Pausing Purkinje Cells in the Cerebellum of the Awake Cat

A recent controversy has emerged concerning the existence of long pauses, presumably reflecting bistability of membrane potential, in the cerebellar Purkinje cells (PC) of awake animals. It is generally agreed that in the anesthetized animals and in vitro, these cells switch between two stable membrane potential states: a depolarized state (the ‘up-state’) characterized by continuous firing of simple spikes (SS) and a hyperpolarized state (the ‘down-state’) characterized by long pauses in the SS activity. To address the existence of long pauses in the neural activity of cerebellar PCs in the awake and behaving animal we used extracellular recordings in cats and find that approximately half of the recorded PCs exhibit such long pauses in the SS activity and transition between activity – periods with uninterrupted SS lasting an average of 1300 ms – and pauses up to several seconds. We called these cells pausing Purkinje cells (PPC) and they can easily be distinguished from continuous firing Purkinje cells. In most PPCs, state transitions in both directions were often associated (25% of state transitions) with complex spikes (CSs). This is consistent with intracellular findings of CS-driven state transitions. In sum, we present proof for the existence of long pauses in the PC SS activity that probably reflect underlying bistability, provide the first in-depth analysis of these pauses and show for the first time that transitions in and out of these pauses are related to CS firing in the awake and behaving animal

Asymptotic analysis for the generalized langevin equation

Various qualitative properties of solutions to the generalized Langevin equation (GLE) in a periodic or a confining potential are studied in this paper. We consider a class of quasi-Markovian GLEs, similar to the model that was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem (invariance principle), short time asymptotics and the white noise limit are studied. Our proofs are based on a careful analysis of a hypoelliptic operator which is the generator of an auxiliary Markov process. Systematic use of the recently developed theory of hypocoercivity \cite{Vil04HPI} is made.Comment: 27 pages, no figures. Submitted to Nonlinearity

Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force

We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force

Influence of age, social patterns and nasopharyngeal carriage on antibodies to three conserved pneumococcal surface proteins (PhtD, PcpA and PrtA) in healthy young children

The acquisition of specific antibodies is paramount to protect children against pneumococcal diseases, and a better understanding of how age, ethnicity and/or Streptococcus pneumoniae (Spn) nasopharyngeal carriage influence the acquisition of antibodies to pneumococcal surface proteins (PSP) is important for the development of novel serodiagnostic and immunisation strategies. IgG antibody titres against three conserved PSP (PhtD, PcpA and PrtA) in the sera of 451 healthy children aged 1 to 24months from Israel [Jewish (50.1%) and Bedouin (49.9%)] were measured by enzyme-linked immunosorbent assay (ELISA), while nasopharyngeal swabs from these children were assessed for the presence of Spn. Globally, anti-PhtD and anti-PrtA geometric mean concentrations (GMC; EU/ml) were high at <2.5months of age [PhtD: 35.3, 95% confidence interval (CI) 30.6-40.6; PrtA: 71.2, 95 % CI 60-84.5], was lower at 5-7months of age (PhtD: 10, 95 % CI 8-12.4; PrtA: 17.9, 95 % CI 14.4-22.1) and only increased after 11months of age. In contrast, an increase in anti-PcpA was observed at 5-7months of age. Anti-PcpA and anti-PrtA, but not anti-PhtD, were significantly higher in Bedouin children (PcpA: 361.6 vs. 226.3, p = 0.02; PrtA: 67.2 vs. 29.5, p < 0.001) in whom Spn nasopharyngeal carriage was identified earlier (60% vs. 38% of carriers <6months of age, p = 0.002). Spn carriage was associated with significantly higher anti-PSP concentrations in carriers than in non-carriers (p < 0.001 for each PSP). Thus, age, ethnicity and, essentially, nasopharyngeal carriage exert distinct cumulative influences on infant responses to PSP. These specific characteristics are worthwhile to include in the evaluation of pneumococcal seroresponses and the development of new PSP-based vaccine

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Process-based classification of Mediterranean cyclones using potential vorticity

This is the final version. Available on open access from Copernicus Publications via the DOI in this recordCode availability:The code for the SOM classification algorithm is openly available at https://www.mathworks.com/help/deeplearning/gs/cluster-data-with-a-self-organizingmap.html (last access: 29 January 2024).Data availability: The composite cyclone tracks with the resulting cluster attribution are available in the supplementary assets of this paper. The track labels correspond to the composite cyclone track dataset at confidence level 5, made available as a Supplement by Flaounas et al. (2023) (“TRACKS_CL5.dat”).Mediterranean cyclones (MCs) govern extreme weather events across the Euro-African Basin, affecting the lives of hundreds of millions. Despite many studies addressing MCs in the last few decades, their correct simulation and prediction remain a significant challenge to the present day, which may be attributed to the large variability among MCs. Past classifications of MCs are primarily based on geographical and/or seasonal separations; however, here we focus on cyclone genesis and deepening mechanisms. A variety of processes combine to govern MC genesis and evolution, including adiabatic and diabatic processes, topographic influences, land-sea contrasts, and local temperature anomalies. As each process bears a distinct signature on the potential vorticity (PV) field, a PV approach is used to distinguish among different "types"of MCs. Here, a combined cyclone-tracking algorithm is used to detect 3190 Mediterranean cyclone tracks in ECMWF ERA5 from 1979-2020. Cyclone-centered, upper-level isentropic PV structures in the peak time of each cyclone track are classified using a self-organizing map (SOM). The SOM analysis reveals nine classes of Mediterranean cyclones, with distinct Rossby-wave-breaking patterns, discernible in corresponding PV structures. Although classified by upper-level PV structures, each class shows different contributions of lower-tropospheric PV and flow structures down to the surface. Unique cyclone life cycle characteristics, associated hazards (precipitation, winds, and temperature anomalies), and long-term trends, as well as synoptic, thermal, dynamical, seasonal, and geographical features of each cyclone class, indicate dominant processes in their evolution. Among others, the classification reveals the importance of topographically induced Rossby wave breaking to the generation of the most extreme Mediterranean cyclones. These results enhance our understanding of MC predictability by linking the large-scale Rossby wave formations and life cycles to coherent classes of under-predicted cyclone aspects.de Botton Center for Marine ScienceIsraeli Council for Higher Education (CHE)Weizmann Data Science Research CenterWeizmann Institute Sustainability and Energy Research Initiative (SAERI

A weak characterization of slow variables in stochastic dynamical systems

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system