The Debiased Spatial Whittle likelihood.

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle likelihood, makes important corrections to the well-known Whittle likelihood to account for large sources of bias caused by boundary effects and aliasing. We generalize the approach to flexibly allow for significant volumes of missing data including those with lower-dimensional substructure, and for irregular sampling boundaries. We build a theoretical framework under relatively weak assumptions which ensures consistency and asymptotic normality in numerous practical settings including missing data and non-Gaussian processes. We also extend our consistency results to multivariate processes. We provide detailed implementation guidelines which ensure the estimation procedure can be conducted in O ( n log n ) operations, where n is the number of points of the encapsulating rectangular grid, thus keeping the computational scalability of Fourier and Whittle-based methods for large data sets. We validate our procedure over a range of simulated and realworld settings, and compare with state-of-the-art alternatives, demonstrating the enduring practical appeal of Fourier-based methods, provided they are corrected by the procedures developed in this paper.

Network histograms and universality of blockmodel approximation.

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks--political weblogs and student friendships--and discuss how to interpret the network histogram when additional information related to node and edge labeling is present.

Cortical activity evoked by an acute painful tissue-damaging stimulus in healthy adult volunteers.

Everyday painful experiences are usually single events accompanied by tissue damage, and yet most experimental studies of cutaneous nociceptive processing in the brain use repeated laser, thermal, or electrical stimulations that do not damage the skin. In this study the nociceptive activity in the brain evoked by tissue-damaging skin lance was analyzed with electroencephalography (EEG) in 20 healthy adult volunteers (13 men and 7 women) aged 21-40 yr. Time-frequency analysis of the evoked activity revealed a distinct late event-related vertex potential (lance event-related potential, LERP) at 100-300 ms consisting of a phase-locked energy increase between 1 and 20 Hz (delta-beta bands). A pairwise comparison between lance and sham control stimulation also revealed a period of ultralate stronger desynchronization after lance in the delta band (1-5 Hz). Skin application of mustard oil before lancing, which sensitizes a subpopulation of nociceptors expressing the cation channel TRPA1, did not affect the ultralate desynchronization but reduced the phase-locked energy increase in delta and beta bands, suggesting a central interaction between different modalities of nociceptive inputs. Verbal descriptor screening of individual pain experience revealed that lance pain is predominantly due to Aδ fiber activation, but when individuals describe lances as C fiber mediated, an ultralate delta band event-related desynchronization occurs in the brain-evoked activity. We conclude that pain evoked by acute tissue damage is associated with distinct Aδ and C fiber-mediated patterns of synchronization and desynchronization of EEG oscillations in the brain.

A developmental shift in habituation to pain in human neonates.

Habituation to recurrent non-threatening or unavoidable noxious stimuli is an important aspect of adaptation to pain. Neonates, especially if preterm, are exposed to repeated noxious procedures during their clinical care. They can mount strong behavioral, autonomic, spinal, and cortical responses to a single noxious stimulus; however, it is not known whether the developing nervous system can adapt to the recurrence of these inputs. Here, we used electroencephalography to investigate changes in cortical microstates (representing the complex sequential processing of noxious inputs) following two consecutive clinically required heel lances in term and preterm infants. We show that stimulus repetition dampens the engagement of initial microstates and associated behavioral and autonomic responses in term infants, while preterm infants do not show signs of habituation. Nevertheless, both groups engage different longer-latency cortical microstates to each lance, which is likely to reflect changes in higher-level stimulus processing with repeated stimulation. These data suggest that while both age groups are capable of encoding contextual differences in pain, the preterm brain does not regulate the initial cortical, behavioral, and autonomic responses to repeated noxious stimuli. Habituation mechanisms to pain are already in place at term age but mature over the equivalent of the last trimester of gestation and are not fully functional in preterm neonates.

The memory of spatial patterns: changes in local abundance and aggregation in a tropical forest.

The current spatial pattern of a population is the result of previous individual birth, death, and dispersal events. We present a simple model followed by a comparative analysis for a species-rich plant community to show how the current spatial aggregation of a population may hold information about recent population dynamics. Previous research has shown how locally restricted seed dispersal often leads to stronger aggregation in less abundant populations than it does in more abundant populations. In contrast, little is known about how changes in the local abundance of a species may affect the spatial distribution of individuals. If the level of aggregation within a species depends to some extent on the abundance of the species, then changes in abundance should lead to subsequent changes in aggregation. However, an overall change of spatial pattern relies on many individual birth and death events, and a surplus of deaths or births may have short-term effects on aggregation that are opposite to the long-term change predicted by the change in abundance. The change in aggregation may therefore lag behind the change in abundance, and consequently, the current aggregation may hold information about recent population dynamics. Using an individual-based simulation model with local dispersal and density-dependent competition, we show that, on average, recently growing populations should be more aggregated than shrinking populations of the same current local abundance. We tested this hypothesis using spatial data on individuals from a long-term tropical rain forest plot, and find support for this relationship in canopy trees, but not in understory and shrub species. On this basis we argue that current spatial aggregation is an important characteristic that contains information on recent changes in local abundance, and may be applied to taxonomic groups where dispersal is limited and within-species aggregation is observed.

