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Register a new userMoving bumps in theta neuron networks
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We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable bumps of activity, which move along the ring if the coupling kernel is asymmetric. We investigate the effects of the kernel asymmetry on the existence, stability and speed of these moving bumps using continuum equations formally describing infinite networks. Depending on the level of heterogeneity within the network we find complex sequences of bifurcations as the amount of asymmetry is varied, in strong contrast to the behaviour of a classical neural field model.
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We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics of neurons with the same in-degree. A Gaussian copula is used to introduce correlations between a neurons in- and out-degree and numerical bifurcation analysis is used determine the effects of these correlations on the networks dynamics. For excitatory coupling we find that inducing positive correlations has a similar effect to increasing the coupling strength between neurons, while for inhibitory coupling it has the opposite effect. We also determine the propensity of various two- and three-neuron motifs to occur as correlations are varied and give a plausible explanation for the observed changes in dynamics.
The search for young planets had its first breakthrough with the detection of the accreting planet PDS70b. In this study, we aim to broaden our understanding towards the formation of multi-planet systems such as HR8799 or the Solar System. Our previous study on HD169142, one of the closest Herbig stars, points towards a shadow-casting protoplanetary candidate. Here, we present follow-up observations to test our previously proposed hypothesis. We set our new data into context with previous observations to follow structural changes in the disk over the course of 6 years. We find spatially resolved systematic changes in the position of the previously described surface brightness dip in the inner ring. We further find changes in the brightness structure in azimuthal direction along the ring. And finally, a comparison of our SPHERE data with recent ALMA observations reveals a wavelength dependent radial profile of the bright ring. The time-scale on which the changes in the rings surface brightness occur suggest that they are caused by a shadow cast by a 1-10Mj planet surrounded by dust, an orbit comparable to those of the giant planets in our own Solar System. Additionally, we find the first indications for temperature-induced instabilities in the ring. And finally, we trace a pressure maxima, for the first time spatially resolved, with a width of 4.5au. The density distribution of the ring at mm wavelengths around the pressure maxima could further indicate effects from snow lines or even the dynamics and feedback of the larger grains.
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing driving external fields $h rightarrow 0$. Considering that this is rarely the case for natural systems, such a restriction poses a challenge to the explanatory power of these models. Besides that, in models of dissipative systems like earthquakes, forest fires and neuronal networks, there is no true critical behavior, as expressed in clean power laws obeying finite-size scaling, but a scenario called dirty criticality or self-organized quasi-criticality (SOqC). Here, we propose simple homeostatic mechanisms which promote self-organization of coupling strengths, gains, and firing thresholds in neuronal networks. We show that near criticality can be reached and sustained even in the presence of external inputs because the firing thresholds adapt to and cancel the inputs, a phenomenon similar to perfect adaptation in sensory systems. Similar mechanisms can be proposed for the couplings and local thresholds in spin systems and cellular automata, which could lead to applications in earthquake, forest fire, stellar flare, voting and epidemic modeling.
We study the strategy to optimally maximize the dynamic range of excitable networks by removing the minimal number of links. A network of excitable elements can distinguish a broad range of stimulus intensities and has its dynamic range maximized at criticality. In this study, we formulate the activation propagation in excitable networks as a message passing process in which the critical state is reached when the largest eigenvalue of the weighted non-backtracking (WNB) matrix is exactly one. By considering the impact of single link removal on the largest eigenvalue, we develop an efficient algorithm that aims to identify the optimal set of links whose removal will drive the system to the critical state. Comparisons with other competing heuristics on both synthetic and real-world networks indicate that the proposed method can maximize the dynamic range by removing the smallest number of links, and at the same time maintain the largest size of the giant connected component.
In practical terms, controlling a network requires manipulating a large number of nodes with a comparatively small number of external inputs, a process that is facilitated by paths that broadcast the influence of the (directly-controlled) driver nodes to the rest of the network. Recent work has shown that surprisingly, temporal networks can enjoy tremendous control advantages over their static counterparts despite the fact that in temporal networks such paths are seldom instantaneously available. To understand the underlying reasons, here we systematically analyze the scaling behavior of a key control cost for temporal networks--the control energy. We show that the energy costs of controlling temporal networks are determined solely by the spectral properties of an effective Gramian matrix, analogous to the static network case. Surprisingly, we find that this scaling is largely dictated by the first and the last network snapshot in the temporal sequence, independent of the number of intervening snapshots, the initial and final states, and the number of driver nodes. Our results uncover the intrinsic laws governing why and when temporal networks save considerable control energy over their static counterparts.
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