21,039 research outputs found
The interleaved multichromatic number of a graph
For , we consider interleaved -tuple colorings of the nodes of a
graph, that is, assignments of 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 distinct numbers to provide graph with such a
coloring, then the interleaved multichromatic number of is
and is known to be given by a
function of the simple cycles of under acyclic orientations if 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 ,
nor does it resort to the possible applications of interleaved -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
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