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The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020 [37]. In view of most recent information on testing activity [32], we present here an update of our initial work [4]. In this work, mathematical models have been developed to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended here to account for undetected infections, as well as for stages of infections and age groups. The models are calibrated on data until April 5, data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases and reduced contact to risk groups.
COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. In this work, several mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Considering different starting times of infection, parameters sets that represent infectivity of SARS-CoV-2 are computed and compared with other viral infections that can also cause pandemics.
Based on the target cell model, SARS-CoV-2 infecting time between susceptible cells (mean of 30 days approximately) is much slower than those reported for Ebola (about 3 times slower) and influenza (60 times slower). The within-host reproductive number for SARS-CoV-2 is consistent to the values of influenza infection (1.7-5.35). The best model to fit the data was including immune responses, which suggest a slow cell response peaking between 5 to 10 days post onset of symptoms. The model with eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, both, the target cell model and the model with immune responses, predict that virus may replicate very slowly in the first days after infection, and it could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work.
The production of the Λ(1520) baryonic resonance has been measured at midrapidity in inelastic pp collisions at s√ = 7 TeV and in p-Pb collisions at sNN−−−√ = 5.02 TeV for non-single diffractive events and in multiplicity classes. The resonance is reconstructed through its hadronic decay channel Λ(1520) → pK− and the charge conjugate with the ALICE detector. The integrated yields and mean transverse momenta are calculated from the measured transverse momentum distributions in pp and p-Pb collisions. The mean transverse momenta follow mass ordering as previously observed for other hyperons in the same collision systems. A Blast-Wave function constrained by other light hadrons (π, K, K0S, p, Λ) describes the shape of the Λ(1520) transverse momentum distribution up to 3.5 GeV/c in p-Pb collisions. In the framework of this model, this observation suggests that the Λ(1520) resonance participates in the same collective radial flow as other light hadrons. The ratio of the yield of Λ(1520) to the yield of the ground state particle Λ remains constant as a function of charged-particle multiplicity, suggesting that there is no net effect of the hadronic phase in p-Pb collisions on the Λ(1520) yield.
The study of (anti-)deuteron production in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high energy hadronic collisions. In this paper the production of (anti-)deuterons is studied as a function of the charged particle multiplicity in inelastic pp collisions at s√=13 TeV using the ALICE experiment. Thanks to the large accumulated integrated luminosity, it has been possible to measure (anti-)deuteron production in pp collisions up to the same charged particle multiplicity (dNch/dη∼26) as measured in p-Pb collisions at similar centre-of-mass energies. Within the uncertainties, the deuteron yield in pp collisions resembles the one in p-Pb interactions, suggesting a common formation mechanism behind the production of light nuclei in hadronic interactions. In this context the measurements are compared with the expectations of coalescence and Statistical Hadronisation Models (SHM).
The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe, with about 571,700 confirmed cases and about 26,500 deaths as of March 28th, 2020. We present here the preliminary results of a mathematical study directed at informing on the possible application or lifting of control measures in Germany. The developed mathematical models allow to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions.
Individual differences in perception are widespread. Considering inter-individual variability, synesthetes experience stable additional sensations; schizophrenia patients suffer perceptual deficits in e.g. perceptual organization (alongside hallucinations and delusions). Is there a unifying principle explaining inter-individual variability in perception? There is good reason to believe perceptual experience results from inferential processes whereby sensory evidence is weighted by prior knowledge about the world. Different perceptual phenotypes may result from different precision weighting of sensory evidence and prior knowledge. We tested this hypothesis by comparing visibility thresholds in a perceptual hysteresis task across medicated schizophrenia patients, synesthetes, and controls. Participants rated the subjective visibility of stimuli embedded in noise while we parametrically manipulated the availability of sensory evidence. Additionally, precise long-term priors in synesthetes were leveraged by presenting either synesthesia-inducing or neutral stimuli. Schizophrenia patients showed increased visibility thresholds, consistent with overreliance on sensory evidence. In contrast, synesthetes exhibited lowered thresholds exclusively for synesthesia-inducing stimuli suggesting high-precision long-term priors. Additionally, in both synesthetes and schizophrenia patients explicit, short-term priors – introduced during the hysteresis experiment – lowered thresholds but did not normalize perception. Our results imply that distinct perceptual phenotypes might result from differences in the precision afforded to prior beliefs and sensory evidence, respectively.
