Exploiting relationship directionality to enhance statistical modeling of peer-influence across social networks.

Risky-prescribing is the excessive or inappropriate prescription of drugs that singly or in combination pose significant risks of adverse health outcomes. In the United States, prescribing of opioids and other "risky" drugs is a national public health concern. We use a novel data framework-a directed network connecting physicians who encounter the same patients in a sequence of visits-to investigate if risky-prescribing diffuses across physicians through a process of peer-influence. Using a shared-patient network of 10 661 Ohio-based physicians constructed from Medicare claims data over 2014-2015, we extract information on the order in which patients encountered physicians to derive a directed patient-sharing network. This enables the novel decomposition of peer-effects of a medical practice such as risky-prescribing into directional (outbound and inbound) and bidirectional (mutual) relationship components. Using this framework, we develop models of peer-effects for contagion in risky-prescribing behavior as well as spillover effects. The latter is measured in terms of adverse health events suspected to be related to risky-prescribing in patients of peer-physicians. Estimated peer-effects were strongest when the patient-sharing relationship was mutual as opposed to directional. Using simulations we confirmed that our modeling and estimation strategies allows simultaneous estimation of each type of peer-effect (mutual and directional) with accuracy and precision. We also show that failing to account for these distinct mechanisms (a form of model mis-specification) produces misleading results, demonstrating the importance of retaining directional information in the construction of physician shared-patient networks. These findings suggest network-based interventions for reducing risky-prescribing.

Estimating the impact of physician risky-prescribing on the network structure underlying physician shared-patient relationships.

Social network analysis and shared-patient physician networks have become effective ways of studying physician collaborations. Assortative mixing or "homophily" is the network phenomenon whereby the propensity for similar individuals to form ties is greater than for dissimilar individuals. Motivated by the public health concern of risky-prescribing among older patients in the United States, we develop network models and tests involving novel network measures to study whether there is evidence of geographic homophily in prescribing and deprescribing in the specific shared-patient network of physicians linked to the US state of Ohio in 2014. Evidence of homophily in risky-prescribing would imply that prescribing behaviors help shape physician networks and could inform interventions to reduce risky-prescribing (e.g., should interventions target groups of physicians or select physicians at random). Furthermore, if such effects varied depending on the structural features of a physician's position in the network (e.g., by whether or not they are involved in cliques - groups of actors that are fully connected to each other - such as closed triangles in the case of three actors), this would further strengthen the case for targeting of select physicians for interventions. Using accompanying Medicare Part D data, we converted patient longitudinal prescription receipts into novel measures of the intensity of each physician's risky-prescribing. Exponential random graph models were used to simultaneously estimate the importance of homophily in prescribing and deprescribing in the network beyond the characteristics of physician specialty (or other metadata) and network-derived features. In addition, novel network measures were introduced to allow homophily to be characterized in relation to specific triadic (three-actor) structural configurations in the network with associated non-parametric randomization tests to evaluate their statistical significance in the network against the null hypothesis of no such phenomena. We found physician homophily in prescribing and deprescribing in both the state-wide and multiple HRR sub-networks, and that the level of homophily varied across HRRs. We also found that physicians exhibited within-triad homophily in risky-prescribing, with the prevalence of homophilic triads significantly higher than expected by chance absent homophily. These results may explain why communities of prescribers emerge and evolve, helping to justify group-level prescriber interventions. The methodology could be applied to arbitrary shared-patient networks and even more generally to other kinds of network data that underlies other kinds of social phenomena.

Judicial hierarchy and discursive influence.

We apply a dynamic influence model to the opinions of the US federal courts to examine the role of the US Supreme Court in influencing the direction of legal discourse in the federal courts. We propose two mechanisms for how the Court affects innovation in legal language: a selection mechanism where the Court's influence primarily derives from its discretionary jurisdiction, and an authorship mechanism in which the Court's influence derives directly from its own innovations. To test these alternative hypotheses, we develop a novel influence measure based on a dynamic topic model that separates the Court's own language innovations from those of the lower courts. Applying this measure to the US federal courts, we find that the Supreme Court primarily exercises influence through the selection mechanism, with modest additional influence attributable to the authorship mechanism. This article is part of the theme issue 'A complexity science approach to law and governance'.

Complex systems of secrecy: the offshore networks of oligarchs.

