Fast algorithm for detecting community structure in networks

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for detecting such structure. These algorithms however are computationally demanding, which limits their application to small networks. Here we describe a new algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster than previous algorithms. We give several example applications, including one to a collaboration network of more than 50000 physicists.Comment: 5 pages, 4 figure

Expanding Universe Illusion

We present a new induced movement illusion from global expansion or contraction in a triangular region filled with rising or falling textures. Objective global expansion or contraction induces lateral movement in the oblique edges of the triangle. The effects may be due to common and relative movements operating within a single texture

Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices

We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and kagome lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLC, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), high-temperature expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo simulations.For many models and properties NLC results are substantially more accurate than HTE and ED.Comment: 14 pages, 16 figures, as publishe

In search of Leonardo: Computer-based facial image analysis of Renaissance artworks for identifying Leonardo as subject

One of the enduring mysteries in the history of the Renaissance is the adult appearance of the archetypical "Renaissance Man," Leonardo da Vinci. His only acknowledged self-portrait is from an advanced age, and various candidate images of younger men are difficult to assess given the absence of documentary evidence. One clue about Leonardo's appearance comes from the remark of the contemporary historian, Vasari, that the sculpture of David by Leonardo's master, Andrea del Verrocchio, was based on the appearance of Leonardo when he was an apprentice. Taking a cue from this statement, we suggest that the more mature sculpture of St. Thomas, also by Verrocchio, might also have been a portrait of Leonardo. We tested the possibility Leonardo was the subject for Verrocchio's sculpture by a novel computational technique for the comparison of three-dimensional facial configurations. Based on quantitative measures of similarities, we also assess whether another pair of candidate two-dimensional images are plausibly attributable as being portraits of Leonardo as a young adult. Our results are consistent with the claim Leonardo is indeed the subject in these works, but we need comparisons with images in a larger corpora of candidate artworks before our results achieve statistical significance

The perceived depth from disparity as function of luminance contrast

Does human vision show the contrast invariance expected of an ideal stereoscopic system for computing depth from disparity? We used random-dot stereograms to investigate the luminance contrast effect on perceived depth from disparity. The perceived depth of disparity corrugations was measured by adjusting the length of a horizontal line to match the perceived depth of the corrugations at various luminance contrasts. At each contrast, the perceived depth increased with disparity up to a critical value, decreasing with further increases in disparity. Both the maximum perceived depth and the disparity modulation level where this maximum occurred changed as a sigmoid function of luminance contrast. These results show that perceived depth from disparity depends in a complex manner on the luminance contrast in the image, providing significant limitations on depth perception at low contrasts in a lawful manner but that are incompatible with existing models of cortical disparity processing

Finding community structure in very large networks

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Vortex Formation by Interference of Multiple Trapped Bose-Einstein Condensates

We report observations of vortex formation as a result of merging together multiple $^{87}$Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a trapping potential is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated condensates. The three condensates then merge together into one BEC, either by removal of the barrier, or during the final stages of evaporative cooling if the barrier energy is low enough; both processes can naturally produce vortices within the trapped BEC. We interpret the vortex formation mechanism as originating in interference between the initially independent condensates, with indeterminate relative phases between the three initial condensates and the condensate merging rate playing critical roles in the probability of observing vortices in the final, single BEC.Comment: 5 pages, 3 figure

White Matter Abnormalities in Patients with Treatment-Resistant Genetic Generalized Epilepsies.

BACKGROUND Genetic generalized epilepsies (GGEs) are associated with microstructural brain abnormalities that can be evaluated with diffusion tensor imaging (DTI). Available studies on GGEs have conflicting results. Our primary goal was to compare the white matter structure in a cohort of patients with video/EEG-confirmed GGEs to healthy controls (HCs). Our secondary goal was to assess the potential effect of age at GGE onset on the white matter structure. MATERIAL AND METHODS A convenience sample of 23 patients with well-characterized treatment-resistant GGEs (13 female) was compared to 23 HCs. All participants received MRI at 3T. DTI indices, including fractional anisotropy (FA) and mean diffusivity (MD), were compared between groups using Tract-Based Spatial Statistics (TBSS). RESULTS After controlling for differences between groups, abnormalities in DTI parameters were observed in patients with GGEs, including decreases in functional anisotropy (FA) in the hemispheric (left>right) and brain stem white matter. The examination of the effect of age at GGE onset on the white matter integrity revealed a significant negative correlation in the left parietal white matter region FA (R=-0.504; p=0.017); similar trends were observed in the white matter underlying left motor cortex (R=-0.357; p=0.103) and left posterior limb of the internal capsule (R=-0.319; p=0.148). CONCLUSIONS Our study confirms the presence of widespread white matter abnormalities in patients with GGEs and provides evidence that the age at GGE onset may have an important effect on white matter integrity