1,720,958 research outputs found
A journey through structured populations and the numerics for their linear stability analysis
Full text linkIn questa tesi sviluppiamo metodi numerici per l'analisi della stabilità lineare di alcune classi di modelli deterministici di popolazione con struttura continua. Per questi modelli, quando lo scopo è valutare la stabilità locale degli equilibri o di altri invarianti, si è tipicamente portati a indagare lo spettro di operatori linear(izzati) infinito-dimensionali. Questo obiettivo può raramente essere raggiunto analiticamente e i metodi numerici sono spesso necessari.
L'idea alla base dei metodi presentati in questa tesi è quella di discretizzare tali operatori infinito-dimensionali attraverso matrici ottenute tramite tecniche di proiezione basate su metodi (pseudo)spettrali. Il vantaggio di questi metodi è che il loro ordine di convergenza dipende dalla regolarità delle funzioni coinvolte. In particolare, si ottiene ordine infinito quando le funzioni approssimate sono differenziabili infinite volte.
La prima parte della tesi è dedicata all'approssimazione dei numeri di riproduzione, che nel caso di modelli di popolazione con struttura continua sono caratterizzati come raggio spettrale di operatori infinito-dimensionali [DIEKMANN, HEESTERBEEK, METZ, J. Math. Biol. 7, 1990].
In questa tesi consideriamo tre classi di modelli. Primo, consideriamo un'ampia classe di modelli di popolazione strutturati per età, con intervallo d'età finito e formulati come equazioni Integro-Differenziali alle Derivate Parziali (IPDE) con condizioni al bordo non locali, per i quali estendiamo il metodo presentato in [BREDA, FLORIAN, RIPOLL, VERMIGLIO, J. Comput. Appl. Matematica. 384, 2021] per consentire una completa flessibilità nel calcolo dei numeri di riproduzione.
Dopodiché consideriamo modelli di popolazione formulati come Equazioni Differenziali Ordinarie (ODE) con coefficienti periodici [BACAER, GUERNAOUI, J. Math. Biol. 69, 2006]. Qui la periodicità introduce una struttura nella popolazione che è l'istante di tempo nell'intervallo del periodo in cui un individuo viene generato/infettato.
Infine, consideriamo modelli epidemici con strategie di test di massa, dove a intervalli di tempo fissati gli individui infetti vengono testati e isolati se positivi. La classe di interesse è quella dei modelli SIR e SEIR formulati come ODE impulsive. Qui, per calcolare il numero di riproduzione (di controllo), è necessario tenere conto dell'eterogeneità introdotta dagli eventi di test di massa, che è il tempo trascorso dall'ultimo test.
Gli operatori risultanti vengono discretizzati mediante opportuni metodi di collocazione pseudospettrale, ed i numeri di riproduzione vengono approssimati attraverso il raggio spettrale delle matrici.
La seconda parte della tesi è dedicata allo studio di metodi numerici per l'analisi di stabilità di modelli di popolazione lineari strutturati per età con intervallo di età finito, formulati come IPDE con condizioni al contorno non locali, in cui la variabile età è accoppiata con una struttura aggiuntiva.
Prima, consideriamo modelli in cui la struttura aggiuntiva è una variabile spaziale e la diffusione degli individui è modellata da un operatore di convoluzione non locale [KANG, RUAN, XI, J. Dyn. Diff. Eq. 34, 2022].
Dopo, consideriamo modelli con una variabile d'età aggiuntiva [KANG, RUAN, XI, Ann. di Mat. Pura 200, 2021].
Per entrambe queste classi di modelli, la stabilità dell'equilibrio nullo è determinata dallo spettro del generatore infinitesimale associato al semigruppo soluzione. Per approssimare questi spettri, discretizziamo i generatori associati tramite combinazioni di metodi pseudospettrali e spettrali.
I metodi sono presentati insieme a dimostrazioni di convergenza e risultati numerici che attestano la validità degli approcci. Un'ulteriore novità di questa tesi è l'uso di errori di interpolazione in spazi L1 per le prove di convergenza, i quali sono motivati dall'interpretazione biologica associata alla norma L1 nel contesto di popolazioni strutturate.In this thesis, we develop numerical methods for the linear stability analysis of some classes of deterministic continuously structured population models. For these models, when the aim is to assess the local stability of equilibria or other invariants, one is typically led to investigate the spectrum of linear(ized) infinite-dimensional operators. This target can rarely be achieved analytically, and numerical methods are often required in practical computations.
The fundamental idea underlying the approximation schemes presented in this thesis is that of discretizing the relevant infinite-dimensional operators through matrices obtained by suitable projection techniques based on (pseudo)spectral methods. The main advantage of these methods is that their convergence order depends on the smoothness of the involved functions. In particular, infinite order of convergence is attained when the approximated functions are infinitely times differentiable.
