Consciousness, cognition, and the hierarchy of context: extending the global neuronal workspace model

We adapt an information theory analysis of interacting cognitive biological and social modules to the problem of the global neuronal workspace, the new standard neuroscience paradigm for consciousness. Tunable punctuation emerges in a natural way, suggesting the possibility of fitting appropriate phase transition power law, and away from transition, generalized Onsager relation expressions, to observational data on conscious reaction. The development can be extended in a straightforward manner to include psychosocial stress, culture, or other cognitive modules which constitute a structured, embedding hierarchy of contextual constraints acting at a slower rate than neuronal function itself. This produces a 'biopsychosociocultural' model of individual consciousness that, while otherwise quite close to the standard treatment, meets compelling philosophical and other objections to brain-only descriptions

The fine-grained phase-space structure of Cold Dark Matter halos

We present a new and completely general technique for calculating the fine-grained phase-space structure of dark matter throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real space density of the associated dark matter streams. We also study the evolution of stream density in ellipsoidal NFW halos with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least $10^5$ streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N-body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code GADGET-3 and present tests which demonstrate that N-body discreteness effects can be kept under control in realistic configurations.Comment: 20 pages, 24 figures, submitted to MNRA

Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity

We investigate mobility regimes for localized modes in the discrete nonlinear Schr\"{o}dinger (DNLS) equation with the cubic-quintic onsite terms. Using the variational approximation (VA), the largest soliton's total power admitting progressive motion of kicked discrete solitons is predicted, by comparing the effective kinetic energy with the respective Peierls-Nabarro (PN) potential barrier. The prediction is novel for the DNLS model with the cubic-only nonlinearity too, demonstrating a reasonable agreement with numerical findings. Small self-focusing quintic term quickly suppresses the mobility. In the case of the competition between the cubic self-focusing and quintic self-defocusing terms, we identify parameter regions where odd and even fundamental modes exchange their stability, involving intermediate asymmetric modes. In this case, stable solitons can be set in motion by kicking, so as to let them pass the PN barrier. Unstable solitons spontaneously start oscillatory or progressive motion, if they are located, respectively, below or above a mobility threshold. Collisions between moving discrete solitons, at the competing nonlinearities frame, are studied too.Comment: 12 pages, 15 figure

Inertial waves in rapidly rotating flows: a dynamical systems perspective

An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics is analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.Postprint (author's final draft

Localized Dispersive States in Nonlinear Coupled Mode Equations for Light Propagation in Fiber Bragg Gratings.

Dispersion effects induce new instabilities and dynamics in the weakly nonlinear description of light propagation in fiber Bragg gratings. A new family of dispersive localized pulses that propagate with the group velocity is numerically found, and its stability is also analyzed. The unavoidable different asymptotic order of transport and dispersion effects plays a crucial role in the determination of these localized states. These results are also interesting from the point of view of general pattern formation since this asymptotic imbalance is a generic situation in any transport-dominated (i.e., nonzero group velocity) spatially extended system

New mathematical foundations for AI and Alife: Are the necessary conditions for animal consciousness sufficient for the design of intelligent machines?

Rodney Brooks' call for 'new mathematics' to revitalize the disciplines of artificial intelligence and artificial life can be answered by adaptation of what Adams has called 'the informational turn in philosophy' and by the novel perspectives that program gives into empirical studies of animal cognition and consciousness. Going backward from the necessary conditions communication theory imposes on cognition and consciousness to sufficient conditions for machine design is, however, an extraordinarily difficult engineering task. The most likely use of the first generations of conscious machines will be to model the various forms of psychopathology, since we have little or no understanding of how consciousness is stabilized in humans or other animals

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement

Localized Breathing Modes in Granular Crystals with Defects

We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such "defects", we analyze the problem's linear limit to identify the system eigenfrequencies and the linear defect modes. We then examine the bifurcation of nonlinear defect modes from their linear counterparts and study their linear stability in detail. We identify intriguing differences between the case of impurities in contact and ones that are not in contact. We find that the former bears similarities to the single defect case, whereas the latter features symmetry-breaking bifurcations with interesting static and dynamic implications

Darwin's Rainbow: Evolutionary radiation and the spectrum of consciousness

Evolution is littered with paraphyletic convergences: many roads lead to functional Romes. We propose here another example - an equivalence class structure factoring the broad realm of possible realizations of the Baars Global Workspace consciousness model. The construction suggests many different physiological systems can support rapidly shifting, sometimes highly tunable, temporary assemblages of interacting unconscious cognitive modules. The discovery implies various animal taxa exhibiting behaviors we broadly recognize as conscious are, in fact, simply expressing different forms of the same underlying phenomenon. Mathematically, we find much slower, and even multiple simultaneous, versions of the basic structure can operate over very long timescales, a kind of paraconsciousness often ascribed to group phenomena. The variety of possibilities, a veritable rainbow, suggests minds today may be only a small surviving fraction of ancient evolutionary radiations - bush phylogenies of consciousness and paraconsciousness. Under this scenario, the resulting diversity was subsequently pruned by selection and chance extinction. Though few traces of the radiation may be found in the direct fossil record, exaptations and vestiges are scattered across the living mind. Humans, for instance, display an uncommonly profound synergism between individual consciousness and their embedding cultural heritages, enabling efficient Lamarkian adaptation