Projective, Sparse, and Learnable Latent Position Network Models

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption---that the latent positions are generated according to a Poisson point process---and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.Comment: 51 pages, 2 figure

Strain-induced modifications of transport in gated graphene nanoribbons

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure, and finally becomes completely suppressed at larger strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudo-magnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which either originate from the coupling into Fabry-Perot states that extend through the system, or from the formation of states that are localized near the contacts, where the pseudo-magnetic field is largest. In particular, the n=0 pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.Comment: 10 pages, 6 figure

Bio-inspired ganglion cell models for detecting horizontal and vertical movements

The retina performs the earlier stages of image processing in living beings and is composed of six different groups of cells, namely, the rods, cones, horizontal, bipolar, amacrine and ganglion cells. Each of those group of cells can be sub-divided into other types of cells that vary in shape, size, connectivity and functionality. Each cell is responsible for performing specific tasks in these early stages of biological image processing. Some of those cells are sensitive to horizontal and vertical movements. This paper proposes a multi-hierarchical spiking neural network architecture for detecting horizontal and vertical movements using a custom dataset which was generated in laboratory settings. The proposed architecture was designed to reflect the connectivity, behaviour and the number of layers found in the majority of vertebrates retinas, including humans. The architecture was trained using 2303 images and tested using 816 images. Simulation results revealed that each cell model is sensitive to vertical and horizontal movements with a detection error of 6.75 percent

Hawkes process as a model of social interactions: a view on video dynamics

We study by computer simulation the "Hawkes process" that was proposed in a recent paper by Crane and Sornette (Proc. Nat. Acad. Sci. USA 105, 15649 (2008)) as a plausible model for the dynamics of YouTube video viewing numbers. We test the claims made there that robust identification is possible for classes of dynamic response following activity bursts. Our simulated timeseries for the Hawkes process indeed fall into the different categories predicted by Crane and Sornette. However the Hawkes process gives a much narrower spread of decay exponents than the YouTube data, suggesting limits to the universality of the Hawkes-based analysis.Comment: Added errors to parameter estimates and further description. IOP style, 13 pages, 5 figure

Nonlinear aspects of the EEG during sleep in children

Electroencephalograph (EEG) analysis enables the neuronal behavior of a section of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal and mild OSAS children are evaluated for nonlinear behaviour. We consider how the behaviour of the brain changes with sleep stage and between normal and OSAS children.Comment: 9 pages, 2 figures, 4 table

Power-law distributions in empirical data

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws

Breast cancer diagnosis using a hybrid genetic algorithm for feature selection based on mutual information

Feature Selection is the process of selecting a subset of relevant features (i.e. predictors) for use in the construction of predictive models. This paper proposes a hybrid feature selection approach to breast cancer diagnosis which combines a Genetic Algorithm (GA) with Mutual Information (MI) for selecting the best combination of cancer predictors, with maximal discriminative capability. The selected features are then input into a classifier to predict whether a patient has breast cancer. Using a publicly available breast cancer dataset, experiments were performed to evaluate the performance of the Genetic Algorithm based on the Mutual Information approach with two different machine learning classifiers, namely the k-Nearest Neighbor (KNN), and Support vector machine (SVM), each tuned using different distance measures and kernel functions, respectively. The results revealed that the proposed hybrid approach is highly accurate for predicting breast cancer, and it is very promising for predicting other cancers using clinical data

Spreading in Social Systems: Reflections

In this final chapter, we consider the state-of-the-art for spreading in social systems and discuss the future of the field. As part of this reflection, we identify a set of key challenges ahead. The challenges include the following questions: how can we improve the quality, quantity, extent, and accessibility of datasets? How can we extract more information from limited datasets? How can we take individual cognition and decision making processes into account? How can we incorporate other complexity of the real contagion processes? Finally, how can we translate research into positive real-world impact? In the following, we provide more context for each of these open questions.Comment: 7 pages, chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur