DOI: 10.1145/2240236.2240238

Composable trees for Configurable Behavior

IcOncur whOleheartedly with the composability benefits Bri- an Beckman outlined in his ar- ticle “Why LINQ Matters: Cloud Composability Guaranteed” (Apr. 2012) due to my experience using composability principles to design and implement the message-dissemination mechanism for a mobile ad hoc router in a proprietary network. In it, the message-dissemination functionality of the router emerges from the aggregation of approximately 1,500

nodes in a composable tree that resembles a large version of the lambda-tree diagrams in the article. However, instead of being LINQ-based, each node represents a control element (such as if/else, for-loop, and Boolean operations nodes), as well as nodes that directly access message attributes. Each incoming message traverses the composable tree, with control nodes directing it through pertinent branches based on message attributes (such as message type, timestamp, and sender’s location) until the message reaches processing nodes that complete the dissemination.

Since assembling and maintaining a 1,500-node tree within the code base would be daunting, a parser assembles

 

Nodes verified independently. Verifying the if/else, message-timestamp, and other nodes can be done in isolation;

Routing rules modified for unit testing. As the routing rules mature, their execution requires a full lab- or field-configuration environment, making it difficult to test new features; a quick simplification of a local copy of the DSL specification defines routing rules that bypass irrelevant lab/field constraints while focusing on the feature being tested on the developer’s desktop;

 

a http://en.wikipedia.org/wiki/Domain-specific_ language

Scalable and robust. New routing rules can be added to DSL specification; new routing concepts can be added through the definition of new node types; and new techniques can be added to the overall design; and

Each message traversal recorded by the composable tree. Each node in the composable tree logs a brief one-line statement describing what it was doing and why the message chose a particular traversal path; the aggregation of these statements provides an itinerary describing the journey of each message traversal through the composable tree for confirmation or debugging.

My experience with composable trees defined through a DSL has been so positive I would definitely consider using the technique again to solve problems that are limited in scope but unlimited in variation.

Jim humelsine, Neptune, NJ

Model Dependence in
Sample-Size Calculation

We wish to clarify and expand on several points raised by Martin Schmettow in his article “Sample Size in Usability Studies” (Apr. 2012) regarding sample-size calculation in usability engineering, emphasizing the challenges of calculating sample size for binomial-type studies and identifying promising methodologies for future investigation.

Schmettow interpreted “ overdispersion” as an indication of the variability of the parameter p; that is, when n Bernoulli trials are correlated (dependent), the variance can be shown as np( 1–p) ( 1+C), where C is the correlation parameter, and when C>0 the result is overdispersion. When the Bernoulli trials are negatively correlated, or C<0, the result is “underdispersion.” If the trials are independent, then C=0, corresponding to the binomial model. Bernoulli trials may thus result in overdispersion or underdispersion; in practice, overdispersion is more common due to the heterogeneity of populations/samples.

A widely used approach for model-
ing an overdispersed binomial model
is to consider p as a random variable to
account for all uncertainty. A common
model for p is the beta distribution that
leads to a well-known prototype model
for overdispersion, the “beta-binomial
distribution.” Note this model as-
sumes a particular parametric distri-
bution of the random variable p. How-
ever, sample-size calculations based
on this paradigm also involve compu-
tational challenges; M’Lan et al. 1 con-
cluded that choosing the criterion for
sample-size determination from the
many criteria in the literature is ulti-
mately based on personal taste. Note,
too, that Schmettow’s “zero-truncated
logit-normal binomial model” follows
this scheme. To the best of our knowl-
edge, the Bernstein–Dirichlet process
is a promising family for such a mod-
eling framework; a nice feature of the
related distribution of p is that any den-
sity in (0, 1] can be approximated by
the Bernstein polynomial.

Reference

1. m’lan, C.e., joseph, l., and Wolfson, D.b. bayesian sample size determination for binomial proportions. Bayesian Analysis 3, 2 (feb. 2008), 269–296.

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