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GZ67 In cubical sets, let us write [MATH] for the functor represented by [MATH] Let us denote [MATH] where [MATH] its two points inclusions. Using the techniques of CCHM18 and Sat17 , one may show that there is a combinatorial model structure [MATH] characterized by the following data: |
the cofibrations are the monomorphisms, the fibrations are those maps with the right lifting property against pushout products of [MATH] with monomorphisms. |
Since the details of this construction have not yet been published, we assume the existence of this model structure in the below. |
In the following, we will relate this model structure to the Kan model structure via two Quillen adjunctions. We will freely exploit the equivalence of cubical sets with presheaves over [MATH] and denote the essential geometric embedding [MATH] simply as [MATH] where [MATH] is the full embedding. This is justified by t... |
3.1 It is clear that [MATH] preserves cofibrations. Since [MATH] preserves colimits and products and sends [MATH] to [MATH] , it preserves prism-style generating trivial cofibrations. The reflective embedding of simplicial sets into cubical sets thus forms a Quillen adjunction |
[EQUATION] The interval objects [MATH] and [MATH] induce functorial cylinders in [MATH] and [MATH] via the Cartesian product (note that the latter cylinder preserves representables). These induce evident notions of (elemetary) homotopy and homotopy equivalence in both settings. Since [MATH] and [MATH] respect these int... |
Proposition 3.6 We have a Quillen adjunction [EQUATION] Proof. By Proposition 3.3 , we have that [MATH] preserves cofibrations. It remains to show that [MATH] sends generating trivial cofibrations, i.e. horn inclusions, to weak equivalences. |
Note first that [MATH] is weakly contractible as there is a contracting homotopy [MATH] that sends [MATH] to [MATH] and [MATH] to [MATH] By 2-out-of-3, it follows that the action of [MATH] on maps is valued in weak equivalences. |
In the standard fashion of simplicial homotopy theory, one may now show by induction on [MATH] that [MATH] sends [MATH] to a weak equivalence where [MATH] and [MATH] denotes the [MATH] -horn, the union over [MATH] of the [MATH] -th face of [MATH] The base case [MATH] of a face inclusion is covered by the preceding para... |
[EQUATION] and uses cocontinuity of [MATH] and closure of trivial cofibrations under pushout. The original claim is obtained for maximal choices of [MATH] |
# Source: arxiv 1805.04343 # Title: Dynamics of new strain emergence on a temporal network # Sections: all # Downloaded: 2026-03-02T08:40:18.957932+00:00 |
Dynamics of new strain emergence on a temporal network Abstract Multi-strain competition on networks is observed in many contexts, including infectious disease ecology, information dissemination or behavioral adaptation to epidemics. Despite a substantial body of research has been developed considering static, time-agg... |
Sukankana Chakraborty Xavier R. Hoffmann 2,3 Marc G. Leguia 4,5 Felix Nolet Elisenda Ortiz 2,3 Ottavia Prunas 7,8,9 Leonardo Zavojanni 10 Eugenio Valdano 11 Chiara Poletto 12 |
Department of Electronics and Computer Science (ECS), University of Southampton, Highfield Campus, SO17 1BJ, Southampton, United Kingdom. |
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Spain. Universitat de Barcelona Institute of Complex Systems (UBICS), Spain. |
Faculty of Information Studies, Novo Mesto, Slovenia. Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Catalonia, Spain. |
Laboratory of Dynamics in Biological Systems; Department of Cellular and Molecular Medicine, KU Leuven; Leuven, Belgium. ISI Foundation; Via Chisola 5; 10126; Torino; Italy. |
Complex Systems for Life Sciences, Universitá degli Studi di Torino, 10124 Torino, Italy. GSK Vaccines, 53100 Siena, Italy. 10 Section for the Science of Complex Systems; CeMSIIS; Medical University of Vienna; Spitalgasse 23; A-1090; Vienna, Austria. |
11 Departament d’Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili. 12 Sorbonne Universités, UPMC Univ. Paris 06, INSERM, Institut Pierre Louis d’Epidémiologie et de Santé Publique (IPLESP UMR-S 1136), 75012 Paris, France. |
Introduction The study of infection spread on contact networks has been the focus of epidemiological research for a significantly long time. Recently, increasing attention is being devoted to studying the co-circulation of multiple infections on the same networked population, and the impact of competitive and cooperati... |
. An important goal is to elucidate dynamical mechanisms underlying the emergence of new pathogen strains and the associated phenomena of vaccine failure and antibiotic resistance |
. Applications, however, go beyond infectious disease epidemiology, and include the spread of competing (or cooperating) ideas, memes,computer viruses and products. |
Overall the goal of multi-strain models is the understanding of the co-existence outcome in varying key epidemiological parameters - e.g. transmissibility and duration of infection period. For instance, it was shown that two competing strains rarely coexist |
