If we consider the Brier score (B) in the context of the signal detection theory and assume that it makes sense to consider the existence of B as a parameter for the population (let B be this B), and if we assume that the calibration in the observer's probability estimate is perfect, we find that there is a theoretical relationship between B and the area under the binormal receiver operating ch...

Monotonically monolithic spaces were recently introduced by V.V. Tkachuk, and monotonically κ-monolithic spaces by O.Alas, Tkachuk, and R. Wilson. In this note we answer some of their questions by showing that monotonically ω-monolithic compact spaces must be Corson compact, yet there is a Corson compact space which is not monotonically ω-monolithic. We obtain a characterization of monotonic mo...

A detailed structure theorem is shown for locally compact, locally connected, hereditarily normal spaces and for normal, locally compact, locally connected, hereditarily ω1-scwH spaces in models of PFA(S)[S], and for the latter kinds of spaces in models of PFA. Corollaries include a powerful refinement theorem like that for monotonically normal spaces, and the corollary that the spaces involved...

Nucleation is considered for nonzero rate of change of the dimensionless barrier B, which is characterized by a finite, slowly varying "nonstationary index" N∝-(dB/dt). In the standard adiabatic approximation it is assumed that after the start of nucleation an N-independent nucleation flux is established instantaneously, with a quasi-steady-state (QSS) value determined by the current barrier B(...

A monotonically labelled binary tree is a binary tree with integer labels attached to the internal nodes in such a way that the labels along any path from the root are nondecreasing. If there is only one label, we are dealing with ordinary binary trees. Prodinger and Urbanek [6] introduced a variety of families of monotonically labelled trees and obtained enumerative results about many of them....

The parametric variation in neuronal discharge according to the values of sensory or motor variables strongly influences the collective behavior of neuronal populations. A multitude of studies on the populations of broadly tuned neurons (e.g., cosine tuning) have led to such well-known computational principles as population coding, noise suppression, and line attractors. Much less is known abou...

Changes in the voltage clamp currents of squid giant axons wrought by low axoplasmic TEA+ (tetraethylammonium chloride) concentrations (0.3 mM and above) are described. They are: (a) For positive steps from the resting potential in sea water, the K+ current increases, decreases, then increases, instead of increasing monotonically. (b) For positive steps from the resting potential in 440 mM exte...