Equivariant embedding of finite-dimensional dynamical systems

We prove an equivariant version of the classical Menger-Nobeling theorem. Whenever a group $G$ acts on a finite-dimensional compact metric space $X$, there exists an equivariant topological embedding of $X$ to into $([0,1]^d)^G$, provided that for every positive integer $N$ the space of points in $X$ with orbit size at most $N$ has topological dimension strictly less than $\frac{d}{2}N$. Moreover, under the above assumptions, a generic continuous equivariant function from $X$ into $([0,1]^d)^G$ is a topological embedding. We emphasize that the result imposes no restrictions whatsoever on the acting group $G$ (beyond the existence of an action on a finite-dimensional space).Comment: 12 page

Within-Host Whole-Genome Deep Sequencing and Diversity Analysis of Human Respiratory Syncytial Virus Infection Reveals Dynamics of Genomic Diversity in the Absence and Presence of Immune Pressure

Human respiratory syncytial virus (RSV) is the leading cause of lower respiratory tract disease in infants and young children and an important respiratory pathogen in the elderly and immunocompromised. While population-wide molecular epidemiology studies have shown multiple cocirculating RSV genotypes and revealed antigenic and genetic change over successive seasons, little is known about the extent of viral diversity over the course of an individual infection, the origins of novel variants, or the effect of immune pressure on viral diversity and potential immune-escape mutations. To investigate viral population diversity in the presence and absence of selective immune pressures, we studied whole-genome deep sequencing of RSV in upper airway samples from an infant with severe combined immune deficiency syndrome and persistent RSV infection. The infection continued over several months before and after bone marrow transplant (BMT) from his RSV-immune father. RSV diversity was characterized in 26 samples obtained over 78 days. Diversity increased after engraftment, as defined by T-cell presence, and populations reflected variation mostly within the G protein, the major surface antigen. Minority populations with known palivizumab resistance mutations emerged after its administration. The viral population appeared to diversify in response to selective pressures, showing a statistically significant growth in diversity in the presence of pressure from immunity. Defining escape mutations and their dynamics will be useful in the design and application of novel therapeutics and vaccines. These data can contribute to future studies of the relationship between within-host and population-wide RSV phylodynamics

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Is Bicuspid Aortic Valve Morphology Genetically Determined? A Family-Based Study

International audienceBicuspid aortic valve (BAV) is a common congenital heart disease, with a 10-fold higher prevalence in first-degree relatives. BAV has different phenotypes based on the morphology of cusp fusion. These phenotypes are associated with different clinical courses and prognoses. Currently, the determinants of the valve phenotype are unknown. In this study we evaluated the role of genetics using familial cohorts. Patients with BAV and their first-degree relatives were evaluated by echocardiography. The concordance in BAV phenotype between pairs of family members was calculated and compared with the concordance expected by chance. We then performed a systematic literature review to identify additional reports and calculated the overall concordance rate. During the study period, 70 cases from 31 families and 327 sporadic cases were identified. BAV was diagnosed in 14% of the screened relatives. The proportions of the morphologies identified was: 12.3% for type 0, 66.2% for type 1-LR, 15.4% for type 1-RN, 4.6% for type 1-NL, and 1.5% for type 2. For the assessment of morphologic concordance, we included 120 pairs of first-degree relatives with BAV from our original cohort and the literature review. Concordance was found only in 62% of the pairs which was not significantly higher than expected by chance. In conclusion, our finding demonstrates intrafamilial variability in BAV morphology, suggesting that morphology is determined by factors other than Mendelian genetics. As prognosis differs by morphology, our findings may suggest that clinical outcomes may vary even between first-degree relatives