子晶体光纤的非线性效应及其应用研究进展

光子晶体光纤在光器件的集成化、小型化乃至大幅降低其成本方面都有着重要的应用前景。介绍了光子晶体光纤的各类非线性效应及其潜在应用,重点讨论基于光子晶体光纤的光开关实现方案,并提出一种基于M Z干涉的光子晶体光纤光开关方案,对其可行性进行了探讨。     

On Characterizations of a Mixture of Exponential Distributions

Several results characterizing a mixture of exponential distributions are presented. Section 2 generalizes two of Govindarajulu's results, using sequences of moments of order statistics. A necessary and sufficient condition is given in section 3 that an absolutely continuous positive r.v. follow a mixture of two exponential distributions. The conditions are based on the absolute difference of two i.i.d. random variables. Using conditional s-expectations, we generalize Shanbhag's result, in section 4.     

Consonance Sets for 2-Parameter Weibull and Exponential Distributions

This paper describes a general method for constructing consonance sets based on the Kolmogorov-Smirnov goodness-of-fit statistic. The method is applied to constructing consonance sets for two widely applicable distributions in reliability, the 2-parameter Weibull and exponential distributions. The paper concludes with a numerical example.     

Nonlinear Regularization for Per Voxel Estimation of Magnetic Susceptibility Distributions From MRI Field Maps

Magnetic susceptibility is an important physical property of tissues, and can be used as a contrast mechanism in magnetic resonance imaging (MRI). Recently, targeting contrast agents by conjugation with signaling molecules and labeling stem cells with contrast agents have become feasible. These contrast agents are strongly paramagnetic, and the ability to quantify magnetic susceptibility could allow accurate measurement of signaling and cell localization. Presented here is a technique to estimate arbitrary magnetic susceptibility distributions by solving an ill-posed inversion problem from field maps obtained in an MRI scanner. Two regularization strategies are considered: conventional Tikhonov regularization and a sparsity promoting nonlinear regularization using the $ell_{1}$ norm. Proof of concept is demonstrated using numerical simulations, phantoms, and in a stroke model in a rat. Initial experience indicates that the nonlinear regularization better suppresses noise and streaking artifacts common in susceptibility estimation.      

Bessel函数与三角函数之积的级数展开及在微波滤波器中的应用

根据对平面波函数运用Fourier-Bessel定理,经过一系列推导并进行反Fourier变换,得到了直角坐标系下Bessel函数与三角函数之积的一种级数展开,该表达式应用到矩-圆波导结的计算中,能解析地推出其广义S参数,得到与文献和HFSS软件较为一致的结果.计算了Ku和Ka频段多种尺寸的有厚度的矩形孔的耦合系数,并与文献、实验数据进行了比较,吻合较好,设计了一个Ku频段6阶类椭圆函数滤波器,实验性能与理论结果一致.     

Eigenvalue Distributions of Sums and Products of Large Random Matrices Via Incremental Matrix Expansions

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using - and -transforms in free probability theory. We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free. This is used to determine the asymptotic signal-to-interference-ratio of a multiuser code-division multiple-access (CDMA) system with a minimum mean-square error linear receiver.     

高非线性指数的压敏瓷

传统配方制成的压敏瓷元件,非线性指数较低,一般不超过60。在负荷时,元件的非线性指数会不断降低,电气性能也很快劣化。在高纯氧化锌粉中添加适量Zn、BaCO3、TiO2等添加剂配制成的瓷料,按传统工艺制成的压敏瓷元件,非线性指数较高,可达100,其压敏特性好,残压低,运行稳定可靠。     

Discriminating Among the Log-Normal, Weibull, and Generalized Exponential Distributions

We consider model selection and discrimination among three important lifetime distributions. These three distributions have been used quite effectively to analyze lifetime data. We study the probability of correct selection using the maximized likelihood method, as it has been used in the literature. We further compute the asymptotic probability of correct selection, and compare the theoretical, and simulation results for different sample sizes, and for different model parameters. The results have been extended for Type-I censored data also. The theoretical, and simulation results match quite well. Two real data sets have been analyzed for illustrative purposes. We also suggest a method to determine the minimum sample size required to discriminate among the three distributions for a given probability of correct selection, and a user specified protection level.     

A Test of the Equality of Survival Distributions Based on Paired Observations from Conditionally Independent Exponential Distributions

A model describes the joint distribution of paired survival times based on certain reasonable assumptions appropriate for biological data generated in a clinical trial setting or for certain failure data. An exact parametric test for equality of mean survival times for data following this distribution is developed. The power of the exact test is investigated by a computer simulation study for various sample sizes and values of the model parameters and compared to that of alternative tests. Heretofore, researchers desiring to analyze paired survival data have resorted to paired t tests or nonparametric procedures such as the sign test or signed ranks test. The t-test is invalid for non-normally distributed data although the robustness of the test might minimize the difficulty. The nonparametric tests, by their nature, fail to use the data completely. This paper presents an exact parametric test based on a distribution whose justification requires rather modest and reasonable assumptions. Critical values for the test can be obtained from a table of the chi-square distribution. This exact test appears to be a viable alternative to non-parametric approaches to the analysis of paired survival data. It is extremely easy to calculate on a hand calculator. In fact, since no data storage is required (unlike the signed ranks test), the calculations can be readily programmed on a programmable calculator. The modeling of bivariate and multivariate survival data we believe has not been adequately addressed in the statistical and engineering literature. We hope that this paper will spark additional work.     

具有均匀差分分布的一类置换

本文研究了置换的差分分布，证明了如果一个置换的坐标函数的每个线性组合都有非零线性结构，则该置换具有均匀差分分布的充要条件，是它的坐标函数的每个非零线性组合都是只有一个恒变线性结构的部分ｂｅｎｔ函数，并且它的坐标函数的不同非零线性组合所具有的非零线性结构互不相同。还证明了如果一个偶数维置换的坐标函数的每个线性组合都有非零线性结构，则该置换一定不具有均匀差分分布。本文还研究了Ｋ．Ｎｙｂｅｒｇ构造的能够达到最大非线性度的置换，证明了这些置换都具有均匀差分分布，从而解决了具有均匀差分分布的置换的存在性问题。     

A New Family of Ternary Almost Perfect Nonlinear Mappings

A mapping f(x) from GF(pⁿ) to GF(pⁿ) is differentially k-uniform if k is the maximum number of solutions x isin GF(pⁿ) of f(x+a) - f(x) = b, where a, b isin GF(pⁿ) and a ne 0. A 2-uniform mapping is called almost perfect nonlinear (APN). This correspondence describes new families of ternary APN mappings over GF(3ⁿ), n>3 odd, of the form f(x) = ux^d + x^{d 2} where d₁ = (3^n-1)/2 - 1 and d₂ = 3ⁿ - 2.