The Morse theory of \v{C}ech and Delaunay complexes

Given a finite set of points in $\mathbb R^n$ and a radius parameter, we study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the \v{C}ech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which are explicitly described by a single discrete gradient field.Comment: 21 pages, 2 figures, improved expositio

\v{C}ech-Delaunay gradient flow and homology inference for self-maps

We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior. We establish a sampling theorem to recover the eigenspace of the endomorphism on homology induced by the self-map. Using a combinatorial gradient flow arising from the discrete Morse theory for \v{C}ech and Delaunay complexes, we construct a chain map to transform the problem from the natural but expensive \v{C}ech complexes to the computationally efficient Delaunay triangulations. The fast chain map algorithm has applications beyond dynamical systems.Comment: 22 pages, 8 figure

Restriction of task processing time affects cortical activity during processing of a cognitive task: an event-related slow cortical potential study

As is known from psychometrics, restriction of task processing time by the instruction to respond as quickly and accurately as possible leads to task-unspecific cognitive processing. Since this task processing mode is used in most functional neuroimaging studies of human cognition, this may evoke cortical activity that is functionally not essential for the particular task under investigation. Using topographic recordings of event-related slow cortical potentials, two experiments have been performed to investigate whether cortical activity during processing of a visuo-spatial imagery task is substantially influenced by the time provided to process the task. Furthermore, it was investigated whether this effect is additionally modulated by a subject’s task-specific ability. The instruction to respond as quickly and accurately as possible led to increased negative slow cortical potential amplitudes over parietal and frontal regions and significantly interacted with task-specific ability. While cortical activity recorded over parietal and frontal regions was different between subjects with low and high spatial ability when processing time was unrestricted, no such differences were found between ability groups when subjects were instructed to answer both quickly and accurately. These results suggest that restricting processing time has considerable effects on the amount and the pattern of brain activity during cognitive processing and should be taken into account more explicitly in the experimental design and interpretation of neuroimaging studies of cognition

Direct Current Auditory Evoked Potentials During Wakefulness, Anesthesia, and Emergence from Anesthesia

Direct current auditory evoked potentials (DC-AEPs) are a sensitive indicator of depth of anesthesia in ani-mals. However, they have never been investigated in humans. To assess the potential usefulness of DC-AEPs as an indicator of anesthesia in humans, we performed an explorative study in which DC-AEPs were recorded during propofol and methohexital anesthesia in hu-mans. DC-AEPs were recorded via 22 scalp electrodes in 19 volunteers randomly assigned to receive either propofol or methohexital. DC-AEPs were evoked by binaurally presented 2-s, 60-dB, 800-Hz tones; meas-urements were taken during awake baseline, anesthesia, and emergence. Statistical analysis included analy-sis of variance and discriminant analysis of data acquired during these three conditions. About 500 ms after stimulus presentation, DC-AEPs could be ob-served. These potentials were present only during base-line and emergence—not during anesthesia. Statistically significant differences were found between baseline and anesthesia and between anesthesia and emergence. In conclusion, similar effects, as reported in animal studies of anesthetics on the DC-AEPs, could be observed in anesthetized humans. These results dem-onstrate that DC-AEPs are potentially useful in the assessment of cortical function during anesthesia and might qualify the method for monitoring anesthesia in humans

The role of demonstrator familiarity and language cues on infant imitation from television

An imitation procedure was used to investigate the impact of demonstrator familiarity and language cues on infant learning from television. Eighteen-month-old infants watched two pre-recorded videos showing an adult demonstrating a sequence of actions with two sets of stimuli. Infants' familiarity with the demonstrator and the language used during the demonstration varied as a function of experimental condition. Immediately after watching each video, infants' ability to reproduce the target actions was assessed. A highly familiar demonstrator did not enhance infants' performance. However, the addition of a narrative, developed from mothers' naturalistic description of the event, facilitated learning from an unfamiliar demonstrator. We propose that the differential effect of demonstrator familiarity and language cues may reflect the infants' ability to distinguish between important and less important aspects in a learning situation. (C) 2010 Elsevier Inc. All rights reserved

All about the Money – External Performance Monitoring is Affected by Monetary, but Not by Socially Conveyed Feedback Cues in More Antisocial Individuals

This study investigated the relationship between feedback processing and antisocial personality traits measured by the PSSI questionnaire (Kuhl and Kazén, 1997) in a healthy undergraduate sample. While event-related potentials [feedback related negativity (FRN), P300] were recorded, participants encountered expected and unexpected feedback during a gambling task. As recent findings suggest learning problems and deficiencies during feedback processing in clinical populations of antisocial individuals, we performed two experiments with different healthy participants in which feedback about monetary gains or losses consisted either of social–emotional (facial emotion displays) or non-social cues (numerical stimuli). Since the FRN and P300 are both sensitive to different aspects of feedback processing we hypothesized that they might help to differentiate between individuals scoring high and low on an antisocial trait measure. In line with previous evidence FRN amplitudes were enhanced after negative and after unexpected feedback stimuli. Crucially, participants scoring high on antisocial traits displayed larger FRN amplitudes than those scoring low only in response to expected and unexpected negative numerical feedback, but not in response to social–emotional feedback – irrespective of expectancy. P300 amplitudes were not modulated by antisocial traits at all, but by subjective reward probabilities. The present findings indicate that individuals scoring high on antisociality attribute higher motivational salience to monetary compared to emotional–social feedback which is reflected in FRN amplitude enhancement. Contrary to recent findings, however, no processing deficiencies concerning social–emotional feedback stimuli were apparent in those individuals. This indicates that stimulus salience is an important aspect in learning and feedback processes in individuals with antisocial traits which has potential implications for therapeutic interventions in clinical populations