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Graph Theory

Sanchari Sircar, Nita Parekh, Gaurav Sablok
Identifying functionally coexpressed genes and modules has increasingly become important to understand the transcriptional flux and to understand large scale gene association. Application of the graph theory and combination of tools has allowed to understand the genic interaction and to understand the role of hub and non-hub proteins in plant development and its ability to cope with stress. Association genetics has also been coupled with network modules to map these key genes as e-QTLs. High throughput sequencing approaches has revolutionized the mining of the gene behavior and also the association of the genes over time-series...
2018: Methods in Molecular Biology
Miao Yu, Zhengjia Dai, Xiaowei Tang, Xiang Wang, Xiaobin Zhang, Weiwei Sha, Shuqiao Yao, Ni Shu, Xindi Wang, Jiaying Yang, Xiangyang Zhang, Xiangrong Zhang, Yong He, Zhijun Zhang
Deficit schizophrenia (DS), characterized by primary and enduring negative symptoms, has been considered as a pathophysiologically distinct schizophrenic subgroup. Neuroimaging characteristics of DS, especially functional brain network architecture, remain largely unknown. Resting-state functional magnetic resonance imaging and graph theory approaches were employed to investigate the topological organization of whole-brain functional networks of 114 male participants including 33 DS, 41 non-deficit schizophrenia (NDS) and 40 healthy controls (HCs)...
July 20, 2017: Schizophrenia Bulletin
Plamen P Angelov, Xiaowei Gu, Jose C Pr
Based on a critical analysis of data analytics and its foundations, we propose a functional approach to estimate data ensemble properties, which is based entirely on the empirical observations of discrete data samples and the relative proximity of these points in the data space and hence named empirical data analysis (EDA). The ensemble functions include the nonparametric square centrality (a measure of closeness used in graph theory) and typicality (an empirically derived quantity which resembles probability)...
October 12, 2017: IEEE Transactions on Cybernetics
Josepheen De Asis-Cruz, Mary T Donofrio, Gilbert Vezina, Catherine Limperopoulos
Newborns with congenital heart disease (CHD) requiring open heart surgery are at increased risk for neurodevelopmental disabilities. Recent quantitative MRI studies have reported disrupted growth, microstructure, and metabolism in fetuses and newborns with complex CHD. To date, no study has examined whether functional brain connectivity is altered in this high-risk population after birth, before surgery. Our objective was to compare whole-brain functional connectivity of resting state networks in healthy, term newborns (n = 82) and in term neonates with CHD before surgery (n = 30) using graph theory and network-based statistics...
2018: NeuroImage: Clinical
Yunxiao Chen, Xiaoou Li, Jingchen Liu, Gongjun Xu, Zhiliang Ying
Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster analysis...
2017: Applied Psychological Measurement
Joana B Pereira, Danielle van Westen, Erik Stomrud, Tor Olof Strandberg, Giovanni Volpe, Eric Westman, Oskar Hansson
Alzheimer's disease has a long preclinical phase during which amyloid pathology and neurodegeneration accumulate in the brain without producing overt cognitive deficits. It is currently unclear whether these early disease stages are associated with a progressive disruption in the communication between brain regions that subsequently leads to cognitive decline and dementia. In this study we assessed the organization of structural networks in cognitively normal (CN) individuals harboring amyloid pathology (A+N-), neurodegeneration (A-N+), or both (A+N+) from the prospective and longitudinal Swedish BioFINDER study...
October 3, 2017: Cerebral Cortex
Robert Griffiths, Paul A Jenkins, Dario Spanò
This paper considers the coalescent genealogy in a Wright-Fisher diffusion process, modelling the frequency of an allele, when the frequency is fixed in a bridge at two times 0 and T. Particular attention is paid to beginning and ending at zero frequency. The coalescent genealogy of the population at time t is described by two coalescent processes from t to 0 and from t to T. If the frequencies are fixed at zero then the coalescent processes have single lineages at 0 and T. Genealogy of the neutral Wright-Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright-Fisher diffusion...
October 6, 2017: Theoretical Population Biology
Thomas J O'Neill, Elizabeth M Davenport, Gowtham Murugesan, Albert Montillo, Joseph A Maldjian
Traumatic brain injury (TBI) is an important public health issue. TBI includes a broad spectrum of injury severities and abnormalities. Functional MR imaging (fMR imaging), both resting state (rs) and task, has been used often in research to study the effects of TBI. Although rs-fMR imaging is not currently applicable in clinical diagnosis of TBI, computer-aided tools are making this a possibility for the future. Specifically, graph theory is being used to study the change in networks after TBI. Machine learning methods allow researchers to build models capable of predicting injury severity and recovery trajectories...
November 2017: Neuroimaging Clinics of North America
Gerta Rücker, Guido Schwarzer
Network meta-analysis has evolved into a core method for evidence synthesis in health care. In network meta-analysis, three or more treatments for a given medical condition are compared, based on a number of clinical studies, usually randomized controlled trials. Often many different endpoints are investigated, related to different aspects of the patient's outcome, such as efficacy, safety, acceptability or costs of a treatment. Different outcomes may lead to different rankings of the treatments. We use the existing theory of partially ordered sets and show how the relations between the treatments in a network meta-analysis can be illustrated by Hasse diagrams, that is, directed graphs showing the partial order relations, and by structured scatter plots and biplots...
