The Higher Order Schwarzian Derivative: Its Applications for Chaotic Behavior and New Invariant Sufficient Condition of Chaos

The Schwarzian derivative of a function f(x) which is defined in the interval (a, b) having higher order derivatives is given by Sf(x)=(f''(x)/f'(x))'-1/2(f''(x)/f'(x))^2 . A sufficient condition for a function to behave chaotically is that its Schwarzian derivative is negative. In this paper, we try to find a sufficient condition for a non-linear dynamical system to behave chaotically. The solution function of this system is a higher degree polynomial. We define n-th Schwarzian derivative to examine its general properties. Our analysis shows that the sufficient condition for chaotic behavior of higher order polynomial is provided if its highest order three terms satisfy an inequality which is invariant under the degree of the polynomial and the condition is represented by Hankel determinant of order 2. Also the n-th order polynomial can be considered to be the partial sum of real variable analytic function. Let this analytic function be the solution of non-linear differential equation, then the sufficient condition for the chaotical behavior of this function is the Hankel determinant of order 2 negative, where the elements of this determinant are the coefficient of the terms of n, n-1, n-2 in Taylor expansion.Comment: 8 page

Inattentional Deafness: Visual Load Leads to Time-Specific Suppression of Auditory Evoked Responses

UNLABELLED: Due to capacity limits on perception, conditions of high perceptual load lead to reduced processing of unattended stimuli (Lavie et al., 2014). Accumulating work demonstrates the effects of visual perceptual load on visual cortex responses, but the effects on auditory processing remain poorly understood. Here we establish the neural mechanisms underlying "inattentional deafness"--the failure to perceive auditory stimuli under high visual perceptual load. Participants performed a visual search task of low (target dissimilar to nontarget items) or high (target similar to nontarget items) load. On a random subset (50%) of trials, irrelevant tones were presented concurrently with the visual stimuli. Brain activity was recorded with magnetoencephalography, and time-locked responses to the visual search array and to the incidental presence of unattended tones were assessed. High, compared to low, perceptual load led to increased early visual evoked responses (within 100 ms from onset). This was accompanied by reduced early (∼ 100 ms from tone onset) auditory evoked activity in superior temporal sulcus and posterior middle temporal gyrus. A later suppression of the P3 "awareness" response to the tones was also observed under high load. A behavioral experiment revealed reduced tone detection sensitivity under high visual load, indicating that the reduction in neural responses was indeed associated with reduced awareness of the sounds. These findings support a neural account of shared audiovisual resources, which, when depleted under load, leads to failures of sensory perception and awareness. SIGNIFICANCE STATEMENT: The present work clarifies the neural underpinning of inattentional deafness under high visual load. The findings of near-simultaneous load effects on both visual and auditory evoked responses suggest shared audiovisual processing capacity. Temporary depletion of shared capacity in perceptually demanding visual tasks leads to a momentary reduction in sensory processing of auditory stimuli, resulting in inattentional deafness. The dynamic "push-pull" pattern of load effects on visual and auditory processing furthers our understanding of both the neural mechanisms of attention and of cross-modal effects across visual and auditory processing. These results also offer an explanation for many previous failures to find cross-modal effects in experiments where the visual load effects may not have coincided directly with auditory sensory processing

Endothelial dysfunction and lung capillary injury in cardiovascular diseases

Cardiac dysfunction of both systolic and diastolic origins leads to increased left atrial pressure, lung capillary injury and increased resistance to gas transfer. Acutely, pressure-induced trauma disrupts the endothelial and alveolar anatomical configuration and definitively causes an impairment of cellular pathways involved in fluid-flux regulation and gas exchange efficiency, a process well identified as stress failure of the alveolar-capillary membrane. In chronic heart failure (HF), additional stimuli other than pressure may trigger the true remodeling process of capillaries and small arteries characterized by endothelial dysfunction, proliferation of myofibroblasts, fibrosis and extracellular matrix deposition. In parallel there is a loss of alveolar gas diffusion properties due to the increased path from air to blood (thickening of extracellular matrix) and loss of fine molecular mechanism involved in fluid reabsorption and clearance. Deleterious changes in gas transfer not only reflect the underlying lung tissue damage but also portend independent prognostic information and may play a role in the pathogenesis of exercise limitation and ventilatory abnormalities observed in these patients. Few currently approved treatments for chronic HF have the potential to positively affect structural remodeling of the lung capillary network; angiotensin-converting enzyme inhibitors are one of the few currently established options. Recently, more attention has been paid to novel therapies specifically targeting the nitric oxide pathway as a suitable target to improve endothelial function and permeability as well as alveolar gas exchange properties

