Approximation Algorithms for Covering/Packing Integer Programs

Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min {c.x: x in Z^n_+, Ax > a, Bx < b, x < d}. We give a bicriteria-approximation algorithm that, given epsilon in (0, 1], finds a solution of cost O(ln(m)/epsilon^2) times optimal, meeting the covering constraints (Ax > a) and multiplicity constraints (x < d), and satisfying Bx < (1 + epsilon)b + beta, where beta is the vector of row sums beta_i = sum_j B_ij. Here m denotes the number of rows of A. This gives an O(ln m)-approximation algorithm for CIP -- minimum-cost covering integer programs with multiplicity constraints, i.e., the special case when there are no packing constraints Bx < b. The previous best approximation ratio has been O(ln(max_j sum_i A_ij)) since 1982. CIP contains the set cover problem as a special case, so O(ln m)-approximation is the best possible unless P=NP.Comment: Preliminary version appeared in IEEE Symposium on Foundations of Computer Science (2001). To appear in Journal of Computer and System Science

A Motion Illusion Reveals Mechanisms of Perceptual Stabilization

Visual illusions are valuable tools for the scientific examination of the mechanisms underlying perception. In the peripheral drift illusion special drift patterns appear to move although they are static. During fixation small involuntary eye movements generate retinal image slips which need to be suppressed for stable perception. Here we show that the peripheral drift illusion reveals the mechanisms of perceptual stabilization associated with these micromovements. In a series of experiments we found that illusory motion was only observed in the peripheral visual field. The strength of illusory motion varied with the degree of micromovements. However, drift patterns presented in the central (but not the peripheral) visual field modulated the strength of illusory peripheral motion. Moreover, although central drift patterns were not perceived as moving, they elicited illusory motion of neutral peripheral patterns. Central drift patterns modulated illusory peripheral motion even when micromovements remained constant. Interestingly, perceptual stabilization was only affected by static drift patterns, but not by real motion signals. Our findings suggest that perceptual instabilities caused by fixational eye movements are corrected by a mechanism that relies on visual rather than extraretinal (proprioceptive or motor) signals, and that drift patterns systematically bias this compensatory mechanism. These mechanisms may be revealed by utilizing static visual patterns that give rise to the peripheral drift illusion, but remain undetected with other patterns. Accordingly, the peripheral drift illusion is of unique value for examining processes of perceptual stabilization

Phrase Frequency Effects in Language Production

A classic debate in the psychology of language concerns the question of the grain-size of the linguistic information that is stored in memory. One view is that only morphologically simple forms are stored (e.g., ‘car’, ‘red’), and that more complex forms of language such as multi-word phrases (e.g., ‘red car’) are generated on-line from the simple forms. In two experiments we tested this view. In Experiment 1, participants produced noun+adjective and noun+noun phrases that were elicited by experimental displays consisting of colored line drawings and two superimposed line drawings. In Experiment 2, participants produced noun+adjective and determiner+noun+adjective utterances elicited by colored line drawings. In both experiments, naming latencies decreased with increasing frequency of the multi-word phrase, and were unaffected by the frequency of the object name in the utterance. These results suggest that the language system is sensitive to the distribution of linguistic information at grain-sizes beyond individual words

The developmental pattern of stimulus and response interference in a color-object Stroop task: an ERP study

<p>Abstract</p> <p>Background</p> <p>Several studies have shown that Stroop interference is stronger in children than in adults. However, in a standard Stroop paradigm, stimulus interference and response interference are confounded. The purpose of the present study was to determine whether interference at the stimulus level and the response level are subject to distinct maturational patterns across childhood. Three groups of children (6–7 year-olds, 8–9 year-olds, and 10–12 year-olds) and a group of adults performed a manual Color-Object Stroop designed to disentangle stimulus interference and response interference. This was accomplished by comparing three trial types. In congruent (C) trials there was no interference. In stimulus incongruent (SI) trials there was only stimulus interference. In response incongruent (RI) trials there was stimulus interference and response interference. Stimulus interference and response interference were measured by a comparison of SI with C, and RI with SI trials, respectively. Event-related potentials (ERPs) were measured to study the temporal dynamics of these processes of interference.</p> <p>Results</p> <p>There was no behavioral evidence for stimulus interference in any of the groups, but in 6–7 year-old children ERPs in the SI condition in comparison with the C condition showed an occipital P1-reduction (80–140 ms) and a widely distributed amplitude enhancement of a negative component followed by an amplitude reduction of a positive component (400–560 ms). For response interference, all groups showed a comparable reaction time (RT) delay, but children made more errors than adults. ERPs in the RI condition in comparison with the SI condition showed an amplitude reduction of a positive component over lateral parietal (-occipital) sites in 10–12 year-olds and adults (300–540 ms), and a widely distributed amplitude enhancement of a positive component in all age groups (680–960 ms). The size of the enhancement correlated positively with the RT response interference effect.</p> <p>Conclusion</p> <p>Although processes of stimulus interference control as measured with the color-object Stroop task seem to reach mature levels relatively early in childhood (6–7 years), development of response interference control appears to continue into late adolescence as 10–12 year-olds were still more susceptible to errors of response interference than adults.</p