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.

The internal structure of the state protection of children in Mendoza: the actors and their movements (1995-1999)

The state protection of children in the last 30 years has a critical reflection of the ratification of the first human rights treaty for children and adolescents. Multiple glances focused on the bureaucratic normative apparatuses that operated/operate on children's bodies, to glimpse the configuration of institutional practices. This article attempts to reconstruct the circuits generated through the articulation and power networks related to the state protection of institutionalized childhood (1995 - 1999), through the study of the actors involved in the institutionalization in the province of Mendoza. The methodology used is hermeneutical, heuristic and will be carried out from the analysis of the case of the “witnesses”. For this, three cases of institutionalized boys, girls, and adolescents have been chosen, reflected in institutional files. The results raise the relevance of four institutional actors that are key in institutional actions, whose profiles could be translated into the decision-maker, the communicational control, the sentinel, and the public force. On the other hand, in the minimal networks of the cases presented, the subordination of one (executive) power over another state (judicial) power is proposed. Finally, differentiated power dynamics are indicated between the center and the peripheries of the province of Mendoza, Argentina.

Perturbation analysis of a multi-morphogen Turing reaction-diffusion stripe patterning system reveals key regulatory interactions

ABSTRACTPeriodic patterning is widespread in development and can be modelled by reaction-diffusion (RD) processes. However, minimal two-component RD descriptions are vastly simpler than the multi-molecular events that actually occur and are often hard to relate to real interactions measured experimentally. Addressing these issues, we investigated the periodic striped patterning of the rugae (transverse ridges) in the mammalian oral palate, focusing on multiple previously implicated pathways: FGF, Hh, Wnt and BMP. For each, we experimentally identified spatial patterns of activity and distinct responses of the system to inhibition. Through numerical and analytical approaches, we were able to constrain substantially the number of network structures consistent with the data. Determination of the dynamics of pattern appearance further revealed its initiation by ‘activators’ FGF and Wnt, and ‘inhibitor’ Hh, whereas BMP and mesenchyme-specific-FGF signalling were incorporated once stripes were formed. This further limited the number of possible networks. Experimental constraint thus limited the number of possible minimal networks to 154, just 0.004% of the number of possible diffusion-driven instability networks. Together, these studies articulate the principles of multi-morphogen RD patterning and demonstrate the utility of perturbation analysis for constraining RD systems.This article has an associated ‘The people behind the papers’ interview.