Necessary Conditions for Differentiability of Distance Functions

Necessary conditions for the Gâteaux differentiability of the distance function to a set are considered. A series of characterizing results is obtained.     

Bit-parallel approximate string matching algorithms with transposition

Using bit-parallelism has resulted in fast and practical algorithms for approximate string matching under Levenshtein edit distance, which permits a single edit operation to insert, delete or substitute a character. Depending on the parameters of the search, currently the fastest non-filtering algorithms in practice are the O(km/wn) algorithm of Wu and Manber, the O((k+2)(m−k)/wn) algorithm of Baeza-Yates and Navarro, and the O(m/wn) algorithm of Myers, where m is the pattern length, n is the text length, k is the error threshold and w is the computer word size. In this paper we discuss a uniform way of modifying each of these algorithms to permit also a fourth type of edit operation: transposing two adjacent characters in the pattern. This type of edit distance is also known as Damerau edit distance. In the end we also present an experimental comparison of the resulting algorithms.     

基于MMD算法的HMM参数重估计的矩阵表示

本文提出的MMD算法用于提高模型区别错误信息和正确信息的能力．利用该算法在对模型的参数进行重估计时．涉及到复杂的目标函数的梯度运算．击运用矩阵运算使得梯度运算变得简单明了，因此本文给出了MMD算法下的HMM参数重估计的矩阵表示形式并给出了证明．     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Pearson-χ~2距离的若干性质

本文对数理统计中常用的 Pearson- χ2距离的分析特性进行了讨论 ,得到了这一距离的一些解析性质 ,最后我们还给出了几个常用距离的关系 .     

Violin frequency response - bridge mobility and bridge feet distance

Good violins have a broad hill in the 2-3 kHz range of their frequency response. This hill has previously been attributed to the first in-plane resonance of the violin bridge. Experiments prove, however, that the hill is the result of two forces acting in opposite directions at the bridge feet. The experiments reported here show that the hill can be “tuned” by altering the distance between the bridge feet. It can be tuned both in terms of frequency and level but the properties of the violin cannot be neglected.     

Simultaneous approximation for the Bézier variant of Baskakov-Beta operators

In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation.     

Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.