Trinets encode tree-child and level-2 phylogenetic networks

Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all “recoverable” rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets

Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups

Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some positive invertible elliptic operator, we investigate the geometry of loop groups in the light of the cohomology of pseudo-differential operators. We set up a geometric framework to study a class of infinite dimensional manifolds in which we recover some results on the geometry of loop groups, using again weighted traces. Along the way, we investigate properties of extensions of the Radul and Schwinger cocycles defined with the help of weighted traces.Comment: 36 page

Ultrafast dephasing of coherent optical phonons in atomically controlled GeTe/Sb2_{2}Te3_{3} superlattices

Femtosecond dynamics of coherent optical phonons in GeTe/Sb$_{2}$Te$_{3}$ superlattices (SLs), a new class of semiconductor SLs with three different states, have been investigated by using a reflection-type pump-probe technique at various lattice temperatures. The time-resolved transient reflectivity (TR) obtained in as-grown SLs exhibits the coherent A$_{1}$ optical modes at 5.10 THz and 3.78 THz, while only the single A$_{1}$ mode at 3.68 THz is observed in annealed SLs. The decay rate of the A$_{1}$ mode in annealed SLs is strongly temperature dependent, while that in as-grown SLs is not temperature dependent. This result indicates that the damping of the coherent A$_{1}$ phonons in amorphous SLs is governed by the phonon-defect (vacancy) scattering rather than the anharmonic phonon-phonon coupling.Comment: 5 pages, 5 figure

Can a Course on Sexuality Counseling Increase Empathy when Working with Sex- and Gender-Minoritized Individuals?

This study examined whether a sexuality counseling course could increase self-perceived empathy for working with Sex and Gender minoritized (SGM)individuals. Forty-two students enrolled in a sexuality counseling course completed empathy assessments prior to starting the course and after completing it. Statistically significant increases in empathy towards gay/lesbian, bisexual, and transgender individuals were found (moderate to a large effect sizes). Results indicate that, at least under some circumstances, empathy levels for SGM individuals in counselors-in-training (CITs) could be increased through coursework. Increases in practitioner empathy for SGM individuals can translate into lower uniliteral termination rates and better counseling and psychotherapy outcomes

Isotope effects on the lattice parameter of cubic SiC

Path-integral molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble have been carried out to study the dependence of the lattice parameter of 3C-SiC upon isotope mass. This computational method allows a quantitative and nonperturbative study of such anharmonic effect. Atomic nuclei were treated as quantum particles interacting via a tight-binding-type potential. At 300 K, the difference Delta a between lattice parameters of 3C-SiC crystals with 12C and 13C amounts to 2.1 x 10^{-4} A. The effect due to Si isotopes is smaller, and amounts to 3.5 x 10^{-5} A when replacing 28Si by 29Si. Results of the PIMD simulations are interpreted in terms of a quasiharmonic approximation for the lattice vibrations.Comment: 4 pages, 3 figure

Raman scattering study of electron-doped Prx_xCa1−x_{1-x}Fe2_2As2_2 superconductors

Temperature-dependent polarized Raman spectra of electron-doped superconducting Pr$_x$Ca$_{1-x}$Fe$_2$As$_2$ ($x \approx 0.12$) single crystals are reported. All four allowed by symmetry even-parity phonons are identified. Phonon mode of B$_{1g}$ symmetry at 222 cm$^{-1}$, which is associated with the c-axis motion of Fe ions, is found to exhibit an anomalous frequency hardening at low temperatures, that signals non-vanishing electron-phonon coupling in the superconducting state and implies that the superconducting gap magnitude $2\Delta_c < 27$meV.Comment: 4 pages, 3 figure

Quantum interference effects in resonant Raman spectroscopy of single- and triple-layer MoTe2_2 from first principles

We present a combined experimental and theoretical study of resonant Raman spectroscopy in single- and triple-layer MoTe$_2$. Raman intensities are computed entirely from first principles by calculating finite differences of the dielectric susceptibility. In our analysis, we investigate the role of quantum interference effects and the electron-phonon coupling. With this method, we explain the experimentally observed intensity inversion of the $A^\prime_1$ vibrational modes in triple-layer MoTe2 with increasing laser photon energy. Finally, we show that a quantitative comparison with experimental data requires the proper inclusion of excitonic effects.Comment: Main Text (5 Figures, 1 Tables) + Supporting Information (6 Figures

Phonons in single and few-layer MoS2 and WS2

We report ab-initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS2 and WS2. We explore in detail the behavior of the Raman active modes, A1g and E2g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et. al., ACS Nano Vol. 4, 2695 (2010)] we find that the A1g mode increases in frequency with increasing layer number while the E2g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with growing number of layers. This decrease in the long-range part over-compensates the increase of the short-range interaction due to the weak inter-layer interaction.Comment: 8 pages, 6 figure