The development of binocular vision is an active learning process comprising the development of disparity tuned neurons in visual cortex and the establishment of precise vergence control of the eyes. We present a computational model for the learning and self-calibration of active binocular vision based on the Active Efficient Coding framework, an extension of classic efficient coding ideas to active perception. Under normal rearing conditions, the model develops disparity tuned neurons and precise vergence control, allowing it to correctly interpret random dot stereogramms. Under altered rearing conditions modeled after neurophysiological experiments, the model qualitatively reproduces key experimental findings on changes in binocularity and disparity tuning. Furthermore, the model makes testable predictions regarding how altered rearing conditions impede the learning of precise vergence control. Finally, the model predicts a surprising new effect that impaired vergence control affects the statistics of orientation tuning in visual cortical neurons.
Active efficient coding explains the development of binocular vision and its failure in amblyopia
(2020)
The development of vision during the first months of life is an active process that comprises the learning of appropriate neural representations and the learning of accurate eye movements. While it has long been suspected that the two learning processes are coupled, there is still no widely accepted theoretical framework describing this joint development. Here we propose a computational model of the development of active binocular vision to fill this gap. The model is based on a new formulation of the Active Efficient Coding theory, which proposes that eye movements, as well as stimulus encoding, are jointly adapted to maximize the overall coding efficiency. Under healthy conditions, the model self-calibrates to perform accurate vergence and accommodation eye movements. It exploits disparity cues to deduce the direction of defocus, which leads to co-ordinated vergence and accommodation responses. In a simulated anisometropic case, where the refraction power of the two eyes differs, an amblyopia-like state develops, in which the foveal region of one eye is suppressed due to inputs from the other eye. After correcting for refractive errors, the model can only reach healthy performance levels if receptive fields are still plastic, in line with findings on a critical period for binocular vision development. Overall, our model offers a unifying conceptual framework for understanding the development of binocular vision.
Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction
(2020)
Class I ventral posterior dendritic arborisation (c1vpda) proprioceptive sensory neurons respond to contractions in the Drosophila larval body wall during crawling. Their dendritic branches run along the direction of contraction, possibly a functional requirement to maximise membrane curvature during crawling contractions. Although the molecular machinery of dendritic patterning in c1vpda has been extensively studied, the process leading to the precise elaboration of their comb-like shapes remains elusive. Here, to link dendrite shape with its proprioceptive role, we performed long-term, non-invasive, in vivo time-lapse imaging of c1vpda embryonic and larval morphogenesis to reveal a sequence of differentiation stages. We combined computer models and dendritic branch dynamics tracking to propose that distinct sequential phases of targeted growth and stochastic retraction achieve efficient dendritic trees both in terms of wire and function. Our study shows how dendrite growth balances structure–function requirements, shedding new light on general principles of self-organisation in functionally specialised dendrites.
The spike (S) protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is required for cell entry and is the major focus for vaccine development. We combine cryo electron tomography, subtomogram averaging and molecular dynamics simulations to structurally analyze S in situ. Compared to recombinant S, the viral S is more heavily glycosylated and occurs predominantly in a closed pre-fusion conformation. We show that the stalk domain of S contains three hinges that give the globular domain unexpected orientational freedom. We propose that the hinges allow S to scan the host cell surface, shielded from antibodies by an extensive glycan coat. The structure of native S contributes to our understanding of SARS-CoV-2 infection and the development of safe vaccines. The large scale tomography data set of SARS-CoV-2 used for this study is therefore sufficient to resolve structural features to below 5 Ångstrom, and is publicly available at EMPIAR-10453.
Learning in the eyes: specific changes in gaze patterns track explicit and implicit visual learning
(2020)
What is the link between eye movements and sensory learning? Although some theories have argued for a permanent and automatic interaction between what we know and where we look, which continuously modulates human information- gathering behavior during both implicit and explicit learning, there exist surprisingly little evidence supporting such an ongoing interaction. We used a pure form of implicit learning called visual statistical learning and manipulated the explicitness of the task to explore how learning and eye movements interact. During both implicit exploration and explicit visual learning of unknown composite visual scenes, eye movement patterns systematically changed in accordance with the underlying statistical structure of the scenes. Moreover, the degree of change was directly correlated with the amount of knowledge the observers acquired. Our results provide the first evidence for an ongoing and specific interaction between hitherto accumulated knowledge and eye movements during both implicit and explicit learning.
