42 research outputs found
Ground state at high density
Weak limits as the density tends to infinity of classical ground states of
integrable pair potentials are shown to minimize the mean-field energy
functional. By studying the latter we derive global properties of high-density
ground state configurations in bounded domains and in infinite space. Our main
result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the
density increases, while high-density ground states show some pattern if the
Fourier transform is partially negative. The latter confirms the conclusion of
earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and
Likos et al. (2007). Other results include the proof that there is no Bravais
lattice among high-density ground states of interactions whose Fourier
transform has a negative part and the potential diverges or has a cusp at zero.
We also show that in the ground state configurations of the penetrable sphere
model particles are superposed on the sites of a close-packed lattice.Comment: Note adde
Spectra of complex networks
We propose a general approach to the description of spectra of complex
networks. For the spectra of networks with uncorrelated vertices (and a local
tree-like structure), exact equations are derived. These equations are
generalized to the case of networks with correlations between neighboring
vertices. The tail of the density of eigenvalues at large
is related to the behavior of the vertex degree distribution
at large . In particular, as , . We propose a simple approximation, which enables us to
calculate spectra of various graphs analytically. We analyse spectra of various
complex networks and discuss the role of vertices of low degree. We show that
spectra of locally tree-like random graphs may serve as a starting point in the
analysis of spectral properties of real-world networks, e.g., of the Internet.Comment: 10 pages, 4 figure
A p53-TLR3 axis ameliorates pulmonary hypertension by inducing BMPR2 via IRF3
Pulmonary arterial hypertension (PAH) features pathogenic and abnormal endothelial cells (ECs), and one potential origin is clonal selection. We studied the role of p53 and toll-like receptor 3 (TLR3) in clonal expansion and pulmonary hypertension (PH) via regulation of bone morphogenetic protein (BMPR2) signaling. ECs of PAH patients had reduced p53 expression. EC-specific p53 knockout exaggerated PH, and clonal expansion reduced p53 and TLR3 expression in rat lung CD117+ ECs. Reduced p53 degradation (Nutlin 3a) abolished clonal EC expansion, induced TLR3 and BMPR2, and ameliorated PH. Polyinosinic/polycytidylic acid [Poly(I:C)] increased BMPR2 signaling in ECs via enhanced binding of interferon regulatory factor-3 (IRF3) to the BMPR2 promoter and reduced PH in p53−/− mice but not in mice with impaired TLR3 downstream signaling. Our data show that a p53/TLR3/IRF3 axis regulates BMPR2 expression and signaling in ECs. This link can be exploited for therapy of PH
Mixing patterns in networks
We study assortative mixing in networks, the tendency for vertices in
networks to be connected to other vertices that are like (or unlike) them in
some way. We consider mixing according to discrete characteristics such as
language or race in social networks and scalar characteristics such as age. As
a special example of the latter we consider mixing according to vertex degree,
i.e., according to the number of connections vertices have to other vertices:
do gregarious people tend to associate with other gregarious people? We propose
a number of measures of assortative mixing appropriate to the various mixing
types, and apply them to a variety of real-world networks, showing that
assortative mixing is a pervasive phenomenon found in many networks. We also
propose several models of assortatively mixed networks, both analytic ones
based on generating function methods, and numerical ones based on Monte Carlo
graph generation techniques. We use these models to probe the properties of
networks as their level of assortativity is varied. In the particular case of
mixing by degree, we find strong variation with assortativity in the
connectivity of the network and in the resilience of the network to the removal
of vertices.Comment: 14 pages, 2 tables, 4 figures, some additions and corrections in this
versio
Quantitative analyses and modelling to support achievement of the 2020 goals for nine neglected tropical diseases
Quantitative analysis and mathematical models are useful tools in informing strategies to control or eliminate disease. Currently, there is an urgent need to develop these tools to inform policy to achieve the 2020 goals for neglected tropical diseases (NTDs). In this paper we give an overview of a collection of novel model-based analyses which aim to address key questions on the dynamics of transmission and control of nine NTDs: Chagas disease, visceral leishmaniasis, human African trypanosomiasis, leprosy, soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. Several common themes resonate throughout these analyses, including: the importance of epidemiological setting on the success of interventions; targeting groups who are at highest risk of infection or re-infection; and reaching populations who are not accessing interventions and may act as a reservoir for infection,. The results also highlight the challenge of maintaining elimination 'as a public health problem' when true elimination is not reached. The models elucidate the factors that may be contributing most to persistence of disease and discuss the requirements for eventually achieving true elimination, if that is possible. Overall this collection presents new analyses to inform current control initiatives. These papers form a base from which further development of the models and more rigorous validation against a variety of datasets can help to give more detailed advice. At the moment, the models' predictions are being considered as the world prepares for a final push towards control or elimination of neglected tropical diseases by 2020