Illustration of the Retino-Cortical Mapping Process

<div><p>(A) Iso-density contours of photoreceptors (red crosses) for four selected values of the parameter <i>a</i>. The photoreceptors are arranged as 18 concentric rings. The mapping “template” is composed of nonoverlapping 32-ring sectors (receptive fields) formed by the intersection of rays originating at the center of the retina. The value of the photoreceptor is the average of the intensities of the photoreceptors (pixels) within the receptive field's boundary.</p><p>(B) Inverse mapping of “cortical” images back to the retinal (input) domain. The cortical magnification effect is due to inhomogeneous distribution of photoreceptors. A “Cartesian” visual image (here, a checkerboard; 512 × 512 pixels) is mapped onto a “cortical” plane. Mapping is dependent on the linear parameter <i>a</i>. The foveal part of visual field is magnified, that is, a larger piece of cortical area is devoted to processing.</p></div

Robots, Sensorimotor Interactions, and Neural Control Architecture

<div><p>(A1) <i>Roboto</i> has a total of 14 DOF, five of which are used in the current set of experiments. Note the head-mounted CCD camera, the pan-tilt head system (2 DOF), and the moveable left arm with shoulder, elbow, and wrist joints (3 DOF). The object is a red ball (1.25 inches diameter) attached to the tip of the last joint.</p><p>(A2) <i>Strider</i> has a total of 14 DOF, with four legs of 3 DOF each and 2 DOF in the pan-tilt head system. Objects are red and blue blocks (1 inch cubes). <i>Strider</i> is situated in an environmental enclosure with black walls.</p><p>(A3) <i>Madame</i> has 4 DOF, with 2 DOF in the pan-tilt system and 2 DOF for the wheels, which are both located on an axis vertical to the main body axis. The environment is a square arena bounded by blue walls containing 20 red-colored floating spheres.</p><p>(B1) <i>Roboto</i> engages in sensorimotor interactions via the head system and arm movements; sensory → motor (dotted arrows), motor → sensory (dashed arrows).</p><p>(B2) <i>Strider</i> engages in sensorimotor interactions via the head system, as well as via steering signals generated by the head and transmitted to the four legs.</p><p>(B3) <i>Madame</i>'s behavior consists of a series of approaches to colored objects and ovations. Fixations to the objects are maintained by independent action of head and body.</p><p>(C) Neural control architecture. The architecture common to all robots is composed of color image arrays <i>I_R, I_G, I_B,</i> color- intensity map<b><i>Col</i></b><i>_RGBY</i>, and saliency map <i>Sal</i> (see text for details). The peak of the saliency map (blue cross) determines the pan-tilt camera motion and body steering. In addition, <i>Strider</i>'s neural system contains a value system with taste sensory inputs relayed via a virtual taste sensor (blue square in visual image) to taste neurons (<i>T_AP,AV</i>), which in turn generates reward and aversiveness signals (rew, ave). These signals are used to modulate the strengths of the saliency factors <i>η_RGBY</i> (see text for details).</p></div

Properties of Networks (<i>n</i> = 10) Optimized for Structural and Functional Motif Number

<div><p>(A) Maximization of functional motif number (<i>N</i> = 30, <i>K</i> = 311). Each maximization starts from different random initial conditions, including a different set of 10 random networks. From left to right, each graph shows plots of functional motif number, structural motif number, motif frequency spectrum (<i>M</i> = 3) of optimized networks, and clustering coefficient.</p> <p>(B) Maximization of structural motif number (<i>N</i> = 30, <i>K</i> = 311). Graphs are as in (A). Compare the motif frequency spectrum in (A) with the corresponding plot for the macaque visual cortex in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020369#pbio-0020369-g002" target="_blank">Figure 2</a>A (first row, left bar graph). Initially, random networks in generation 1 exhibited frequency spectra identical to those for random networks in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020369#pbio-0020369-g002" target="_blank">Figure 2</a>A (first row, middle panel).</p></div

Structural Motifs that Occurred in Significantly Increased Numbers at Motif Sizes <i>M</i> = 3 and <i>M</i> = 4

