Bounds on the capacity of constrained two-dimensional (2-D) codes are presented. The bounds of Calkin and Wilf apply to first-order symmetric constraints. The bounds are generalized in a weaker form to higher order and nonsymmetric constraints. Results are given for constraints specified by run-length limits or a minimum distance between pixels of a given value.

We show that there is no batch-means estimation procedure for consistently estimating the asymptotic variance when the number of batches is held fixed as the run length increases. This result suggests that the number of batches should increase as the run length increases for sequential stopping rules based on batch means.

For many Internet applications, the ability to protect the identity of participants in a distributed applications is critical. For such applications, a number of anonymous communication systems have been realized over the recent years. The effectiveness of these systems relies greatly on the way messages are routed among the participants. (We call this the route selection strategy.) In this pap...

In a recent paper, Brlek, Jamet and Paquin showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: are they the only ones? If no, what do the infinite smooth words that are also Lyndon words look like? In this paper, we give the answer, proving that the only infinite smooth Lyndon words are m{a<b}, with a, b even, m{1<b} and ∆ −1 1 ...

in statistical quality control a very widely used measure is average run length (arl) which may be worked out by different methods like integral equation, approximations, and monte carlo simulations. the arl measure and the other related measures are of major significance in every type of production process. an omission in its computation (and hence its related measures such as extra quadratic ...

in many industrial and non-industrial applications the quality of a process or product is characterized by a relationship between a response variable and one or more explanatory variables. this relationship is referred to as profile. in the past decade, profile monitoring has been extensively studied under the normal response variable, but it has paid a little attention to the profile with the ...