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Graph Theory

Ankit N Khambhati, Ann E Sizemore, Richard F Betzel, Danielle S Bassett
Recent advances in brain imaging techniques, measurement approaches, and storage capacities have provided an unprecedented supply of high temporal resolution neural data. These data present a remarkable opportunity to gain a mechanistic understanding not just of circuit structure, but also of circuit dynamics, and its role in cognition and disease. Such understanding necessitates a description of the raw observations, and a delineation of computational models and mathematical theories that accurately capture fundamental principles behind the observations...
June 20, 2017: NeuroImage
Elena Fimmel, Christian J Michel, Lutz Strüngmann
Comma-free codes constitute a class of circular codes, which has been widely studied, in particular by Golomb et al. (Biologiske Meddelelser, Kongelige Danske Videnskabernes Selskab 23:1-34, 1958a, Can J Math 10:202-209, 1958b), Michel et al. (Comput Math Appl 55:989-996, 2008a, Theor Comput Sci 401:17-26, 2008b, Inf Comput 212:55-63, 2012), Michel and Pirillo (Int J Comb 2011:659567, 2011), and Fimmel and Strüngmann (J Theor Biol 389:206-213, 2016). Based on a recent approach using graph theory to study circular codes Fimmel et al...
June 22, 2017: Bulletin of Mathematical Biology
Bo Gong, Benjamin Schullcke, Sabine Krueger-Ziolek, Marko Vauhkonen, Gerhard Wolf, Ullrich Mueller-Lisse, Knut Moeller
The objective of Electrical Impedance Tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite element method framework. In previous studies, standard sparse regularization was used for difference EIT to achieve a sparse solution. However, regarding element-wise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise...
June 16, 2017: IEEE Transactions on Medical Imaging
João Ricardo Sato, Claudinei Eduardo Biazoli, Giovanni Abrahão Salum, Ary Gadelha, Nicolas Crossley, Gilson Vieira, André Zugman, Felipe Almeida Picon, Pedro Mario Pan, Marcelo Queiroz Hoexter, Edson Amaro, Mauricio Anés, Luciana Monteiro Moura, Marco Antonio Gomes Del'Aquilla, Philip Mcguire, Luis Augusto Rohde, Euripedes Constantino Miguel, Andrea Parolin Jackowski, Rodrigo Affonseca Bressan
OBJECTIVES: One of the major challenges facing psychiatry is how to incorporate biological measures in the classification of mental health disorders. Many of these disorders affect brain development and its connectivity. In this study, we propose a novel method for assessing brain networks based on the combination of a graph theory measure (eigenvector centrality) and a one-class support vector machine (OC-SVM). METHODS: We applied this approach to resting-state fMRI data from 622 children and adolescents...
February 8, 2017: World Journal of Biological Psychiatry
R A I Bethlehem, R Romero-Garcia, E Mak, E T Bullmore, S Baron-Cohen
Background: While autism and attention-deficit/hyperactivity disorder (ADHD) are considered distinct conditions from a diagnostic perspective, clinically they share some phenotypic features and have high comorbidity. Regardless, most studies have focused on only one condition, with considerable heterogeneity in their results. Taking a dual-condition approach might help elucidate shared and distinct neural characteristics. Method: Graph theory was used to analyse topological properties of structural covariance networks across both conditions and relative to a neurotypical (NT; n = 87) group using data from the ABIDE (autism; n = 62) and ADHD-200 datasets (ADHD; n = 69)...
June 13, 2017: Cerebral Cortex
Tetsuya Takahashi, Teruya Yamanishi, Sou Nobukawa, Shinya Kasakawa, Yuko Yoshimura, Hirotoshi Hiraishi, Chiaki Hasegawa, Takashi Ikeda, Tetsu Hirosawa, Toshio Munesue, Haruhiro Higashida, Yoshio Minabe, Mitsuru Kikuchi
OBJECTIVE: Altered brain connectivity has been theorized as a key neural underpinning of autism spectrum disorder (ASD), but recent investigations have revealed conflicting patterns of connectivity, particularly hyper-connectivity and hypo-connectivity across age groups. The application of graph theory to neuroimaging data has become an effective approach for characterizing topographical patterns of large-scale functional networks. We used a graph approach to investigate alteration of functional networks in childhood ASD...
May 23, 2017: Clinical Neurophysiology: Official Journal of the International Federation of Clinical Neurophysiology
Ying Wang, Junjing Wang, Yanbin Jia, Shuming Zhong, Meiqi Niu, Yao Sun, Zhangzhang Qi, Ling Zhao, Li Huang, Ruiwang Huang
Identifying brain differences and similarities between bipolar disorder (BD) and major depressive disorder (MDD) is necessary for increasing our understanding of the pathophysiology and for developing more effective treatments. However, the features of whole-brain intrinsic functional connectivity underlying BD and MDD have not been directly compared. We collected resting-state fMRI data from 48 BD patients, 48 MDD patients, and 51 healthy subjects. We constructed voxel-wise whole-brain functional networks and computed regional functional connectivity strength (FCS) using graph-theory and further divided the regional FCS into long-range FCS (lFCS) and short-range FCS (sFCS)...
June 15, 2017: Scientific Reports
Keiichi Onoda, Toshikazu Kawagoe, Haixia Zheng, Shuhei Yamaguchi
Dorsal anterior cingulate cortex (dACC) is an important region in the processing of both cognition and affect. Recently, transcranial brain stimulation has been used to modulate cortical activity, but it is unclear whether this stimulation has a specific effect on dACC. Based on EEG evidence that frontal midline theta activity is generated in dACC, we hypothesized that transcranial alternating current stimulation (tACS) with theta band frequency would modulate neural networks including dACC. In this study, we examined the effects of theta band tACS on functional networks and emotional state...
