Generalized Convexity Properties and Shape-Based Approximation in Networks Reliability

Some properties of generalized convexity for sets and functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is developed based on their mutual complementarity properties. The approximating objects are from the class of quadratic spline functions, constructed based on both interpolation conditions and shape knowledge. It is proved that the approximant objects preserve both the high-order convexity and some extremum properties of the exact reliability polynomials. It leads to pointing out the area of the network where the maximum number of paths is achieved. Numerical examples and simulations show the performance of the algorithm, both in terms of low complexity, small error and shape preserving. Possibilities of increasing the accuracy of approximation are discussed.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington’s landscape theory and bifurcation analysis, we have shown that both Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining positive feedback motifs with different types of incoherent feedback motifs. Our study demonstrates that the intrinsic bi-stable dynamics due to the presence of the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these proposed minimal networks to orchestrate these complex bifurcations. These modeling insights will be useful in identifying and analyzing possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

Exploiting heterogeneity in operational neural networks by synaptic plasticity

The recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are based on a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, the default search method to find optimal operators in ONNs, the so-called Greedy Iterative Search (GIS) method, usually takes several training sessions to find a single operator set per layer. This is not only computationally demanding, also the network heterogeneity is limited since the same set of operators will then be used for all neurons in each layer. To address this deficiency and exploit a superior level of heterogeneity, in this study the focus is drawn on searching the best-possible operator set(s) for the hidden neurons of the network based on the “Synaptic Plasticity” paradigm that poses the essential learning theory in biological neurons. During training, each operator set in the library can be evaluated by their synaptic plasticity level, ranked from the worst to the best, and an “elite” ONN can then be configured using the top-ranked operator sets found at each hidden layer. Experimental results over highly challenging problems demonstrate that the elite ONNs even with few neurons and layers can achieve a superior learning performance than GIS-based ONNs and as a result, the performance gap over the CNNs further widens.

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

ICM cells can be partitioned robustly through transient synchronization using secreted FGF4

The differentiation of ICM cells into epiblast (EPI) and primitive endoderm (PE) is central in embryonic development. It is known that FGF4 signaling is important in this process, but it remains unclear how cells can be correctly partitioned. Here we model the NANOG-GATA6-FGF4 network, and test all 64 logical regulatory combinations for their ability to partition a group of cells. We found that nearly all the logic combinations allowed for correct partitioning, including a minimal network where self-activation of NANOG and GATA6 was inactivated. However such self-activation increased the robustness of the system. Furthermore, the model also captured the reported changes in cell proportions in response to FGF perturbations. This constrains the possible regulatory logic and predicts the presence of an “OR” gate in cell-cell communication. We repeatedly found that FGF4 coordinated the decision in two phases: A convergence and a bifurcation phase. First FGF4 negative feedback drives the cells to a balanced “battle” state where most cells have intermediate levels of both regulators, thus being double positive. Subsequent bifurcation happens at constant FGF4 level. Together our results suggest that the frequently observed state of multipotency during differentiation may be an emergent phenomenon resulting from inter-cellular negative feedbacks.

Reconfigurable Web-Interface Remote Lab for Instrumentation and Electronic Learning

Lab sessions in engineering education are designed to reinforce theoretical concepts. However, usually there are not enough time to reinforce all of them. Remote and virtual lab give students more time for reinforce those concepts. In particular, with remote labs, this can be done interacting with real lab equipment and specific configurations. This work proposes a flexible configuration for Remote Lab Sessions, based on some of 2019 most popular programming languages (Python and JavaScript). This configuration needed minimal network privileges, it is easily to scale and reconfigure. Its structure is based on a unique Reception-Server (which hosts User database, and Time Shift Manager, it is accessible from The Internet, and connect Users with Instruments-Servers) and some Instrument-Servers (which manage hardware connection and host experiences). Users always connect to Reception-Server, and book a shift for an experience. During the time range associate to that shift, User is internally forwarded to Instrument-Server associated with selected experience, so User is still connected to Reception-Serer. In this way, Reception-Server acts as a firewall, protecting Instrument-Servers, which never are open to The Internet. A triple evaluation system is implemented, User session logging and auto-evaluation (objectives accomplished) a knowledge test and an interaction survey. An experience is implemented, controlling a DC source using Standard Commands for Programmable Instruments.

CDC-42 Interactions with Par Proteins Are Critical for Proper Patterning in Polarization

Many cells rearrange proteins and other components into spatially distinct domains in a process called polarization. This asymmetric patterning is required for a number of biological processes including asymmetric division, cell migration, and embryonic development. Proteins involved in polarization are highly conserved and include members of the Par and Rho protein families. Despite the importance of these proteins in polarization, it is not yet known how they interact and regulate each other to produce the protein localization patterns associated with polarization. In this study, we develop and analyse a biologically based mathematical model of polarization that incorporates interactions between Par and Rho proteins that are consistent with experimental observations of CDC-42. Using minimal network and eFAST sensitivity analyses, we demonstrate that CDC-42 is predicted to reinforce maintenance of anterior PAR protein polarity which in turn feedbacks to maintain CDC-42 polarization, as well as supporting posterior PAR protein polarization maintenance. The mechanisms for polarity maintenance identified by these methods are not sufficient for the generation of polarization in the absence of cortical flow. Additional inhibitory interactions mediated by the posterior Par proteins are predicted to play a role in the generation of Par protein polarity. More generally, these results provide new insights into the role of CDC-42 in polarization and the mutual regulation of key polarity determinants, in addition to providing a foundation for further investigations.