Network Graph Theory Research Articles

Brain Degeneration in ALS vs ALS-FTD is Not on a Continuum as Revealed by MRI White Matter Graph Theory Network Analysis (2593)

Brain Degeneration in ALS vs ALS-FTD is Not on a Continuum as Revealed by MRI White Matter Graph Theory Network Analysis (2593)

Application of Bipolar-Fuzzy-Graphof a Semigroup in Fuzzy Logic Systems and Networks

The ultimate objective of a piece of research work is to correlate bipolar fuzzy, Computer Network Systems( CNS) and graph theory with a semigroup. Here, we present the thought of BFG symptomatic of a network systemon SG , it’s isomorphism, the thought of BFGS, group, and the idea of anti-BF-IGS as a speculation of anti- BF-IS , BFG , and graph. We concentrate a portion of their properties and demonstrate that the CNS , Gr (V 1, A 1, B 1, µ A1, σ B1) and Gr (V 2, A 2, B 2, µ A2, σ B2) be BFGS are isomorphic if their complements are isomorphic and vice versa.

Graph theory in paediatric epilepsy: A systematic review.

Graph theoretical studies have been designed to investigate network topologies during life. Network science and graph theory methods may contribute to a better understanding of brain function, both normal and abnormal, throughout developmental stages. The degree to which childhood epilepsies exert a significant effect on brain network organisation and cognition remains unclear. The hypothesis suggests that the formation of abnormal networks associated with epileptogenesis early in life causes a disruption in normal brain network development and cognition, reflecting abnormalities in later life. Neurological diseases with onset during critical stages of brain maturation, including childhood epilepsy, may threaten this orderly neurodevelopmental process. According to the hypothesis that the formation of abnormal networks associated with epileptogenesis in early life causes a disruption in normal brain network development, it is then mandatory to perform a proper examination of children with new-onset epilepsy early in the disease course and a deep study of their brain network organisation over time. In regards, graph theoretical analysis could add more information. In order to facilitate further development of graph theory in childhood, we performed a systematic review to describe its application in functional dynamic connectivity using electroencephalographic (EEG) analysis, focussing on paediatric epilepsy.

Visualizing research trends and research theme evolution in E-learning field: 1999\u20132018

This paper aims to provide a comprehensive understanding of the evolution of major research themes and trends in e-learning research. A co-word analysis is applied for the analysis of the 21,656 keywords collected from 7214 articles published in 10 journals in the field of e-learning from the years 1999 to 2018. Specifically, a cluster analysis, social network analysis, strategic diagram, and graph theory were applied in the analysis for two time periods: 1999–2008 and 2009–2018. The study detects the bridging, popular, and core topics in e-learning research for the two periods. The research results indicate that e-learning research has undergone a health evolution over the past two decades. There is a temporal continuity of e-learning research because some research topics have kept their continuity over the studied 20 years. Meanwhile, the research traditions in the e-learning field are also continuously evolving with the development of new technologies. The results also offer useful hints on the future direction of how the field may evolve.

Beyond traditional approaches: a partial directed coherence with graph theory-based mental load assessment using EEG modality

Brain connectivity-based methods are efficient and reliable for assessing the mental workload during high task demands as the human brain is functionally interconnected during any psychological task. On the other hand, the graph theory approach is a mathematical study that draws the pairwise relationships between objects. This paper covers the deployment of graph theory concepts on the brain connectivity methods to find the complex underlying behaviors of the brain in the simplest way. Furthermore, in this work, mental workload assessments on multimedia animations were performed using a brain connectivity approach based on partial directed coherence (PDC) with graph theory analysis. Electroencephalography (EEG) data were collected from 34 adult participants at baseline and during multimedia learning tasks. The results revealed that the EEG-based connectivity approach with graph theory offers more promising results than the traditional feature extraction techniques. The connectivity approach achieved an accuracy of 85.77% in comparison with the 78.50% accuracy achieved by the existing feature extraction techniques. It is concluded that the proposed PDC method with graph theory network analysis is a better solution for cognitive load assessment during any cognitive task.

