2,724 research outputs found
Hypersensitivity and chaos signatures in the quantum baker's maps
Classical chaotic systems are distinguished by their sensitive dependence on
initial conditions. The absence of this property in quantum systems has lead to
a number of proposals for perturbation-based characterizations of quantum
chaos, including linear growth of entropy, exponential decay of fidelity, and
hypersensitivity to perturbation. All of these accurately predict chaos in the
classical limit, but it is not clear that they behave the same far from the
classical realm. We investigate the dynamics of a family of quantizations of
the baker's map, which range from a highly entangling unitary transformation to
an essentially trivial shift map. Linear entropy growth and fidelity decay are
exhibited by this entire family of maps, but hypersensitivity distinguishes
between the simple dynamics of the trivial shift map and the more complicated
dynamics of the other quantizations. This conclusion is supported by an
analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure
Evolutionary Neural Gas (ENG): A Model of Self Organizing Network from Input Categorization
Despite their claimed biological plausibility, most self organizing networks
have strict topological constraints and consequently they cannot take into
account a wide range of external stimuli. Furthermore their evolution is
conditioned by deterministic laws which often are not correlated with the
structural parameters and the global status of the network, as it should happen
in a real biological system. In nature the environmental inputs are noise
affected and fuzzy. Which thing sets the problem to investigate the possibility
of emergent behaviour in a not strictly constrained net and subjected to
different inputs. It is here presented a new model of Evolutionary Neural Gas
(ENG) with any topological constraints, trained by probabilistic laws depending
on the local distortion errors and the network dimension. The network is
considered as a population of nodes that coexist in an ecosystem sharing local
and global resources. Those particular features allow the network to quickly
adapt to the environment, according to its dimensions. The ENG model analysis
shows that the net evolves as a scale-free graph, and justifies in a deeply
physical sense- the term gas here used.Comment: 16 pages, 8 figure
Linear, Deterministic, and Order-Invariant Initialization Methods for the K-Means Clustering Algorithm
Over the past five decades, k-means has become the clustering algorithm of
choice in many application domains primarily due to its simplicity, time/space
efficiency, and invariance to the ordering of the data points. Unfortunately,
the algorithm's sensitivity to the initial selection of the cluster centers
remains to be its most serious drawback. Numerous initialization methods have
been proposed to address this drawback. Many of these methods, however, have
time complexity superlinear in the number of data points, which makes them
impractical for large data sets. On the other hand, linear methods are often
random and/or sensitive to the ordering of the data points. These methods are
generally unreliable in that the quality of their results is unpredictable.
Therefore, it is common practice to perform multiple runs of such methods and
take the output of the run that produces the best results. Such a practice,
however, greatly increases the computational requirements of the otherwise
highly efficient k-means algorithm. In this chapter, we investigate the
empirical performance of six linear, deterministic (non-random), and
order-invariant k-means initialization methods on a large and diverse
collection of data sets from the UCI Machine Learning Repository. The results
demonstrate that two relatively unknown hierarchical initialization methods due
to Su and Dy outperform the remaining four methods with respect to two
objective effectiveness criteria. In addition, a recent method due to Erisoglu
et al. performs surprisingly poorly.Comment: 21 pages, 2 figures, 5 tables, Partitional Clustering Algorithms
(Springer, 2014). arXiv admin note: substantial text overlap with
arXiv:1304.7465, arXiv:1209.196
Frequency planning for clustered jointly processed cellular multiple access channel
Owing to limited resources, it is hard to guarantee minimum service levels to all users in conventional cellular systems. Although global cooperation of access points (APs) is considered promising, practical means of enhancing efficiency of cellular systems is by considering distributed or clustered jointly processed APs. The authors present a novel `quality of service (QoS) balancing scheme' to maximise sum rate as well as achieve cell-based fairness for clustered jointly processed cellular multiple access channel (referred to as CC-CMAC). Closed-form cell level QoS balancing function is derived. Maximisation of this function is proved as an NP hard problem. Hence, using power-frequency granularity, a modified genetic algorithm (GA) is proposed. For inter site distance (ISD) <; 500 m, results show that with no fairness considered, the upper bound of the capacity region is achievable. Applying hard fairness restraints on users transmitting in moderately dense AP system, 20% reduction in sum rate contribution increases fairness by upto 10%. The flexible QoS can be applied on a GA-based centralised dynamic frequency planner architecture
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