Lightening the Load: Perceptual Load Impairs Visual Detection in Typical Adults but Not in Autism

Autism spectrum disorder (ASD) research portrays a mixed picture of attentional abilities with demonstrations of enhancements (e.g., superior visual search) and deficits (e.g., higher distractibility). Here we test a potential resolution derived from the Load Theory of Attention (e.g., Lavie, 2005). In Load Theory, distractor processing depends on the perceptual load of the task and as such can only be eliminated under high load that engages full capacity. We hypothesize that ASD involves enhanced perceptual capacity, leading to the superior performance and increased distractor processing previously reported. Using a signal-detection paradigm, we test this directly and demonstrate that, under higher levels of load, perceptual sensitivity was reduced in typical adults but not in adults with ASD. These findings confirm our hypothesis and offer a promising solution to the previous discrepancies by suggesting that increased distractor processing in ASD results not from a filtering deficit but from enhanced perceptual capacity

Establishing gaze markers of perceptual load during multi-target visual search

Highly-automated technologies are increasingly incorporated into existing systems, for instance in advanced car models. Although highly automated modes permit non-driving activities (e.g. internet browsing), drivers are expected to reassume control upon a 'take over' signal from the automation. To assess a person's readiness for takeover, non-invasive eye tracking can indicate their attentive state based on properties of their gaze. Perceptual load is a well-established determinant of attention and perception, however, the effects of perceptual load on a person's ability to respond to a takeover signal and the related gaze indicators are not yet known. Here we examined how load-induced attentional state affects detection of a takeover-signal proxy, as well as the gaze properties that change with attentional state, in an ongoing task with no overt behaviour beyond eye movements (responding by lingering the gaze). Participants performed a multi-target visual search of either low perceptual load (shape targets) or high perceptual load (targets were two separate conjunctions of colour and shape), while also detecting occasional auditory tones (the proxy takeover signal). Across two experiments, we found that high perceptual load was associated with poorer search performance, slower detection of cross-modal stimuli, and longer fixation durations, while saccade amplitude did not consistently change with load. Using machine learning, we were able to predict the load condition from fixation duration alone. These results suggest monitoring fixation duration may be useful in the design of systems to track users' attentional states and predict impaired user responses to stimuli outside of the focus of attention

On the coupling and decoupling of mind wandering and perception: a shared metabolism account

INTRODUCTION: Mind wandering (MW) has been associated with reduced responsiveness to external stimuli ("perceptual decoupling"). Conversely, increased perceptual demands of a task result in reduced MW. Here we propose a neurobiological account attributing the mutually-limiting relationship of MW and perception to brain-wide limits on cerebral metabolism. Since overall cerebral metabolism is known to remain constant, despite increased mental task demands, we tested whether increased perceptual processing load in a visual task will result in reduced oxygen metabolism in MW-related medial prefrontal cortex (mPFC) regions. METHODS: We used broadband near-infrared spectroscopy to measure oxidation states of the cytochrome-c-oxidase enzyme (oxCCO), an intracellular marker of metabolism, in mPFC while sampling participants' MW experiences during their performance of a visual task of either low (feature search) or high(conjunction search) perceptual load. RESULTS: Increased perceptual load in the task resulted in reduced oxCCO signal in mPFC regions related to MW reports. High perceptual load was also found to specifically suppress detailed (and hence more metabolism-demanding) rather than vague MW. DISCUSSION: Overall, the results support a shared metabolism account of the relationship between MW and perception and demonstrate that attentional-regulation of metabolism only supports ongoing detailed MW when perceptual processing demands are low

Visual perceptual load induces inattentional deafness

In this article, we establish a new phenomenon of “inattentional deafness” and highlight the level of load on visual attention as a critical determinant of this phenomenon. In three experiments, we modified an inattentional blindness paradigm to assess inattentional deafness. Participants made either a low- or high-load visual discrimination concerning a cross shape (respectively, a discrimination of line color or of line length with a subtle length difference). A brief pure tone was presented simultaneously with the visual task display on a final trial. Failures to notice the presence of this tone (i.e., inattentional deafness) reached a rate of 79% in the high-visual-load condition, significantly more than in the low-load condition. These findings establish the phenomenon of inattentional deafness under visual load, thereby extending the load theory of attention (e.g., Lavie, Journal of Experimental Psychology. Human Perception and Performance, 25, 596–616, 1995) to address the cross-modal effects of visual perceptual load