A Blueprint for the Hard Problem of Consciousness

A Blueprint for the Hard Problem of Consciousness addresses the fundamental mechanism that allows physical events to transcend into subjective experiences, termed the Hard Problem of Consciousness. Consciousness is made available as the abstract product of self-referent realization of information by strange loops through the levels of processing of the brain. Readers are introduced to the concept of the Hard Problem of Consciousness and related concepts followed by a critical discourse of different theories of consciousness. Next, the author identifies the fundamental flaw of the Integrated Information Theory (IIT) and proposes an alternative that avoids the cryptic intelligent design and panpsychism of the IIT. This author also demonstrates how something can be created out of nothing without resorting to quantum theory, while pointing out neurobiological alternatives to the bottom-up approach of quantum theories of consciousness. The book then delves into the philosophy of qualia in different physiological knowledge networks (spatial, temporal and olfactory, cortical signals, for example) to explain an action-based model consistent with the generational principles of Predictive Coding, which maps prediction and predictive-error signals for perceptual representations supporting integrated goal-directed behaviors. Conscious experiences are considered the outcome of abstractions realized out of map overlays and provided by sustained oscillatory activity. The key feature of this blueprint is that it offers a perspective of the Hard Problem of Consciousness from the point of view of the subject; the experience of ‘being the subject’ is predicted to be the realization of inference inversely mapped out of hidden causes of global integrated actions. The author explains the consistencies of his blueprint with ideas of the Global Neuronal Workspace and the Adaptive Resonance Theory of consciousness as well as with the empirical evidence supporting the Integrated Information Theory. A Blueprint for the Hard Problem of Consciousness offers a unique perspective to readers interested in the scientific philosophy and cognitive neuroscience theory in relation to models of the theory of consciousness

Anyons, group theory and planar physics

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell groups.Comment: 22 pages, journal reference added, bibliography update

The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories

In this paper, we investigate the main algebraic properties of the maximally superintegrable system known as "Perlick system type I". All possible values of the relevant parameters, $K$ and $\beta$, are considered. In particular, depending on the sign of the parameter $K$ entering in the metrics, the motion will take place on compact or non compact Riemannian manifolds. To perform our analysis we follow a classical variant of the so called factorization method. Accordingly, we derive the full set of constants of motion and construct their Poisson algebra. As it is expected for maximally superintegrable systems, the algebraic structure will actually shed light also on the geometric features of the trajectories, that will be depicted for different values of the initial data and of the parameters. Especially, the crucial role played by the rational parameter $\beta$ will be seen "in action".Comment: 16 pages, 7 figure

Integrability, Supersymmetry and Coherent States. A volume in honour of Professor Véronique Hussin

ISBN 978-3-030-20087-

Solutions to the Painlev\'e V equation through supersymmetric quantum mechanics

In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlev\'e V (PV) equation, a second-order non-linear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator, while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.Comment: 39 pages, 18 figures, 4 tables, 70 reference