Scale dependence of distributions of hotspots

We consider a random field $\phi(\mathbf{r})$ in $d$ dimensions which is largely concentrated around small `hotspots', with `weights', $w_i$. These weights may have a very broad distribution, such that their mean does not exist, or else is not a useful estimate. In such cases, the median $\overline W$ of the total weight $W$ in a region of size $R$ is an informative characterisation of the weights. We define the function $F$ by $\ln \overline W=F(\ln R)$. If $F'(x)>d$, the distribution of hotspots is dominated by the largest weights. In the case where $F'(x)-d$ approaches a constant positive value when $R\to \infty$, the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term \emph{ultradimensional}. The form of the function $F(x)$ is determined for a model of diffusion in a random potential.Comment: 18 pages, 10 figure

A high-resolution flux-matrix model describes the spread of diseases in a spatial network and the effect of mitigation strategies

Propagation of an epidemic across a spatial network of communities is described by a variant of the SIR model accompanied by an intercommunity infectivity matrix. This matrix is estimated from fluxes between communities, obtained from cell-phone tracking data recorded in the USA between March 2020 and February 2021. We apply this model to the SARS-CoV-2 pandemic by fitting just one global parameter representing the frequency of interaction between individuals. We find that the predicted infections agree reasonably well with the reported cases. We clearly see the effect of “shelter-in-place” policies introduced at the onset of the pandemic. Interestingly, a model with uniform transmission rates produces similar results, suggesting that the epidemic transmission was deeply influenced by air travel. We then study the effect of alternative mitigation policies, in particular restricting long-range travel. We find that this policy is successful in decreasing the epidemic size and slowing down the spread, but less effective than the shelter-in-place policy. This policy can result in a pulled wave of infections. We express its velocity and characterize the shape of the traveling front as a function of the epidemiological parameters. Finally, we discuss a policy of selectively constraining travel based on an edge-betweenness criterion.journal articl

A minimal model for household-based testing and tracing in epidemics

In a previous work (Huberet al.2020Phys. Biol.17065010), we discussed virus transmission dynamics modified by a uniform clustering of contacts in the population: close contacts within households and more distant contacts between households. In this paper, we discuss testing and tracing in such a stratified population. We propose a minimal tracing strategy consisting of random testing of the entire population plus full testing of the households of those persons found positive. We provide estimates of testing frequency for this strategy to work

Simple Mathematical Model Of Pathologic Microsatellite Expansions: When Self-Reparation Does Not Work

We propose a simple model of pathologic microsatellite expansion, and describe an inherent self-repairing mechanism working against expansion. We prove that if the probabilities of elementary expansions and contractions are equal, microsatellite expansions are always self-repairing. If these probabilities are different, self-reparation does not work. Mosaicism, anticipation and reverse mutation cases are discussed in the framework of the model. We explain these phenomena and provide some theoretical evidence for their properties, for example the rarity of reverse mutations

Biomedical Open Source Software: Crucial Packages and Hidden Heroes

Despite the importance of scientific software for research, it is often not formally recognized and rewarded. This is especially true for foundation libraries, which are used by the software packages visible to the users, being "hidden" themselves. The funders and other organizations need to understand the complex network of computer programs that the modern research relies upon. In this work we used CZ Software Mentions Dataset to map the dependencies of the software used in biomedical papers and find the packages critical to the software ecosystems. We propose the centrality metrics for the network of software dependencies, analyze three ecosystems (PyPi, CRAN, Bioconductor) and determine the packages with the highest centrality