Atomic subgraphs and the statistical mechanics of networks.

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extensive numbers of triangles and other network motifs commonly observed in many real-world networks. More specifically, we focus on maximum entropy ensembles under constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such models. We also present a procedure for combining distributions of multiple atomic subgraphs that enables the construction of models with fewer parameters. Expanding the model to include atoms with edge and vertex labels we obtain a general class of models that can be parametrized in terms of basic building blocks and their distributions that include many widely used models as special cases. These models include random graphs with arbitrary distributions of subgraphs, random hypergraphs, bipartite models, stochastic block models, models of multilayer networks and their degree-corrected and directed versions. We show that the entropy for all these models can be derived from a single expression that is characterized by the symmetry groups of atomic subgraphs.

When do we have the power to detect biological interactions in spatial point patterns?

Uncovering the roles of biotic interactions in assembling and maintaining species-rich communities remains a major challenge in ecology. In plant communities, interactions between individuals of different species are expected to generate positive or negative spatial interspecific associations over short distances. Recent studies using individual-based point pattern datasets have concluded that (a) detectable interspecific interactions are generally rare, but (b) are most common in communities with fewer species; and (c) the most abundant species tend to have the highest frequency of interactions. However, it is unclear how the detection of spatial interactions may change with the abundances of each species, or the scale and intensity of interactions. We ask if statistical power is sufficient to explain all three key results.We use a simple two-species model, assuming no habitat associations, and where the abundances, scale and intensity of interactions are controlled to simulate point pattern data. In combination with an approximation to the variance of the spatial summary statistics that we sample, we investigate the power of current spatial point pattern methods to correctly reject the null model of pairwise species independence.We show the power to detect interactions is positively related to both the abundances of the species tested, and the intensity and scale of interactions, but negatively related to imbalance in abundances. Differences in detection power in combination with the abundance distributions found in natural communities are sufficient to explain all the three key empirical results, even if all pairwise interactions are identical. Critically, many hundreds of individuals of both species may be required to detect even intense interactions, implying current abundance thresholds for including species in the analyses are too low. Sy n thesis. The widespread failure to reject the null model of spatial interspecific independence could be due to low power of the tests rather than any key biological process. Since we do not model habitat associations, our results represent a first step in quantifying sample sizes required to make strong statements about the role of biotic interactions in diverse plant communities. However, power should be factored into analyses and considered when designing empirical studies.

Hyperanalytic denoising.

A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of "replicates" of the image. The "replicates" are calculated by extending the image into a vector-valued hyperanalytic signal. More than one hyperanalytic signal may be chosen, and either the hypercomplex or Riesz transforms are used, to calculate this object. The deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal, at a fixed scale and position index, are determined. A "universal" threshold is calculated for the proposed procedure. An expression for the risk of an individual coefficient is derived. The risk is calculated explicitly when the "universal" threshold is used and is shown to be less than the risk of "universal" hard thresholding, under certain conditions. The proposed method is implemented and the derived theoretical risk reductions substantiated.

Encoding of mechanical nociception differs in the adult and infant brain.

Newborn human infants display robust pain behaviour and specific cortical activity following noxious skin stimulation, but it is not known whether brain processing of nociceptive information differs in infants and adults. Imaging studies have emphasised the overlap between infant and adult brain connectome architecture, but electrophysiological analysis of infant brain nociceptive networks can provide further understanding of the functional postnatal development of pain perception. Here we hypothesise that the human infant brain encodes noxious information with different neuronal patterns compared to adults. To test this we compared EEG responses to the same time-locked noxious skin lance in infants aged 0-19 days (n = 18, clinically required) and adults aged 23-48 years (n = 21). Time-frequency analysis revealed that while some features of adult nociceptive network activity are present in infants at longer latencies, including beta-gamma oscillations, infants display a distinct, long latency, noxious evoked 18-fold energy increase in the fast delta band (2-4 Hz) that is absent in adults. The differences in activity between infants and adults have a widespread topographic distribution across the brain. These data support our hypothesis and indicate important postnatal changes in the encoding of mechanical pain in the human brain.

