Approaching the non-linear Shannon limit

We review the recent progress of information theory in optical communications, and describe the current experimental results and associated advances in various individual technologies which increase the information capacity. We confirm the widely held belief that the reported capacities are approaching the fundamental limits imposed by signal-to-noise ratio and the distributed non-linearity of conventional optical fibres, resulting in the reduction in the growth rate of communication capacity. We also discuss the techniques which are promising to increase and/or approach the information capacity limit.

Nonlinear signal transformations:path to capacity above the linear AWGN Shannon limit

We present a methodology for simultaneous optimization of modulation format and regenerative transformations in nonlinear communication channels. We derived analytically the maximum regenerative Shannon capacity, towards which any regenerative channel tends at high SNR and large number of regenerators.

The potential for networks with capacities exceeding the nonlinear-Shannon limit

We examine the network benefits of various forms of nonlinearity compensation, showing that total network capacities that are more than double the capacity of a network with reaches determined by the Nonlinear-Shannon limit © 2015 OSA.

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

Characterizing graph symmetries through quantum Jensen-Shannon divergence

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph. © 2013 American Physical Society.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

The impact of phase conjugation on the nonlinear-Shannon limit:the difference between optical and electrical phase conjugation

We show that optical and electrical phase conjugation enable effective nonlinear compensation, The impact of polarization mode dispersion and finite processing bandwidth on the ultimate limits are also considered.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Biodiversity context of selected samples from the Tara Oceans Expedition (2009-2013)

The present data set provides contextual data for samples from the Tara Oceans Expedition (2009-2013) that were selected for publication in a special issue of the SCIENCE journal (see related references below). Contextual data include various diversity indexes calculated for the sampling location using satellite and model climatologies (Darwin project, Physat) and results from the sequencing of Tara Oceans samples.