Coloring Mixed and Directional Interval Graphs

A mixed graph has a set of vertices, a set of undirected egdes, and a set ofdirected arcs. A proper coloring of a mixed graph $G$ is a function $c$ thatassigns to each vertex in $G$ a positive integer such that, for each edge $uv$in $G$, $c(u) \ne c(v)$ and, for each arc $uv$ in $G$, $c(u) mixed graph$G$, the chromatic number$\chi(G)$is the smallest number ofcolors in any proper coloring of$G$. A directional interval graph is a mixedgraph whose vertices correspond to intervals on the real line. Such a graph hasan edge between every two intervals where one is contained in the other and anarc between every two overlapping intervals, directed towards the interval thatstarts and ends to the right. Coloring such graphs has applications in routing edges in layered orthogonalgraph drawing according to the Sugiyama framework; the colors correspond to thetracks for routing the edges. We show how to recognize directional intervalgraphs, and how to compute their chromatic number efficiently. On the otherhand, for mixed interval graphs, i.e., graphs where two intersecting intervalscan be connected by an edge or by an arc in either direction arbitrarily, weprove that computing the chromatic number is NP-hard.<br

Cryo-EM structures reveal intricate Fe-S cluster arrangement and charging in Rhodobacter capsulatus formate dehydrogenase

Metal-containing formate dehydrogenases (FDH) catalyse the reversible oxidation of formate to carbon dioxide at their molybdenum or tungsten active site. They display a diverse subunit and cofactor composition, but structural information on these enzymes is limited. Here we report the cryo-electron microscopic structures of the soluble Rhodobacter capsulatus FDH (RcFDH) as isolated and in the presence of reduced nicotinamide adenine dinucleotide (NADH). RcFDH assembles into a 360 kDa dimer of heterotetramers revealing a putative interconnection of electron pathway chains. In the presence of NADH, the RcFDH structure shows charging of cofactors, indicative of an increased electron load

Outcome uncertainty influences probability perception and risk attitudes

Subjective inferences of probability play a critical role in decision-making. How we learn about choice options, through description or experience, influences how we perceive their likelihoods, an effect known as the description–experience (DE) gap. Classically, the DE gap details how low probability described options are perceptually inflated as compared to equiprobable experience ones. However, these studies assessed probability perception relative to a ‘sure-bet’ option, and it remained unclear whether the DE gap occurs when humans directly trade-off equiprobable description and experience options and whether choice patterns are influenced by the prospects of gain and loss. We addressed these questions through two experiments where humans chose between description and experience options with equal probabilities of either winning or losing points. Contrary to early studies, we found that gain-seeking participants preferred experience options across all probability levels and, by contrast, loss-mitigating participants avoided the experience options across all probability levels, with a maximal effect at 50%. Our results suggest that the experience options were perceived as riskier than descriptive options due to the greater uncertainty associated with their outcomes. We conclude by outlining a novel theory of probabilistic inference where outcome uncertainty modulates probability perception and risk attitudes