Following the invasion of Ukraine, the USA, UK, and EU governments-among others-sanctioned oligarchs close to Putin. This approach has come under scrutiny, as evidence has emerged of the oligarchs' successful evasion of these punishments. To address this problem, we analyze the role of an overlooked but highly influential group: the secretive professional intermediaries who create and administer the oligarchs' offshore financial empires. Drawing on the Offshore Leaks Database provided by the International Consortium of Investigative Journalists (ICIJ), we examine the ties linking offshore expert advisors (lawyers, accountants, and other wealth management professionals) to ultra-high-net-worth individuals from four countries: Russia, China, the USA, and Hong Kong. We find that resulting nation-level "oligarch networks" share a scale-free structure characterized by a heterogeneity of heavy-tailed degree distributions of wealth managers; however, network topologies diverge across clients from democratic versus autocratic regimes. While generally robust, scale-free networks are fragile when targeted by attacks on highly connected nodes. Our "knock-out" experiments pinpoint this vulnerability to the small group of wealth managers themselves, suggesting that sanctioning these professional intermediaries may be more effective and efficient in disrupting dark finance flows than sanctions on their wealthy clients. This vulnerability is especially pronounced amongst Russian oligarchs, who concentrate their offshore business in a handful of boutique wealth management firms. The distinctive patterns we identify suggest a new approach to sanctions, focused on expert intermediaries to disrupt the finances and alliances of their wealthy clients. More generally, our research contributes to the larger body of work on complexity science and the structures of secrecy.

Towards intelligent complex networks: the space and prediction of information walks.

In this paper we study the problem of walk-specific information spread in directed complex social networks. Classical models usually analyze the "explosive" spread of information on social networks (e.g., Twitter) - a broadcast or epidemiological model focusing on the dynamics of a given source node "infecting" multiple targets. Less studied, but of equal importance is the case of single-track information flow, wherein the focus is on the node-by-node (and not necessarily a newly visited node) trajectory of information transfer. An important and motivating example is the sequence of physicians visited by a given patient over a presumed course of treatment or health event. This is the so-called a referral sequence which manifests as a path in a network of physicians. In this case the patient (and her health record) is a source of "information" from one physician to the next. With this motivation in mind we build a Bayesian Personalized Ranking (BPR) model to predict the next node on a walk of a given network navigator using network science features. The problem is related to but different from the well-investigated link prediction problem. We present experiments on a dataset of several million nodes derived from several years of U.S. patient referral records, showing that the application of network science measures in the BPR framework boosts hit-rate and mean percentile rank for the task of next-node prediction. We then move beyond the simple information walk to consider the derived network space of all information walks within a period, in which a node represents an information walk and two information walks are connected if have nodes in common from the original (social) network. To evaluate the utility of such a network of information walks, we simulate outliers of information walks and distinguish them with the other normal information walks, using five distance metrics for the derived feature vectors between two information walks. The experimental results of such a proof-of-concept application shows the utility of the derived information walk network for the outlier monitoring of information flow on an intelligent network.

Analysis of the U.S. patient referral network.

In this paper, we analyze the US Patient Referral Network (also called the Shared Patient Network) and various subnetworks for the years 2009 to 2015. In these networks, two physicians are linked if a patient encounters both of them within a specified time interval, according to the data made available by the Centers for Medicare and Medicaid Services. We find power law distributions on most state-level data as well as a core-periphery structure. On a national and state level, we discover a so-called small-world structure as well as a "gravity law" of the type found in some large-scale economic networks. Some physicians play the role of hubs for interstate referral. Strong correlations between certain network statistics with health care system statistics at both the state and national levels are discovered. The patterns in the referral network evinced using several statistical analyses involving key metrics derived from the network illustrate the potential for using network analysis to provide new insights into the health care system and opportunities or mechanisms for catalyzing improvements.

Referral paths in the U.S. physician network.

In this paper, we analyze the millions of referral paths of patients' interactions with the healthcare system for each year in the 2006-2011 time period and relate them to U.S. cardiovascular treatment records. For a patient, a "referral path" records the chronological sequence of physicians encountered by a patient (subject to certain constraints on the times between encounters). It provides a basic unit of analysis in a broader referral network that encodes the flow of patients and information between physicians in a healthcare system. We consider referral networks defined over a range of interactions as well as the characteristics of referral paths, producing a characterization of the various networks as well as the physicians they comprise. We further relate these metrics and findings to outcomes in the specific area of cardiovascular care. In particular, we match a referral path to occurrences of Acute Myocardial Infarction (AMI) and use the summary measures of the referral path to predict the treatment a patient receives and medical outcomes following treatment. Some referral path features are more significant with respect to their ability to boost a tree-based predictive model, and have stronger correlations with numerical treatment outcome variables. The patterns of referral paths and the derived informative features illustrate the potential for using network science to optimize patient referrals in healthcare systems for improved treatment outcomes and more efficient utilization of medical resources.

