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Human visual grouping processes consolidate independent visual objects into grouped visual features on the basis of shared characteristics; these visual features can themselves be grouped, resulting in a hierarchical representation of visual grouping information. This “grouping hierarchy“ promotes ef- ficient attention in the support of goal-directed behavior, but improper grouping of elements of a visual scene can also re- sult in critical behavioral errors. Understanding of how visual object/features characteristics such as size and form influences perception of hierarchical visual groups can further theory of human visual grouping behavior and contribute to effective in- terface design. In the present study, participants provided free- response groupings of a set of stimuli that contained consistent structural relationships between a limited set of visual features. These grouping patterns were evaluated for relationships be- tween specific characteristics of the constituent visual features and the distribution of features across levels of the indicated grouping hierarchy. We observed that while the relative size of the visual features differentiated groupings across levels of the grouping hierarchy, the form of visual objects and features was more likely to distinguish separate groups within a partic- ular level of hierarchy. These consistent relationships between visual feature characteristics and placement within a grouping hierarchy can be leveraged to advance computational theories of human visual grouping behavior, which can in turn be ap- plied to effective design for interfaces such as voter ballots. 

Human visual grouping processes consolidate independent visual objects into grouped visual features on the basis of shared characteristics; these visual features can themselves be grouped, resulting in a hierarchical representation of visual grouping information. This “grouping hierarchy“ promotes ef- ficient attention in the support of goal-directed behavior, but improper grouping of elements of a visual scene can also re- sult in critical behavioral errors. Understanding of how visual object/features characteristics such as size and form influences perception of hierarchical visual groups can further theory of human visual grouping behavior and contribute to effective in- terface design. In the present study, participants provided free- response groupings of a set of stimuli that contained consistent structural relationships between a limited set of visual features. These grouping patterns were evaluated for relationships be- tween specific characteristics of the constituent visual features and the distribution of features across levels of the indicated grouping hierarchy. We observed that while the relative size of the visual features differentiated groupings across levels of the grouping hierarchy, the form of visual objects and features was more likely to distinguish separate groups within a partic- ular level of hierarchy. These consistent relationships between visual feature characteristics and placement within a grouping hierarchy can be leveraged to advance computational theories of human visual grouping behavior, which can in turn be ap- plied to effective design for interfaces such as voter ballots. 

Four inter-related measures of phase are described to study the phase synchronization of cellular oscillators, and computation of these measures is described and illustrated on single cell fluorescence data from the model filamentous fungus, Neurospora crassa. One of these four measures is the phase shift ϕ in a sinusoid of the form x(t) = A(cos(ωt + ϕ), where t is time. The other measures arise by creating a replica of the periodic process x(t) called the Hilbert transform x̃(t), which is 90 degrees out of phase with the original process x(t). The second phase measure is the phase angle FH(t) between the replica x̃(t) and X(t), taking values between -π and π. At extreme values the Hilbert Phase is discontinuous, and a continuous form FC(t) of the Hilbert Phase is used, measuring time on the nonnegative real axis (t). The continuous Hilbert Phase FC(t) is used to define the phase MC(t1,t0) for an experiment beginning at time t0 and ending at time t1. In that phase differences at time t0 are often of ancillary interest, the Hilbert Phase FC(t0) is subtracted from FC(t1). This difference is divided by 2π to obtain the phase MC(t1,t0) in cycles. Both the Hilbert Phase FC(t) and the phase MC(t1,t0) are functions of time and useful in studying when oscillators phase-synchronize in time in signal processing and circadian rhythms in particular. The phase of cellular clocks is fundamentally different from circadian clocks at the macroscopic scale because there is an hourly cycle superimposed on the circadian cycle.