Convergence and Energy Landscape for Cheeger Cut Clustering

This paper provides both theoretical and algorithmic results for the l 1-relaxation of the Cheeger cut problem. The l2- relaxation, known as spectral clustering, only loosely relates to the Cheeger cut; however, it is convex and leads to a simple optimization problem. The l1-relaxation, in contrast, is non-convex but is provably equivalent to the original problem. The l1-relaxation therefore trades convexity for exactness, yielding improved clustering results at the cost of a more challenging optimization. The first challenge is understanding convergence of algorithms. This paper provides the first complete proof of convergence for algorithms that minimize the l1-relaxation. The second challenge entails comprehending the l1-energy landscape, i.e. the set of possible points to which an algorithm might converge. We show that l 1-algorithms can get trapped in local minima that are not globally optimal and we provide a classification theorem to interpret these local minima. This classification gives meaning to these suboptimal solutions and helps to explain, in terms of graph structure, when the l1-relaxation provides the solution of the original Cheeger cut problem

Connectivity of Soft Random Geometric Graphs Over Annuli

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.Comment: 12 pages, 6 figure

Multisensory and Motor Representations in Rat Oral Somatosensory Cortex

Abstract In mammals, a complex array of oral sensors assess the taste, temperature and haptic properties of food. Although the representation of taste has been extensively studied in the gustatory cortex, it is unclear how the somatosensory cortex encodes information about the properties of oral stimuli. Moreover, it is poorly understood how different oral sensory modalities are integrated and how sensory responses are translated into oral motor actions. To investigate whether oral somatosensory cortex processes food-related sensations and movements, we performed in vivo whole-cell recordings and motor mapping experiments in rats. Neurons in oral somatosensory cortex showed robust post-synaptic and sparse action potential responses to air puffs. Membrane potential showed that cold water evoked larger responses than room temperature or hot water. Most neurons showed no clear tuning of responses to bitter, sweet and neutral gustatory stimuli. Finally, motor mapping experiments with histological verification revealed an initiation of movements related to food consumption behavior, such as jaw opening and tongue protrusions. We conclude that somatosensory cortex: (i) provides a representation of the temperature of oral stimuli, (ii) does not systematically encode taste information and (iii) influences orofacial movements related to food consummatory behavior

Population vulnerability to COVID-19 in Europe: A burden of disease analysis

Background: Evidence has emerged showing that elderly people and those with pre-existing chronic health conditions may be at higher risk of developing severe health consequences from COVID-19. In Europe, this is of particular relevance with ageing populations living with non-communicable diseases, multi-morbidity and frailty. Published estimates of Years Lived with Disability (YLD) from the Global Burden of Disease (GBD) study help to characterise the extent of these effects. Our aim was to identify the countries across Europe that have populations at highest risk from COVID-19 by using estimates of population age structure and YLD for health conditions linked to severe illness from COVID-19. Methods: Population and YLD estimates from GBD 2017 were extracted for 45 countries in Europe. YLD was restricted to a list of specific health conditions associated with being at risk of developing severe consequences from COVID-19 based on guidance from the United Kingdom Government. This guidance also identified individuals aged 70 years and above as being at higher risk of developing severe health consequences. Study outcomes were defined as: (i) proportion of population aged 70 years and above; and (ii) rate of YLD for COVID-19 vulnerable health conditions across all ages. Bivariate groupings were established for each outcome and combined to establish overall population-level vulnerability. Results: Countries with the highest proportions of elderly residents were Italy, Greece, Germany, Portugal and Finland. When assessments of population-level YLD rates for COVID-19 vulnerable health conditions were made, the highest rates were observed for Bulgaria, Czechia, Croatia, Hungary and Bosnia and Herzegovina. A bivariate analysis indicated that the countries at high-risk across both measures of vulnerability were: Bulgaria; Portugal; Latvia; Lithuania; Greece; Germany; Estonia; and Sweden. Conclusion: Routine estimates of population structures and non-fatal burden of disease measures can be usefully combined to create composite indicators of vulnerability for rapid assessments, in this case to severe health consequences from COVID-19. Countries with available results for sub-national regions within their country, or national burden of disease studies that also use sub-national levels for burden quantifications, should consider using non-fatal burden of disease estimates to estimate geographical vulnerability to COVID-19

The neurobiology of Etruscan shrew active touch

The Etruscan shrew, Suncus etruscus, is not only the smallest terrestrial mammal, but also one of the fastest and most tactile hunters described to date. The shrew's skeletal muscle consists entirely of fast-twitch types and lacks slow fibres. Etruscan shrews detect, overwhelm, and kill insect prey in large numbers in darkness. The cricket prey is exquisitely mechanosensitive and fast-moving, and is as big as the shrew itself. Experiments with prey replica show that shape cues are both necessary and sufficient for evoking attacks. Shrew attacks are whisker guided by motion- and size-invariant Gestalt-like prey representations. Shrews often attack their prey prior to any signs of evasive manoeuvres. Shrews whisk at frequencies of approximately 14 Hz and can react with latencies as short as 25–30 ms to prey movement. The speed of attacks suggests that shrews identify and classify prey with a single touch. Large parts of the shrew's brain respond to vibrissal touch, which is represented in at least four cortical areas comprising collectively about a third of the cortical volume. Etruscan shrews can enter a torpid state and reduce their body temperature; we observed that cortical response latencies become two to three times longer when body temperature drops from 36°C to 24°C, suggesting that endothermy contributes to the animal's high-speed sensorimotor performance. We argue that small size, high-speed behaviour and extreme dependence on touch are not coincidental, but reflect an evolutionary strategy, in which the metabolic costs of small body size are outweighed by the advantages of being a short-range high-speed touch and kill predator