Using graph theory and social media data to assess cultural ecosystem services in coastal areas: Method development and application

The use of social media (SM) data has emerged as a promising tool for the assessment of cultural ecosystem services (CES). Most studies have focused on the use of single SM platforms and on the analysis of photo content to assess the demand for CES. Here, we introduce a novel methodology for the assessment of CES using SM data through the application of graph theory network analyses (GTNA) on hashtags associated to SM posts and compare it to photo content analysis. We applied the proposed methodology on two SM platforms, Instagram and Twitter, on three worldwide known case study areas, namely Great Barrier Reef, Galapagos Islands and Easter Island. Our results indicate that the analysis of hashtags through graph theory offers similar capabilities to photo content analysis in the assessment of CES provision and the identification of CES providers. More importantly, GTNA provides greater capabilities at identifying relational values and eudaimonic aspects associated to nature, elusive aspects for photo content analysis. In addition, GTNA contributes to the reduction of the interpreter’s bias associated to photo content analyses, since GTNA is based on the tags provided by the users themselves. The study also highlights the importance of considering data from different SM platforms, as the type of users and the information offered by these platforms can show different CES attributes. The ease of application and relative short computing processing times involved in the application of GTNA makes it a cost-effective method with the potential of being applied to large geographical scales.

TDCS effects on brain network properties during physiological aging.

Brain neural networks undergo relevant changes during physiological aging, which affect cognitive and behavioral functions. Currently, non-invasive brain stimulation techniques, such as transcranial direct current stimulation (tDCS), are proposed as tools able to modulate cognitive functions in brain aging, acting on networks properties and connectivity. Segregation and integration measures are used and evaluated by means of local clustering (segregation) and path length (integration). Moreover, to assess the balancing between them, the Small World (SW) parameter is employed, evaluating functional coupling in normal brain aging and in pathological conditions including neurodegeneration. The aim of this study was to systematically investigate the tDCS-induced effects on brain network proprieties in physiological aging. In order to reach this aim, cortical activity was acquired from healthy young and elderly subjects by means of EEG recorded before, during, and after anodal, cathodal, and sham tDCS sessions. Specifically, the aim to exploring tDCS polarity-dependent changes in the age-dependent network dynamics was based on a network graph theory application on two groups divided in young and elderly subjects. Eighteen healthy young (9 females; mean age = 24.7, SD = 3.2) and fifteen elderly subjects (9 females; mean = 70.1, SD = 5.1) were enrolled. Each participant received anodal, cathodal, or sham tDCS over the left prefrontal cortex (PFC) in three separate experimental sessions performed 1week apart. SW was computed to evaluate brain network organization. The present study demonstrates that tDCS delivered in PFC can change brain network dynamics, and tDCS-EEG coregistration data can be analyzed using graph theory to understand the induced effects of different tDCS polarities in physiological and pathological brain aging.

RETRACTED ARTICLE: An investigation of unicyclic graphs in which the isolate bondage number is equal to three in graph network theory

A set $$S $$ (of vertices) of a graph $$G$$ is termed a dominating set of $$G$$ if each vertex in $$V - S$$ is adjacent to a node in $$ S$$. A dominating set $$ S$$ such as the subgraph induced by $$S$$ has an isolated vertex is termed an isolate dominating set and also the minimum count of an isolate dominating set is termed the isolate domination number of $$G$$ and it is represented by $$\gamma_{is} (G)$$. A subset $$X \subseteq E $$ is said to be an edge dominating set if each edge in $$X - E $$ is adjacent to some edge in $$S$$. The edge domination number is that the count of the smallest edge dominating set of $$G$$ and is employed by $$\gamma^{\prime}$$. A collection of edges $$X$$ of $$E$$ is claimed to be a perfect edge dominating set if each edge not in $$ X$$ is adjacent to precisely one edge in $$X$$. The ideal edge domination number is that the minimum cardinality has taken perfect edge dominating sets of $$G$$ and is denoted by $$\gamma_{p}^{^{\prime}}$$. In this paper, we initiate the survey of bondage related to isolate domination. The isolate bondage number $$b_{is} (G)$$ is outlined to be the minimum cardinality of a collection of edges whose relieved from $$G$$ ends up in a graph $$G^{\prime}$$ fulfilling $$\gamma_{is} (G^{\prime}) > \gamma_{is} (G)$$. We obtain several results for isolate dominating set and identical values of isolate bondage number. Moreover, we investigate some bounds for the isolate bondage number, and this bound is keen and analyze under which conditions the domination parameter and isolate domination parameter are equal. Also, we found some more results for perfect edge domination, and we characterize trees for which $$\gamma^{\prime} = \gamma_{p}^{^{\prime}}$$ and further exciting results.

Computerized features of spatial arrangement of tumor-infiltrating lymphocytes from H&E images predicts survival and response to checkpoint inhibitors in gynecologic cancers.

6074 Background: Immune checkpoint inhibitors (ICI) have demonstrated success in solid tumors. In gynecologic cancers (GC), the response rate is still low (~10-15%) except in MSI-H endometrial cancer (~ 50%). Current biomarkers (e.g. PDL1 expression) have limited utility in identifying benefit from ICI in GC. In this work we evaluated the ability of computational measurements of spatial arrangement of tumor infiltrating lymphocytes (TIL) from H&E slide images in predicting overall survival (OS) and response to ICI in ovarian, cervical and endometrial cancers. Methods: The study included 151 patients, including 102 ovarian carcinomas treated with surgery and chemotherapy (D1) and another set (D2) of n=49 patients (n=14 ovarian, n=27 endometrial and n=8 cervical), treated with different ICI agents (Pembrolizumab, Nivolumab, Ipilimumab, Avelumab) in the second line setting. Progressors and non-progressors in D2 were classified according to clinical improvement and radiologic assessment by RECIST. A machine learning approach was employed to identify tumor regions on the diagnostic slides from D1 and D2 and then used to automatically identify TILs within the tumor regions. Subsequently machine learning was used to define TIL clusters based on TIL proximity, and graph network theory was used to capture measurements relating to spatial arrangement of TIL clusters. The multivariable Cox regression model (MCRM) was trained on n=51 patients from D1 to predict OS and then independently evaluated in predicting (1) OS on the hold-out n=51 patients in D1 and (2) response and progression-free survival (PFS) in D2. Results: Statistical analysis identified 7 prognostic features relating to interaction of TIL clusters with cancer nuclei. MCRM was prognostic of OS on the n=51 hold out patients in D1 (hazard ratio (HR)=2.06, 95% confidence interval [1.04- 4.07], p=0.008) and predictive of PFS in D2 (HR=2.24, CI=[1.13-4.44], p=0.03). The AUC for MCRM in predicting progression in D2 was 82%. Conclusions: Computerized features of spatial arrangement of TILs on H&E images were prognostic of OS and PFS and predicted response to ICI in three gynecological cancers. These findings need to be validated in larger, multi-site validation sets. [Table: see text]

Graph theoretical quantification of white matter reorganization after cortical stroke in mice

Stroke is a devastating disease leading to cell death and disconnection between neurons both locally and remote, often resulting in severe long-term disability. Spontaneous reorganization of areas and pathways not primarily affected by ischemia is, however, associated with albeit limited recovery of function. Quantitative mapping of whole-brain changes of structural connectivity concerning the ischemia-induced sensorimotor deficit and recovery thereof would help to target structural plasticity in order to improve rehabilitation. Currently, only in vivo diffusion MRI can extract the structural whole-brain connectome noninvasively. This approach is, however, used primarily in human studies. Here, we applied atlas-based MRI analysis and graph theory to DTI in wild-type mice with cortical stroke lesions. Using a DTI network approach and graph theory, we aimed at gaining insights into the dynamics of the spontaneous reorganization after stroke related to the recovery of function. We found evidence for altered structural integrity of connections of specific brain regions, including the breakdown of connections between brain regions directly affected by stroke as well as long-range rerouting of intra- and transhemispheric connections related to improved sensorimotor behavior.

Identification of filamentary structures in the environment of superclusters of galaxies in the Local Universe

Context.Characterization of the internal structure of the superclusters of galaxies (walls, filaments, and knots where the clusters are located) is crucial for understanding the formation of the large-scale structure and for outlining the environment where galaxies evolved in the last few gigayears.Aims.We aim to detect the compact regions of high relative density (clusters and rich groups of galaxies), to map the elongated structures of low relative density (filaments, bridges, and tendrils of galaxies), and to characterize the galaxies that populate the filaments and study the environmental effects they are subject to.Methods.We used optical galaxies with spectroscopic redshifts from the SDSS-DR13 inside rectangular boxes encompassing the volumes of a sample of 46 superclusters of galaxies up toz= 0.15. A virial approximation was applied to correct the positions of the galaxies in the redshift space for the “finger of God” projection effect. Our methodology implements different classical pattern recognition and machine-learning techniques (Voronoi tessellation, hierarchical clustering, graph-network theory, and minimum spanning trees, among others), pipelined in the Galaxy System-Finding algorithm and the Galaxy Filament-Finding algorithm.Results.In total, we detected 2705 galaxy systems (clusters and groups, of which 159 are new) and 144 galaxy filaments in the 46 superclusters of galaxies. The filaments we detected have a density contrast of above 3, with a mean value of around 10, a radius of about 2.5 h70−1Mpc, and lengths of between 9 and 130 h70−1Mpc. Correlations between the galaxy properties (mass, morphology, and activity) and the environment in which they reside (systems, filaments, and the dispersed component) suggest that galaxies closer to the skeleton of the filaments are more massive by up to 25% compared to those in the dispersed component; 70% of the galaxies in the filament region present early-type morphologies and the fractions of active galaxies (both AGNs and star-forming galaxies) seem to decrease as galaxies approach the filament.Conclusions.Our results support the idea that galaxies in filaments are subject to environmental effects leading them to be more massive (probably due to larger rates of both merging and gas accretion), less active both in star formation and nuclear activity, and prone to the density–morphology relation. These results suggest that preprocessing in large-scale filaments could have significant effects on galaxy evolution.

