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

HELIOS-Retrieval: An Open-source, Nested Sampling Atmospheric Retrieval Code, Application to the HR 8799 Exoplanets and Inferred Constraints for Planet Formation

We present an open-source retrieval code named HELIOS-Retrieval (hereafter HELIOS-R), designed to obtain chemical abundances and temperature-pressure profiles from inverting the measured spectra of exoplanetary atmospheres. In the current implementation, we use an exact solution of the radiative transfer equation, in the pure absorption limit, in our forward model, which allows us to analytically integrate over all of the outgoing rays (instead of performing Gaussian quadrature). Two chemistry models are considered: unconstrained chemistry (where the mixing ratios are treated as free parameters) and equilibrium chemistry (enforced via analytical formulae, where only the elemental abundances are free parameters). The nested sampling algorithm allows us to formally implement Occam's Razor based on a comparison of the Bayesian evidence between models. We perform a retrieval analysis on the measured spectra of the HR 8799b, c, d and e directly imaged exoplanets. Chemical equilibrium is disfavored by the Bayesian evidence for HR 8799b, c and d. We find supersolar C/O, C/H and O/H values for the outer HR 8799b and c exoplanets, while the inner HR 8799d and e exoplanets have substellar C/O, substellar C/H and superstellar O/H values. If these retrieved properties are representative of the bulk compositions of the exoplanets, then they are inconsistent with formation via gravitational instability (without late-time accretion) and consistent with a core accretion scenario in which late-time accretion of ices occurred differently for the inner and outer exoplanets. For HR 8799e, we find that spectroscopy in the K band is crucial for constraining C/O and C/H. HELIOS-R is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).Comment: 27 pages, 21 figures, 3 tables, published in A