1
|
Friedman EJ, Young K, Tremper G, Liang J, Landsberg AS, Schuff N. Directed network motifs in Alzheimer's disease and mild cognitive impairment. PLoS One 2015; 10:e0124453. [PMID: 25879535 PMCID: PMC4400037 DOI: 10.1371/journal.pone.0124453] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2014] [Accepted: 03/05/2015] [Indexed: 11/26/2022] Open
Abstract
Directed network motifs are the building blocks of complex networks, such as human brain networks, and capture deep connectivity information that is not contained in standard network measures. In this paper we present the first application of directed network motifs in vivo to human brain networks, utilizing recently developed directed progression networks which are built upon rates of cortical thickness changes between brain regions. This is in contrast to previous studies which have relied on simulations and in vitro analysis of non-human brains. We show that frequencies of specific directed network motifs can be used to distinguish between patients with Alzheimer’s disease (AD) and normal control (NC) subjects. Especially interesting from a clinical standpoint, these motif frequencies can also distinguish between subjects with mild cognitive impairment who remained stable over three years (MCI) and those who converted to AD (CONV). Furthermore, we find that the entropy of the distribution of directed network motifs increased from MCI to CONV to AD, implying that the distribution of pathology is more structured in MCI but becomes less so as it progresses to CONV and further to AD. Thus, directed network motifs frequencies and distributional properties provide new insights into the progression of Alzheimer’s disease as well as new imaging markers for distinguishing between normal controls, stable mild cognitive impairment, MCI converters and Alzheimer’s disease.
Collapse
Affiliation(s)
- Eric J. Friedman
- International Computer Science Institute, Berkeley, CA, United States of America
- Department of Computer Science, University of California, Berkeley, Berkeley, CA, United States of America
- * E-mail:
| | - Karl Young
- Department of Radiology & Biomedical Imaging, University of California San Francisco, San Francisco, CA, United States of America
- VA Medical Center, San Francisco, CA, United States of America
| | - Graham Tremper
- Department of Computer Science, University of California, Berkeley, Berkeley, CA, United States of America
| | - Jason Liang
- Department of Computer Science, University of California, Berkeley, Berkeley, CA, United States of America
| | - Adam S. Landsberg
- W.M. Keck Science Department, Claremont McKenna College, Pitzer College, and Scripps College, Claremont, CA, United States of America
| | - Norbert Schuff
- Department of Radiology & Biomedical Imaging, University of California San Francisco, San Francisco, CA, United States of America
- VA Medical Center, San Francisco, CA, United States of America
| | | |
Collapse
|
2
|
Friedman EJ, Young K, Asif D, Jutla I, Liang M, Wilson S, Landsberg AS, Schuff N. Directed progression brain networks in Alzheimer's disease: properties and classification. Brain Connect 2015; 4:384-93. [PMID: 24901258 DOI: 10.1089/brain.2014.0235] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
This article introduces a new approach in brain connectomics aimed at characterizing the temporal spread in the brain of pathologies like Alzheimer's disease (AD). The main instrument is the development of "directed progression networks" (DPNets), wherein one constructs directed edges between nodes based on (weakly) inferred directions of the temporal spreading of the pathology. This stands in contrast to many previously studied brain networks where edges represent correlations, physical connections, or functional progressions. In addition, this is one of a few studies showing the value of using directed networks in the study of AD. This article focuses on the construction of DPNets for AD using longitudinal cortical thickness measurements from magnetic resonance imaging data. The network properties are then characterized, providing new insights into AD progression, as well as novel markers for differentiating normal cognition (NC) and AD at the group level. It also demonstrates the important role of nodal variations for network classification (i.e., the significance of standard deviations, not just mean values of nodal properties). Finally, the DPNets are utilized to classify subjects based on their global network measures using a variety of data-mining methodologies. In contrast to most brain networks, these DPNets do not show high clustering and small-world properties.