PERBANDINGAN PEMETAAN PENGETAHUAN PENELITIAN NUTRISI INDONESIA DENGAN THE AMERICAN JOURNAL OF CLINICAL NUTRITION TERINDEKS SCOPUS PENDEKATAN BIBLIOMETRIK DAN SCIENTOMETRICS

Scientometrics closely related to bibliometrics, which is basically the science used to calculate or map research so that it becomes knowledge information. Social Network Analysis (SNA) is a method or strategy for investigating social structures through the use of network theory and graph theory. The aim of this research is comparison mapping of nutrition research knowledge in Indonesia, indexed by Scopus by mapping nutrition research knowledge The American Journal of Clinical Nutrition (AJCN) indexed by Scopus in 2014-2018 with bibliometrics approach and Scientometrics.The research method used a systematic literature review approach consisting of problem identification, data collection, data selection, data synthesis and data analysis. The results of this study indicate that visualization of knowledge mapping of international publications of Indonesian scientific works in the field of nutrition indexed by Scopus with the AJCN 2014-2018 indexed by Scopus using the VOS viewer shows that in Indonesian research, the most researched subjects were Nutrition, Malnutrition, Children. Meanwhile, the AJCN is Obesity, Diet and Nutrition.

Eigenvalues make the difference – A network analysis of the Chinese Super League

To evaluate collective (macro) performance data in the Chinese Super League, social network analyses and graph theory were implemented in team sports performance analyses. For each team, we constructed a weighted and directed network in which nodes corresponded to players and arrows to passes. A total of 1200 matches during the 2014–2018 seasons were analysed. The results showed significant differences in general network measures among team competitive levels, match locations and match outcomes. Successful teams and home teams had significantly higher link, diameter, density and cluster coefficient values than did the unsuccessful teams or visiting teams; however, the winning teams had significantly lower density and cluster coefficient 2 values than did the losing teams. This study suggested that successful teams or teams with advantages (home, winner) have a high level of total passes and eigenvalues. This is the first report in which eigenvalues (the degree of a team’s distribution of the ball during the match) were able to capture changes in dynamics between different teams. There were positive correlations between all the network variables and the total shots and no correlations between all the network variables and goals.

The role of services content for manufacturing competitiveness: A network analysis

This paper explores the phenomenon of international servicification of manufacturing from the period 1995 to 2011. By applying empirical techniques of Social Network Analysis and graph theory, we find that the network of flows of intermediate services embodied in manufacturing exports is still slightly dense and would not correspond to a traditional centre-periphery structure. The mapping shows a numerous, highly cohesive group of countries, with China, the USA and Germany as central economies and an increasing leading role of Asian economies, which would indicate their commitment to upgrading within global value chains. We go a step further by empirically analysing the impact of the countries’ centrality in the global network of intermediate services on manufacturing competitiveness. Our findings reveal that, together with the level of embodiment of intermediate services into manufacturing exports, who the providers of those services inputs are is a key determining factor for manufacturing competitiveness.

Stability of spontaneous, correlated activity in mouse auditory cortex.

Neural systems can be modeled as complex networks in which neural elements are represented as nodes linked to one another through structural or functional connections. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system’s topological organization and to better understand its function. Here, we used two-photon calcium imaging to record spontaneous activity from the same set of cells in mouse auditory cortex over the course of several weeks. We reconstruct functional networks in which cells are linked to one another by edges weighted according to the correlation of their fluorescence traces. We show that the networks exhibit modular structure across multiple topological scales and that these multi-scale modules unfold as part of a hierarchy. We also show that, on average, network architecture becomes increasingly dissimilar over time, with similarity decaying monotonically with the distance (in time) between sessions. Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery. Our work indicates a framework for studying spontaneous activity measured by two-photon calcium imaging using computational methods and graphical models from network science. The methods are flexible and easily extended to additional datasets, opening the possibility of studying cellular level network organization of neural systems and how that organization is modulated by stimuli or altered in models of disease.

