Perturbations of Critical Values in Nonsmooth Critical Point Theory

* Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993). ** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

Sensitivity and Bias within the Binary Signal Detection Theory, BSDT

Similar to classic Signal Detection Theory (SDT), recent optimal Binary Signal Detection Theory (BSDT) and based on it Neural Network Assembly Memory Model (NNAMM) can successfully reproduce Receiver Operating Characteristic (ROC) curves although BSDT/NNAMM parameters (intensity of cue and neuron threshold) and classic SDT parameters (perception distance and response bias) are essentially different. In present work BSDT/NNAMM optimal likelihood and posterior probabilities are analytically analyzed and used to generate ROCs and modified (posterior) mROCs, optimal overall likelihood and posterior. It is shown that for the description of basic discrimination experiments in psychophysics within the BSDT a ‘neural space’ can be introduced where sensory stimuli as neural codes are represented and decision processes are defined, the BSDT’s isobias curves can simultaneously be interpreted as universal psychometric functions satisfying the Neyman-Pearson objective, the just noticeable difference (jnd) can be defined and interpreted as an atom of experience, and near-neutral values of biases are observers’ natural choice. The uniformity or no-priming hypotheses, concerning the ‘in-mind’ distribution of false-alarm probabilities during ROC or overall probability estimations, is introduced. The BSDT’s and classic SDT’s sensitivity, bias, their ROC and decision spaces are compared.