The way in which dendrites spread within neural tissue determines the resulting circuit connectivity and computation. However, a general theory describing the dynamics of this growth process does not exist. Here we obtain the first time-lapse reconstructions of neurons in living fly larvae over the entirety of their developmental stages. We show that these neurons expand in a remarkably regular stretching process that conserves their shape. Newly available space is filled optimally, a direct consequence of constraining the total amount of dendritic cable. We derive a mathematical model that predicts one time point from the previous and use this model to predict dendrite morphology of other cell types and species. In summary, we formulate a novel theory of dendrite growth based on detailed developmental experimental data that optimises wiring and space filling and serves as a basis to better understand aspects of coverage and connectivity for neural circuit formation.
The severity of the COVID-19 pandemic, caused by the SARS-CoV-2 coronavirus, calls for the urgent development of a vaccine. The primary immunological target is the SARS-CoV-2 spike (S) protein. S is exposed on the viral surface to mediate viral entry into the host cell. To identify possible antibody binding sites not shielded by glycans, we performed multi-microsecond molecular dynamics simulations of a 4.1 million atom system containing a patch of viral membrane with four full-length, fully glycosylated and palmitoylated S proteins. By mapping steric accessibility, structural rigidity, sequence conservation and generic antibody binding signatures, we recover known epitopes on S and reveal promising epitope candidates for vaccine development. We find that the extensive and inherently flexible glycan coat shields a surface area larger than expected from static structures, highlighting the importance of structural dynamics in epitope mapping.
Antimicrobial resistance is a major threat to global health and food security today. Scheduling cycling therapies by targeting phenotypic states associated to specific mutations can help us to eradicate pathogenic variants in chronic infections. In this paper, we introduce a logistic switching model in order to abstract mutation networks of collateral resistance. We found particular conditions for which unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimens.
Starting from an optimal-control formulation, the switching policies show their potential in the stabilization of the zero-equilibrium for dynamics governed by logistic maps. However, employing such switching strategies, deserve a specific characterization in terms of limit behaviour. Ultimately, we use evolutionary and control algorithms to find either optimal and sub-optimal switching policies. Simulations results show the applicability of Parrondo’s Paradox to design cycling therapies against drug resistance.
Inspired by the physiology of neuronal systems in the brain, artificial neural networks have become an invaluable tool for machine learning applications. However, their biological realism and theoretical tractability are limited, resulting in poorly understood parameters. We have recently shown that biological neuronal firing rates in response to distributed inputs are largely independent of size, meaning that neurons are typically responsive to the proportion, not the absolute number, of their inputs that are active. Here we introduce such a normalisation, where the strength of a neuron’s afferents is divided by their number, to various sparsely-connected artificial networks. The learning performance is dramatically increased, providing an improvement over other widely-used normalisations in sparse networks. The resulting machine learning tools are universally applicable and biologically inspired, rendering them better understood and more stable in our tests.
We report on the measurement of the size of the particle-emitting source from two-baryon correlations with ALICE in high-multiplicity pp collisions at s√ = 13 TeV. The source radius is studied with low relative momentum p-p, p¯-p¯, p-Λ and p¯-Λ¯ pairs as a function of the pair transverse mass mT considering for the first time in a quantitative way the effect of strong resonance decays. After correcting for this effect, the radii extracted for pairs of different particle species agree. This indicates that protons, antiprotons, Λ, and Λ¯ originate from the same source. Within the measured mT range (1.1-2.2) GeV/c2 the invariant radius of this common source varies between 0.85 and 1.3 fm. These results provide a precise reference for studies of the strong hadron-hadron interactions and for the investigation of collective properties in small colliding systems.
