931 research outputs found
Pattern Formation with a Compartmental Lateral Inhibition System
We propose a compartmental lateral inhibition system that generates
contrasting patterns of gene expression between neighboring compartments. The
system consists of a set of compartments interconnected by channels. Each
compartment contains a colony of cells that produce diffusible molecules to be
detected by the neighboring colony, and each cell is equipped with an
inhibitory circuit that reduces its production when the detected signal is
stronger. We develop a technique to analyze the steady-state patterns emerging
from this lateral inhibition system and apply it to a specific implementation.
The analysis shows that the proposed system indeed exhibits contrasting
patterns within realistic parameter ranges.Comment: 9 pages, 6 figure
Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model
We study variants of the SEIR model for interpreting some qualitative
features of the statistics of the Covid-19 epidemic in France. Standard SEIR
models distinguish essentially two regimes: either the disease is controlled
and the number of infected people rapidly decreases, or the disease spreads and
contaminates a significant fraction of the population until herd immunity is
achieved. After lockdown, at first sight it seems that social distancing is not
enough to control the outbreak. We discuss here a possible explanation, namely
that the lockdown is creating social heterogeneity: even if a large majority of
the population complies with the lockdown rules, a small fraction of the
population still has to maintain a normal or high level of social interactions,
such as health workers, providers of essential services, etc. This results in
an apparent high level of epidemic propagation as measured through
re-estimations of the basic reproduction ratio. However, these measures are
limited to averages, while variance inside the population plays an essential
role on the peak and the size of the epidemic outbreak and tends to lower these
two indicators. We provide theoretical and numerical results to sustain such a
view
Synchronization of coupled stochastic limit cycle oscillators
For a class of coupled limit cycle oscillators, we give a condition on a
linear coupling operator that is necessary and sufficient for exponential
stability of the synchronous solution. We show that with certain modifications
our method of analysis applies to networks with partial, time-dependent, and
nonlinear coupling schemes, as well as to ensembles of local systems with
nonperiodic attractors. We also study robustness of synchrony to noise. To this
end, we analytically estimate the degree of coherence of the network
oscillations in the presence of noise. Our estimate of coherence highlights the
main ingredients of stochastic stability of the synchronous regime. In
particular, it quantifies the contribution of the network topology. The
estimate of coherence for the randomly perturbed network can be used as means
for analytic inference of degree of stability of the synchronous solution of
the unperturbed deterministic network. Furthermore, we show that in large
networks, the effects of noise on the dynamics of each oscillator can be
effectively controlled by varying the strength of coupling, which provides a
powerful mechanism of denoising. This suggests that the organization of
oscillators in a coupled network may play an important role in maintaining
robust oscillations in random environment. The analysis is complemented with
the results of numerical simulations of a neuronal network.
PACS: 05.45.Xt, 05.40.Ca
Keywords: synchronization, coupled oscillators, denoising, robustness to
noise, compartmental modelComment: major revisions; two new section
On resilient control of dynamical flow networks
Resilience has become a key aspect in the design of contemporary
infrastructure networks. This comes as a result of ever-increasing loads,
limited physical capacity, and fast-growing levels of interconnectedness and
complexity due to the recent technological advancements. The problem has
motivated a considerable amount of research within the last few years,
particularly focused on the dynamical aspects of network flows, complementing
more classical static network flow optimization approaches. In this tutorial
paper, a class of single-commodity first-order models of dynamical flow
networks is considered. A few results recently appeared in the literature and
dealing with stability and robustness of dynamical flow networks are gathered
and originally presented in a unified framework. In particular, (differential)
stability properties of monotone dynamical flow networks are treated in some
detail, and the notion of margin of resilience is introduced as a quantitative
measure of their robustness. While emphasizing methodological aspects --
including structural properties, such as monotonicity, that enable tractability
and scalability -- over the specific applications, connections to
well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201
Early warning signs for saddle-escape transitions in complex networks
Many real world systems are at risk of undergoing critical transitions,
leading to sudden qualitative and sometimes irreversible regime shifts. The
development of early warning signals is recognized as a major challenge. Recent
progress builds on a mathematical framework in which a real-world system is
described by a low-dimensional equation system with a small number of key
variables, where the critical transition often corresponds to a bifurcation.
