564 research outputs found
An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
We consider a discrete set of individual agents interacting with a continuum.
Examples might be a predator facing a huge group of preys, or a few shepherd
dogs driving a herd of sheeps. Analytically, these situations can be described
through a system of ordinary differential equations coupled with a scalar
conservation law in several space dimensions. This paper provides a complete
well posedness theory for the resulting Cauchy problem. A few applications are
considered in detail and numerical integrations are provided
Time-evolving measures and macroscopic modeling of pedestrian flow
This paper deals with the early results of a new model of pedestrian flow,
conceived within a measure-theoretical framework. The modeling approach
consists in a discrete-time Eulerian macroscopic representation of the system
via a family of measures which, pushed forward by some motion mappings, provide
an estimate of the space occupancy by pedestrians at successive time steps.
From the modeling point of view, this setting is particularly suitable to
treat nonlocal interactions among pedestrians, obstacles, and wall boundary
conditions. In addition, analysis and numerical approximation of the resulting
mathematical structures, which is the main target of this work, follow more
easily and straightforwardly than in case of standard hyperbolic conservation
laws, also used in the specialized literature by some Authors to address
analogous problems.Comment: 27 pages, 6 figures -- Accepted for publication in Arch. Ration.
Mech. Anal., 201
Pedestrian flows in bounded domains with obstacles
In this paper we systematically apply the mathematical structures by
time-evolving measures developed in a previous work to the macroscopic modeling
of pedestrian flows. We propose a discrete-time Eulerian model, in which the
space occupancy by pedestrians is described via a sequence of Radon positive
measures generated by a push-forward recursive relation. We assume that two
fundamental aspects of pedestrian behavior rule the dynamics of the system: On
the one hand, the will to reach specific targets, which determines the main
direction of motion of the walkers; on the other hand, the tendency to avoid
crowding, which introduces interactions among the individuals. The resulting
model is able to reproduce several experimental evidences of pedestrian flows
pointed out in the specialized literature, being at the same time much easier
to handle, from both the analytical and the numerical point of view, than other
models relying on nonlinear hyperbolic conservation laws. This makes it
suitable to address two-dimensional applications of practical interest, chiefly
the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure
L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method
We consider scalar nonviscous conservation laws with strictly convex flux in
one spatial dimension, and we investigate the behavior of bounded L^2
perturbations of shock wave solutions to the Riemann problem using the relative
entropy method. We show that up to a time-dependent translation of the shock,
the L^2 norm of a perturbed solution relative to the shock wave is bounded
above by the L^2 norm of the initial perturbation.Comment: 17 page
Usefulness of Presepsin (Soluble CD14 Subtype) in the Diagnosis of Neonatal Sepsis
Background: Sepsis is a major cause of morbidity and mortality in neonates. Recently, presepsin (soluble CD14 subtype) has been shown to be beneficial as sepsis marker in adults. Nevertheless, few data are available in neonates.
Objective: To evaluate the diagnostic accuracy of presepsin as a marker of sepsis in the neonatal period.
Design/Methods: All neonates with clinical signs of sepsis admitted to our Unit during a 18\uacmonths period were consecutively enrolled. CDC criteria were used to identify neonates with a suspected sepsis. The subjects enrolled in the study were then classified into 3 groups according to Goldstein's and Wynn's definitions: group 1, infection\u37e group 2, sepsis\u37e group 3, septic shock. To measure presepsin, 100 microliters of blood were collected at the following times: at the onset of clinical signs of sepsis (T0), every 12 h for the next 48 h (T1, T2, T3, T4), and at the end of antibiotic therapy (T5). C\uacreactive protein (CRP) was determined at the same times. Presepsin levels were determined using PathfastTM System (LSI Medience Corporation, Japan/Mitsubishi Chemical Europe).
Results: We enrolled 110 neonates: 36 in group 1 (mean GA 34.6 wks, mean BW 2403 g), 59 in group 2 (mean GA 31 wks, mean BW 1615 g) and 15 in group 3 (mean GA 30.2 wks, mean BW 1441 g). Overall, median presepsin value was 1146 pg/ml at T0, higher than the values we previously reported in healthy neonates (PAS Meeting 2015), and decreased over time to 726 pg/ml at T5. Presepsin levels were significantly higher in neonates with sepsis and in those with septic shock than in the others at T0, T1, T2, T3, and T4 (p < .05). Additionally, neonates with septic shock had higher levels of presepsin than those with sepsis at all times. At enrollment, median presepsin value was 874 pg/ml, 1277 pg/ml, and 1928 pg/ml in group 1, 2, and 3 respectively. No significant difference was found in CRP values among the 3 groups at enrollment. The area under the ROC curve for presepsin at enrollment was 0.839 (95% CI: 0.79\uac0.88). Maximum Youden index was at a cut\uacoff value of 865 pg/ml, corresponding to 75% sensitivity and 80% specificity.
Conclusions: According to our results, presepsin appears an accurate biomarker for the diagnosis of neonatal sepsis and it seems to be earlier than CRP in identifying sepsis and septic shock
A theory of -dissipative solvers for scalar conservation laws with discontinuous flux
We propose a general framework for the study of contractive semigroups
of solutions to conservation laws with discontinuous flux. Developing the ideas
of a number of preceding works we claim that the whole admissibility issue is
reduced to the selection of a family of "elementary solutions", which are
certain piecewise constant stationary weak solutions. We refer to such a family
as a "germ". It is well known that (CL) admits many different contractive
semigroups, some of which reflects different physical applications. We revisit
a number of the existing admissibility (or entropy) conditions and identify the
germs that underly these conditions. We devote specific attention to the
anishing viscosity" germ, which is a way to express the "-condition" of
Diehl. For any given germ, we formulate "germ-based" admissibility conditions
in the form of a trace condition on the flux discontinuity line (in the
spirit of Vol'pert) and in the form of a family of global entropy inequalities
(following Kruzhkov and Carrillo). We characterize those germs that lead to the
-contraction property for the associated admissible solutions. Our
approach offers a streamlined and unifying perspective on many of the known
entropy conditions, making it possible to recover earlier uniqueness results
under weaker conditions than before, and to provide new results for other less
studied problems. Several strategies for proving the existence of admissible
solutions are discussed, and existence results are given for fluxes satisfying
some additional conditions. These are based on convergence results either for
the vanishing viscosity method (with standard viscosity or with specific
viscosities "adapted" to the choice of a germ), or for specific germ-adapted
finite volume schemes
Atmospheric effects on extensive air showers observed with the Surface Detector of the Pierre Auger Observatory
Atmospheric parameters, such as pressure (P), temperature (T) and density,
affect the development of extensive air showers initiated by energetic cosmic
rays. We have studied the impact of atmospheric variations on extensive air
showers by means of the surface detector of the Pierre Auger Observatory. The
rate of events shows a ~10% seasonal modulation and ~2% diurnal one. We find
that the observed behaviour is explained by a model including the effects
associated with the variations of pressure and density. The former affects the
longitudinal development of air showers while the latter influences the Moliere
radius and hence the lateral distribution of the shower particles. The model is
validated with full simulations of extensive air showers using atmospheric
profiles measured at the site of the Pierre Auger Observatory.Comment: 24 pages, 9 figures, accepted for publication in Astroparticle
Physic
The exposure of the hybrid detector of the Pierre Auger Observatory
The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays.
It consists of a surface array to measure secondary particles at ground level
and a fluorescence detector to measure the development of air showers in the
atmosphere above the array. The "hybrid" detection mode combines the
information from the two subsystems. We describe the determination of the
hybrid exposure for events observed by the fluorescence telescopes in
coincidence with at least one water-Cherenkov detector of the surface array. A
detailed knowledge of the time dependence of the detection operations is
crucial for an accurate evaluation of the exposure. We discuss the relevance of
monitoring data collected during operations, such as the status of the
fluorescence detector, background light and atmospheric conditions, that are
used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic
Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter
Data collected by the Pierre Auger Observatory through 31 August 2007 showed
evidence for anisotropy in the arrival directions of cosmic rays above the
Greisen-Zatsepin-Kuz'min energy threshold, \nobreak{eV}. The
anisotropy was measured by the fraction of arrival directions that are less
than from the position of an active galactic nucleus within 75 Mpc
(using the V\'eron-Cetty and V\'eron catalog). An updated
measurement of this fraction is reported here using the arrival directions of
cosmic rays recorded above the same energy threshold through 31 December 2009.
The number of arrival directions has increased from 27 to 69, allowing a more
precise measurement. The correlating fraction is , compared
with expected for isotropic cosmic rays. This is down from the early
estimate of . The enlarged set of arrival directions is
examined also in relation to other populations of nearby extragalactic objects:
galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in
hard X-rays by the Swift Burst Alert Telescope. A celestial region around the
position of the radiogalaxy Cen A has the largest excess of arrival directions
relative to isotropic expectations. The 2-point autocorrelation function is
shown for the enlarged set of arrival directions and compared to the isotropic
expectation.Comment: Accepted for publication in Astroparticle Physics on 31 August 201
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