| 1. |
- Ergon, Mattias, et al.
(författare)
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Monte-Carlo methods for NLTE spectral synthesis of supernovae
- 2018
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Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 620
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Tidskriftsartikel (refereegranskat)abstract
- We present JEKYLL, a new code for modelling of supernova (SN) spectra and lightcurves based on Monte-Carlo (MC) techniques for the radiative transfer. The code assumes spherical symmetry, homologous expansion and steady state for the matter, but is otherwise capable of solving the time-dependent radiative transfer problem in non-local-thermodynamic-equilibrium (NLTE). The method used was introduced in a series of papers by Lucy, but the full time-dependent NLTE capabilities of it have never been tested. Here, we have extended the method to include non-thermal excitation and ionization as well as charge-transfer and two-photon processes. Based on earlier work, the non-thermal rates are calculated by solving the Spencer-Fano equation. Using a method previously developed for the SUMO code, macroscopic mixing of the material is taken into account in a statistical sense. To save computational power a diffusion solver is used in the inner region, where the radiation field may be assumed to be thermalized. In addition, a statistical Markov-chain model is used to sample the emission frequency more efficiently, and we introduce a method to control the sampling of the radiation field, which is used to reduce the noise in the radiation field estimators. Except for a description of JEKYLL, we provide comparisons with the ARTIS, SUMO and CMFGEN codes, which show good agreement in the calculated spectra as well as the state of the gas. In particular, the comparison with CMFGEN, which is similar in terms of physics but uses a different technique, shows that the Lucy method does indeed converge in the time-dependent NLTE case. Finally, as an example of the time-dependent NLTE capabilities of JEKYLL, we present a model of a Type IIb SN, taken from a set of models presented and discussed in detail in an accompanying paper. Based on this model we investigate the effects of NLTE, in particular those arising from non-thermal excitation and ionization, and find strong effects even on the bolometric lightcurve. This highlights the need for full NLTE calculations when simulating the spectra and lightcurves of SNe.
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| 2. |
- Spricer, Kristoffer
(författare)
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An Epidemic on a Weighted Partially Directed Network
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We introduce a weighted partially directed configuration model graph, where the weights on undirected and directed edges correspond to the probability of transmitting an infection. The model is especially useful when the degree distribution is known, but not the exact structure of the network. On such graphs, we study SIR epidemics in discrete time and determine the basic reproduction number R0, the probability of a large outbreak and the relative final size of the outbreak. The analytical results of the model are compared with simulated epidemics on three empirical networks. While the networks are large and have a very high maximum degree, thanks to the sparse nature of the degree distribution for many empirical networks, the analysis is still computationally feasible on standard computers. While results are different on the three networks, we see that for two of them the proposed model is compatible with the simulated epidemics on the empirical networks. This makes the model useful for analyzing such networks.
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| 3. |
- Spricer, Kristoffer, et al.
(författare)
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An SIR epidemic on a weighted network
- 2019
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Ingår i: Network science. - : Cambridge University Press (CUP). - 2050-1242 .- 2050-1250. ; 7:4, s. 556-580
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible-Infectious-Recovered epidemic using both Reed-Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction number R-0, the probability of a major outbreak, and the relative final size of a major outbreak. Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical constructs and empirical network data. In addition, bivariate standard normal copulas are used to model the dependence between the degrees of the two edge types, allowing for modeling the correlation between edge types over a wide range. Among the results are that the weighted graph produces much richer results than the unweighted graph. Also, while R-0 always increases with increasing correlation between the two degrees, this is not necessarily true for the probability of a major outbreak nor for the relative final size of a major outbreak. When using copulas we see that these can produce results that are similar to those of the empirical degree distributions, indicating that in some cases a copula is a viable alternative to using the full empirical data.
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| 4. |
- Spricer, Kristoffer, et al.
(författare)
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Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks
- 2018
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Ingår i: Stochastic Processes and Applications. - Cham : Springer. - 9783030028244 - 9783030028251 ; , s. 315-334
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Konferensbidrag (refereegranskat)abstract
- A key parameter in models for the spread of infectious diseases is the basic reproduction number R0">R 0 R0 , which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by simulating epidemics on empirical networks and by fitting the initial phase of each epidemic to a generalised growth model, allowing for estimating the shape of the growth. For reference, this is repeated on some elementary graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint.
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| 5. |
- Spricer, Kristoffer, 1966-
(författare)
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Random networks with weights and directions, and epidemics thereon
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Networks, consisting of nodes and of edges, can be used to model numerous phenomena, e.g, web pages linking to each other or interactions between people in a population. Edges can be directed, such as a one way link from one web page to another, or undirected (bi-directional), such as physical contacts between pairs of people, which potentially could spread an infection either way between them. Edges can also have weights associated with them, in this thesis corresponding to the probability that an infection is transmitted on the edge.Empirical networks are often only partially known, in the form of ego-centric network data where only a subset of the nodes and the number of adjacent edges of each node have been observed. This situation lends itself well to analysis through the undirected or partially directed configuration model - a random network model where the number of edges of each node (the degree) is given but where the way these edges are connected is random.The four papers in this thesis are concerned with the properties of the configuration model and with the usefulness of it with respect to its ability to model the spread of epidemics on empirical networks. Paper I proves the asymptotic convergence to a given degree distribution for the partially directed configuration model. In Paper II it is shown that epidemics on some empirical and theoretically constructed networks grow exponentially, similarly to what can be seen on the corresponding configuration models. Finally, in Papers III and IV, large population analytical results for the reproduction number, the probability of a large epidemic outbreak and the final size of such an outbreak are derived assuming a configuration model network with weighted and/or partially directed edges. These results are then evaluated on several large empirical networks upon which epidemics are simulated. We find that on some of these networks the analytical expressions are compatible with the results of the simulations. This makes the model useful as a tool for analyzing such networks.
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| 6. |
- Spricer, Kristoffer, et al.
(författare)
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The Configuration Model for Partially Directed Graphs
- 2015
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 161:4, s. 965-985
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Tidskriftsartikel (refereegranskat)abstract
- The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially directed meaning that certain edges are directed and others are undirected. In the paper we define a configuration model for such networks where vertices have in-, out-, and undirected degrees that may be dependent. We prove conditions under which the resulting degree distributions converge to the intended degree distributions. The new model is shown to better approximate several empirical networks compared to undirected and completely directed networks.
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