We study the cyclic color sequences induced at infinity by colored rays with apices being a given balanced finite bichromatic point set. We first study the case in which the rays are required to be pairwise disjoint. We derive a lower bound on the number of color sequences that can be realized from any such fixed point set and examine color sequences that can be realized regardless of the point...

With the advent of high-throughput data recording methods in biology and medicine, the efficient identification of meaningful subspaces within these data sets becomes an increasingly important challenge. Classical dimension reduction techniques such as principal component analysis often do not take the large statistics of the data set into account, and thereby fail if the signal space is for ex...

The Minority Game (MG) [1] provides an ideal playground for studying interacting agent systems such as financial markets [2]. Its stationary states have indeed been understood in great detail [3–5] whose conclusions have been recently confirmed by a fully dynamic theoretical approach [6]. Such a state of the art allows one to address interesting issues on the way in which such complex systems b...

We introduce Colored Resource Allocation Games as a new model for selfish routing and wavelength assignment in multifiber all-optical networks. Colored Resource Allocation Games are a generalization of congestion and bottleneck games where players have their strategies in multiple copies (colors). We focus on two main subclasses of these games depending on the player cost: in Colored Congestion...

We study a problem proposed by Hurtado et al. [10] motivated by sparse set visualization. Given n points in the plane, each labeled with one or more primary colors, a colored spanning graph (CSG) is a graph such that for each primary color, the vertices of that color induce a connected subgraph. The Min-CSG problem asks for the minimum sum of edge lengths in a colored spanning graph. We show th...

We revisit the problem of enumeration of vertex-tricolored planar random triangulations solved in [Nucl. Phys. B 516 [FS] (1998) 543-587] in the light of recent combinatorial developments relating classical planar graph counting problems to the enumeration of decorated trees. We give a direct combinatorial derivation of the associated counting function, involving tricolored trees. This is gener...

In this paper, we present a novel method to embedding secret message in the cover-image. The basic concept of the proposed method is by simple Least Significant Bit (LSB) substitution. We propose a steganography method that applies a technique to embedding a wavelet compressed secret message within the Least Significant Bit (LSB) of the cover image pixels in a specific pattern. The proposed met...

In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of c ≥ 2 colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize ...

418 August 2014 Anesthesiology, V 121 • No 2 418 August 2014 IIn the Neuro/Trauma ICU, the patients were arranged like artwork. Statuesque figures projected their sculptured, angular images in a gallery of haloed subjects suspended in animation. Some were conscious, and some were elsewhere. On this particular dreary day in December, I noticed a group of family members—a mother and two daughters...

We introduce analogues of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. As applications, we recover in a simple way the descent algebras associated with wreath products Γ ≀ Sn and the corresponding generalizations of quasi-symmetric functions. Finally, we obtain Hopf algebras of colored parking functions, colored non-crossing partitions and park...