Effects of dimers on cooperation in the spatial prisoner's dilemma game

We investigate the evolutionary prisoner's dilemma game in structured populations by introducing dimers, which are defined as that two players in each dimer always hold a same strategy. We find that influences of dimers on cooperation depend on the type of dimers and the population structure. For those dimers in which players interact with each other, the cooperation level increases with the number of dimers though the cooperation improvement level depends on the type of network structures. On the other hand, the dimers, in which there are not mutual interactions, will not do any good to the cooperation level in a single community, but interestingly, will improve the cooperation level in a population with two communities. We explore the relationship between dimers and self-interactions and find that the effects of dimers are similar to that of self-interactions. Also, we find that the dimers, which are established over two communities in a multi-community network, act as one type of interaction through which information between communities is communicated by the requirement that two players in a dimer hold a same strategy.Comment: 12 pages and 3 figure

Dynamics and Energetics of Ge(001) Dimers

The dynamic behavior of surface dimers on Ge(001) has been studied by positioning the tip of a scanning tunneling microscope over single flip-flopping dimers and measuring the tunneling current as a function of time. We observe that not just symmetric, but also asymmetric appearing dimers exhibit flip-flop motion. The dynamics of flip-flopping dimers can be used to sensitively gauge the local potential landscape of the surface. Through a spatial and time-resolved measurement of the flip-flop frequency of the dimers, local strain fields near surface defects can be accurately probed

A cluster expansion approach to the Heilmann-Lieb liquid crystal model

A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice $\mathbb{Z}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the horizontal dimers have no long-range traslational order - in agreement with the Heilmann-Lieb conjecture.Comment: 42 pages, 3 figure

Tyrosinase inhibitory and antioxidant activity by bromophenols from the alga Odonthalia corymbifera

In the course of our search for tyrosinase inhibitors and antioxidants, six known bromophenol dimers were purified from methanol extract of the red alga Odonthalia corymbifera. The compounds were identified by comparison with published spectroscopic data. These bromophenols were categorized into symmetric and asymmetric dimers. Among them, the tetrabrominated dimers displayed more potent tyrosinase inhibition than the tribrominated ones. Especially, the asymmetric tetrabrominated compound showed strong inhibition. These results suggest that number of bromine substitution and orientation of bromine and phenolic hydroxy groups are important factors of tyrosinase inhibitory potency. The bromophenols were also investigated for antioxidant activities by using DPPH and ABTS radical scavenging, CUPRAC and FRAP metal reducing and copper chelation assays. All dimers showed comparable antioxidant activities to the positive controls examined. Symmetric dimers displayed relatively higher antioxidant activities than asymmetric ones

Para to Ortho transition of metallic dimers on Si(001)

Extensive electronic structure calculations are performed to obtain the stable geometries of metals like Al, Ga and In on the Si(001) surface at 0.5 ML and 1 ML coverages. Our results coupled with previous theoretical findings explain the recent experimental data in a comprehensive fashion. At low coverages, as shown by previous works, `Para' dimers give the lowest energy structure. With increasing coverage beyond 0.5 ML, `Ortho' dimers become part of low energy configurations leading toward a `Para' to `Ortho' transition at 1 ML coverage. For In mixed staggered dimers (`Ortho' and `Para') give the lowest energy configuration. For Ga, mixed dimers are non-staggered, while for Al `Para' to `Ortho' transition of dimers is complete. Thus at intermediate coverages between 0.5 and 1 ML, the `Ortho' and `Para' dimers may coexist on the surface. Consequently, this may be an explanation of the fact that the experimental observations can be successfully interpreted using either orientation. A supported zigzag structure at 0.5 ML, which resembles ${\rm (CH)_x}$, does not undergo a dimerization transition, and hence stays semi-metallic. Also, unlike ${\rm (CH)_x}$ the soliton formation is ruled out for this structure.Comment: 8 pages, 6 figure

Coupling of hard dimers to dynamical lattices via random tensors

We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the critical behavior of the continuum limit is the one of pure random lattices. We find a negative critical activity where the universality class is changed as dimers become critical, in a very similar way hard dimers exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents are calculated exactly. An alternative description as a system of `color-sensitive hard-core dimers' on random branched polymers is provided.Comment: 12 page