Bayesian learning of sparse multiscale image representations.

Multiscale representations of images have become a standard tool in image analysis. Such representations offer a number of advantages over fixed-scale methods, including the potential for improved performance in denoising, compression, and the ability to represent distinct but complementary information that exists at various scales. A variety of multiresolution transforms exist, including both orthogonal decompositions such as wavelets as well as nonorthogonal, overcomplete representations. Recently, techniques for finding adaptive, sparse representations have yielded state-of-the-art results when applied to traditional image processing problems. Attempts at developing multiscale versions of these so-called dictionary learning models have yielded modest but encouraging results. However, none of these techniques has sought to combine a rigorous statistical formulation of the multiscale dictionary learning problem and the ability to share atoms across scales. We present a model for multiscale dictionary learning that overcomes some of the drawbacks of previous approaches by first decomposing an input into a pyramid of distinct frequency bands using a recursive filtering scheme, after which we perform dictionary learning and sparse coding on the individual levels of the resulting pyramid. The associated image model allows us to use a single set of adapted dictionary atoms that is shared--and learned--across all scales in the model. The underlying statistical model of our proposed method is fully Bayesian and allows for efficient inference of parameters, including the level of additive noise for denoising applications. We apply the proposed model to several common image processing problems including non-Gaussian and nonstationary denoising of real-world color images.

Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.

In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store.

Quantitative patterns of stylistic influence in the evolution of literature.

Literature is a form of expression whose temporal structure, both in content and style, provides a historical record of the evolution of culture. In this work we take on a quantitative analysis of literary style and conduct the first large-scale temporal stylometric study of literature by using the vast holdings in the Project Gutenberg Digital Library corpus. We find temporal stylistic localization among authors through the analysis of the similarity structure in feature vectors derived from content-free word usage, nonhomogeneous decay rates of stylistic influence, and an accelerating rate of decay of influence among modern authors. Within a given time period we also find evidence for stylistic coherence with a given literary topic, such that writers in different fields adopt different literary styles. This study gives quantitative support to the notion of a literary "style of a time" with a strong trend toward increasingly contemporaneous stylistic influence.

Empirical mode decomposition analysis for visual stylometry.

In this paper, we show how the tools of empirical mode decomposition (EMD) analysis can be applied to the problem of "visual stylometry," generally defined as the development of quantitative tools for the measurement and comparisons of individual style in the visual arts. In particular, we introduce a new form of EMD analysis for images and show that it is possible to use its output as the basis for the construction of effective support vector machine (SVM)-based stylometric classifiers. We present the methodology and then test it on collections of two sets of digital captures of drawings: a set of authentic and well-known imitations of works attributed to the great Flemish artist Pieter Bruegel the Elder (1525-1569) and a set of works attributed to Dutch master Rembrandt van Rijn (1606-1669) and his pupils. Our positive results indicate that EMD-based methods may hold promise generally as a technique for visual stylometry.

Nonparametric sparsification of complex multiscale networks.

Many real-world networks tend to be very dense. Particular examples of interest arise in the construction of networks that represent pairwise similarities between objects. In these cases, the networks under consideration are weighted, generally with positive weights between any two nodes. Visualization and analysis of such networks, especially when the number of nodes is large, can pose significant challenges which are often met by reducing the edge set. Any effective "sparsification" must retain and reflect the important structure in the network. A common method is to simply apply a hard threshold, keeping only those edges whose weight exceeds some predetermined value. A more principled approach is to extract the multiscale "backbone" of a network by retaining statistically significant edges through hypothesis testing on a specific null model, or by appropriately transforming the original weight matrix before applying some sort of threshold. Unfortunately, approaches such as these can fail to capture multiscale structure in which there can be small but locally statistically significant similarity between nodes. In this paper, we introduce a new method for backbone extraction that does not rely on any particular null model, but instead uses the empirical distribution of similarity weight to determine and then retain statistically significant edges. We show that our method adapts to the heterogeneity of local edge weight distributions in several paradigmatic real world networks, and in doing so retains their multiscale structure with relatively insignificant additional computational costs. We anticipate that this simple approach will be of great use in the analysis of massive, highly connected weighted networks.

Improved IBD detection using incomplete haplotype information.