. The most efficiently spreading strain quickly becomes dominant, and leads the other to extinction. Moreover, a key result is that the conditions on disease parameters leading to dominance often depend on the properties of the network substrate |
So far, most works have considered static networks and only very few have accounted for the dynamics of contacts . The spread of single infections on temporal networks, on the other hand, is being extensively studied, the interest in the subject being prompted by the increasing availability of time resolved contact dat... |
. Face-to-face interactions have been measured by RFID technology in school, workplaces and hospitals, among the others . Time resolved data on sexual encounters are also available |
. These data highlight the dynamical properties of human interactions, such as node turnover, burstiness, heterogeneous activity potential, presence of temporal motifs and correlations, that were shown to profoundly alter in some cases the epidemic spread |
Here we study the competition between an endemic and an emerging strain on an empirical temporal network of face-to-face contacts collected in a hospital. We reconstruct the outcome of the emergence (either replacement or extinction) in varying transmissibility and infection duration of the emerging strain. We focus on... |
Methods 2.1 Contact network We use the network of face-to-face proximity interactions among patients and health care workers in a hospital ward, collected by the SocioPatterns group |
. The data contain [MATH] individuals, and their proximity interactions with the time of occurrence. The data collection period spans 4 days. We aggregate contacts over a 30-minute windows. The resulting temporal network is a sequence of [MATH] time steps, each encoding the topology of contacts at that time. |
2.2 Pathogen dynamics We model both the endemic and the emergent strain through Susceptible-Infectious-Susceptible (SIS) compartmental models. The nodes in the network can be either Susceptible, or infected by either strain. The two strains are mutually exclusive so that concurrent infection of the same nodes by both s... |
In order to study pathogen emergence and takeover, we set up our stochastic simulations as follows ) We fix [MATH] and [MATH] , which corresponds to an average infectious period of [MATH] hours. |
ii ) We let the endemic strain evolve to equilibrium, using a relaxation time of 24 hours. iii ) We fix the time of emergence [MATH] of the emergent strain. We use two values: 7PM on the second day, and 7AM of the third day. We dub these two points AP (after peak) and BP (before peak), respectively. At [MATH] we seed o... |
2.3 Randomized null model In order to gauge the impact of the temporal and topological properties of the contact network, we set up a randomized null model, aimed at breaking the correlations between time and topology. At each time step of the spreading simulation we sample randomly with replacement a network configura... |
2.4 Parameter exploration We explore values of [MATH] in the range [MATH] , and [MATH] in [MATH] , using steps of 0.025, 0.0025, respectively. Then, in order to accumulate sufficient statistics for our measures, we run [MATH] iterations for each parameter configuration. |
Results By varying the epidemiological parameters of the emergent strain ( [MATH] ), we study the phenomenology of pathogen interaction at different parameter values, and investigate the successful replacement of the endemic strain by the emergent one. We also probe the temporal and topological features of the network ... |
3.1 Strain replacement For each [MATH] we compute the probability of replacement [MATH] ), i.e., the probability that, after emergence, the emergent strain takes over the population and drives the endemic strain to extinction. Unsurprisingly, Fig. shows that high values of transmissibility [MATH] favor replacement (hig... |
However, the picture is substantially different when the strain is injected at BP, and two scenarios are revealed: for long infectious periods (low [MATH] ), the null model still shows a higher [MATH] , while with short ones, replacement ins more likely in the real network. |
3.2 Time of coexistence While [MATH] tells us how likely the emergent strain is to take over, it gives no information on how it gets to fixation. One simple measure to gauge that is the time of coexistence , i.e., the number of time units in which the prevalence of both strains is higher than zero. Panels A,D in Fig. s... |
In the null model, in the absence of bottlenecks, the critical region witnesses the highest values of time of coexistence, as the disease spreads slowly up to takeover. In the plots Fig. C,F ), for selected values of [MATH] close to the critical region, we show the full distribution of the time of coexistence, showing ... |
Discussion & Conclusion We studied the dynamics of emergence of a new strain on a temporal network of contacts in the regime in which the spreading time scales are comparable with the time scale of the network evolution. By comparing results on an empirical network and on a randomized null model we found that the tempo... |
