Phase coexistence in proton glass

Proton glasses are crystals of composition M{sub 1{minus}x}(NW{sub 4}){sub x}W{sub 2}AO{sub 4}, where M = K,Rb, W = H,D, A = P,As. For x = 0 there is a ferroelectric (FE) transition, while for x = 1 there is an antiferroelectric (AFE) transition. In both cases, the transition is from a paraelectric (PE) state of tetragonal structure with dynamically disordered hydrogen bonds to an ordered state of orthorhombic structure. For an intermediate x range there is no transition, but the hydrogen rearrangements slow down, and eventually display nonergodic behavior characteristic of glasses. The authors and other have shown from spontaneous polarization, dielectric permittivity, nuclear magnetic resonance, and neutron diffraction experiments that for smaller x there is coexistence of ferroelectric and paraelectric phases, and for larger x there is coexistence of antiferroelectric and paraelectric phases. The authors present a method for analytically describing this coexistence, and the degree to which this coexistence is spatial or temporal

Phase coexistence in proton glass

Proton glasses are crystals of composition M{sub 1{minus}x}(NW{sub 4}){sub x}W{sub 2}AO{sub 4}, where M = K,Rb, W = H,D, A = P,As. For x = 0 there is a ferroelectric (FE) transition, while for x = 1 there is an antiferroelectric (AFE) transition. In both cases, the transition is from a paraelectric (PE) state of tetragonal structure with dynamically disordered hydrogen bonds to an ordered state of orthorhombic structure. For an intermediate x range there is no transition, but the hydrogen rearrangements slow down, and eventually display nonergodic behavior characteristic of glasses. The authors and other have shown from spontaneous polarization, dielectric permittivity, nuclear magnetic resonance, and neutron diffraction experiments that for smaller x there is coexistence of ferroelectric and paraelectric phases, and for larger x there is coexistence of antiferroelectric and paraelectric phases. The authors present a method for analytically describing this coexistence, and the degree to which this coexistence is spatial or temporal

Measures and Limits of Models of Fixation Selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection . We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced