Mechanistic description of spontaneous loss of memory persistent activity based on neuronal synaptic strength.

Persistent neural activity associated with working memory (WM) lasts for a limited time duration. Current theories suggest that its termination is actively obtained via inhibitory currents, and there is currently no theory regarding the possibility of a passive memory-loss mechanism that terminates memory persistent activity. Here, we develop an analytical-framework, based on synaptic strength, and show via simulations and fitting to wet-lab experiments, that passive memory-loss might be a result of an ionic-current long-term plateau, i.e., very slow reduction of memory followed by abrupt loss. We describe analytically the plateau, when the memory state is just below criticality. These results, including the plateau, are supported by experiments performed on rats. Moreover, we show that even just above criticality, forgetfulness can occur due to neuronal noise with ionic-current fluctuations, yielding a plateau, representing memory with very slow decay, and eventually a fast memory decay. Our results could have implications for developing new medications, targeted against memory impairments, through modifying neuronal noise.

Efficient network immunization under limited knowledge.

Targeted immunization of centralized nodes in large-scale networks has attracted significant attention. However, in real-world scenarios, knowledge and observations of the network may be limited, thereby precluding a full assessment of the optimal nodes to immunize (or quarantine) in order to avoid epidemic spreading such as that of the current coronavirus disease (COVID-19) epidemic. Here, we study a novel immunization strategy where only n nodes are observed at a time and the most central among these n nodes is immunized. This process can globally immunize a network. We find that even for small n (≈10) there is significant improvement in the immunization (quarantine), which is very close to the levels of immunization with full knowledge. We develop an analytical framework for our method and determine the critical percolation threshold p c and the size of the giant component P ∞ for networks with arbitrary degree distributions P(k). In the limit of n → ∞ we recover prior work on targeted immunization, whereas for n = 1 we recover the known case of random immunization. Between these two extremes, we observe that, as n increases, p c increases quickly towards its optimal value under targeted immunization with complete information. In particular, we find a new general scaling relationship between |p c (∞) - p c (n)| and n as |p c (∞) - p c (n)| ∼ n -1exp(-αn). For scale-free (SF) networks, where P(k) ∼ k -γ, 2 < γ < 3, we find that p c has a transition from zero to nonzero when n increases from n = 1 to O(log N) (where N is the size of the network). Thus, for SF networks, having knowledge of ≈log N nodes and immunizing the most optimal among them can dramatically reduce epidemic spreading. We also demonstrate our limited knowledge immunization strategy on several real-world networks and confirm that in these real networks, p c increases significantly even for small n.

Impact of food distribution on lifetime of a forager with or without sense of smell.

Modeling foraging via basic models is a problem that has been recently investigated from several points of view. However, understanding the effect of the spatial distribution of food on the lifetime of a forager has not been achieved yet. We explore here how the distribution of food in space affects the forager's lifetime in several different scenarios. We analyze a random forager and a smelling forager in both one and two dimensions. We first consider a general food distribution, and then analyze in detail specific distributions including constant distance between food, certain probability of existence of food at each site, and power-law distribution of distances between food. For a forager in one dimension without smell we find analytically the lifetime, and for a forager with sense of smell we find the condition for immortality. In two dimensions we find based on analytical considerations that the lifetime (T) scales with the starving time (S) and food density (f) as T∼S^{4}f^{3/2}.

Distance distribution in extreme modular networks.

Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks, and social media. Having the knowledge of the shortest paths length distribution between random pairs of nodes in such networks is important for understanding many processes, including diffusion or flow. Here, we provide analytical methods which are in good agreement with simulations on large scale networks with an extreme modular structure. By extreme modular, we mean that two modules or communities may be connected by maximum one link. As a result of the modular structure of the network, we obtain a distribution showing many peaks that represent the number of modules a typical shortest path is passing through. We present theory and results for the case where interlinks are weighted, as well as cases in which the interlinks are spread randomly across nodes in the community or limited to a specific set of nodes.

Interconnections between networks acting like an external field in a first-order percolation transition.

Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we show how the effects of such interconnections can be described as an external field for interdependent networks experiencing a first-order percolation transition. We find that the critical exponents γ and δ, related to the external field, can also be defined for first-order transitions but that they have different values than those found for second-order transitions. Surprisingly, we find that both sets of different exponents (for first and second order) can even be found within a single model of interdependent networks, depending on the dependency coupling strength. Nevertheless, in both cases both sets satisfy Widom's identity, δ-1=γ/ß, which further supports the validity of their definitions. Furthermore, we find that both Erdos-Rényi and scale-free networks have the same values of the exponents in the first-order regime, implying that these models are in the same universality class. In addition, we find that in k-core percolation the values of the critical exponents related to the field are the same as for interdependent networks, suggesting that these systems also belong to the same universality class.

Spatio-temporal propagation of cascading overload failures in spatially embedded networks.

Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The cascading overload failures are found to spread radially from the centre of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict the dynamics of cascading overload failures in realistic systems.