These factors, however, were found to be unimportant in other circumstances. For instance, the competition between two SIS processes starting at the same time on a static network was found to be unaffected by the network topology under the quenched mean field approximation |
(where the spectral radius that rules the strength of spreading factorizes and disappears from the inequalities). An analytical formulation of the competition dynamics in the temporal case, based on the quenched mean field approximation would allow a direct comparison with the static case. The quenched mean field has b... |
. The extension of this theory to the case of two competing pathogens is the subject of future research. A second result is that strong fluctuations in the overall volume of contacts make the timing of emergence critical for the likelihood of replacement. Right after the peak of activity, the prevalence of the endemic ... |
The values of the average infectious period (around 6 hours for the endemic strain and between 5.5 hours and 50 hours for the emerging one) were chosen to be comparable with the time scale of network dynamics, that is dominated by daily activity cycles. This was motivated by the interest in probing the interacting dyna... |
Our work is just a preliminary attempt at uncovering how the complex interplay between network and pathogen time scales shape the rise and fixation of emerging strains. The theoretical interest in the problem is motivated by the importance of the emergence of new strains in disease ecology (pandemic strains, selection ... |
Acknowledgements This work is the output of the Complexity72h workshop, held at IMT School in Lucca, 7-11 May 2018. S.C. acknowledges support from the DAIS-ITA project: "This research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence under Agreement Number W911NF-16-3-0001. The views a... |
# Source: arxiv 1805.05359 # Title: Theoretical open-loop model of respiratory mechanics in the extremely preterm infant # Sections: all # Downloaded: 2026-03-03T05:17:57.634306+00:00 |
Theoretical open-loop model of respiratory mechanics in the extremely preterm infant Laura Ellwein Fix 1* Joseph Khoury Russell R Moores, Jr. Lauren Linkous Matthew Brandes Henry J. Rozycki |
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA Division of Neonatal Medicine, Children’s Hospital of Richmond, Virginia Commonwealth University, Richmond, VA |
VCU School of Medicine, Virginia Commonwealth University, Richmond, VA * lellwein@vcu.edu Abstract Non-invasive ventilation is increasingly used for respiratory support in preterm infants, and is associated with a lower risk of chronic lung disease. However, this mode is often not successful in the extremely preterm in... |
Introduction The extremely preterm infant, born at [MATH] weeks gestation and usually [MATH] g, is at risk of developing chronic lung disease despite established treatments such as surfactant replacement therapy. Currently the survival rate of this group ranges from [MATH] at 27 weeks to as low as [MATH] at 23 weeks |
, with survivors living with varying degrees of morbidity. One risk factor for lung disease remains the trauma associated with traditional mechanical ventilation including endotracheal tube injury, high cyclic tidal volumes pressures, and hyperoxia. Non-invasive methods of ventilation such as continuous positive airway... |
. One hypothesis for the failure of non-invasive ventilation and the need for increasing invasive respiratory support is the markedly increased compliance (floppiness) of the chest wall in the extremely preterm infant resulting from ribcage undermineralization common at the start of the third trimester |
. In the preterm infant chest wall compliance can be up to five times lung tissue compliance When the chest wall is not sufficiently rigid, the negative pressure within the pleural space between the lung and chest wall |
. In many cases this leads to progressive lung collapse (atelectasis) with each breath as the forces needed to open airspaces after each exhalation become insurmountable |
, leading to decreasing lung compliance and functional residual capacity (FRC) . This progression of events is observed clinically in X-rays and by symptoms of respiratory distress such as chest retractions and rapid breathing. The clinical result is progressively reduced tidal volumes and end-expiratory lung volume (E... |
Despite this being repeatedly observed clinically, there remains little quantification of the impact of variable nonlinear chest wall compliance on tidal breathing dynamics, and even fewer computational modeling efforts investigating the underlying mechanics of progressive volume loss. Most computational models of brea... |
. Existing computer models of tidal breathing have not fully accounted for the physiology particular to premature infants and thus have limited applicability. Often, methods of providing ventilator support have been developed in adults and children, then refined and scaled for newborns and premature infants, limiting i... |
In this work, we have developed a nonlinear computational model of respiratory mechanics parameterized for the extremely preterm infant that demonstrates differential volume loss under high vs low chest wall compliance conditions. We adapt a model first presented by Athanasiades et al |
