Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices

We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block-diagonalization of matrices. We obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower-dimensional problems and test the predictions of our low-dimensional analysis through numerical simulations. Under certain conditions, this technique may yield a substantial reduction of the dimensionality of the problem. For example, for a class of dynamical hypernetworks analyzed in the paper, we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2. We apply our reduction techique to a number of different examples, including a class of undirected unweighted hypermotifs of three nodes.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.

Synchronization of hypernetworks of coupled dynamical systems

We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each of which corresponds to a distinct type of interaction), and we refer to such a system as a hypernetwork. Applications include neural networks formed of both electrical gap junctions and chemical synapses, the coordinated motion of shoals of fishes communicating through both vision and flow sensing, and hypernetworks of coupled chaotic oscillators. We first analyze the case of a hypernetwork formed of $m=2$ networks. We look for necessary and sufficient conditions for synchronization. We attempt at reducing the linear stability problem in a master stability function form, i.e., at decoupling the effects of the coupling functions from the structure of the networks. Unfortunately, we are unable to obtain a reduction in a master stability function form for the general case. However, we show that such a reduction is possible in three cases of interest: (i) the Laplacian matrices associated with the two networks commute; (ii) one of the two networks is unweighted and fully connected; (iii) one of the two networks is such that the coupling strength from node $i$ to node $j$ is a function of $j$ but not of $i$. Furthermore, we define a class of networks such that if either one of the two coupling networks belongs to this class, the reduction can be obtained independently of the other network. As an example of interest, we study synchronization of a neural hypernetwork for which the connections can be either chemical synapses or electrical gap junctions. We propose a generalization of our stability results to the case of hypernetworks formed of $m\geq 2$ networks.Comment: Accepted for publication in New Journal of Physic

Network synchronization of groups

In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both continuous time and discrete time systems are considered. We initially focus on the case where two groups are present and the network has bipartite topology (i.e., links exist between nodes in different groups but not between nodes in the same group). We also show that group synchronous motions are compatible with more general network topologies, where there are also connections within the groups

Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page

FKBP12 associates tightly with the skeletal muscle type 1 ryanodine receptor, but not with other intracellular calcium release channels

AbstractThis study compared the relative levels of ryanodine receptor (RyR) isoforms, inositol 1,4,5-trisphosphate receptor (IP3R) isoforms, and calcineurin, plus their association with FKBP12 in brain, skeletal and cardiac tissue. FKBP12 demonstrated a very tight, high affinity association with skeletal muscle microsomes, which was displaced by FK506. In contrast, FKBP12 was not tightly associated with brain or cardiac microsomes and did not require FK506 for removal from these organelles. Furthermore, of the proteins solubilised from skeletal muscle, cardiac muscle and brain microsomes, only skeletal muscle RyR1 bound to an FKBP12–glutathione-S-transferase fusion protein, in a high affinity FK506 displaceable manner. These results suggest that RyR1 has distinctive FKBP12 binding properties when compared to RyR2, RyR3, all IP3R isoforms and calcineurin

Antegrade common femoral artery closure device use is associated with decreased complications.

ObjectiveAntegrade femoral artery access is often used for ipsilateral infrainguinal peripheral vascular intervention. However, the use of closure devices (CD) for antegrade access (AA) is still considered outside the instructions for use for most devices. We hypothesized that CD use for antegrade femoral access would not be associated with an increased odds of access site complications.MethodsThe Vascular Quality Initiative was queried from 2010 to 2019 for infrainguinal peripheral vascular interventions performed via femoral AA. Patients who had a cutdown or multiple access sites were excluded. Cases were then stratified into whether a CD was used or not. Hierarchical multivariable logistic regressions controlling for hospital-level variation were used to examine the independent association between CD use and access site complications. A sensitivity analysis using coarsened exact matching was performed using factors different between treatment groups to reduce imbalance between the groups.ResultsOverall, 11,562 cases were identified and 5693 (49.2%) used a CD. Patients treated with a CD were less likely to be white (74.1% vs 75.2%), have coronary artery disease (29.7% vs 33.4%), use aspirin (68.7% vs 72.4%), and have heparin reversal with protamine (15.5% vs 25.6%; all P < .05). CD patients were more likely to be obese (31.6% vs 27.0%), have an elective operation (82.6% vs 80.1%), ultrasound-guided access (75.5% vs 60.6%), and a larger access sheath (6.0 ± 1.0 F vs 5.5 ± 1.0 F; P < .05 for all). CD cases were less likely to develop any access site hematoma (2.55% vs 3.53%; P < .01) or a hematoma requiring reintervention (0.63% vs 1.26%; P < .01) and had no difference in access site stenosis or occlusion (0.30% vs 0.22%; P = .47) compared with no CD. On multivariable analysis, CD cases had significantly decreased odds of developing any access site hematoma (odds ratio, 0.75; 95% confidence interval, 0.59-0.95) and a hematoma requiring intervention (odds ratio, 0.56; 95% confidence interval, 0.38-0.81). A sensitivity analysis after coarsened exact matching confirmed these findings.ConclusionsIn this nationally representative sample, CD use for AA was associated with a lower odds of hematoma in selected patients. Extending the instructions for use indications for CDs to include femoral AA may decrease the incidence of access site complications, patient exposure to reintervention, and costs to the health care system