13,905 research outputs found
Adaptive, locally-linear models of complex dynamics
The dynamics of complex systems generally include high-dimensional,
non-stationary and non-linear behavior, all of which pose fundamental
challenges to quantitative understanding. To address these difficulties we
detail a new approach based on local linear models within windows determined
adaptively from the data. While the dynamics within each window are simple,
consisting of exponential decay, growth and oscillations, the collection of
local parameters across all windows provides a principled characterization of
the full time series. To explore the resulting model space, we develop a novel
likelihood-based hierarchical clustering and we examine the eigenvalues of the
linear dynamics. We demonstrate our analysis with the Lorenz system undergoing
stable spiral dynamics and in the standard chaotic regime. Applied to the
posture dynamics of the nematode our approach identifies
fine-grained behavioral states and model dynamics which fluctuate close to an
instability boundary, and we detail a bifurcation in a transition from forward
to backward crawling. Finally, we analyze whole-brain imaging in
and show that the stability of global brain states changes with oxygen
concentration.Comment: 25 pages, 16 figure
Predictive Processing and the Phenomenology of Time Consciousness: A Hierarchical Extension of Rick Grush’s Trajectory Estimation Model
This chapter explores to what extent some core ideas of predictive processing can be applied to the phenomenology of time consciousness. The focus is on the experienced continuity of consciously perceived, temporally extended phenomena (such as enduring processes and successions of events). The main claim is that the hierarchy of representations posited by hierarchical predictive processing models can contribute to a deepened understanding of the continuity of consciousness. Computationally, such models show that sequences of events can be represented as states of a hierarchy of dynamical systems. Phenomenologically, they suggest a more fine-grained analysis of the perceptual contents of the specious present, in terms of a hierarchy of temporal wholes. Visual perception of static scenes not only contains perceived objects and regions but also spatial gist; similarly, auditory perception of temporal sequences, such as melodies, involves not only perceiving individual notes but also slightly more abstract features (temporal gist), which have longer temporal durations (e.g., emotional character or rhythm). Further investigations into these elusive contents of conscious perception may be facilitated by findings regarding its neural underpinnings. Predictive processing models suggest that sensorimotor areas may influence these contents
A Dynamic Approach to Rhythm in Language: Toward a Temporal Phonology
It is proposed that the theory of dynamical systems offers appropriate tools
to model many phonological aspects of both speech production and perception. A
dynamic account of speech rhythm is shown to be useful for description of both
Japanese mora timing and English timing in a phrase repetition task. This
orientation contrasts fundamentally with the more familiar symbolic approach to
phonology, in which time is modeled only with sequentially arrayed symbols. It
is proposed that an adaptive oscillator offers a useful model for perceptual
entrainment (or `locking in') to the temporal patterns of speech production.
This helps to explain why speech is often perceived to be more regular than
experimental measurements seem to justify. Because dynamic models deal with
real time, they also help us understand how languages can differ in their
temporal detail---contributing to foreign accents, for example. The fact that
languages differ greatly in their temporal detail suggests that these effects
are not mere motor universals, but that dynamical models are intrinsic
components of the phonological characterization of language.Comment: 31 pages; compressed, uuencoded Postscrip
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
From modular to centralized organization of synchronization in functional areas of the cat cerebral cortex
Recent studies have pointed out the importance of transient synchronization
between widely distributed neural assemblies to understand conscious
perception. These neural assemblies form intricate networks of neurons and
synapses whose detailed map for mammals is still unknown and far from our
experimental capabilities. Only in a few cases, for example the C. elegans, we
know the complete mapping of the neuronal tissue or its mesoscopic level of
description provided by cortical areas. Here we study the process of transient
and global synchronization using a simple model of phase-coupled oscillators
assigned to cortical areas in the cerebral cat cortex. Our results highlight
the impact of the topological connectivity in the developing of
synchronization, revealing a transition in the synchronization organization
that goes from a modular decentralized coherence to a centralized synchronized
regime controlled by a few cortical areas forming a Rich-Club connectivity
pattern.Comment: 24 pages, 8 figures. Final version published in PLoS On
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