June 15, 2017: Scientific Reports
Carmen Keller, Alex Junghans
BACKGROUND: Individuals with low numeracy have difficulties with understanding complex graphs. Combining the information-processing approach to numeracy with graph comprehension and information-reduction theories, we examined whether high numerates' better comprehension might be explained by their closer attention to task-relevant graphical elements, from which they would expect numerical information to understand the graph. Furthermore, we investigated whether participants could be trained in improving their attention to task-relevant information and graph comprehension...
June 1, 2017: Medical Decision Making: An International Journal of the Society for Medical Decision Making
Marcello A Budroni, Andrea Baronchelli, Romualdo Pastor-Satorras
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterization of empirical data. Here we investigate the effects of the (multi)fractal properties of a signal, common in time series arising from chaotic dynamics or strange attractors, on the topology of a suitably projected network. Relying on the box-counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation...
May 2017: Physical Review. E
Barbara Dietz, Vitalii Yunko, Małgorzata Białous, Szymon Bauch, Michał Ławniczak, Leszek Sirko
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs...
May 2017: Physical Review. E
E Aurell, G Del Ferraro, E Domínguez, R Mulet
We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model...
May 2017: Physical Review. E
Marianna Milano, Pietro Hiram Guzzi, Olga Tymofieva, Duan Xu, Christofer Hess, Pierangelo Veltri, Mario Cannataro
BACKGROUND: Recently the study of the complex system of connections in neural systems, i.e. the connectome, has gained a central role in neurosciences. The modeling and analysis of connectomes are therefore a growing area. Here we focus on the representation of connectomes by using graph theory formalisms. Macroscopic human brain connectomes are usually derived from neuroimages; the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network - this process is referred to as parcellation...
June 6, 2017: BMC Bioinformatics
Jessica Zamborain-Mason, Garry R Russ, Rene A Abesamis, Abner A Bucol, Sean R Connolly
Network analysis is gaining increasing importance in conservation planning. However, which network metrics are the best predictors of metapopulation persistence is still unresolved. Here, we identify a critical limitation of graph theory-derived network metrics that have been proposed for this purpose: their omission of node self-connections. We resolve this by presenting modifications of existing network metrics, and developing entirely new metrics, that account for node self-connections. Then, we illustrate the performance of these new and modified metrics with an age-structured metapopulation model for a real-world marine reserve network case study, and we evaluate the robustness of our findings by systematically varying particular features of that network...
July 2017: Ecology Letters
Laura Ortiz-Terán, Ibai Diez, Tomás Ortiz, David L Perez, Jose Ignacio Aragón, Victor Costumero, Alvaro Pascual-Leone, Georges El Fakhri, Jorge Sepulcre
Sensory deprivation reorganizes neurocircuits in the human brain. The biological basis of such neuroplastic adaptations remains elusive. In this study, we applied two complementary graph theory-based functional connectivity analyses, one to evaluate whole-brain functional connectivity relationships and the second to specifically delineate distributed network connectivity profiles downstream of primary sensory cortices, to investigate neural reorganization in blind children compared with sighted controls. We also examined the relationship between connectivity changes and neuroplasticity-related gene expression profiles in the cerebral cortex...
June 12, 2017: Proceedings of the National Academy of Sciences of the United States of America
Volkmar Heinrich, Wooten D Simpson, Emmet A Francis
The ability of motile immune cells to detect and follow gradients of chemoattractant is critical to numerous vital functions, including their recruitment to sites of infection and-in emerging immunotherapeutic applications-to malignant tumors. Facilitated by a multitude of chemotactic receptors, the cells navigate a maze of stimuli to home in on their target. Distinct chemotactic processes direct this navigation at particular times and cell-target distances. The expedient coordination of this spatiotemporal hierarchy of chemotactic stages is the central element of a key paradigm of immunotaxis...
2017: Frontiers in Immunology
Dimitris A Pinotsis, Scott L Brincat, Earl K Miller
Memories are assumed to be represented by groups of co-activated neurons, called neural ensembles. Describing ensembles is a challenge: complexity of the underlying micro-circuitry is immense. Current approaches use a piecemeal fashion, focusing on single neurons and employing local measures like pairwise correlations. We introduce an alternative approach that identifies ensembles and describes the effective connectivity between them in a holistic fashion. It also links the oscillatory frequencies observed in ensembles with the spatial scales at which activity is expressed...
June 9, 2017: NeuroImage
Mitchell Eithun, Anne Shiu
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems, which require an enzyme and substrate to bind several times in order to add multiple phosphate groups, can be bistable. Processive systems, in contrast, require only one binding to add all phosphate groups, and were recently shown to be globally stable...
June 6, 2017: Mathematical Biosciences
Pengyun Chen, Yichen Zhang, Zhenhong Jia, Jie Yang, Nikola Kasabov
Traditional image change detection based on a non-subsampled contourlet transform always ignores the neighborhood information's relationship to the non-subsampled contourlet coefficients, and the detection results are susceptible to noise interference. To address these disadvantages, we propose a denoising method based on the non-subsampled contourlet transform domain that uses the Hidden Markov Tree model (NSCT-HMT) for change detection of remote sensing images. First, the ENVI software is used to calibrate the original remote sensing images...
June 6, 2017: Sensors
Arvid Sjölander, Johan Zetterqvist
The sibling comparison design is an important epidemiologic tool to control for unmeasured confounding, in studies of the causal effect of an exposure on an outcome. It is routinely argued that within-family associations are automatically controlled for all measured and unmeasured covariates that are shared (constant) within sets of siblings, such as early childhood environment and parental genetic makeup. However, an important lesson from modern causal inference theory is that not all types of covariate control are desirable...
July 2017: Epidemiology
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