We study the site percolation under Achlioptas process with a product rule in a two-dimensional square lattice. From the measurement of the cluster size distribution P(s), we find that P(s) has a very robust power-law regime followed by a stable hump near the transition threshold. Based on the careful analysis on the PP(s) distribution, we show that the transition should be discontinuous. The e...

We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid (VBS) ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the d...

A relation between the MacDowell-Mansouri theory of gravity and the Pontrjagin toplogical invariant in (3 + 1) dimensions is discussed. This relation may be of especial interest in the quest of finding a mechanism to go from non-dynamical to dynamical gravity.

An aggressive (and delinquent) personality can be shown to exist when observations are made across a large enough sampling of exemplars. Arguments against the existence of such a personality are based on a failure to use sufficiently aggregated measures. Numerous estimates are preferable in order to average out idiosyncratic variance thereby leaving a clearer view of underlying dimensions of be...

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous works in which the Wick rotation was used to make the model well defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit ...

The literature on numerical perception is reviewed from the standpoint of research on selective attention, and predictions are made concerning the dimensional interaction between physical and numerical size of numerals. We manipulated stimulus differences to make the classification of numerical value slightly better (Experiment 1), substantially better (Experiment 2), or worse (Experiments 3-4)...

Five normal listeners were tested in detail for their auditory gap-detection thresholds, using stimuli in which the narrow-band noise markers of the gap differed in one or both of two auditory dimensions ~frequency composition and ear stimulated!. Gap thresholds for stimuli in which the markers differed along either single dimension averaged about 18 ms, while thresholds for markers differing a...

In multi-alternative choice, the attraction, compromise, and similarity effects demonstrate that the value of an alternative is not independent of the other alternatives in the choice-set. Rather, these effects suggest that a choice is reached through the comparison of alternatives. We investigated exactly how alternatives are compared against each other using eye-movement data. The results ind...

We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the underlying theory.