Here we show that in high-dimensional systems, containing many variables, we
frequently encounter an additional non-bifurcative saddle-type mechanism
leading to critical transitions. This generic class of transitions has been
missed in the search for early-warnings up to now. In fact, the saddle-type
mechanism also applies to low-dimensional systems with saddle-dynamics. Near a
saddle a system moves slowly and the state may be perceived as stable over
substantial time periods. We develop an early warning sign for the saddle-type
transition. We illustrate our results in two network models and epidemiological
data. This work thus establishes a connection from critical transitions to
networks and an early warning sign for a new type of critical transition. In
complex models and big data we anticipate that saddle-transitions will be
encountered frequently in the future.Comment: revised versio
Dangerous connections: on binding site models of infectious disease dynamics
We formulate models for the spread of infection on networks that are amenable
to analysis in the large population limit. We distinguish three different
levels: (1) binding sites, (2) individuals, and (3) the population. In the
tradition of Physiologically Structured Population Models, the formulation
starts on the individual level. Influences from the `outside world' on an
individual are captured by environmental variables. These environmental
variables are population level quantities. A key characteristic of the network
models is that individuals can be decomposed into a number of conditionally
independent components: each individual has a fixed number of `binding sites'
for partners. The Markov chain dynamics of binding sites are described by only
a few equations. In particular, individual-level probabilities are obtained
from binding-site-level probabilities by combinatorics while population-level
quantities are obtained by averaging over individuals in the population. Thus
we are able to characterize population-level epidemiological quantities, such
as , , the final size, and the endemic equilibrium, in terms of the
corresponding variables
Advanced model-based control studies for the induction and maintenance of intravenous anaesthesia
This paper describes strategies toward model-based automation of intravenous anaesthesia employing advanced control techniques. In particular, based on a detailed compartmental mathematical model featuring pharmacokinetic and pharmacodynamics information, two alternative model predictive control strategies are presented: a model predictive control strategy, based on online optimization, the extended predictive self-adaptive control and a multiparametric control strategy based on offline optimization, the multiparametric model predictive control. The multiparametric features to account for the effect of nonlinearity and the impact of estimation are also described. The control strategies are tested on a set of 12 virtually generated patient models for the regulation of the depth of anaesthesia by means of the bispectral index (BIS) using Propofol as the administrated anaesthetic. The simulations show fast response, suitability of dose, and robustness to induce and maintain the desired BIS setpoint
Preclinical pharmacokinetic evaluation of novel antimalarial and antituberculosis drug leads
Preclinical pharmacokinetics relies on efficient and accurate screening to select clinical candidates from early leads. Poor pharmacokinetic interpretation can disadvantage drug discovery by promoting inadequate compounds and expelling potential drug candidates. Objectives of this project included pharmacokinetic evaluation of antimalarial and anti-tuberculosis lead compounds with techniques aimed at improving preclinical pharmacokinetic outcomes. This included mechanistic pharmacokinetic approaches such as non-linear mixed effects (NLME) modelling in comparison with traditional non-compartmental analysis. Where appropriate, pharmacokinetic methods were expanded to include organ distribution and capsule dosing in mice to bridge our techniques from discovery to early development. Three benzoxazole amodiaquine analogues possessing equipotent in vitro antiplasmodial activity and showed diverse in vivo efficacy in a malaria mouse model. Evaluation of their respective pharmacokinetics in mice showed their in vivo exposures could translate to in vivo efficacy. Retrospective PK/PD simulations point to a time above IC50 drive in efficacy. Pharmacokinetic evaluation of an aminopyridine antimalarial compound in its cyclodextrin inclusion complex revealed a pH dependent increase in solubility that reduced variance, likely due to favoured intestinal absorption. Investigation of two novel fusidic acid C-3 ester prodrugs aimed at repositioning fusidic acid for tuberculosis, showed high concentrations of the rodent specific 3-epifusidic acid metabolite that greatly reduced exposure of fusidic acid in mice. Further organ distribution studies showed a prodrug strategy is still viable for repositioning fusidic acid for tuberculosis, but that rodent models are inappropriate for further evaluation. NLME modelling successfully provided unique mechanistic and mathematical insight of pharmacokinetic profiles of new leads. The level of interpretation on pharmacology parameters improved and aided in understanding why drug leads are likely to fail or succeed, assisting future compound optimisation
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