Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution

On the geometric interpretation of the Polynomial Lie Bracket for nonlinear time-delay systems

Time-delay systems are infinite dimensional, thus standard differential geometric tools can not be applied in a straightforward way. Though, thanks to a suitable extended Lie Bracket - or Polynomial Lie Bracket - which has been introduced recently, it is still possible to build up a geometric framework to tackle the analysis and synthesis problems for nonlinear time delay systems. The major contribution herein is to show that those geometric generalizations are not just formal, but are interpreted in terms of successive forward and backward flows similarly to the Lie Bracket of delay free vector fields

Recovering low molecular weight extractives from degraded straw by oyster mushroom at the farm scale for high value use

The cultivation of mushrooms on wheat straw can be considered a solid state fermentation, yet following harvest the residual, partially degraded straw is discarded. During cultivation, the degradation of lignocellulose in the straw takes place by the fungus under the action of enzymes releasing degradation products with small molecular weight, some of which are potentially valuable. These compounds may be extracted from straw after mushroom cultivation in two stages: an aqueous extraction followed by a solvent extraction. The present work is focused on the first stage of the process. The aqueous extraction releases water soluble compounds, such as sugars and phenolics with lower molecular weight, which are easily obtained. The partially degraded straw may then be treated with organic solvents to release water insoluble lignin breakdown products, such as fatty acids, phenolics and other aromatics. It is important to conduct scale-up experiments at a scale that would reflect the amount of waste straw generated by a mushroom farm. A study was performed using a vessel of 300 L capacity with mixing impeller, by observing the influence of the temperature (20oC, 25oC, 40oC, 60oC and 80oC) and water-to-dry straw ratio (from 40:1 to 90:1) on the total extracted matter and especially on sugar and phenolic compounds yields. A microbial study of the aqueous extract was also performed at 20oC and 25oC to explain the high concentration of organic carbon in the extract under certain circumstances. The optimum extraction conditions were determined by taking into account the yield and the energy consumption of the process. The conclusion was that the extraction temperature can be conducted between 20oC and 25oC with good results for obtaining liquor which can be used in a biogas installation. The extraction should be conducted at 80oC to obtain greater yields of sugars and phenolics

Mobilizing the Trump Train: Understanding Collective Action in a Political Trolling Community

Political trolls initiate online discord not only for the lulz (laughs) but also for ideological reasons, such as promoting their desired political candidates. Political troll groups recently gained spotlight because they were considered central in helping Donald Trump win the 2016 US presidential election, which involved difficult mass mobilizations. Political trolls face unique challenges as they must build their own communities while simultaneously disrupting others. However, little is known about how political trolls mobilize sufficient participation to suddenly become problems for others. We performed a quantitative longitudinal analysis of more than 16 million comments from one of the most popular and disruptive political trolling communities, the subreddit /r/The\_Donald (T\D). We use T_D as a lens to understand participation and collective action within these deviant spaces. In specific, we first study the characteristics of the most active participants to uncover what might drive their sustained participation. Next, we investigate how these active individuals mobilize their community to action. Through our analysis, we uncover that the most active employed distinct discursive strategies to mobilize participation, and deployed technical tools like bots to create a shared identity and sustain engagement. We conclude by providing data-backed design implications for designers of civic media

GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization

In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general c\`adl\`ag martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of F\"ollmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994).Comment: 22 page