Simultaneous Domination in Graphs

Let \({F_1, F_2, \ldots, F_k}\) be graphs with the same vertex set V. A subset \({S \subseteq V}\) is a simultaneous dominating set if for every i, 1 ≤ i ≤ k, every vertex of F _i not in S is adjacent to a vertex in S in F _i ; that is, the set S is simultaneously a dominating set in each graph F _i . The cardinality of a smallest such set is the simultaneous domination number. We present general upper bounds on the simultaneous domination number. We investigate bounds in special cases, including the cases when the factors, F _i , are r-regular or the disjoint union of copies of K _r . Further we study the case when each factor is a cycle.     

On (non-) monotonicity of cooperative solutions

Aggregate monotonicity of cooperative solutions is widely accepted as a desirable property, and examples where certain solution concepts (such as the nucleolus) violate this property are scarce and have no economic interpretation. We provide an example of a simple four-player game that points out at a class of economic contexts where aggregate monotonicity is not appealing.     

On the generalized Erdös-Szekeres Conjecture — a new upper bound

We prove the following result: For every two natural numbers n and q, n q + 2, there is a natural number E(n, q) satisfying the following:

1. (1) Let S be any set of points in the plane, no three on a line. If |S| E(n, q), then there exists a convex n-gon whose points belong to S, for which the number of points of S in its interior is 0 (mod q).

2. (2) For fixed q, E(n,q) 2^c(q)·n, c(q) is a constant depends on q only.

Part (1) was proved by Bialostocki et al. [2] and our proof is aimed to simplify the original proof. The proof of Part (2) is completely new and reduces the huge upper bound of [2] (a super-exponential bound) to an exponential upper bound.     

Perturbed projections and subgradient projections for the multiple-sets split feasibility problem

We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in a suitable product space we are able to present a simultaneous subgradients projections algorithm that generates convergent sequences of iterates in the feasible case. We further derive and analyze a perturbed projection method for the multiple-sets split feasibility problem and, additionally, furnish alternative proofs to two known results.     

Nonequilibrium statistical mechanics of dividing cell populations

We present and study a model for the nonequilibrium statistical mechanics of protein distributions in a proliferating cell population. Our model describes how the total protein variation is shaped by two processes: variation in protein production internal to the cells and variation in division and inheritance at the population level. It enables us to assess the contribution of each of these components separately. We find that, even if production is deterministic, cell division can generate a large variation in protein distribution. In this limit we solve exactly a special case and draw an analogy between protein distribution along cell generations and stress distribution in layers of granular material. At the other limit of extremely noisy protein production, we find that the population structure restrains variation and that the details of division do not affect the tail of the distribution.     

Investigation of proton-proton short-range correlations via the 12C(e,e'pp) reaction

We investigated simultaneously the 12C(e,e'p) and 12C(e,e'pp) reactions at Q2=2 (GeV/c)2, xB=1.2, and in an (e, e'p) missing-momentum range from 300 to 600 MeV/c. At these kinematics, with a missing momentum greater than the Fermi momentum of nucleons in a nucleus and far from the delta excitation, short-range nucleon-nucleon correlations are predicted to dominate the reaction. For (9.5+/-2)% of the 12C(e,e'p) events, a recoiling partner proton was observed back-to-back to the 12C(e,e'p) missing-momentum vector, an experimental signature of correlations.     

Influence of Solution Volume on the Dissolution Rate of Silicon Dioxide in Hydrofluoric Acid

Experimental data and modeling of the dissolution of various Si/SiO₂ thermal coatings in different volumes of hydrofluoric acid (HF) are reported. The rates of SiO₂‐film dissolution, measured by means of various electrochemical techniques, and alteration in HF activity depend on the thickness of the film coating. Despite the small volumes (0.6–1.2 mL) of the HF solution, an effect of SiO₂‐coating thickness on the dissolution rate was detected. To explain alterations detected in HF activity after SiO₂ dissolution, spectroscopic analyses (NMR and FTIR) of the chemical composition of the solutions were conducted. This is associated with a modification in the chemical composition of the HF solution, which results in either the formation of an oxidized species in solution or the precipitation of dissolution products. HF₂^? accumulation in the HF solution, owing to SiO₂ dissolution was identified as the source of the chemical alteration.     

Manifestations of probe presence on probe dynamics in supercooled liquids

Experimental studies that follow behavior of single probes embedded in heterogeneous systems are increasingly common. The presence of probes may perturb the system, and such perturbations may or may not affect interpretation of host behavior from the probe observables typically measured. In this study, the manifestations of potential probe-induced changes to host dynamics in supercooled liquids are investigated via molecular dynamics simulations. It is found that probe dynamics do not necessarily mirror host dynamics as they exist either in the probe-free or probe-bearing systems. In particular, for a binary supercooled liquid, we find that smooth probes larger than the host particles induce increased translational diffusion in the host system; however, the diffusion is anisotropic and enhances caging of the probe, suppressing probe translational diffusion. This in turn may lead experiments that follow probe diffusion to suggest Stokes-Einstein behavior of the system even while both the probe-free and probe-bearing systems exhibit deviations from that behavior.     

Buzzwords on their way to a tipping‐point: A view from the blogosphere

“Buzzwords” are new words (i.e., neologisms) that enter the language and acquire great popularity as “fashion words.” To date, the dynamic aspect of buzzwords has not been the subject of a rigorous scientific analysis. In this study, we analyzed the appearance of buzzwords in the blogosphere and compared their dynamics to the one of nonpopular neologisms and well‐established words. It was found that the growth rate of buzzwords is exponential and higher than that of the blogosphere. Moreover, we have identified general early warning signals for an approaching tipping point in the dynamics of buzzwords indicating that as fashion words they are on their way to a tipping‐point of decline. The article presents these findings and others and concludes by presenting a model for studying the dynamics of new words entering the language. © 2010 Wiley Periodicals, Inc. Complexity 16: 58‐68, 2011