We present a tree di erence algorithm with expected sequential execution timeO(n log log n) and expected parallel execution time of O(log n), for trees of size n. The algorithm assumes unique labels and permits operations only on leaves and frontier subtrees. Despite these limitations, it can be useful in the analysis of structured text. 1 Applications of Tree Di erence In this paper we describ...

TD( ) is a popular family of algorithms for approximate policy evaluation in large MDPs. TD( ) works by incrementally updating the value function after each observed transition. It has two major drawbacks: it makes ine cient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squ...

It is shown that there does not exist a reversible abelian Hadamard diierence set in

Conventional numerical di erentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simpli ed to one of the nite di erence approximations based on Taylor series, and closed-form expressions of these nite di erence formulas have already been presented. In this paper, we present new nite di erence formulas, which are more accurate than the available ones, espe...

A family of scaling corrections aimed to improve the chi-square approximation of goodness-oft test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall t of a model, but on...

The concept of weighted f Gini mean di¤ erence for convex and symmetric functions in linear spaces is introduced. Some fundamental inequalities and applications for norms are also provided. 1. Introduction The Gini mean di¤erence of the sample a = (a1; : : : ; an) 2 R is de…ned by G (a) = 1 2n2 n X

We propose a generalization of the Hukuhara di¤erence. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara di¤erence of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is suggested to attempt a generalization of division for real intervals.

A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

The maximum time diierence pipelining is an eeective way to increase the clock rate of a circuit. The maximum time diierence pipelined 8 8 2's complement multiplier based on a 1:5m semi-custom HCMOS process discussed in this paper can work nearly three times faster than an ordinary multiplier based on the same technology. Test result shows the majority of the multiplier's time diierence is caus...

This paper considers the security of iterated block ciphers against the di erential cryptanalysis introduced by Biham and Shamir. Di erential cryptanalysis is a chosen-plaintext attack on secret-key block ciphers that are based on iterating a cryptographically weak function r times (e.g., the 16-round Data Encryption Standard (DES) ). It is shown that the success of such attacks on an r-round c...