MRD codes with maximum idealizers

Left and right idealizers are important invariants of linear rank-distance codes. In the case of maximum rank-distance (MRD for short) codes in $\mathbb{F}_q^{n\times n}$ the idealizers have been proved to be isomorphic to finite fields of size at most $q^n$. Up to now, the only known MRD codes with maximum left and right idealizers are generalized Gabidulin codes, which were first constructed in 1978 by Delsarte and later generalized by Kshevetskiy and Gabidulin in 2005. In this paper we classify MRD codes in $\mathbb{F}_q^{n\times n}$ for $n\leq 9$ with maximum left and right idealizers and connect them to Moore-type matrices. Apart from generalized Gabidulin codes, it turns out that there is a further family of rank-distance codes providing MRD ones with maximum idealizers for $n=7$, $q$ odd and for $n=8$, $q\equiv 1 \pmod 3$. These codes are not equivalent to any previously known MRD code. Moreover, we show that this family of rank-distance codes does not provide any further examples for $n\geq 9$.Comment: Reviewers' comments implemented, we changed the titl

Estimating infectious disease parameters from data on social contacts and serological status

In dynamic models of infectious disease transmission, typically various mixing patterns are imposed on the so-called Who-Acquires-Infection-From-Whom matrix (WAIFW). These imposed mixing patterns are based on prior knowledge of age-related social mixing behavior rather than observations. Alternatively, one can assume that transmission rates for infections transmitted predominantly through non-sexual social contacts, are proportional to rates of conversational contact which can be estimated from a contact survey. In general, however, contacts reported in social contact surveys are proxies of those events by which transmission may occur and there may exist age-specific characteristics related to susceptibility and infectiousness which are not captured by the contact rates. Therefore, in this paper, transmission is modeled as the product of two age-specific variables: the age-specific contact rate and an age-specific proportionality factor, which entails an improvement of fit for the seroprevalence of the varicella-zoster virus (VZV) in Belgium. Furthermore, we address the impact on the estimation of the basic reproduction number, using non-parametric bootstrapping to account for different sources of variability and using multi-model inference to deal with model selection uncertainty. The proposed method makes it possible to obtain important information on transmission dynamics that cannot be inferred from approaches traditionally applied hitherto.Comment: 25 pages, 6 figure

Downdating high-resolution population density maps using sealed surface cover time series

Many countries in Europe and North America see their natural and agricultural landscapes being replaced by a fragmented, sprawled landscape. Spatially detailed modelling of changes in land use, population and transport could help to forecast the impact of scenarios aimed at mitigating the process of urban sprawl. A common problem with land-use change models however, is the lack of historical data for proper model calibration. In this paper we describe an approach for developing historical population density maps by downdating a recent high-resolution population density raster, using a time series of sealed surface data and historical census data as an input. In the proposed approach, we hypothesise a local relationship between increasing population densities and increasing sealed surface fraction estimates, the latter obtained from remote sensing imagery. We apply the method to Flanders, Belgium, a region where population growth and improved transport networks led to a diffuse urban expansion, with ribbon development along many roads and a strong fragmentation of open space. The resulting population and sealed surface maps provide interesting data on the urban sprawl phenomenon in the past decades. By computing a densification index we observe that most urban areas witness a recent population density increase while in several rural areas the built-up area per inhabitant is still growing. The downdated time series of population maps obtained in this study will be used to set up a historical calibration for an activity-based cellular automata model for Flanders and Brussels which, among other data, needs high-resolution population maps

Estimating infectious disease parameters from data on social contacts and serological status

In dynamic models of infectious disease transmission, typically various mixing patterns are imposed on the so-called 'who acquires infection from whom' matrix. These imposed mixing patterns are based on prior knowledge of age-related social mixing behaviour rather than observations. Alternatively, we can assume that transmission rates for infections transmitted predominantly through non-sexual social contacts are proportional to rates of conversational contact which can be estimated from a contact survey. In general, however, contacts reported in social contact surveys are proxies of those events by which transmission may occur and there may be age-specific characteristics that are related to susceptibility and infectiousness which are not captured by the contact rates. Therefore, we model transmission as the product of two age-specific variables: the age-specific contact rate and an age-specific proportionality factor, which entails an improvement of fit for the seroprevalence of the varicella zoster virus in Belgium. Furthermore, we address the effect on the estimation of the basic reproduction number, using non-parametric bootstrapping to account for different sources of variability and using multimodel inference to deal with model selection uncertainty. The method proposed makes it possible to obtain important information on transmission dynamics that cannot be inferred from approaches that have been traditionally applied hitherto. Copyright (c) 2010 Royal Statistical Society.