<div><p>(A) Structural motifs found in all three large-scale cortical networks analyzed in this study (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020369#pbio-0020369-t002" target="_blank">Table 2</a>).</p> <p>(B) Structural motifs found in networks optimized for functional motif number (see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020369#pbio-0020369-t004" target="_blank">Table 4</a>). Numbers refer to the motif's ID.</p></div

Effect of Retinal Morphology on Information Flow

<p>Transfer entropy between sensor (S) and motor variables (M) as a function of parameter <i>a</i> in <i>Madame</i>. The linear parameter <i>a</i> determines the distribution of the photoreceptors in the retina and thus the eye morphology. Transfer entropy is calculated for every pixel of a visual region (S; 6 × 6 pixel patch) and the difference between left and right wheel speed (M; angular velocity). Squares show information flow from M to S; triangles indicate information flow from S to M. Pixels were selected from a central visual region (continuous lines) and a peripheral region (dashed lines). Data in all graphs are averages of five representative experiments consisting of 4,096 samples each, error bars show standard deviations.</p

Information Flow (Transfer Entropy) between Sensory Input, Neural Representation of Saliency, and Motor Variables in <i>Roboto</i>

<div><p>(A1) Transfer entropy between array <i>I_R</i> (variable S) and pan-tilt amplitude (variable M). Series of plots show maps of transfer entropy from S to M (S → M) and from M to S (M → S) over visual space (55 × 77 pixels), calculated for offsets between −7 (“M leading S”) and +7 (“S leading M”) time steps. Plots show data for conditions “fov” and “rnd.” The gray scale ranges from 0.0 to 0.5 bits (for all plots in panels A1 and B1).</p><p>(A2) Curves show transfer entropy for five individual runs (thin lines) as well as the average over five runs (thick lines) between the single central pixel of array <i>I_R</i> (S) and pan-tilt amplitude (M), for directions M → S (black) and S → M (gray).</p><p>(A3) z-Score maps of significant image regions (plotted between z = 0 and z = 6). The z-scores are expressed as number of standard deviations above background at time offset +1 (S → M) and −1 (M → S). Mean and standard deviation of background is calculated from transfer entropy values at maximal time delays (−7,+7 time steps).</p><p>(B) All three panels have the same format as (A), but the neural activations of the saliency map <i>Sal</i> are substituted as variable S (11 × 11 neural units).</p></div

Definition of Structural and Functional Motifs, and Motif Detection

<div><p>(A) From a network, we select a subset of three vertices and their interconnections, representing a candidate structural motif.</p> <p>(B) The candidate motif is matched to the 13 motif classes for motif size <i>M</i> = 3. Numbers refer to the ID. The candidate motif is detected as a motif with ID = 13. In detecting structural motifs, only exact matches of candidate motif and motif class are counted.</p> <p>(C) A single instance of a structural motif contains many instances of functional motifs. Here, a structural motif (<i>M</i> = 3, ID = 13) is shown to contain, for example, two distinct instances of the functional motif ID = 9, one motif ID = 2, and one motif ID = 7. Many other distinct instances of functional motifs are present that are not shown in the figure. Note that, in order to be counted as a functional motif of size <i>M</i> = 3, all three vertices of the original structural motif must participate. For a very similar distinction between structural and functional motifs (“interlaced circuits”) and an illustration see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020369#pbio-0020369-Ashby1" target="_blank">Ashby (1960)</a>, p. 53.</p></div

Comparison of Structural Motif Frequency Spectra for Macaque Visual Cortex and C. elegans

<div><p>(A) Spectra for structural motifs of size <i>M</i> = 3.</p> <p>(B) Spectra for structural motifs of size <i>M</i> = 4.</p></div

Communication Efficiency and Congestion of Signal Traffic in Large-Scale Brain Networks