Noise reduction in directional signals using multiple morse wavelets illustrated on quadrature Doppler ultrasound.

The use of multiple complex-valued Morse wavelets for the scalogram study of signals which are unidirectional at any time, but are bidirectional overall is considered. These wavelets are well-suited to identifying the forward and reverse components. Scalogram averaging which is possible due to the multiplicity of the complex-valued wavelets leads to a scalogram with reduced noise. Information from positive and negative scales can then be used to estimate a final "cleaned" scalogram. Quadrature Doppler ultrasound blood flow in the femoral artery is taken as an example to clearly illustrate the noise reduction.

A DNA methylation network interaction measure, and detection of network oncomarkers.

Epigenetic processes--including DNA methylation--are increasingly seen as having a fundamental role in chronic diseases like cancer. DNA methylation patterns offer a route to develop prognostic measures based directly on DNA measurements, rather than less-stable RNA measurements. A novel DNA methylation-based measure of the co-ordinated interactive behaviour of genes is developed, in a network context. It is shown that this measure reflects well the co-regulatory behaviour linked to gene expression (at the mRNA level) over the same network interactions. This measure, defined for pairs of genes in a single patient/sample, associates with overall survival outcome independent of known prognostic clinical features, in several independent data sets relating to different cancer types. In total, more than half a billion CpGs in over 1600 samples, taken from nine different cancer entities, are analysed. It is found that groups of gene-pair interactions which associate significantly with survival identify statistically significant subnetwork modules. Many of these subnetwork modules are shown to be biologically relevant by strong correlation with pre-defined gene sets, such as immune function, wound healing, mitochondrial function and MAP-kinase signalling. In particular, the wound healing module corresponds to an increase in co-ordinated interactive behaviour between genes for worse prognosis, and the immune module corresponds to a decrease in co-ordinated interactive behaviour between genes for worse prognosis. This measure has great potential for defining DNA-based cancer biomarkers. Such biomarkers could naturally be developed further, by drawing on the rapidly expanding knowledge base of network science.

Corruption of the intra-gene DNA methylation architecture is a hallmark of cancer.

Epigenetic processes--including DNA methylation--are increasingly seen as having a fundamental role in chronic diseases like cancer. It is well known that methylation levels at particular genes or loci differ between normal and diseased tissue. Here we investigate whether the intra-gene methylation architecture is corrupted in cancer and whether the variability of levels of methylation of individual CpGs within a defined gene is able to discriminate cancerous from normal tissue, and is associated with heterogeneous tumour phenotype, as defined by gene expression. We analysed 270985 CpGs annotated to 18272 genes, in 3284 cancerous and 681 normal samples, corresponding to 14 different cancer types. In doing so, we found novel differences in intra-gene methylation pattern across phenotypes, particularly in those genes which are crucial for stem cell biology; our measures of intra-gene methylation architecture are a better determinant of phenotype than measures based on mean methylation level alone (K-S test [Formula: see text] in all 14 diseases tested). These per-gene methylation measures also represent a considerable reduction in complexity, compared to conventional per-CpG beta-values. Our findings strongly support the view that intra-gene methylation architecture has great clinical potential for the development of DNA-based cancer biomarkers.

A shift in sensory processing that enables the developing human brain to discriminate touch from pain.

When and how infants begin to discriminate noxious from innocuous stimuli is a fundamental question in neuroscience [1]. However, little is known about the development of the necessary cortical somatosensory functional prerequisites in the intact human brain. Recent studies of developing brain networks have emphasized the importance of transient spontaneous and evoked neuronal bursting activity in the formation of functional circuits [2, 3]. These neuronal bursts are present during development and precede the onset of sensory functions [4, 5]. Their disappearance and the emergence of more adult-like activity are therefore thought to signal the maturation of functional brain circuitry [2, 4]. Here we show the changing patterns of neuronal activity that underlie the onset of nociception and touch discrimination in the preterm infant. We have conducted noninvasive electroencephalogram (EEG) recording of the brain neuronal activity in response to time-locked touches and clinically essential noxious lances of the heel in infants aged 28-45 weeks gestation. We show a transition in brain response following tactile and noxious stimulation from nonspecific, evenly dispersed neuronal bursts to modality-specific, localized, evoked potentials. The results suggest that specific neural circuits necessary for discrimination between touch and nociception emerge from 35-37 weeks gestation in the human brain.