Long-range excitations in time-dependent density functional theory

Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency-dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is static correlation created by the step in the exact Kohn-Sham ground-state potential between the two fragments. An approximate non-empirical kernel is derived for excited molecular dissociation curves at large separation. Our result is also relevant for the usual local and semi-local approximations for the ground-state potential, as static correlation there arises from the coalescence of the highest occupied and lowest unoccupied orbital energies as the molecule dissociates.Comment: 7 pages, 2 figure

Bridging the Gap Between the Mode Coupling and the Random First Order Transition Theories of Structural Relaxation in Liquids

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated events (called instantons) which lead to the spatial reorganization of molecules in the region where the instanton pops up. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event which can be derived from the random first order transition theory. The vertex is proportional to $exp(-A/s_{c})$ where $s_{c}$ is the configurational entropy. Close to the glass transition temperature, $T_{g}$, since $s_{c}$ is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor in deeply supercooled liquid fairly well, with a hopping dominated decay following the MCT plateau.Comment: 11 pages, 5 figures, 1 tabl

Dynamical Heterogeneity and the interplay between activated and mode coupling dynamics in supercooled liquids

We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from continuous diffusion, described using general two coupling parameter ($F_{12}$) mode coupling theory (MCT), and from the activated hopping, described using the random first order transition (RFOT) theory, incorporating the effect of dynamical heterogeneity. The theory is valid over the whole temperature plane and shows correct limiting MCT like behavior above $T_{c}$ and goes over to the RFOT theory near the glass transition temperature, $T_{g}$. Between $T_{c}$ and $T_{g}$, the theory predicts that neither the continuous diffusion, described by pure mode coupling theory, nor the hopping motion alone suffices but both contribute to the dynamics while interacting with each other. We show that the interplay between the two contributions conspires to modify the relaxation behavior of the DSF from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Close to $T_c$, coupling between the short time part of MCT dynamics and hopping reduces the stretching given by the F$_{12}$-MCT theory significantly and accelerates structural relaxation. As the temperature is progressively lowered below $T_c$, the equations yield a crossover from MCT dominated regime to the hopping dominated regime. In the combined theory the dynamical heterogeneity is modified because the low barrier components interact with the MCT dynamics to enhance the relaxation rate below $T_c$ and reduces the stretching that would otherwise arise from an input static barrier height distribution.Comment: 7 pages, 4 figure

Identification of two new HMXBs in the LMC: a ∼\sim2013 s pulsar and a probable SFXT

We report on the X-ray and optical properties of two high-mass X-ray binary systems located in the Large Magellanic Cloud (LMC). Based on the obtained optical spectra, we classify the massive companion as a supergiant star in both systems. Timing analysis of the X-ray events collected by XMM-Newton revealed the presence of coherent pulsations (spin period $\sim$2013 s) for XMMU J053108.3-690923 and fast flaring behaviour for XMMU J053320.8-684122. The X-ray spectra of both systems can be modelled sufficiently well by an absorbed power-law, yielding hard spectra and high intrinsic absorption from the environment of the systems. Due to their combined X-ray and optical properties we classify both systems as SgXRBs: the 19$^{\rm th}$ confirmed X-ray pulsar and a probable supergiant fast X-ray transient in the LMC, the second such candidate outside our Galaxy.Comment: 12 pages, 10 figures, accepted for publication in MNRA

Adaptive Seeding for Gaussian Mixture Models

We present new initialization methods for the expectation-maximization algorithm for multivariate Gaussian mixture models. Our methods are adaptions of the well-known $K$-means++ initialization and the Gonzalez algorithm. Thereby we aim to close the gap between simple random, e.g. uniform, and complex methods, that crucially depend on the right choice of hyperparameters. Our extensive experiments indicate the usefulness of our methods compared to common techniques and methods, which e.g. apply the original $K$-means++ and Gonzalez directly, with respect to artificial as well as real-world data sets.Comment: This is a preprint of a paper that has been accepted for publication in the Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD) 2016. The final publication is available at link.springer.com (http://link.springer.com/chapter/10.1007/978-3-319-31750-2 24

Complementation of soluble phosphofructokinase activity in yeast mutants

We describe here the genetic and biochemical analyses of two classes of mutations in the soluble phosphofructokinase (PFK I) of Saccharomyces cerevisiae: those leading to the loss of activity and those giving rise to a kinetically altered enzyme. Complementation and allele-testing between these two classes of mutants show that loss of enzyme activity in vitro can come about not only by mutations in the catalytic subunit but also in the regulatory subunit. Also, a mutation in the catalytic subunit can give rise to an enzyme altered in its kinetic properties in a manner phenomenologically similar to that caused by a mutation in the regulatory subunit. The results of the complementation studies in diploids suggest that, in spite of their distinct functions, both the subunits are essential for activity to be detected in vitro. This is confirmed by the reconstitution of an active PFK I enzyme by mixing cell-free extracts of two complementing parents, each of which lacks the enzyme activity. PFK activity appears in the mixture, reaching a maximum value of 60–100% of that of the diploid in 15–30 min at 24°C. Unlike the catalytic subunit which exists in various multimeric states in cell-free extracts of the mutant bearing only this subunit, the regulatory subunit exists largely as a monomer in a mutant devoid of the catalytic subunit. The reconstituted enzyme, however, is indistinguishable from that of the wild type, as analysed by sedimentation studies and Western blot analysis, demonstrating that only the heteromeric complex of the two subunits is active, while neither of the individual subunits displays activity in vitro