3,271 research outputs found
A stochastic delay differential model of cerebral autoregulation
Mathematical models of the cardiovascular system and of cerebral autoregulation (CAR) have been employed for several years in order to describe the time course of pressures and flows changes subsequent to postural changes. The assessment of the degree of efficiency of cerebral auto regulation has indeed importance in the prognosis of such conditions as cerebro-vascular accidents or Alzheimer. In the quest for a simple but realistic mathematical description of cardiovascular control, which may be fitted onto non-invasive experimental observations after postural changes, the present work proposes a first version of an empirical Stochastic Delay Differential Equations (SDDEs) model. The model consists of a total of four SDDEs and two ancillary algebraic equations, incorporates four distinct delayed controls from the brain onto different components of the circulation, and is able to accurately capture the time course of mean arterial pressure and cerebral blood flow velocity signals, reproducing observed auto-correlated error around the expected drift
Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
We study origin, parameter optimization, and thermodynamic efficiency of
isothermal rocking ratchets based on fractional subdiffusion within a
generalized non-Markovian Langevin equation approach. A corresponding
multi-dimensional Markovian embedding dynamics is realized using a set of
auxiliary Brownian particles elastically coupled to the central Brownian
particle (see video on the journal web site). We show that anomalous
subdiffusive transport emerges due to an interplay of nonlinear response and
viscoelastic effects for fractional Brownian motion in periodic potentials with
broken space-inversion symmetry and driven by a time-periodic field. The
anomalous transport becomes optimal for a subthreshold driving when the driving
period matches a characteristic time scale of interwell transitions. It can
also be optimized by varying temperature, amplitude of periodic potential and
driving strength. The useful work done against a load shows a parabolic
dependence on the load strength. It grows sublinearly with time and the
corresponding thermodynamic efficiency decays algebraically in time because the
energy supplied by the driving field scales with time linearly. However, it
compares well with the efficiency of normal diffusion rocking ratchets on an
appreciably long time scale
Good and Bad Optimization Models: Insights from Rockafellians
A basic requirement for a mathematical model is often that its solution (output) shouldnât
change much if the modelâs parameters (input) are perturbed. This is important because the exact values
of parameters may not be known and one would like to avoid being misled by an output obtained using
incorrect values. Thus, itâs rarely enough to address an application by formulating a model, solving the
resulting optimization problem and presenting the solution as the answer. One would need to confirm
that the model is suitable, i.e., âgood,â and this can, at least in part, be achieved by considering a
family of optimization problems constructed by perturbing parameters as quantified by a Rockafellian
function. The resulting sensitivity analysis uncovers troubling situations with unstable solutions, which
we referred to as âbadâ models, and indicates better model formulations. Embedding an actual problem
of interest within a family of problems via Rockafellians is also a primary path to optimality conditions
as well as computationally attractive, alternative problems, which under ideal circumstances, and when
properly tuned, may even furnish the minimum value of the actual problem. The tuning of these
alternative problems turns out to be intimately tied to finding multipliers in optimality conditions and
thus emerges as a main component of several optimization algorithms. In fact, the tuning amounts to
solving certain dual optimization problems. In this tutorial, weâll discuss the opportunities and insights
afforded by Rockafellians.Office of Naval ResearchAir Force Office of Scientific ResearchMIPR F4FGA00350G004MIPR N0001421WX0149
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