and modified for newborn lambs by LeRolle et al . In the latter, differences such as smaller diameter airways, higher respiratory rates, higher lung resistance, and higher chest wall compliances were considered, however many of the critical physiological nonlinearities contributing to long-term dynamics were not includ... |
. Dynamic alterations of compliance curves based on breath-to-breath end-inspiratory lung volume (EILV) and peak inspiratory pressure (PIP) are shown to influence tidal volume and EELV, thus simulating progressive lung volume loss. We also demonstrate the effect of two simulated interventions that raise alveolar pressu... |
Mathematical model The lumped-parameter respiratory mechanics model describes dynamic volumes and pressures in the airways, lungs, chest wall, and intrapleural space between lungs and chest. A signal that represents diaphragm pressure generated during spontaneous breathing drives the model. A compartment is assumed to ... |
State equations Each non-rigid compartment has an associated compliance [MATH] [ml/cm H O], describing the change in compartmental volume [MATH] given a change in transmural pressure [MATH] across its boundary with compartment [MATH] |
[EQUATION] The nature of [MATH] does not change explicitly with time but instead is implicitly determined by the relationship between volume and pressure. This can be reformulated in terms of dynamic changes of state: |
[EQUATION] Bidirectional airflow through the trachea, bronchi, bronchioles, and to and from the lungs results from contraction and relaxation of the diaphragm generating a pressure difference. Airflow is opposed by the resistance of the airways as functions of their radaii or tissue properties. This relationship is des... |
[EQUATION] where [MATH] [cm H [MATH] s/ml] is the resistance to airflow prior to compartment [MATH] . If a compartment includes inertial effects, the pressure gradient is also a function of the acceleration of flow, |
[EQUATION] where [MATH] is the inertance. Inertial effects are considered for the newborn upper rigid airway because of its smaller radius, but neglected for the rest of the model tissues |
The pressures [MATH] across each compliant compartment include transmural pressure between the compliant airways and the pleural space [MATH] , lung elastic recoil [MATH] , lung viscoelastic component [MATH] , and chest wall elastic recoil [MATH] . Summing pressures over each of three loops according to Kirchhoff’s mes... |
[EQUATION] Using the additional relationships obtained from applying Eq ( ), the system of loop equations can be rewritten as [EQUATION] |
Rearranging Eq ( ) and using Kirchhoff’s current law along with Eq ( ) produces the consolidated set of model differential equations: |
[EQUATION] Conservation laws also maintain that [MATH] , in other words the total system volume equals the chest wall volume, which is the sum of the alveolar and compressible airway volumes. Pressure-volume relationships and compliances [MATH] will be further described below. |
Nonlinear resistance constitutive relations The airways begin with an upper rigid segment characterized by an inertance [MATH] and a nonlinear Rohrer resistance [MATH] |
that increases with airflow: [EQUATION] The constants [MATH] and [MATH] represent laminar and turbulent flow components. A middle collapsible portion is modeled as a cylinder with constant length having nonlinear resistance [MATH] that depends inversely on the 4th power of the radius according to Poiseuille’s law. Ther... |
[EQUATION] where [MATH] equals its minimum value [MATH] when [MATH] , an estimate of dead space. An inverse relationship between resistance in the smaller peripheral airways [MATH] and lung volume [MATH] reflects high resistance at low or near-zero volumes |
. To avoid [MATH] as [MATH] from a strict exponential decay model, we adopt the formulation used by both Liu et al and Athanasiades et al |
, a decaying exponential function of relative lung volume with finite [MATH] at [MATH] [EQUATION] where [MATH] . This parameterization gives that [MATH] when [MATH] , and [MATH] when [MATH] (residual volume). |
Nonlinear compliance constitutive relations The volumes [MATH] [MATH] , and [MATH] representing physiological compartments are assumed to have nonlinear compliance which are modeled implicitly with a pressure-volume curve or explicitly by [MATH] |
The compliance curve for the collapsible airway volume [MATH] as a function of [MATH] represents data depicted in following a sigmoidal function |
[EQUATION] Maximal compliance occurs at the middle of the sigmoid [MATH] , with [MATH] characterizing the slope of the sigmoid. In newborns and infants an exponential-like chest-wall compliance curve is observed |
but with compliance being near infinite for [MATH] . We chose to model the static compliance of the chest wall as a “softplus” function of the form [MATH] , the smooth approximation of the rectifier activation function [MATH] . Accounting for translations and scaling, this is represented by |
[EQUATION] The asymptotic volume at large negative pressure is thus assumed to equal RV. The “transition point” where the softplus function slope has the greatest rate of change from horizontal to affine occurs at [MATH] . The chest wall relaxation volume [MATH] is set using an estimate from literature at 25% of VC (vi... |
. From this parameterization, [MATH] . The single degree of freedom [MATH] then characterizes the slope of the chest wall compliance curve and is adjusted to produce a range of dynamic compliance values. |
The volume of the lung compartment [MATH] is modeled as the product of distention of lung units [MATH] and fraction of recruited alveoli [MATH] |
. To obtain [MATH] near [MATH] , lung volume is given as [EQUATION] Alveolar compliance [MATH] as used in the system of differential equations ( ) is found with symbolic computation as [MATH] |
The first term [MATH] represents the volume due to aggregate elasticity of the lung unit structure, which is modeled here as a saturated exponential |
[EQUATION] where [MATH] characterizes the lung stiffness. This representation has been found to suffice in cases of a healthy or surfactant-treated lung. The second term of the lung compliance [MATH] represents the contribution of recruitment and derecruitment of alveoli to compliance, which has been modeled previously... |
. It can be represented by a sigmoid which resembles the probability density function of a Gaussian distribution describing aggregate opening or closing pressures of individual alveolar sacs or ducts |
. We adopt the formulation of Hamlington et al [EQUATION] It follows that [MATH] is the baseline fraction of lung recruited at [MATH] [MATH] represents the maximum recruitable fraction of lung, [MATH] is mean opening pressure at which recruitment is maximum, and [MATH] describes the transition to full recruitment captu... |
could be captured in the parameterization of [MATH] The viscoelastic properties of pulmonary tissue are represented with a linear Kelvin-Voigt model consisting of scalar compliance [MATH] and resistance [MATH] , which contributes a viscoelastic pressure component [MATH] in series with lung elastic recoil [MATH] , see F... |
Respiratory muscle driving pressure The pressure [MATH] describes the effective action of the respiratory muscles driving the model dynamics with [MATH] negative in the outward direction. We used a sinusoidal function to describe tidal breathing, with maximum equaling zero at end-expiration: |
[EQUATION] where [MATH] is the amplitude of the cosine wave and [MATH] is the frequency. The wave generates a negative pressure with total magnitude [MATH] outward from the body. Though simple, the sinusoidal function can admit time-varying frequency, show dynamics over multiple breaths, is used in artificial ventilati... |
). More sophisticated functions can model inhalation and exhalation with different durations or qualitative forms, however the breath-to-breath dynamics displayed in this study can be captured sufficiently with the sinusoidal function. |
Progressive volume loss The complete mechanism of interaction between inefficient inhalation resulting from high chest wall compliance and the progressive nature of lung volume loss and respiratory distress is not fully understood. Clinical X-ray evidence of delayed atelectasis and subsequent acute respiratory distress... |
The lung compliance curve shifts slightly with each breath via changes in mean threshold opening pressure based on number of collapsed alveoli. A volume loss associated with derecruited alveoli necessitates an increase in expanded volume of recruited alveoli relative to the radius cubed, with an increased distending pr... |
using a simple example of expansion of 3 alveoli that double in volume with a 25% increase in radius; if 1 alveolus closes, the other two radaii must now increase by 35% to achieve the same overall volume change and the required distending pressure increases proportionally. This proportion applied to [MATH] and [MATH] ... |
. If tidal breathing begins on the steepest part of the lung compliance curve, compliance decreases monotonically until eventually tidal breathing occurs on the low compliance tail on the left part of the curve and [MATH] . Tidal breathing may begin at a higher position towards the flatter upper part of the curve, in w... |
Assuming constant amplitude of the sinusoidal muscle pressure pressure function and no stochasticity, the maximum recruitable fraction of alveoli is achieved at end-inspiration (EI) during steady-state oscillatory breathing and additional fraction will not be recruited under a pressure of this same amplitude in subsequ... |
Simulation conditions Parameterization The lung curve was parameterized to obtain an approximate dynamic lung compliance [MATH] of 2.3 ml/cm H |
calculated as the slope [MATH] during normal breathing with no interventions. In particular, [MATH] was tuned to produce a curve [MATH] between RV and TLC with the calculated slope, and the parameters of [MATH] produced a curve that is [MATH] for the whole range of normal breathing to represent a nearly fully recruited... |
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