The first part of the thesis is devoted to the numerical computation of the reproduction numbers, which for the case of continuously structured population models are characterized as the spectral radius of infinite-dimensional operators [DIEKMANN, HEESTERBEEK, METZ, J. Math. Biol. 7, 1990].
In this thesis, we consider three classes of models. First, we consider a large class of age-structured population models with finite age-span formulated as Integro-Partial Differential Equations (IPDEs) with nonlocal boundary conditions, for which we extend the method presented [BREDA, FLORIAN, RIPOLL, VERMIGLIO, J. Comput. Appl. Math. 384, 2021] to allow for complete flexibility in the computation of the reproduction numbers.
Then, we consider population models formulated as Ordinary Differential Equations (ODEs) with time periodic coefficients [BACAER, GUERNAOUI, J. Math. Biol. 69, 2006]. Here, the time-periodicity introduces a structure in the population which is the instant of time in the period interval at which an individual is generated/infected.
Lastly, we consider epidemic models with mass testing strategies, where at fixed intervals of times, the infected individuals are tested and isolated if positive. The class of interest is that of SIR and SEIR models formulated as impulsive ODEs. Here, to compute the (control) reproduction number, one must take into account the heterogeneity introduced by the mass testing events, which is the time elapsed since last testing.
The relevant operators are discretized by suitable pseudospectral collocation methods, and the reproduction numbers are approximated through the spectral radius of matrices.
The second part of the thesis is devoted to the study of numerical methods for the stability analysis of linear age-structured population models with finite age-span, formulated as IPDEs with nonlocal boundary conditions, in which the age-variable is coupled with an additional structure.
First, we consider models where the additional structure is a spatial variable, and the spread of individuals is modeled by a nonlocal convolution operator [KANG, RUAN, XI, J. Dyn. Diff. Eq. 34, 2022].
Secondly, we consider models with an additional age variable [KANG, RUAN, XI, Ann. di Mat. Pura 200, 2021].
For both of these classes of models, the stability of the null equilibrium is determined by the spectrum of the infinitesimal generator associated to the solution semigroup. To approximate those spectra, we discretize the relevant generators through combinations of pseudospectral and spectral methods.
The methods are presented alongside convergence proofs and numerical results attesting the validity of the approaches. An additional novelty of this thesis is the use of interpolation error bounds in L1-spaces for the convergence proofs, which is motivated by the biological interpretation attached to the L1 norm in the context of structured populations
A numerical method for the stability analysis of linear age-structured models with nonlocal diffusion
Full text linkWe numerically address the stability analysis of linear age-structured
population models with nonlocal diffusion, which arise naturally in describing
dynamics of infectious diseases. Compared to Laplace diffusion, models with
nonlocal diffusion are more challenging since the associated semigroups have no
regularizing properties in the spatial variable. Nevertheless, the asymptotic
stability of the null equilibrium is determined by the spectrum of the
infinitesimal generator associated to the semigroup. We propose a numerical
method to approximate the leading part of this spectrum by first reformulating
the problem via integration of the age-state and then by discretizing the
generator combining a spectral projection in space with a pseudospectral
collocation in age. A rigorous convergence analysis proving spectral accuracy
is provided in the case of separable model coefficients. Results are confirmed
experimentally and numerical tests are presented also for the more general
instance.Comment: 23 pages, 11 figure
A pseudospectral method for investigating the stability of linear population models with two physiological structures
Full text linkThe asymptotic stability of the null equilibrium of a linear population model
with two physiological structures formulated as a first-order hyperbolic PDE is
determined by the spectrum of its infinitesimal generator. We propose an
equivalent reformulation of the problem in the space of absolutely continuous
functions in the sense of Carath\'eodory, so that the domain of the
corresponding infinitesimal generator is defined by trivial boundary
conditions. Via bivariate collocation, we discretize the reformulated operator
as a finite-dimensional matrix, which can be used to approximate the spectrum
of the original infinitesimal generator. Finally, we provide test examples
illustrating the converging behavior of the approximated eigenvalues and
eigenfunctions, and its dependence on the regularity of the model coefficients
Bivariate collocation for computing R0 in epidemic models with two structures
Full text linkStructured epidemic models can be formulated as first-order hyperbolic PDEs, where the “spatial” variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate 0, which measures the transmissibility of an infectious disease and, rigorously, is defined as the dominant eigenvalue of a next generation operator. Via bivariate collocation and cubature on tensor grids, the latter is approximated with a finite-dimensional matrix, so that its dominant eigenvalue can easily be computed with standard techniques. We use test examples to investigate experimentally the behavior of the approximation: the convergence order appears to be infinite when the corresponding eigenfunction is smooth, and finite for less regular eigenfunctions. To demonstrate the effectiveness of the technique for more realistic applications, we present a new epidemic model structured by demographic age and immunity, and study the approximation of 0 in some particular cases of interest
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