The production of π±, K±, K0S, K∗(892)0, p, ϕ(1020), Λ, Ξ−, Ω−, and their antiparticles was measured in inelastic proton-proton (pp) collisions at a center-of-mass energy of s√ = 13 TeV at midrapidity (|y|<0.5) as a function of transverse momentum (pT) using the ALICE detector at the CERN LHC. Furthermore, the single-particle pT distributions of K0S, Λ, and Λ¯¯¯¯ in inelastic pp collisions at s√ = 7 TeV are reported here for the first time. The pT distributions are studied at midrapidity within the transverse momentum range 0≤pT≤20 GeV/c, depending on the particle species. The pT spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower s√ and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high pT with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and xT≡2pT/s√ scaling properties of hadron production are also studied. As the collision energy increases from s√ = 7 to 13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of s√, while ratios for multi-strange hadrons indicate enhancements. The pT-differential cross sections of π±, K± and p (p¯¯¯) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for π± and p (p¯¯¯) at high pT.
In this Letter, we report the first measurement of the antideuteron inelastic cross section at low particle momenta, covering a range of 0.3≤p<4 GeV/c. The measurement is carried out using p-Pb collisions at a center-of-mass energy per nucleon-nucleon pair of sNN−−−√ = 5.02 TeV, recorded with the ALICE detector at the CERN LHC and utilizing the detector material as an absorber for antideuterons and antiprotons. The extracted raw primary antiparticle-to-particle ratios are compared to the results from detailed ALICE simulations based on the GEANT4 toolkit for the propagation of antiparticles through the detector material. The analysis of the raw primary (anti)proton spectra serves as a benchmark for this study, since their hadronic interaction cross sections are well constrained experimentally. The first measurement of the antideuteron inelastic cross section averaged over the ALICE detector material with atomic mass numbers ⟨A⟩ = 17.4 and 31.8 is obtained. The measured inelastic cross section points to a possible excess with respect to the Glauber model parameterization in the lowest momentum interval of 0.3≤p<0.47 GeV/c up to a factor 2.1. This result is relevant for the understanding of antimatter propagation and the contributions to antinuclei production from cosmic ray interactions within the interstellar medium. In addition, the momentum range covered by this measurement is of particular importance to evaluate signal predictions for indirect dark-matter searches.
Jet fragmentation transverse momentum distributions in pp and p–Pb collisions at √sNN = 5.02 TeV
(2020)
Jet fragmentation transverse momentum (jT) distributions are measured in proton-proton (pp) and proton-lead (p-Pb) collisions at sNN−−−√ = 5.02 TeV with the ALICE experiment at the LHC. Jets are reconstructed with the ALICE tracking detectors and electromagnetic calorimeter using the anti-kT algorithm with resolution parameter R=0.4 in the pseudorapidity range |η|<0.25. The jT values are calculated for charged particles inside a fixed cone with a radius R=0.4 around the reconstructed jet axis. The measured jT distributions are compared with a variety of parton-shower models. Herwig and PYTHIA 8 based models describe the data well for the higher jT region, while they underestimate the lower jT region. The jT distributions are further characterised by fitting them with a function composed of an inverse gamma function for higher jT values (called the "wide component"), related to the perturbative component of the fragmentation process, and with a Gaussian for lower jT values (called the "narrow component"), predominantly connected to the hadronisation process. The width of the Gaussian has only a weak dependence on jet transverse momentum, while that of the inverse gamma function increases with increasing jet transverse momentum. For the narrow component, the measured trends are successfully described by all models except for Herwig. For the wide component, Herwig and PYTHIA 8 based models slightly underestimate the data for the higher jet transverse momentum region. These measurements set constraints on models of jet fragmentation and hadronisation.
The elliptic flow (v2) of (anti-)3He is measured in Pb-Pb collisions at sNN−−−√ = 5.02 TeV in the transverse-momentum (pT) range of 2-6 GeV/c for the centrality classes 0-20%, 20-40%, and 40-60% using the event-plane method. This measurement is compared to that of pions, kaons, and protons at the same center-of-mass energy. A clear mass ordering is observed at low pT, as expected from relativistic hydrodynamics. The violation of the scaling of v2 with the number of constituent quarks at low pT, already observed for identified hadrons and deuterons at LHC energies, is confirmed also for (anti-)3He. The elliptic flow of (anti-)3He is underestimated by the Blast-Wave model and overestimated by a simple coalescence approach based on nucleon scaling. The elliptic flow of (anti-)3He measured in the centrality classes 0-20% and 20-40% is well described by a more sophisticated coalescence model where the phase-space distributions of protons and neutrons are generated using the iEBE-VISHNU hybrid model with AMPT initial conditions.