A Fast and Efficient Incremental Approach toward Dynamic Community Detection

Community detection is a discovery tool used by network scientists to analyze the structure of real-world networks. It seeks to identify natural divisions that may exist in the input networks that partition the vertices into coherent modules (or communities). While this problem space is rich with efficient algorithms and software, most of this literature caters to the static use-case where the underlying network does not change. However, many emerging real-world use-cases give rise to a need to incorporate dynamic graphs as inputs. In this paper, we present a fast and efficient incremental approach toward dynamic community detection. The key contribution is a generic technique called $\Delta-screening$, which examines the most recent batch of changes made to an input graph and selects a subset of vertices to reevaluate for potential community (re)assignment. This technique can be incorporated into any of the community detection methods that use modularity as its objective function for clustering. For demonstration purposes, we incorporated the technique into two well-known community detection tools. Our experiments demonstrate that our new incremental approach is able to generate performance speedups without compromising on the output quality (despite its heuristic nature). For instance, on a real-world network with 63M temporal edges (over 12 time steps), our approach was able to complete in 1056 seconds, yielding a 3x speedup over a baseline implementation. In addition to demonstrating the performance benefits, we also show how to use our approach to delineate appropriate intervals of temporal resolutions at which to analyze an input network

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Random Matrix Theory and Classical Statistical Mechanics. I. Vertex Models

A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and spectral rigidity). For Yang-Baxter integrable cases, including free-fermion solutions, we have found a Poissonian behavior, whereas level repulsion close to the Wigner distribution is found for non-integrable models. For the asymmetric eight-vertex model, however, the level repulsion can also disappearand the Poisson distribution be recovered on (non Yang--Baxter integrable) algebraic varieties, the so-called disorder varieties. We also present an infinite set of algebraic varieties which are stable under the action of an infinite discrete symmetry group of the parameter space. These varieties are possible loci for free parafermions. Using our numerical criterion we have tested the generic calculability of the model on these algebraic varieties.Comment: 25 pages, 7 PostScript Figure

Caractérisation de la colonisation du chevreuil en zone méditerranéenne française.

Sept ans après la première enquête réalisée en 1987 sur 12 départements méditerranéens, la réactualisation, par la même méthodologie, permet de constater que l'espèce du chevreuil progresse de manière significative vers le sud de la zone enquêtée

Modeling affirmative and negated action processing in the brain with lexical and compositional semantic models

Recent work shows that distributional semantic models can be used to decode patterns of brain activity associated with individual words and sentence meanings. However, it is yet unclear to what extent such models can be used to study and ecode fMRI patterns associated with specific aspects of semantic composition such as the negation function. In this paper, we apply lexical and compositional semantic models to decode fMRI patterns associated with negated and affirmative sentences containing hand-action verbs. Our results show reduced decoding (correlation) of sentences where the verb is in the negated context, as compared to the affirmative one, within brain regions implicated in action-semantic processing. This supports behavioral and brain imaging studies, suggesting that negation involves reduced access to aspects of the affirmative mental representation. The results pave the way for testing alternate semantic models of negation against human semantic processing in the brain

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Multicritical Points of Potts Spin Glasses on the Triangular Lattice

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure

ENaC activity in collecting ducts modulates NCC in cirrhotic mice.

Cirrhosis is a frequent and severe disease, complicated by renal sodium retention leading to ascites and oedema. A better understanding of the complex mechanisms responsible for renal sodium handling could improve clinical management of sodium retention. Our aim was to determine the importance of the amiloride-sensitive epithelial sodium channel (ENaC) in collecting ducts in compensate and decompensate cirrhosis. Bile duct ligation was performed in control mice (CTL) and collecting duct-specific αENaC knockout (KO) mice, and ascites development, aldosterone plasma concentration, urinary sodium/potassium ratio and sodium transporter expression were compared. Disruption of ENaC in collecting ducts (CDs) did not alter ascites development, urinary sodium/potassium ratio, plasma aldosterone concentrations or Na,K-ATPase abundance in CCDs. Total αENaC abundance in whole kidney increased in cirrhotic mice of both genotypes and cleaved forms of α and γ ENaC increased only in ascitic mice of both genotypes. The sodium chloride cotransporter (NCC) abundance was lower in non-ascitic KO, compared to non-ascitic CTL, and increased when ascites appeared. In ascitic mice, the lack of αENaC in CDs induced an upregulation of total ENaC and NCC and correlated with the cleavage of ENaC subunits. This revealed compensatory mechanisms which could also take place when treating the patients with diuretics. These compensatory mechanisms should be considered for future development of therapeutic strategies

Universality in phase boundary slopes for spin glasses on self dual lattices

We study the effects of disorder on the slope of the disorder--temperature phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal or irrelevant cases of disorder. Using duality arguments, as well as exact Pfaffian techniques we reproduce these analytical estimates. In addition, we obtain different estimates for spin-glass models on hierarchical lattices where the effects of disorder are relevant. We show that the phase-boundary slope near the Onsager point can be used to probe for the relevance of disorder effects.Comment: 8 pages, 6 figure

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure