Stability of Self Similar Flows of Second Kind in the Neighbourhood of a Critical Point

Following method developed by Bhatnagar & Prasad, based on the investigations of Kulikovskii & Slobodkina, we study the stability of self-similar flows generated by the propagation of shock-wave in an inhomogeneous medium with density varying either exponentially or as a power of distance. Also we consider the shocks produced by impulsive load. We find that all these flows are stable in the neighbourhood of critical point, which is a saddle point of the system of differential equations governing the flow in its neighbourhood

Dynamics of modulationally unstable ionacoustic wave packets in plasmas with negative ions

In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schrödinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory

Electron acoustic solitons in the Earth's magnetotail

International audienceSmall amplitude electron - acoustic solitons are studied in a magnetized plasma consisting of two types of electrons, namely cold electron beam and background plasma electrons and two temperature ion plasma. The analysis predicts rarefactive solitons. The model may provide a possible explanation for the perpendicular polarization of the low-frequency component of the broadband electrostatic noise observed in the Earth's magnetotail

Ion-Acoustic Solitons in Bi-Ion Dusty Plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg-de-Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compressi- on and rarefaction solitons depends continuously on the dust density. A modified Korteveg-de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of the dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.Comment: 17 pages, 5 figure

Solitary Dust--Acoustic Waves in a Plasma with Two-Temperature Ions and Distributed Grain Size

The propagation of weakly nonlinear dust--acoustic waves in a dusty plasma containing two ion species with different temperatures is explored. The nonlinear equations describing both the quadratic and cubic plasma nonlinearities are derived. It is shown that the properties of dust--acoustic waves depend substantially on the grain size distribution. In particular, for solitary dust--acoustic waves with a positive potential to exist in a plasma with distributed grain size, it is necessary that the difference between the temperatures of two ion species be large that that in the case of unusized grains.Comment: 16 pages, 6 figure

Continuous flexibility analysis of SARS-CoV-2 spike prefusion structures

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results.The authors would like to acknowledge financial support from CSIC (PIE/COVID-19 No. 202020E079), the Comunidad de Madrid through grant CAM (S2017/BMD-3817), the Spanish Ministry of Science and Innovation through projects SEV 2017-0712, FPU-2015/264 and PID2019-104757RB-I00/AEI/ FEDER, the Instituto de Salud Carlos III [PT17/0009/0010 (ISCIII-SGEFI/ERDF)], and the European Union and Horizon 2020 through grants INSTRUCT–ULTRA (INFRADEV-03-2016-2017, Proposal 731005), EOSC Life (INFRAEOSC-04-2018, Proposal 824087), HighResCells (ERC-2018-SyG, Proposal 810057), IMpaCT (WIDESPREAD- 03-2018, Proposal 857203), CORBEL (INFRADEV-1-2014-1, Proposal 654248) and EOSC–Synergy (EINFRA-EOSC-5, Proposal 857647). HDT and BF were supported by NIH grant GM125769 and JSM was supported by NIH grant R01-AI12752

Comparison of machine learning and semi-quantification algorithms for (I123)FP-CIT classification: the beginning of the end for semi-quantification?

Background Semi-quantification methods are well established in the clinic for assisted reporting of (I123) Ioflupane images. Arguably, these are limited diagnostic tools. Recent research has demonstrated the potential for improved classification performance offered by machine learning algorithms. A direct comparison between methods is required to establish whether a move towards widespread clinical adoption of machine learning algorithms is justified. This study compared three machine learning algorithms with that of a range of semi-quantification methods, using the Parkinson’s Progression Markers Initiative (PPMI) research database and a locally derived clinical database for validation. Machine learning algorithms were based on support vector machine classifiers with three different sets of features: Voxel intensities Principal components of image voxel intensities Striatal binding radios from the putamen and caudate. Semi-quantification methods were based on striatal binding ratios (SBRs) from both putamina, with and without consideration of the caudates. Normal limits for the SBRs were defined through four different methods: Minimum of age-matched controls Mean minus 1/1.5/2 standard deviations from age-matched controls Linear regression of normal patient data against age (minus 1/1.5/2 standard errors) Selection of the optimum operating point on the receiver operator characteristic curve from normal and abnormal training data Each machine learning and semi-quantification technique was evaluated with stratified, nested 10-fold cross-validation, repeated 10 times. Results The mean accuracy of the semi-quantitative methods for classification of local data into Parkinsonian and non-Parkinsonian groups varied from 0.78 to 0.87, contrasting with 0.89 to 0.95 for classifying PPMI data into healthy controls and Parkinson’s disease groups. The machine learning algorithms gave mean accuracies between 0.88 to 0.92 and 0.95 to 0.97 for local and PPMI data respectively. Conclusions Classification performance was lower for the local database than the research database for both semi-quantitative and machine learning algorithms. However, for both databases, the machine learning methods generated equal or higher mean accuracies (with lower variance) than any of the semi-quantification approaches. The gain in performance from using machine learning algorithms as compared to semi-quantification was relatively small and may be insufficient, when considered in isolation, to offer significant advantages in the clinical context

Prototypes for Content-Based Image Retrieval in Clinical Practice

Content-based image retrieval (CBIR) has been proposed as key technology for computer-aided diagnostics (CAD). This paper reviews the state of the art and future challenges in CBIR for CAD applied to clinical practice