A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate. (C) 2012 Elsevier B.V. All rights reserved.

Harmonic deformation of Delaunay triangulations

We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process. (C) 2012 Elsevier B.V All rights reserved.

Semi-supervised learning guided by the modularity measure in complex networks

Semi-supervised learning techniques have gained increasing attention in the machine learning community, as a result of two main factors: (1) the available data is exponentially increasing; (2) the task of data labeling is cumbersome and expensive, involving human experts in the process. In this paper, we propose a network-based semi-supervised learning method inspired by the modularity greedy algorithm, which was originally applied for unsupervised learning. Changes have been made in the process of modularity maximization in a way to adapt the model to propagate labels throughout the network. Furthermore, a network reduction technique is introduced, as well as an extensive analysis of its impact on the network. Computer simulations are performed for artificial and real-world databases, providing a numerical quantitative basis for the performance of the proposed method.

Effective number of accessed nodes in complex networks

The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Electroluminescence of phenylene-vinylene random copolymers with different conjugation lengths

PPV random derivates were synthesized and characterized. Polymer light emitting diodes (PLEDs) were assembled using the random copolymers as emissive layer and showed EL in the blue-green region in function of the method of preparation. The increase in the average conjugation degree in the polymer chain led to the reduction of the turn-on voltage of the device. The addition of Alq3 as ETL increased tenfold the luminescence efficiency. (C) 2009 Elsevier B.V. All rights reserved.

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

Complex network classification using partially self-avoiding deterministic walks

Complex networks have attracted increasing interest from various fields of science. It has been demonstrated that each complex network model presents specific topological structures which characterize its connectivity and dynamics. Complex network classification relies on the use of representative measurements that describe topological structures. Although there are a large number of measurements, most of them are correlated. To overcome this limitation, this paper presents a new measurement for complex network classification based on partially self-avoiding walks. We validate the measurement on a data set composed by 40000 complex networks of four well-known models. Our results indicate that the proposed measurement improves correct classification of networks compared to the traditional ones. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4737515]

A Note on Large Deviations for the Stable Marriage of Poisson and Lebesgue with Random Appetites

Let IaS,a"e (d) be a set of centers chosen according to a Poisson point process in a"e (d) . Let psi be an allocation of a"e (d) to I in the sense of the Gale-Shapley marriage problem, with the additional feature that every center xi aI has an appetite given by a nonnegative random variable alpha. Generalizing some previous results, we study large deviations for the distance of a typical point xaa"e (d) to its center psi(x)aI, subject to some restrictions on the moments of alpha.

Alzheimer random walk model: Two previously overlooked diffusion regimes

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

Effects of 830 and 670 nm Laser on Viability of Random Skin Flap in Rats

Objective: This study aimed to investigate the effect of 830 and 670 nm diode laser on the viability of random skin flaps in rats. Background data: Low-level laser therapy (LLLT) has been reported to be successful in stimulating the formation of new blood vessels and reducing the inflammatory process after injury. However, the efficiency of such treatment remains uncertain, and there is also some controversy regarding the efficacy of different wavelengths currently on the market. Materials and methods: Thirty Wistar rats were used and divided into three groups, with 10 rats in each. A random skin flap was raised on the dorsum of each animal. Group 1 was the control group, group 2 received 830 nm laser radiations, and group 3 was submitted to 670 nm laser radiation (power density = 0.5 mW/cm(2)). The animals underwent laser therapy with 36 J/cm(2) energy density (total energy = 2.52 J and 72 sec per session) immediately after surgery and on the 4 subsequent days. The application site of laser radiation was one point at 2.5 cm from the flap's cranial base. The percentage of skin flap necrosis area was calculated on the 7th postoperative day using the paper template method. A skin sample was collected immediately after to determine the vascular endothelial growth factor (VEGF) expression and the epidermal cell proliferation index (KiD67). Results: Statistically significant differences were found among the percentages of necrosis, with higher values observed in group 1 compared with groups 2 and 3. No statistically significant differences were found among these groups using the paper template method. Group 3 presented the highest mean number of blood vessels expressing VEGF and of cells in the proliferative phase when compared with groups 1 and 2. Conclusions: LLLT was effective in increasing random skin flap viability in rats. The 670 nm laser presented more satisfactory results than the 830 nm laser.