BACKGROUND: The availability of high density genetic maps and genotyping platforms has transformed human genetic studies. The use of these platforms has enabled population-based genome-wide association studies. However, in inheritance-based studies, current methods do not take full advantage of the information present in such genotyping analyses. RESULTS: In this paper we describe an improved method for identifying genetic regions shared identical-by-descent (IBD) from recent common ancestors. This method improves existing methods by taking advantage of phase information even if it is less than fully accurate or missing. We present an analysis of how using phase information increases the accuracy of IBD detection compared to using only genotype information. CONCLUSIONS: Our algorithm should have utility in a wide range of genetic studies that rely on identification of shared genetic material in large families or small populations.

Deblurring of Class-Averaged Images in Single-Particle Electron Microscopy.

This paper proposes a method for deblurring of class-averaged images in single-particle electron microscopy (EM). Since EM images of biological samples are very noisy, the images which are nominally identical projection images are often grouped, aligned and averaged in order to cancel or reduce the background noise. However, the noise in the individual EM images generates errors in the alignment process, which creates an inherent limit on the accuracy of the resulting class averages. This inaccurate class average due to the alignment errors can be viewed as the result of a convolution of an underlying clear image with a blurring function. In this work, we develop a deconvolution method that gives an estimate for the underlying clear image from a blurred class-averaged image using precomputed statistics of misalignment. Since this convolution is over the group of rigid body motions of the plane, SE(2), we use the Fourier transform for SE(2) in order to convert the convolution into a matrix multiplication in the corresponding Fourier space. For practical implementation we use a Hermite-function-based image modeling technique, because Hermite expansions enable lossless Cartesian-polar coordinate conversion using the Laguerre-Fourier expansions, and Hermite expansion and Laguerre-Fourier expansion retain their structures under the Fourier transform. Based on these mathematical properties, we can obtain the deconvolution of the blurred class average using simple matrix multiplication. Tests of the proposed deconvolution method using synthetic and experimental EM images confirm the performance of our method.

Quantification of artistic style through sparse coding analysis in the drawings of Pieter Bruegel the Elder.

Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison based on a single relevant statistic, offers a natural and potentially more germane alternative to wavelet-based classification techniques that rely on more complicated statistical frameworks. Specifically, we show that our model provides a method capable of discriminating between authentic and imitation Bruegel drawings that numerically outperforms well-known existing approaches. Finally, we discuss the applications and constraints of our technique.

Accurate image rotation using hermite expansions.

In this paper, we propose an approach for the accurate rotation of a digital image using Hermite expansions. This exploits the fact that if a 2-D continuous bandlimited Hermite expansion is rotated, the resulting function can be expressed as a Hermite expansion with the same bandlimit. Furthermore, the Hermite coefficients of the initial 2-D expansion and the rotated expansion are mapped through an invertible linear relationship. Two efficient methods to compute the mapping between Hermite coefficients during rotation are proposed. We also propose a method for connecting the Hermite expansion and a discrete image. Using this method, we can obtain the Hermite expansion from a discrete image and vice versa. Combining these techniques, we propose new methods for the rotation of discrete images. We assess the accuracy of our methods and compare them with an existing FFT-based method implementing three shears. We find that the method proposed here consistently has better accuracy than the FFT-based method.

A SNP streak model for the identification of genetic regions identical-by-descent.

The availability of very dense genetic maps is changing in a fundamental way the methods used to identify the genetic basis of both rare and common inherited traits. The ability to directly compare the genomes of two related individuals and quickly identify those regions that are inherited identical-by-descent (IBD) from a recent common ancestor would be of utility in a wide range of genetic mapping methods. Here, we describe a simple method for using dense SNP maps to identify regions of the genome likely to be inherited IBD by family members. This method is based on identifying obligate recombination events and examining the pattern of distribution of such events along the genetic map. Specifically, we use the length of a consecutive set of biallelic markers that have a high probability of having avoided such obligate recombination events. This ;;SNP streak" is derived from subsets of samples within a pedigree and allows us to make statistical inferences about the ancestry of the region(s) containing stretches of markers with these properties. We show that the use of subsets of more than two samples has the advantage of identifying shorter shared subsegments as significant. This mitigates the effects of errors in SNP calls. We provide specific examples of microarray-based SNP data, using a family with a complex pedigree and with a rare form of inherited kidney disease, to illustrate this approach.

A Fast Hermite Transform.

We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Trade-offs between approximation in bandlimit (in the Hermite sense) and size of the support region are addressed. Numerical experiments are presented that show the feasibility and utility of our approach. Generalizations to any family of orthogonal polynomials are outlined. Applications to various problems in tomographic reconstruction, including the determination of protein structure, are discussed.