Simultaneous Representation of Proper and Unit Interval Graphs

In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary

Social Comparisons as a device for cooperation in simultaneous-move games

This paper analyzes the effects of players' relative comparisons in complete information simultaneous-move games. In particular, every individual is assumed to evaluate the kindness she infers from other players'choices by comparing these choices with respect to a given refer- ence level. Specifically, this paper identifies under what conditions the introduction of relative comparisons leads players to be more cooperative than in standard game-theoretic models. I show that this result holds under certain conditions on the specific reference point that players use in their relative comparisons, and on whether players'relative comparisons leads them to regard each others' actions as more strategic complementary or substitutable. The model is then applied to different examples in public good games which enhance the intuition behind the results. Finally, I show that some existing models in the literature of intentions-based reciprocity and social status acquisition can be rationalized as special cases.Relative comparisons, Reference points, Simultaneous-move games, Kindness, Strategic complementarities.

Simultaneous junction formation

High-risk, high-payoff improvements to a baseline process sequence of simultaneous junction formation of silicon solar cells are discussed. The feasibility of simultaneously forming front and back junctions of solar cells using liquid dopants on dendritic web silicon was studied. Simultaneous diffusion was compared to sequential diffusion. A belt furnace for the diffusion process was tested

Simultaneous Orthogonal Planarity

We introduce and study the $\textit{OrthoSEFE}-k$ problem: Given $k$ planar graphs each with maximum degree 4 and the same vertex set, do they admit an OrthoSEFE, that is, is there an assignment of the vertices to grid points and of the edges to paths on the grid such that the same edges in distinct graphs are assigned the same path and such that the assignment induces a planar orthogonal drawing of each of the $k$ graphs? We show that the problem is NP-complete for $k \geq 3$ even if the shared graph is a Hamiltonian cycle and has sunflower intersection and for $k \geq 2$ even if the shared graph consists of a cycle and of isolated vertices. Whereas the problem is polynomial-time solvable for $k=2$ when the union graph has maximum degree five and the shared graph is biconnected. Further, when the shared graph is biconnected and has sunflower intersection, we show that every positive instance has an OrthoSEFE with at most three bends per edge.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Combining simultaneous with temporal masking

Simultaneous and temporal masking are two frequently used techniques in psychology and vision science. Although there are many studies and theories related to each masking technique, there are no systematic investigations of their mutual relationship, even though both techniques are often applied together. Here, the authors show that temporal masking can both undo and enhance the deteriorating effects of simultaneous masking depending on the stimulus onset asynchrony between the simultaneous and temporal masks. For the task and stimuli used in this study, temporal masking was largely unaffected by the properties of the simultaneous mask. In contrast, simultaneous masking seems to depend strongly on spatial grouping and was strongly affected by the properties of the temporal mask. These findings help to identify the nature of both temporal and simultaneous masking and promote understanding of the role of spatial and temporal grouping in visual perception