ABSTRACT
A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature. Classically, synchronization was characterized in terms of macroscopic parameters, such as the spectrum of Lyapunov exponents. Recently, however, we attempted a microscopic description of synchronization, called topological synchronization, and showed that chaotic synchronization is, in fact, a continuous process that starts in low-density areas of the attractor. Here we analyze the relation between the two emergent phenomena by shifting the descriptive level of topological synchronization to account for the multifractal nature of the visited attractors. Namely, we measure the generalized dimension of the system and monitor how it changes while increasing the coupling strength. We show that during the gradual process of topological adjustment in phase space, the multifractal structures of each strange attractor of the two coupled oscillators continuously converge, taking a similar form, until complete topological synchronization ensues. According to our results, chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what we termed as the 'zipper effect', a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. Topological synchronization offers, therefore, a more detailed microscopic description of chaotic synchronization and reveals new information about the process even in cases of high mismatch parameters.
ABSTRACT
In recent decades, the scientific study of consciousness has significantly increased our understanding of this elusive phenomenon. Yet, despite critical development in our understanding of the functional side of consciousness, we still lack a fundamental theory regarding its phenomenal aspect. There is an "explanatory gap" between our scientific knowledge of functional consciousness and its "subjective," phenomenal aspects, referred to as the "hard problem" of consciousness. The phenomenal aspect of consciousness is the first-person answer to "what it's like" question, and it has thus far proved recalcitrant to direct scientific investigation. Naturalistic dualists argue that it is composed of a primitive, private, non-reductive element of reality that is independent from the functional and physical aspects of consciousness. Illusionists, on the other hand, argue that it is merely a cognitive illusion, and that all that exists are ultimately physical, non-phenomenal properties. We contend that both the dualist and illusionist positions are flawed because they tacitly assume consciousness to be an absolute property that doesn't depend on the observer. We develop a conceptual and a mathematical argument for a relativistic theory of consciousness in which a system either has or doesn't have phenomenal consciousness with respect to some observer. Phenomenal consciousness is neither private nor delusional, just relativistic. In the frame of reference of the cognitive system, it will be observable (first-person perspective) and in other frame of reference it will not (third-person perspective). These two cognitive frames of reference are both correct, just as in the case of an observer that claims to be at rest while another will claim that the observer has constant velocity. Given that consciousness is a relativistic phenomenon, neither observer position can be privileged, as they both describe the same underlying reality. Based on relativistic phenomena in physics we developed a mathematical formalization for consciousness which bridges the explanatory gap and dissolves the hard problem. Given that the first-person cognitive frame of reference also offers legitimate observations on consciousness, we conclude by arguing that philosophers can usefully contribute to the science of consciousness by collaborating with neuroscientists to explore the neural basis of phenomenal structures.
ABSTRACT
Sleep deprivation (SD) critically affects a range of cognitive and affective functions, typically assessed during task performance. Whether such impairments stem from changes to the brain's intrinsic functional connectivity remain largely unknown. To examine this hypothesis, we applied graph theoretical analysis on resting-state fMRI data derived from 18 healthy participants, acquired during both sleep-rested and sleep-deprived states. We hypothesized that parameters indicative of graph connectivity, such as modularity, will be impaired by sleep deprivation and that these changes will correlate with behavioral outcomes elicited by sleep loss. As expected, our findings point to a profound reduction in network modularity without sleep, evident in the limbic, default-mode, salience and executive modules. These changes were further associated with behavioral impairments elicited by SD: a decrease in salience module density was associated with worse task performance, an increase in limbic module density was predictive of stronger amygdala activation in a subsequent emotional-distraction task and a shift in frontal hub lateralization (from left to right) was associated with increased negative mood. Altogether, these results portray a loss of functional segregation within the brain and a shift towards a more random-like network without sleep, already detected in the spontaneous activity of the sleep-deprived brain. Hum Brain Mapp 38:3300-3314, 2017. © 2017 Wiley Periodicals, Inc.