Collapse
Affiliation(s)
- Eric J Friedman
- 1 International Computer Science Institute , Berkeley, California
| | | | | | | | | | | | | | | | | |
Collapse
|
3
|
Abstract
We show that in networks with a hierarchical architecture, critical dynamical behaviors can emerge even when the underlying dynamical processes are not critical. This finding provides explicit insight into current studies of the brain's neuronal network showing power-law avalanches in neural recordings, and provides a theoretical justification of recent numerical findings. Our analysis shows how the hierarchical organization of a network can itself lead to power-law distributions of avalanche sizes and durations, scaling laws between anomalous exponents, and universal functions-even in the absence of self-organized criticality or critical points. This hierarchy-induced phenomenon is independent of, though can potentially operate in conjunction with, standard dynamical mechanisms for generating power laws.
Collapse
Affiliation(s)
- Eric J Friedman
- Department of Computer Science, International Computer Science Institute, University of California Berkeley, California 94704, USA
| | | |
Collapse
|
4
|
Morrison RE, Friedman EJ, Landsberg AS. Combinatorial games with a pass: a dynamical systems approach. Chaos 2011; 21:043108. [PMID: 22225345 DOI: 10.1063/1.3650234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim, we observe that the introduction of the pass dramatically alters the game's underlying structure, rendering it considerably more complex, while for Chomp, the pass move is found to have relatively minimal impact. We show how these results can be understood by recasting these games as dynamical systems describable by dynamical recursion relations. From these recursion relations, we are able to identify underlying structural connections between these "games with passes" and a recently introduced class of "generic (perturbed) games." This connection, together with a (non-rigorous) numerical stability analysis, allows one to understand and predict the effect of a pass on a game.
Collapse
Affiliation(s)
- Rebecca E Morrison
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA.
| | | | | |
Collapse
|
5
|
Friedman EJ, Landsberg AS. Construction and analysis of random networks with explosive percolation. Phys Rev Lett 2009; 103:255701. [PMID: 20366263 DOI: 10.1103/physrevlett.103.255701] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2009] [Revised: 11/01/2009] [Indexed: 05/29/2023]
Abstract
The existence of explosive phase transitions in random (Erdös Rényi-type) networks has been recently documented by Achlioptas, D'Souza, and Spencer [Science 323, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism behind these first-order phase transitions and develop tools that allow us to identify (and predict) when a random network will exhibit an explosive transition. Several interesting new models displaying explosive transitions are also presented.
Collapse
Affiliation(s)
- Eric J Friedman
- School of ORIE and Center for Applied Mathematics, Cornell University, Ithaca, New York 14850, USA
| | | |
Collapse
|
6
|
Abstract
We study the nature of statistical correlations that develop between systems of interacting self-organized critical automata (sandpiles). Numerical and analytical findings are presented describing the emergence of "synchronization" between sandpiles and the dependency of this synchronization on factors such as variations in coupling strength, toppling rule probabilities, symmetric versus asymmetric coupling rules, and numbers of sandpiles.
Collapse
Affiliation(s)
- Reuben Gann
- W. M. Keck Science Center, 925 N. Mills Avenue, Claremont McKenna, Pitzer, and Scripps Colleges, Claremont, CA 91711, USA
| | | | | | | |
Collapse
|
7
|
Friedman EJ, Landsberg AS. Large-scale synchrony in weakly interacting automata. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 63:051303. [PMID: 11414898 DOI: 10.1103/physreve.63.051303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2000] [Indexed: 05/23/2023]
Abstract
We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.
Collapse
Affiliation(s)
- E J Friedman
- Department of Economics, Rutgers University, New Brunswick, New Jersey 08903, USA
| | | |
Collapse
|
8
|
Landsberg AS, Friedman EJ. Dynamical effects of partial orderings in physical systems. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 54:3135-3141. [PMID: 9965454 DOI: 10.1103/physreve.54.3135] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
9
|
Landsberg AS, Knobloch E. Oscillatory bifurcation with broken translation symmetry. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 53:3579-3600. [PMID: 9964668 DOI: 10.1103/physreve.53.3579] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
10
|
Landsberg AS, Knobloch E. Oscillatory doubly diffusive convection in a finite container. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 53:3601-3609. [PMID: 9964669 DOI: 10.1103/physreve.53.3601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
11
|
Landsberg AS, Braiman Y, Wiesenfeld K. Effect of disorder on synchronization in prototype two-dimensional Josephson arrays. Phys Rev B Condens Matter 1995; 52:15458-15474. [PMID: 9980903 DOI: 10.1103/physrevb.52.15458] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
12
|
|