A notification service alerts a large number of recipients to attend to important or emergency events. Prompt notification using multiple modes is critical to handle a disaster. This paper proposes an "escalation hierarchy" method as an enhancement to the combinatorial testing approach to provide capacity evaluation of a notification service involving interaction of multiple factors. Our trial of the method on an industrial large-scale notification service showed the effectiveness of our method in reducing testing efforts through automating both consistency checking of measurement data and identification of causes for capacity overflow.

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles. In this paper we consider the basic building blocks of these rules, irreducible Apollonian configurations. Our main result is to show how to find a small field that can realize such a configuration and also give a method to relate the bends of the new circles to the bends of the circles forming the curvilinear triangle.

We present LEASE, a new system and framework for location estimation assisted by stationary emitters for indoor RF wireless networks. Unlike previous studies, we emphasize the deployment aspect of location estimation engines. Motivated thus, we present an adaptable infrastructure-based system that uses a small number of stationary emitters (SEs) and sniffers employed in a novel way to locate standard wireless clients in an enterprise. We present the components of the system and its architecture, and new non-parametric techniques for location estimation that work with a small number of SEs. Our techniques for location estimation can also be used in a client-based deployment. We present experimental results of using our techniques at two sites demonstrating the ability to perform location estimation with good accuracy in our new adaptable framework.

Recently, a class of experimental designs has been devised that guarantee input domain coverage up to all combinations of k test factors taken t at a time.With such designs, all pairwise combinations (or triplets or quadruplets, etc.) are selected at least once.To evaluate their applicability to software testing, we analyzed the extent to which software coverage (i.e., code execution) achieved by these designs for t=1, ... ,k is representative of that achieved by exhaustively testing all factor combinations.The block coverage obtained for t;5;2 was comparable with that achieved by exhaustively testing all factor combinations but higher-order values of t were required for path coverage.Implications of these results for software testing are discussed.

It is noted that the developers of large software systems must decide how much software should be tested before releasing it. An explicit tradeoff between the costs of testing and releasing is considered. The former may include the opportunity cost of continued testing, and the latter may include the cost of customer dissatisfaction and of fixing faults found in the field. Exact stopping rules were obtained by Dalal and Mallows (J. Amer., Statist. Assoc., vol.83, p.872, 1988), under the assumption that the distribution of the fault finding rate is known. Here, two important variants where the fault finding distribution is not completely known are considered. They are (i) the distribution is exponential with unknown mean and (ii) the distribution is locally exponential with the rate changing smoothly over time. New procedures for both cases are presented. In case (i) it is shown how to incorporate information from related projects and subjective inputs. Several novel graphical procedures which are easy to implement are proposed, and these are illustrated for data from a large telecommunications software system.>

Lagarias and Reeds showed that iterates $Q^{(i)} (x) = Q(Q^{(i - 1)} (x))$ of a polynomial $Q (x)$ satisfy certain identities. It is shown that their result can be interpreted as a symbolic generalization of the result “the $(p + 1)$st-difference of a polynomial of degree p is zero,” in which powers of an independent variable are replaced by iterates of a polynomial transformation. $(Q,x)$-binomial coefficients $\begin{bmatrix} n \\ i \end{bmatrix}_{Q,x} $ are defined where Q is a polynomial and x a scalar, which are defined by a two-term recurrence showing that $\begin{bmatrix} n \\ i \end{bmatrix}_{Q,x} $ are in the polynomial ring $\mathbb{Z} [ Q,x ]$ generated by x and the coefficients of Q. For polynomial $P(x)$ of degree n, the iterates $Q^{(k)} (x)$ satisfy the identity $P(Q^{(n + 1)} (x)) = \sum_{j = 0}^n ( - 1)^j \begin{bmatrix} n \\ j \end{bmatrix}_{Q,x} P(Q^{(j)} (x))$ . If $Q(x) = qx + a$ is linear, then $\begin{bmatrix} n \\ j \end{bmatrix}_{Q,x} = q^{(\begin{smallmatrix} {n - j} \\ 2 \end{smallmatrix})} \begin{bmatrix} n \\ j \end{bmatrix}_q $ where $\left[ {\begin{array}{*{20}c} n \\ j \\ \end{array} } \right]_q $, is a q-binomial coefficient. It is shown by example that other q-formulae have $(Q,x)$-analogues.

The class of nonnegative definite Toeplitz matrices that can be embedded in nonnegative definite circulant matrices of a larger size is characterized. An equivalent characterization in terms of the spectrum of the underlying process is also presented, together with the corresponding extremal processes. It is shown that a given finite-duration sequence rho can be extended to be the covariance of a periodic stationary processes whenever the Toeplitz matrix R generated by this sequence is strictly positive definite. The sequence rho =1, cos alpha , cos 2 alpha with ( alpha / pi ) irrational, which has a unique nonperiodic extension as a covariance sequence, demonstrates that the strictness is needed. A simple constructive proof supplies a bound on the abovementioned period in terms of the minimal eigenvalue of R. It also yields, under the same conditions, an extension of rho to covariances that eventually decay to zero. For the maximum-likelihood estimate of the covariance of a stationary Gaussian process, the extension length required for using the estimate-maximize iterative algorithm is determined.>

Gleason has recently shown that the weight enumerators of binary and ternary self-dual codes are polynomials in two given polynomials. In this paper it is shown that classical invariant theory permits a straightforward and systematic proof of Gleason's theorems and their generalizations. The joint weight enumerator of two codes (analogous to the joint density function of two random variables) is defined and shown to satisfy a MacWilliams theorem. Invariant theory is then applied to generalize Gleason's theorem to the complete weight enumerator of self-dual codes overGF(3), the Lee metric enumerator overGF(5)(given by Klein in 1884!) and overGF(7)(given by Maschke in 1893!), the Hamming enumerator overGF(q), and overGF(4)with all weights divisible by 2, the joint enumerator of two self-dual codes overGF(2), and a number of other results.