Psychometric Curve and Behavioral Strategies for Whisker-Based Texture Discrimination in Rats

The rodent whisker system is a major model for understanding neural mechanisms for tactile sensation of surface texture (roughness). Rats discriminate surface texture using the whiskers, and several theories exist for how texture information is physically sensed by the long, moveable macrovibrissae and encoded in spiking of neurons in somatosensory cortex. However, evaluating these theories requires a psychometric curve for texture discrimination, which is lacking. Here we trained rats to discriminate rough vs. fine sandpapers and grooved vs. smooth surfaces. Rats intermixed trials at macrovibrissa contact distance (nose >2 mm from surface) with trials at shorter distance (nose <2 mm from surface). Macrovibrissae were required for distant contact trials, while microvibrissae and non-whisker tactile cues were used for short distance trials. A psychometric curve was measured for macrovibrissa-based sandpaper texture discrimination. Rats discriminated rough P150 from smoother P180, P280, and P400 sandpaper (100, 82, 52, and 35 µm mean grit size, respectively). Use of olfactory, visual, and auditory cues was ruled out. This is the highest reported resolution for rodent texture discrimination, and constrains models of neural coding of texture information

Local circuits targeting parvalbumin-containing interneurons in layer IV of rat barrel cortex

Interactions between inhibitory interneurons and excitatory spiny neurons and also other inhibitory cells represent fundamental network properties which cause the so-called thalamo-cortical response transformation and account for the well-known receptive field differences of cortical layer IV versus thalamic neurons. We investigated the currently largely unknown morphological basis of these interactions utilizing acute slice preparations of barrel cortex in P19-21 rats. Layer IV spiny (spiny stellate, star pyramidal and pyramidal) neurons or inhibitory (basket and bitufted) interneurons were electrophysiologically characterized and intracellularly biocytin-labeled. In the same slice, we stained parvalbumin-immunoreactive (PV-ir) interneurons as putative target cells after which the tissue was subjected to confocal image acquisition. Parallel experiments confirmed the existence of synaptic contacts in these types of connection by correlated light and electron microscopy. The axons of the filled neurons differentially targeted barrel PV-ir interneurons: (1) The relative number of all contacted PV-ir cells within the axonal sphere was 5–17% for spiny (n = 10), 32 and 58% for basket (n = 2) and 12 and 13% for bitufted (n = 2) cells. (2) The preferential subcellular site which was contacted on PV-ir target cells was somatic for four and dendritic for five spiny cells; for basket cells, there was a somatic and for bitufted cells a dendritic preference in each examined case. (3) The highest number of contacts on a single PV-ir cell was 9 (4 somatic and 5 dendritic) for spiny neurons, 15 (10 somatic and 5 dendritic) for basket cells and 4 (1 somatic and 3 dendritic) for bitufted cells. These patterns suggest a cell type-dependent communication within layer IV microcircuits in which PV-ir interneurons provide not only feed-forward but also feedback inhibition thus triggering the thalamo-cortical response transformation

Swarming on Random Graphs II

We consider an individual-based model where agents interact over a random network via first-order dynamics that involve both attraction and repulsion. In the case of all-to-all coupling of agents in Rd this system has a lowest energy state in which an equal number of agents occupy the vertices of the d-dimensional simplex. The purpose of this paper is to sharpen and extend a line of work initiated in [56], which studies the behavior of this model when the interaction between the N agents occurs according to an Erdős-Rényi random graph G(N, p) instead of all-to-all coupling. In particular, we study the effect of randomness on the stability of these simplicial solutions, and provide rigorous results to demonstrate that stability of these solutions persists for probabilities greater than Np = O(logN). In other words, only a relatively small number of interactions are required to maintain stability of the state. The results rely on basic probability arguments together with spectral properties of random graphs.

The P2 Receptor Antagonist PPADS Supports Recovery from Experimental Stroke In Vivo

BACKGROUND: After ischemia of the CNS, extracellular adenosine 5'-triphosphate (ATP) can reach high concentrations due to cell damage and subsequent increase of membrane permeability. ATP may cause cellular degeneration and death, mediated by P2X and P2Y receptors. METHODOLOGY/PRINCIPAL FINDINGS: The effects of inhibition of P2 receptors by pyridoxalphosphate-6-azophenyl-2',4'-disulphonic acid (PPADS) on electrophysiological, functional and morphological alterations in an ischemia model with permanent middle cerebral artery occlusion (MCAO) were investigated up to day 28. Spontaneously hypertensive rats received PPADS or vehicle intracerebroventricularly 15 minutes prior MCAO for up to 7 days. The functional recovery monitored by qEEG was improved by PPADS indicated by an accelerated recovery of ischemia-induced qEEG changes in the delta and alpha frequency bands along with a faster and sustained recovery of motor impairments. Whereas the functional improvements by PPADS were persistent at day 28, the infarct volume measured by magnetic resonance imaging and the amount of TUNEL-positive cells were significantly reduced by PPADS only until day 7. Further, by immunohistochemistry and confocal laser scanning microscopy, we identified both neurons and astrocytes as TUNEL-positive after MCAO. CONCLUSION: The persistent beneficial effect of PPADS on the functional parameters without differences in the late (day 28) infarct size and apoptosis suggests that the early inhibition of P2 receptors might be favourable for the maintenance or early reconstruction of neuronal connectivity in the periinfarct area after ischemic incidents