Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models—also known as firing rate models or firing rate equations—to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings

Tropospheric and stratospheric smoke over Europe as observed within EARLINET/ACTRIS in summer 2017

For several weeks in summer 2017, strong smoke layers were observed over Europe at numerous EARLINET stations. EARLINET is the European research lidar network and part of ACTRIS and comprises more than 30 ground-based lidars. The smoke layers were observed in the troposphere as well as in the stratosphere up to 25 km from Northern Scandinavia over whole western and central Europe to the Mediterranean regions. Backward trajectory analysis among other tools revealed that these smoke layers originated from strong wild fires in western Canada in combination with pyrocumulus convection. An extraordinary fire event in the mid of August caused intense smoke layers that were observed across Europe for several weeks starting on 18 August 2017. Maximum aerosol optical depths up to 1.0 at 532 nm were observed at Leipzig, Germany, on 22 August 2017 during the peak of this event. The stratospheric smoke layers reached extinction coefficient values of more than 600 Mm−1 at 532 nm, a factor of 10 higher than observed for volcanic ash after the Pinatubo eruption in the 1990s. First analyses of the intensive optical properties revealed low particle depolarization values at 532 nm for the tropospheric smoke (spherical particles) and rather high values (up to 20%) in the stratosphere. However, a strong wavelength dependence of the depolarization ratio was measured for the stratospheric smoke. This indicates irregularly shaped stratospheric smoke particles in the size range of the accumulation mode. This unique depolarization feature makes it possible to distinguish clearly smoke aerosol from cirrus clouds or other aerosol types by polarization lidar measurements. Particle extinction-to-backscatter ratios were rather low in the order of 40 to 50 sr at 355 nm, while values between 70-90 sr were measured at higher wavelengths. In the western and central Mediterranean, stratospheric smoke layers were most prominent in the end of August at heights between 16 and 20 km. In contrast, stratospheric smoke started to occur in the eastern Mediterranean (Cyprus and Israel) in the beginning of September between 18 and 23 km. Stratospheric smoke was still visible in the beginning of October at certain locations (e.g. Evora, Portugal), while tropospheric smoke was mainly observed until the end of August within Europe. An overview of the smoke layers measured at several EARLINET sites will be given. The temporal development of these layers as well as their geometrical and optical properties will be presented

Comprehensive genomic meta-analysis identifies intra-tumoural stroma as a predictor of survival in patients with gastric cancer

10.1136/gutjnl-2011-301373Gut6281100-1111GUTT

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations without an explicit time delay. We show that this discrepancy is due to a voltage-dependent spike-synchronization mechanism inherent in networks of spiking neurons which is not captured by standard firing rate equations. Here we investigate an exact low-dimensional description for a network of heterogeneous canonical Class 1 inhibitory neurons which includes the sub-threshold dynamics crucial for generating synchronous states. In the limit of slow synaptic kinetics the spike-synchrony mechanism is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inputs are also slow. However, even in this limit synchronous spiking can be elicited by inputs which fluctuate on a time-scale of the membrane time-constant of the neurons. Our meanfield equations therefore represent an extension of the standard Wilson-Cowan equations in which spike synchrony is also correctly described.FD and EM acknowledge support by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement No. 642563. AR acknowledges a project grant from the Spanish ministry of Economics and Competitiveness, Grants No. BFU2012-33413 and MTM2015-71509. AR has been partially funded by the CERCA progam of the Generalitat de Catalunya. EM acknowledges the projects grants from the Spanish ministry of Economics and Competitiveness, Grants No. PSI2016-75688- P and No. PCIN-2015- 127. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Coronal Heating as Determined by the Solar Flare Frequency Distribution Obtained by Aggregating Case Studies

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating.Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 7