Robust Hypothesis Tests for Detecting Statistical Evidence of 2D and 3D Interactions in Single-Molecule Measurements

A variety of experimental techniques have improved the 2D and 3D spatial resolution that can be extracted from \emph{in vivo} single-molecule measurements. This enables researchers to quantitatively infer the magnitude and directionality of forces experienced by biomolecules in their native cellular environments. Situations where such forces are biologically relevant range from mitosis to directed transport of protein cargo along cytoskeletal structures. Models commonly applied to quantify single-molecule dynamics assume that effective forces and velocity in the $x,y$ (or $x,y,z$) directions are statistically independent, but this assumption is physically unrealistic in many situations. We present a hypothesis testing approach capable of determining if there is evidence of statistical dependence between positional coordinates in experimentally measured trajectories; if the hypothesis of independence between spatial coordinates is rejected, then a new model accounting for 2D (3D) interactions should be considered to more faithfully represent the underlying experimental kinetics. The technique is robust in the sense that 2D (3D) interactions can be detected via statistical hypothesis testing even if there is substantial inconsistency between the physical particle's actual noise sources and the simplified model's assumed noise structure. For example, 2D (3D) interactions can be reliably detected even if the researcher assumes normal diffusion, but the experimental data experiences "anomalous diffusion" and/or is subjected to a measurement noise characterized by a distribution differing from that assumed by the fitted model. The approach is demonstrated on control simulations and on experimental data (IFT88 directed transport in the primary cilium).Comment: 7 pages, 6 figure

Tight binding model for iron pnictides

We propose a five-band tight-binding model for the Fe-As layers of iron pnictides with the hopping amplitudes calculated within the Slater-Koster framework. The band structure found in DFT, including the orbital content of the bands, is well reproduced using only four fitting parameters to determine all the hopping amplitudes. The model allows to study the changes in the electronic structure caused by a modification of the angle $\alpha$ formed by the Fe-As bonds and the Fe-plane and recovers the phenomenology previously discussed in the literature. We also find that changes in $\alpha$ modify the shape and orbital content of the Fermi surface sheets.Comment: 12 pages, 6 eps figures. Figs 1 and 2 modified, minor changes in the text. A few references adde

Axial-vector mesons from τ→APντ\tau\to AP\nu_\tau decays

Axial-vector mesons $a_1(1260)$, $f_1(1285)$, $h_1(1170)$, $K_1(1270)$, and $K_1(1400)$ can be produced in semileptonic $\tau\to A P \nu_{\tau}$ decays, where $P$ stands for the pseudoscalar mesons $\pi$ or $K$. We calculate the branching ratios based in a meson dominance model. The exclusive channels $\tau^-\to a_1(1260)^-\pi^0\nu$, $\tau^-\to a_1(1260)^0\pi^-\nu$, and $\tau^-\to h_1(1170)\pi^-\nu$ turn out to be of order ${\cal O}(10^{-3})$, the channel $\tau^-\to f_1(1285)\pi^-\nu$ of order ${\cal O}(10^{-4})$, and channels $\tau^-\to K_1(1270)^-\pi^0\nu$, $\tau^-\to K_1(1270)^0\pi^-\nu$, $\tau^-\to K_1(1400)^-\pi^0\nu$, and $\tau^-\to K_1(1400)^0\pi^-\nu$ of order ${\cal O}(10^{-6})$. These results indicate that the branching ratios could be measured in experiments.Comment: 7 pages, 1 table, 1 figure, version published in PR

Optical conductivity and Raman scattering of iron superconductors

We discuss how to analyze the optical conductivity and Raman spectra of multi-orbital systems using the velocity and the Raman vertices in a similar way Raman vertices were used to disentangle nodal and antinodal regions in cuprates. We apply this method to iron superconductors in the magnetic and non-magnetic states, studied at the mean field level. We find that the anisotropy in the optical conductivity at low frequencies reflects the difference between the magnetic gaps at the X and Y electron pockets. Both gaps are sampled by Raman spectroscopy. We also show that the Drude weight anisotropy in the magnetic state is sensitive to small changes in the lattice structure.Comment: 14 pages, 10 figures, as accepted in Phys. Rev. B, explanations/discussion added in Secs. II, III and V

Low magnetization and anisotropy in the antiferromagnetic state of undoped iron pnictides

We examine the magnetic phase diagram of iron pnictides using a five band model. For the intermediate values of the interaction expected to hold in the iron pnictides, we find a metallic low moment state characterized by antiparallel orbital magnetic moments. The anisotropy of the interorbital hopping amplitudes is the key to understanding this low moment state. This state accounts for the small magnetization measured in undoped iron pnictides and leads to the strong exchange anisotropy found in neutron experiments. Orbital ordering is concomitant with magnetism and produces the large zx orbital weight seen at Gamma in photoemission experiments.Comment: 4 pages, 4 eps figures. Small changes in the text. Modification of colors in Figs. Final version as accepted in PR