Inferring epidemiological parameters from phylogenetic information for the HIV-1 epidemic among MSM

The HIV-1 epidemic in Europe is primarily sustained by a dynamic topology of sexual interactions among MSM who have individual immune systems and behavior. This epidemiological process shapes the phylogeny of the virus population. Both fields of epidemic modeling and phylogenetics have a long history, however it remains difficult to use phylogenetic data to infer epidemiological parameters such as the structure of the sexual network and the per-act infectiousness. This is because phylogenetic data is necessarily incomplete and ambiguous. Here we show that the cluster-size distribution indeed contains information about epidemiological parameters using detailed numberical experiments. We simulate the HIV epidemic among MSM many times using the Monte Carlo method with all parameter values and their ranges taken from literature. For each simulation and the corresponding set of parameter values we calculate the likelihood of reproducing an observed cluster-size distribution. The result is an estimated likelihood distribution of all parameters from the phylogenetic data, in particular the structure of the sexual network, the per-act infectiousness, and the risk behavior reduction upon diagnosis. These likelihood distributions encode the knowledge provided by the observed cluster-size distrbution, which we quantify using information theory. Our work suggests that the growing body of genetic data of patients can be exploited to understand the underlying epidemiological process.     

Mossbauer effect study of surface magnetization processes in iron

Magnetization processes at the surface of iron plates were investigated in a variable external field by means of Mössbauer emission and scattering spectroscopy of⁵⁷Fe. It is shown that the 90? walls of closure domains do not move until an externally applied field reaches a certain value. The “starting” values of the field determined from the Mössbauer measurements agree with those at which a sudden decrease in the growth rate of the bulk magnetization starts. Blocking of the surface domain wall movement occurs in a layer of at least 10 Μm thickness.     

Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options

In this paper we prove optimal interior regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstacles as well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. The problem considered arises in financial mathematics, when considering path-dependent derivative contracts with early exercise feature.     

Observation of vibrational transitions in (3He 3H)+ after β-decay in the tritium molecule.

We have observed an infrared emission band at (4.69 ± 0.03)μ as a consequence of β-decay in molecular tritium $\text{[}{}^3\text{H}{}_2\text{→}\text{β?}\text{(}{}^3\text{He}{}^3\text{H)}{}^{\mathrm{+}}\text{]}$ at 25 K. This emission is due to β-recoil-induced vibrational excitation.     

Regularity in the obstacle problem for parabolic non-divergence operators of Hörmander type

In this paper we continue the study initiated in [15] concerning the obstacle problem for a class of parabolic non-divergence operators structured on a set of vector fields X={_X1,…,_Xq}$X=\{X_1,\dots ,X_q\}$ in Rⁿ${\mathbf{R}}^n$ with C^∞$C^{\infty }$-coefficients satisfying Hörmander?s finite rank condition, i.e., the rank of Lie[_X1,…,_Xq]$\mathrm{Lie}[X_1,\dots ,X_q]$ equals n   at every point in Rⁿ${\mathbf{R}}^n$. In [15] we proved, under appropriate assumptions on the operator and the obstacle, the existence and uniqueness of strong solutions to a general obstacle problem. The main result of this paper is that we establish further regularity, in the interior as well as at the initial state, of strong solutions. Compared to [15] we in this paper assume, in addition, that there exists a homogeneous Lie group G=(Rⁿ,°,_δλ)$\mathbf{G}=({\mathbf{R}}^n,°,{\delta }_{\lambda })$ such that _X1,…,_Xq$X_1,\dots ,X_q$ are left translation invariant on G and such that _X1,…,_Xq$X_1,\dots ,X_q$ are _δλ${\delta }_{\lambda }$-homogeneous of degree one.