<div><p>The complex connectivity of the cerebral cortex suggests that inter-regional communication is a primary function. Using computational modeling, we show that anatomical connectivity may be a major determinant for global information flow in brain networks. A macaque brain network was implemented as a communication network in which signal units flowed between grey matter nodes along white matter paths. Compared to degree-matched surrogate networks, information flow on the macaque brain network was characterized by higher loss rates, faster transit times and lower throughput, suggesting that neural connectivity may be optimized for speed rather than fidelity. Much of global communication was mediated by a “rich club” of hub regions: a sub-graph comprised of high-degree nodes that are more densely interconnected with each other than predicted by chance. First, macaque communication patterns most closely resembled those observed for a synthetic rich club network, but were less similar to those seen in a synthetic small world network, suggesting that the former is a more fundamental feature of brain network topology. Second, rich club regions attracted the most signal traffic and likewise, connections between rich club regions carried more traffic than connections between non-rich club regions. Third, a number of rich club regions were significantly under-congested, suggesting that macaque connectivity actively shapes information flow, funneling traffic towards some nodes and away from others. Together, our results indicate a critical role of the rich club of hub nodes in dynamic aspects of global brain communication.</p></div

Multiresolution Consensus Clustering in Networks - Network Data Sets

Network data sets used in:<div><br></div><div>Multiresolution Consensus Clustering in Networks, Scientific Reports, https://doi.org/10.1038/s41598-018-21352-7<br></div><div><br></div><div><b>Data Sets:</b></div><div><br></div><div>Each '.mat' file contains the adjacency matrix 'A', reference partitions 'S' and a label for the reference partition 'gtlabels'. Some files have additional information.</div><div><br></div><div><u>Zachary Karate Club</u></div><div><i>File</i>: 'karate.mat'</div><div><i>Citation</i>: Zachary, W. W. An information flow model for conflict and fission in small groups. <i>Journal of Anthropological Research</i> <b>33</b>, 452–473 (1977).</div><div><i>Source: </i>http://www-personal.umich.edu/~mejn/netdata/</div><div><br></div><div><u>College Football</u></div><div><i>File:</i> 'football.mat'</div><div><i>Citations</i>: Girvan, M. & Newman, M. E. J. Community structure in social and biological networks. <i>Proceedings of the National Academy of Sciences</i> <b>99</b>, 7821–7826 (2002).</div><div>Evans, T. S. Clique graphs and overlapping communities. <i>Journal of Statistical Mechanics: Theory and Experiment</i> <b>2010</b>, P12037 (2010).<br></div><div><i>Source: </i>https://doi.org/10.6084/m9.figshare.93179.v2</div><div><br></div><div><u>Political Blogs</u></div><div><i>File: </i>'polblogs.mat'</div><div><i>Citation</i>: Adamic, L. A. & Glance, N. The political blogosphere and the 2004 U.S. election: Divided they blog. In <i>Proceedings of the 3rd International Workshop on Link Discovery</i>, LinkKDD ’05, 36–43 (ACM, New York, NY, USA 2005).</div><div><i>Source</i>: http://www-personal.umich.edu/~mejn/netdata/</div><div><br></div><div><u>Political Books</u></div><div><i>File</i>: 'polbooks.mat'</div><div><i>Citation</i>: Krebs, V. Books about US politics.</div><div><i>Source</i>: http://www-personal.umich.edu/~mejn/netdata/</div><div><br></div><div><u>Human Structural Brain</u></div><div><i>File:</i> 'DSI_network.mat'</div><div><i>Citation: </i>Hagmann, P. et al. Mapping the structural core of human cerebral cortex. <i>PLOS Biology</i> <b>6</b>, 1–15 (2008).</div><div><i>Raw Data File: '</i>DSI_release2_2011.mat'</div><div><br></div><div><u>Rat Structural Brain</u></div><div><i>File: </i>'rat_cortex.mat'</div><div><i>Additional Data:</i> has extra variable 'labels' which contain the abbreviated names of the anatomical regions</div><div><i>Citation: </i>Bota, M., Sporns, O. & Swanson, L. W. Architecture of the cerebral cortical association connectome underlying cognition. <i>Proceedings of the National Academy of Sciences </i><b>112</b>, E2093–E2101 (2015).</div><div><br></div