Linear colorings of simplicial complexes and collapsing

A vertex coloring of a simplicial complex $\Delta$ is called a linear coloring if it satisfies the property that for every pair of facets $(F_1, F_2)$ of $\Delta$, there exists no pair of vertices $(v_1, v_2)$ with the same color such that $v_1\in F_1\backslash F_2$ and $v_2\in F_2\backslash F_1$. We show that every simplicial complex $\Delta$ which is linearly colored with $k$ colors includes a subcomplex $\Delta'$ with $k$ vertices such that $\Delta'$ is a strong deformation retract of $\Delta$. We also prove that this deformation is a nonevasive reduction, in particular, a collapsing.Comment: 18 page

The Effect of Newer Drugs on Health Spending: Do They Really Increase the Costs?

We analyze the influence of technological progress on pharmaceuticals on rising health expenditures using US State level panel data. Improvements in medical technology are believed to be partly responsible for rapidly rising health expenditures. Even if the technological progress in medicine improves health outcomes and life quality, it can also increase the expenditure on health care. Our findings suggest that newer drugs increase the spending on prescription drugs since they are usually more expensive than their predecessors. However, they lower the demand for other types of medical services, which causes the total spending to decline. A one-year decrease in the average age of prescribed drugs causes per capita health expenditures to decrease by $31.92. The biggest decline occurs in spending on hospital and home health care due to newer drugs.Health care expenditure; pharmaceuticals; technology diffusion

Homotopy decompositions and K-theory of Bott towers

We describe Bott towers as sequences of toric manifolds M^k, and identify the omniorientations which correspond to their original construction as toric varieties. We show that the suspension of M^k is homotopy equivalent to a wedge of Thom complexes, and display its complex K-theory as an algebra over the coefficient ring. We extend the results to KO-theory for several families of examples, and compute the effects of the realification homomorphism; these calculations breathe geometric life into Bahri and Bendersky's recent analysis of the Adams Spectral Sequence. By way of application we investigate stably complex structures on M^k, identifying those which arise from omniorientations and those which are almost complex. We conclude with observations on the role of Bott towers in complex cobordism theory.Comment: 26 page

Vertex decomposable graphs, codismantlability, Cohen-Macaulayness and Castelnuovo-Mumford regularity

We call a (simple) graph G codismantlable if either it has no edges or else it has a codominated vertex x, meaning that the closed neighborhood of x contains that of one of its neighbor, such that G-x codismantlable. We prove that if G is well-covered and it lacks induced cycles of length four, five and seven, than the vertex decomposability, codismantlability and Cohen-Macaulayness for G are all equivalent. The rest deals with the computation of Castelnuovo-Mumford regularity of codismantlable graphs. Note that our approach complements and unifies many of the earlier results on bipartite, chordal and very well-covered graphs

Doğuş-USV unmanned sea vehicle: obstacle localization with stereo vision and path planning

Unmanned vehicle systems are becoming increasingly prevalent on the land, in the sea, and in the air. Navigation and path planning in an unknown environment are important tasks for future generation. The objective of this work is to design an unmanned sea vehicle and necessary software that can perform path planning autonomously with using stereo vision. In this paper using potential field algorithm, collision free path is achieved from a starting point to a terminal point