Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach

Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to the parameters of the system, it is possible to design an effective procedure for parameter adjustment. Stability properties of this procedure are analyzed. Strategies shown in earlier studies to facilitate learning such as randomization of a learning sequence and adding specially designed disturbances during the learning phase are requirements for guaranteeing convergence in the learning scheme proposed.Comment: 30 pages, 7 figure

A pragmatic approach to multi-modality and non-normality in fixation duration studies of cognitive processes

Interpreting eye-fixation durations in terms of cognitive processing load is complicated by the multimodality of their distribution. An important source of multimodality is the distinction between single and multiple fixations to the same object. Based on the distinction, we separated a log-transformed distribution made to an object in non-reading task. We could reasonably conclude that the separated distributions belong to the same, general logistic distribution, which has a finite population mean and variance. This allowed us to use the sample means as dependent variables in a parametric analysis. Six tasks were compared, which required different levels of post-perceptual processing. A no-task control condition was added to test for perceptual processing. Fixation durations differentiated task-specific perceptual, but not post-perceptual processing demands

System, Subsystem, Hive: boundary problems in computational theories of consciousness

A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a system as conscious will do so for some – perhaps most – of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness