The interleaved multichromatic number of a graph

For $k\ge 1$, we consider interleaved $k$-tuple colorings of the nodes of a graph, that is, assignments of $k$ distinct natural numbers to each node in such a way that nodes that are connected by an edge receive numbers that are strictly alternating between them with respect to the relation $<$. If it takes at least $\chi_{int}^k(G)$ distinct numbers to provide graph $G$ with such a coloring, then the interleaved multichromatic number of $G$ is $\chi_{int}^*(G)=\inf_{k\ge 1}\chi_{int}^k(G)/k$ and is known to be given by a function of the simple cycles of $G$ under acyclic orientations if $G$ is connected [1]. This paper contains a new proof of this result. Unlike the original proof, the new proof makes no assumptions on the connectedness of $G$, nor does it resort to the possible applications of interleaved $k$-tuple colorings and their properties

Finding routes in anonymous sensor networks

We consider networks of anonymous sensors and address the problem of constructing routes for the delivery of information from a group of sensors in response to a query by a sink. In order to circumvent the restrictions imposed by anonymity, we rely on using the power level perceived by the sensors in the query from the sink. We introduce a simple distributed algorithm to achieve the building of routes to the sink and evaluate its performance by means of simulations

Quantum density anomaly in optically trapped ultracold gases

We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-like anomalies in the area of ultracold quantum gases

Further insights into the interareal connectivity of a cortical network

Over the past years, network science has proven invaluable as a means to better understand many of the processes taking place in the brain. Recently, interareal connectivity data of the macaque cortex was made available with great richness of detail. We explore new aspects of this dataset, such as a correlation between connection weights and cortical hierarchy. We also look at the link-community structure that emerges from the data to uncover the major communication pathways in the network, and moreover investigate its reciprocal connections, showing that they share similar properties

A novel evolutionary formulation of the maximum independent set problem

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs