Quantifying Triadic Closure in Multi-Edge Social Networks

Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks, because they do not consider that triads can be formed by edges of different multiplicity. We propose a novel measure of triadic closure for multi-edge networks of social interactions based on a shared partner statistic. We demonstrate that our operalization is able to detect meaningful closure in synthetic and empirical multi-edge networks, where common approaches fail. This is a cornerstone in driving inferential network analyses from the analysis of binary networks towards the analyses of multi-edge and weighted networks, which offer a more realistic representation of social interactions and relations.Comment: 19 pages, 5 figures, 6 table

Simultaneous analysis of a sequence of paired ecological tables: A comparison of several methods

A pair of ecological tables is made of one table containing environmental variables (in columns) and another table containing species data (in columns). The rows of these two tables are identical and correspond to the sites where environmental variables and species data have been measured. Such data are used to analyze the relationships between species and their environment. If sampling is repeated over time for both tables, one obtains a sequence of pairs of ecological tables. Analyzing this type of data is a way to assess changes in species-environment relationships, which can be important for conservation Ecology or for global change studies. We present a new data analysis method adapted to the study of this type of data, and we compare it with two other methods on the same data set. All three methods are implemented in the ade4 package for the R environment.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS372 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks

Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states.Comment: 21 pages, 10 figure

Voicing Transformations and a Linear Representation of Uniform Triadic Transformations (Preprint name)

Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup $\mathcal{J}$ of $GL(3,\mathbb{Z}_{12})$ generated by the three voicing reflections. We determine the centralizer of $\mathcal{J}$ in both $GL(3,\mathbb{Z}_{12})$ and the monoid ${Aff}(3,\mathbb{Z}_{12})$ of affine transformations, and recover a Lewinian duality for trichords containing a generator of $\mathbb{Z}_{12}$. We present a variety of musical examples, including Wagner's hexatonic Grail motive and the diatonic falling fifths as cyclic orbits, an elaboration of our earlier work with Satyendra on Schoenberg, String Quartet in $D$ minor, op. 7, and an affine musical map of Joseph Schillinger. Finally, we observe, perhaps unexpectedly, that the retrograde inversion enchaining operation RICH (for arbitrary 3-tuples) belongs to the setwise stabilizer $\mathcal{H}$ in $\Sigma_3 \ltimes \mathcal{J}$ of root position triads. This allows a more economical description of a passage in Webern, Concerto for Nine Instruments, op. 24 in terms of a morphism of group actions. Some of the proofs are located in the Supplementary Material file, so that this main article can focus on the applications

Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis

Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M <= W <= N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's covariance matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series. A real application is to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 4 and 3 years supports the Devil's staircase scenario for the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure

A semiotic analysis of the genetic information

Terms loaded with informational connotations are often employed to refer to genes and their dynamics. Indeed, genes are usually perceived by biologists as basically ‘the carriers of hereditary information.’ Nevertheless, a number of researchers consider such talk as inadequate and ‘just metaphorical,’ thus expressing a skepticism about the use of the term ‘information’ and its derivatives in biology as a natural science. First, because the meaning of that term in biology is not as precise as it is, for instance, in the mathematical theory of communication. Second, because it seems to refer to a purported semantic property of genes without theoretically clarifying if any genuinely intrinsic semantics is involved. Biosemiotics, a field that attempts to analyze biological systems as semiotic systems, makes it possible to advance in the understanding of the concept of information in biology. From the perspective of Peircean biosemiotics, we develop here an account of genes as signs, including a detailed analysis of two fundamental processes in the genetic information system (transcription and protein synthesis) that have not been made so far in this field of research. Furthermore, we propose here an account of information based on Peircean semiotics and apply it to our analysis of transcription and protein synthesis