October 5, 2017: Research Synthesis Methods
Felix Brandl, Satja Mulej Bratec, Xiyao Xie, Afra M Wohlschläger, Valentin Riedl, Chun Meng, Christian Sorg
Cognitive emotion regulation (CER) enables humans to flexibly modulate their emotions. While local theories of CER neurobiology suggest interactions between specialized local brain circuits underlying CER, e.g., in subparts of amygdala and medial prefrontal cortices (mPFC), global theories hypothesize global interaction increases among larger functional brain modules comprising local circuits. We tested the global CER hypothesis using graph-based whole-brain network analysis of functional MRI data during aversive emotional processing with and without CER...
July 13, 2017: Cerebral Cortex
DoHyun Kim, Kendrick Kay, Gordon L Shulman, Maurizio Corbetta
The resting blood oxygen level-dependent (BOLD) signal is synchronized in large-scale brain networks (resting-state networks, RSNs) defined by interregional temporal correlations (functional connectivity, FC). RSNs are thought to place strong constraints on task-evoked processing since they largely match the networks observed during task performance. However, this result may simply reflect the presence of spontaneous activity during both rest and task. Here, we examined the BOLD network structure of natural vision, as simulated by viewing of movies, using procedures that minimized the contribution of spontaneous activity...
July 13, 2017: Cerebral Cortex
Madison S Krieger, Alex McAvoy, Martin A Nowak
In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyse how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march towards fixation or extinction. We describe motion as the swapping of individuals on graphs, and more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth (DB) updating or for any process that combines birth-death (BD) and DB updating...
October 2017: Journal of the Royal Society, Interface
Samson Abramsky, Rui Soares Barbosa, Giovanni Carù, Simon Perdrix
An important class of contextuality arguments in quantum foundations are the all-versus-nothing (AvN) proofs, generalizing a construction originally due to Mermin. We present a general formulation of AvN arguments and a complete characterization of all such arguments that arise from stabilizer states. We show that every AvN argument for an n-qubit stabilizer state can be reduced to an AvN proof for a three-qubit state that is local Clifford-equivalent to the tripartite Greenberger-Horne-Zeilinger state. This is achieved through a combinatorial characterization of AvN arguments, the AvN triple theorem, whose proof makes use of the theory of graph states...
November 13, 2017: Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
Ioannis Gkigkitzis, Ioannis Haranas, Ilias Kotsireas
Mathematical representations of brain networks in neuroscience through the use of graph theory may be very useful for the understanding of neurological diseases and disorders and such an explanatory power is currently under intense investigation. Graph metrics are expected to vary across subjects and are likely to reflect behavioural and cognitive performances. The challenge is to set up a framework that can explain how behaviour, cognition, memory, and other brain properties can emerge through the combined interactions of neurons, ensembles of neurons, and larger-scale brain regions that make information transfer possible...
2017: Advances in Experimental Medicine and Biology
Takayoshi Yoshimura, Satoshi Maeda, Tetsuya Taketsugu, Masaya Sawamura, Keiji Morokuma, Seiji Mori
We explored the reaction mechanism of the cationic rhodium(i)-BINAP complex catalysed isomerisation of allylic amines using the artificial force induced reaction method with the global reaction route mapping strategy, which enabled us to search for various reaction paths without assumption of transition states. The entire reaction network was reproduced in the form of a graph, and reasonable paths were selected from the complicated network using Prim's algorithm. As a result, a new dissociative reaction mechanism was proposed...
June 1, 2017: Chemical Science
M Thilaga, R Vijayalakshmi, R Nadarajan, D Nandagopal
Understanding and analyzing the dynamic interactions among the millions of spatially distributed and functionally connected regions in the human brain constituting a massively parallel communication system is one of the major challenges in computational neuroscience. Many studies in the recent past have employed graph theory to efficiently model, quantitatively analyze and understand the brain's electrical activity. Since, the human brain is believed to broadcast information with reduced material and metabolic costs, identifying various brain regions in the shortest pathways of information dissemination becomes essential to understand the intricacies of brain functioning...
September 28, 2017: Journal of Integrative Neuroscience
Kristy L Schlueter-Kuck, John O Dabiri
We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data are available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified...
September 2017: Chaos
Artee Bansal, Walter G Chapman, D Asthagiri
We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT)...
September 28, 2017: Journal of Chemical Physics
Lizé-Mari Ferreira, Alan Eaby, Jan Dillen
The topology of the Coulomb potential density has been studied within the context of the theory of Atoms in Molecules and has been compared with the topologies of the electron density, the virial energy density and the Ehrenfest force density. The Coulomb potential density is found to be mainly structurally homeomorphic with the electron density. The Coulomb potential density reproduces the non-nuclear attractor which is observed experimentally in the molecular graph of the electron density of a Mg dimer, thus, for the first time ever providing an alternative and energetic foundation for the existence of this critical point...
September 30, 2017: Journal of Computational Chemistry
Y F Weng, R F Qi, X D Zhang, L Zhang, J Ke, Y Zhong, F Chen, Q Xu, G M Lu
Objective: To explore the changes of brain activities in traffic accident survivors with acute stress response (ASR) within a week by using complex networks analysis method based on graph-theory, and to find out the alteration of topological properties in structural brain network. Method: From January, 2013 to February, 2016, twenty traffic accidents survivors with acute stress disorders (Acute Stress Disorder Interview, ASDI>3)and twenty healthy controls underwent the 3T diffusion tensor imaging (DTI) magnetic resonance imaging scan in Nanjing General Hospital...
September 19, 2017: Zhonghua Yi Xue za Zhi [Chinese medical journal]
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