Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Neuronal precision and the limits for acoustic signal recognition in a small neuronal network

Recognition of acoustic signals may be impeded by two factors: extrinsic noise, which degrades sounds before they arrive at the receiver’s ears, and intrinsic neuronal noise, which reveals itself in the trial-to-trial variability of the responses to identical sounds. Here we analyzed how these two noise sources affect the recognition of acoustic signals from potential mates in grasshoppers. By progressively corrupting the envelope of a female song, we determined the critical degradation level at which males failed to recognize a courtship call in behavioral experiments. Using the same stimuli, we recorded intracellularly from auditory neurons at three different processing levels, and quantified the corresponding changes in spike train patterns by a spike train metric, which assigns a distance between spike trains. Unexpectedly, for most neurons, intrinsic variability accounted for the main part of the metric distance between spike trains, even at the strongest degradation levels. At consecutive levels of processing, intrinsic variability increased, while the sensitivity to external noise decreased. We followed two approaches to determine critical degradation levels from spike train dissimilarities, and compared the results with the limits of signal recognition measured in behaving animals

Visual Coding in Locust Photoreceptors

Information capture by photoreceptors ultimately limits the quality of visual processing in the brain. Using conventional sharp microelectrodes, we studied how locust photoreceptors encode random (white-noise, WN) and naturalistic (1/f stimuli, NS) light patterns in vivo and how this coding changes with mean illumination and ambient temperature. We also examined the role of their plasma membrane in shaping voltage responses. We found that brightening or warming increase and accelerate voltage responses, but reduce noise, enabling photoreceptors to encode more information. For WN stimuli, this was accompanied by broadening of the linear frequency range. On the contrary, with NS the signaling took place within a constant bandwidth, possibly revealing a ‘preference’ for inputs with 1/f statistics. The faster signaling was caused by acceleration of the elementary phototransduction current - leading to bumps - and their distribution. The membrane linearly translated phototransduction currents into voltage responses without limiting the throughput of these messages. As the bumps reflected fast changes in membrane resistance, the data suggest that their shape is predominantly driven by fast changes in the light-gated conductance. On the other hand, the slower bump latency distribution is likely to represent slower enzymatic intracellular reactions. Furthermore, the Q10s of bump duration and latency distribution depended on light intensity. Altogether, this study suggests that biochemical constraints imposed upon signaling change continuously as locust photoreceptors adapt to environmental light and temperature conditions

Does transcranial direct current stimulation to prefrontal cortex affect mood and emotional memory retrieval in healthy individuals?

Studies using transcranial direct current stimulation (tDCS) of prefrontal cortex to improve symptoms of depression have had mixed results. We examined whether using tDCS to change the balance of activity between left and right dorsolateral prefrontal cortex (DLPFC) can alter mood and memory retrieval of emotional material in healthy volunteers. Participants memorised emotional images, then tDCS was applied bilaterally to DLPFC while they performed a stimulus-response compatibility task. Participants were then presented with a set of images for memory retrieval. Questionnaires to examine mood and motivational state were administered at the beginning and end of each session. Exploratory data analyses showed that the polarity of tDCS to DLPFC influenced performance on a stimulus-response compatibility task and this effect was dependent on participants' prior motivational state. However, tDCS polarity had no effect on the speed or accuracy of memory retrieval of emotional images and did not influence positive or negative affect. These findings suggest that the balance of activity between left and right DLPFC does not play a critical role in the mood state of healthy individuals. We suggest that the efficacy of prefrontal tDCS depends on the initial activation state of neurons and future work should take this into account. © 2014 Morgan et al