37,418 research outputs found
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon
The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how
the body responds to exogenously supplied insulin and glucagon in patients
affected by Type I diabetes. Based on this model, we design infusion rates of
either insulin (monotherapy) or insulin and glucagon (dual therapy) that can
optimally maintain the blood glucose level within desired limits after
consumption of a meal and prevent the onset of both hypoglycemia and
hyperglycemia. This problem is formulated as a nonlinear optimal control
problem, which we solve using the numerical optimal control package PSOPT.
Interestingly, in the case of monotherapy, we find the optimal solution is
close to the standard method of insulin based glucose regulation, which is to
assume a variable amount of insulin half an hour before each meal. We also find
that the optimal dual therapy (that uses both insulin and glucagon) is better
able to regulate glucose as compared to using insulin alone. We also propose an
ad-hoc rule for both the dosage and the time of delivery of insulin and
glucagon.Comment: Accepted for publication in PLOS ON
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
Decentralized Observability with Limited Communication between Sensors
In this paper, we study the problem of jointly retrieving the state of a
dynamical system, as well as the state of the sensors deployed to estimate it.
We assume that the sensors possess a simple computational unit that is capable
of performing simple operations, such as retaining the current state and model
of the system in its memory.
We assume the system to be observable (given all the measurements of the
sensors), and we ask whether each sub-collection of sensors can retrieve the
state of the underlying physical system, as well as the state of the remaining
sensors. To this end, we consider communication between neighboring sensors,
whose adjacency is captured by a communication graph. We then propose a linear
update strategy that encodes the sensor measurements as states in an augmented
state space, with which we provide the solution to the problem of retrieving
the system and sensor states.
The present paper contains three main contributions. First, we provide
necessary and sufficient conditions to ensure observability of the system and
sensor states from any sensor. Second, we address the problem of adding
communication between sensors when the necessary and sufficient conditions are
not satisfied, and devise a strategy to this end. Third, we extend the former
case to include different costs of communication between sensors. Finally, the
concepts defined and the method proposed are used to assess the state of an
example of approximate structural brain dynamics through linearized
measurements.Comment: 15 pages, 5 figures, extended version of paper accepted at IEEE
Conference on Decision and Control 201
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