The Hidden Convexity of Spectral Clustering

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Independent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.Comment: 22 page

GABAergic compensation in connexin36 knock-out mice evident during low-magnesium seizure-like event activity

Gap junctions within the cerebral cortex may facilitate cortical seizure formation by their ability to synchronize electrical activity. To investigate this, one option is to compare wild-type (WT) animals with those lacking the gene for connexin36 (Cx36 KO); the protein that forms neuronal gap junctions between cortical inhibitory cells. However, genetically modified knock-out animals may exhibit compensatory effects; with the risk that observed differences between WT and Cx36 KO animals could be erroneously attributed to Cx36 gap junction effects. In this study we investigated the effect of GABAA-receptor modulation (augmentation with 16 μM etomidate and blockade with 100 μM picrotoxin) on low-magnesium seizure-like events (SLEs) in mouse cortical slices. In WT slices, picrotoxin enhanced both the amplitude (49% increase, p = 0.0006) and frequency (37% increase, p = 0.005) of SLEs; etomidate also enhanced SLE amplitude (18% increase, p = 0.003) but reduced event frequency (25% decrease, p < 0.0001). In Cx36 KO slices, the frequency effects of etomidate and picrotoxin were preserved, but the amplitude responses were abolished. Pre-treatment with the gap junction blocker mefloquin in WT slices did not significantly alter the drug responses, indicating that the reduction in amplitude seen in the Cx36 KO mice was not primarily mediated by their lack of interneuronal gap junctions, but was rather due to pre-existing compensatory changes in these animals. Conclusions from studies comparing seizure characteristics between WT and Cx36 KO mice must be viewed with a degree of caution because of the possible confounding effect of compensatory neurophysiological changes in the genetically modified animals

A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep

Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input? We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases, the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM

C++ for Heterogeneous Programming: oneAPI (DPC++ and oneTBB)

This tutorial provides hands-on experience programming CPUs, GPUs and FPGAs using a unified, standards-based programming model: oneAPI. oneAPI includes a cross-architecture language: Data Parallel C++ (DPC++). DPC++ is an evolution of C++ that incorporates the SYCL language with extensions for Unified Shared Memory (USM), ordered queues and reductions, among other features. oneAPI also includes libraries for API-based programming, such as domain-specific libraries, math kernel libraries and Threading Building Blocks (TBB). The main benefit of using oneAPI over other heterogeneous programming models is the single programming language approach, which enables one to target multiple devices using the same programming model, and therefore to have a cleaner, portable, and more readable code. In the current heterogeneous era, it is still challenging for developers to match computations to accelerators and to coordinate the use of those accelerators in the context of their larger applications. Therefore, this tutorial’s main goal is not just teaching oneAPI as an easier approach to target heterogeneous platforms, but also to convey techniques to map applications to heterogeneous hardware paying attention to the scheduling and mapping problems (how to achieve load balance and which regions of the application are more suitable to each particular device).Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Mere Expectation to Move Causes Attenuation of Sensory Signals

When a part of the body moves, the sensation evoked by a probe stimulus to that body part is attenuated. Two mechanisms have been proposed to explain this robust and general effect. First, feedforward motor signals may modulate activity evoked by incoming sensory signals. Second, reafferent sensation from body movements may mask the stimulus. Here we delivered probe stimuli to the right index finger just before a cue which instructed subjects to make left or right index finger movements. When left and right cues were equiprobable, we found attenuation for stimuli to the right index finger just before this finger was cued (and subsequently moved). However, there was no attenuation in the right finger just before the left finger was cued. This result suggests that the movement made in response to the cue caused ‘postdictive’ attenuation of a sensation occurring prior to the cue. In a second experiment, the right cue was more frequent than the left. We now found attenuation in the right index finger even when the left finger was cued and moved. This attenuation linked to a movement that was likely but did not in fact occur, suggests a new expectation-based mechanism, distinct from both feedforward motor signals and postdiction. Our results suggest a new mechanism in motor-sensory interactions in which the motor system tunes the sensory inputs based on expectations about future possible actions that may not, in fact, be implemented

Transcriptional Correlates of Proximal-Distal Identify and Regeneration Timing in Axolotl Limbs

Cells within salamander limbs retain memories that inform the correct replacement of amputated tissues at different positions along the length of the arm, with proximal and distal amputations completing regeneration at similar times. We investigated the possibility that positional memory is associated with variation in transcript abundances along the proximal-distal limb axis. Transcripts were deeply sampled from Ambystoma mexicanum limbs at the time they were administered fore arm vs upper arm amputations, and at 19 post-amputation time points. After amputation and prior to regenerative outgrowth, genes typically expressed by differentiated muscle cells declined more rapidly in upper arms while cell cycle transcripts were expressed more highly. These and other expression patterns suggest upper arms undergo more robust tissue remodeling and cell proliferation responses after amputation, and thus provide an explanation for why the overall time to complete regeneration is similar for proximal and distal amputations. Additionally, we identified candidate positional memory genes that were expressed differently between fore and upper arms that encode a surprising number of epithelial proteins and a variety of cell surface, cell adhesion, and extracellular matrix molecules. Also, genes were discovered that exhibited different, bivariate patterns of gene expression between fore and upper arms, implicating dynamic transcriptional regulation for the first time in limb regeneration. Finally, 43 genes expressed differently between fore and upper arm samples showed similar transcriptional patterns during retinoic acid-induced reprogramming of fore arm blastema cells into upper arm cells. Our study provides new insights about the basis of positional information in regenerating axolotl limbs