Modelling and optimizing a system for testing electronic circuit boards.

In this article we consider a difficult combinatorial optimization problem arising from the operation of a system for testing electronic circuit boards (ECB). This problem was proposed to us by a company that makes a system for testing ECBs and is looking for an efficient way of planning the tests on any given ECB. Because of its difficulty, we first split the problem into a covering subproblem and a sequencing subproblem. We also give a global formulation of the test planning problem. Then we present and discuss results pertaining to the covering and sequencing subproblems. These results demonstrate that their solution yields testing plans that are much better than those currently used by the company. Finally we conclude our article by outlining avenues for future research.

The Latent Structure of Dictionaries.

How many words-and which ones-are sufficient to define all other words? When dictionaries are analyzed as directed graphs with links from defining words to defined words, they reveal a latent structure. Recursively removing all words that are reachable by definition but that do not define any further words reduces the dictionary to a Kernel of about 10% of its size. This is still not the smallest number of words that can define all the rest. About 75% of the Kernel turns out to be its Core, a "Strongly Connected Subset" of words with a definitional path to and from any pair of its words and no word's definition depending on a word outside the set. But the Core cannot define all the rest of the dictionary. The 25% of the Kernel surrounding the Core consists of small strongly connected subsets of words: the Satellites. The size of the smallest set of words that can define all the rest-the graph's "minimum feedback vertex set" or MinSet-is about 1% of the dictionary, about 15% of the Kernel, and part-Core/part-Satellite. But every dictionary has a huge number of MinSets. The Core words are learned earlier, more frequent, and less concrete than the Satellites, which are in turn learned earlier, more frequent, but more concrete than the rest of the Dictionary. In principle, only one MinSet's words would need to be grounded through the sensorimotor capacity to recognize and categorize their referents. In a dual-code sensorimotor/symbolic model of the mental lexicon, the symbolic code could do all the rest through recombinatory definition.

Optimal optode montage on electroencephalography/functional near-infrared spectroscopy caps dedicated to study epileptic discharges.

Functional near-infrared spectroscopy (fNIRS), acquired simultaneously with electroencephalography (EEG), allows the investigation of hemodynamic brain responses to epileptic activity. Because the presumed epileptogenic focus is patient-specific, an appropriate source/detector (SD) montage has to be reconfigured for each patient. The combination of EEG and fNIRS, however, entails several constraints on montages, and finding an optimal arrangement of optodes on the cap is an important issue. We present a method for computing an optimal SD montage on an EEG/fNIRS cap that focuses on one or several specific brain regions; the montage maximizes the spatial sensitivity. We formulate this optimization problem as a linear integer programming problem. The method was evaluated on two EEG/fNIRS caps. We simulated absorbers at different locations on a head model and generated realistic optical density maps on the scalp. We found that the maps of optimal SD montages had spatial resolution properties comparable to those of regular SD arrangements for the whole head with significantly fewer sensors than regular SD arrangements. In addition, we observed that optimal montages yielded improved spatial density of fNIRS measurements over the targeted regions together with an increase in signal-to-noise ratio.