Graph-based exploration and clustering analysis of semantic spaces

The goal of this study is to demonstrate how network science and graph theory tools and concepts can be effectively used for exploring and comparing semantic spaces of word embeddings and lexical databases. Specifically, we construct semantic networks based on word2vec representation of words, which is “learnt” from large text corpora (Google news, Amazon reviews), and “human built” word networks derived from the well-known lexical databases: WordNet and Moby Thesaurus. We compare “global” (e.g., degrees, distances, clustering coefficients) and “local” (e.g., most central nodes and community-type dense clusters) characteristics of considered networks. Our observations suggest that human built networks possess more intuitive global connectivity patterns, whereas local characteristics (in particular, dense clusters) of the machine built networks provide much richer information on the contextual usage and perceived meanings of words, which reveals interesting structural differences between human built and machine built semantic networks. To our knowledge, this is the first study that uses graph theory and network science in the considered context; therefore, we also provide interesting examples and discuss potential research directions that may motivate further research on the synthesis of lexicographic and machine learning based tools and lead to new insights in this area.

Bounded Asymmetry in Road Networks

Road networks are a classical stage for applications in network science and graph theory. Meanwhile, many combinatorial problems that arise in road networks are computationally intractable. Thus, an attractive way of tackling them is through efficient heuristics with provable performance guarantees, better known as approximation algorithms. This motivates the intersection of algorithm design with the aforementioned fields. Specifically, identifying measures that characterize graphs and exploiting them in the design of algorithms may yield practical heuristics with rigorous mathematical justification. Herein, we propose a new graph measure, namely the asymmetry factor ΔG of a directed graph G, with immediate algorithmic results via a symmetrization procedure and the black box use of approximation algorithms for symmetric graphs. Crucially, we analyze the asymmetry factors of the road networks from a diverse set of twelve cities, providing empirical evidence that road networks exhibit low bounded asymmetry and thereby justifying the practical use of algorithms for symmetric graphs.

Oxytocin-Induced Changes in Intrinsic Network Connectivity in Cocaine Use Disorder: Modulation by Gender, Childhood Trauma, and Years of Use.

Cocaine use disorder (CUD) is a major public health concern with devastating social, economic, and mental health implications. A better understanding of the underlying neurobiology and phenotypic variations in individuals with CUD is necessary for the development of effective and targeted treatments. In this study, 39 women and 54 men with CUD completed a 6-min resting-state functional magnetic resonance imaging scan after intranasal oxytocin (OXY) or placebo administration. Graph-theory network analysis was used to quantify functional connectivity changes caused by OXY in striatum, anterior cingulate cortex (ACC), insula, and amygdala nodes of interest. OXY increased connectivity in the right ACC and left amygdala in males, whereas OXY increased connectivity in the right ACC and right accumbens in females. Machine learning was then used to associate treatment response (placebo minus OXY) in nodes of interest with years of cocaine use and severity of childhood trauma separately for males and females. Childhood trauma and years of cocaine use were associated with OXY-induced changes in ACC connectivity for both men and women, but connectivity changes in the amygdala were associated with years of cocaine use in men and connectivity changes in the right insula were associated with years of cocaine use in women. These findings suggest that salience network nodes (ACC and insula) are potential OXY treatment targets in CUD, with the amygdala as a treatment target for men and the accumbens as a treatment target for women.

Mapping quantum circuits on 3D nearest-neighbor architectures

In some quantum technologies, an interaction is only allowed between physically adjacent qubits, hence the nearest-neighbor requirement is needed. In such technologies, quantum gates are limited to operate on adjacent qubits. To make a quantum circuit compliant with the nearest-neighbor requirement, SWAP gates are inserted into the circuit to move the interacting qubits of a gate to be adjacent to each other. The mapping of qubits on the physical environment has an important role on reducing the number of SWAP gates and thus the circuit latency. Focusing on this issue, in this paper, a method is proposed that maps a quantum circuit onto a 3D physical hardware such as a 3D optical lattice. A new methodology for this mapping problem is proposed based on a complex network spectral clustering algorithm and graph theory, which are suitable for very large scale networks. It includes three steps: finding the order of qubit mapping, placing physical qubits, and routing. Simulation results show that the proposed mapping approach not only decreases the average number of SWAP gates by about 37% but also improves the average runtime by about 87% for the 2D architecture compared to PAQCS. Moreover, it reduces the average number of SWAP gates for the 3D architecture by 17.1% compared to the best studies in the literatures.

Chapter 11 - Cingulate role in Tourette syndrome

This chapter comprehensively reviews the published record for neurosurgical, neurostimulatory, and neuroimaging evidence of the involvement of the cingulate gyrus in Gilles de la Tourette syndrome (TS). The most noteworthy evidence comes from neuroimaging. Neuroimaging findings were rarely exclusive to the cingulate cortex and tended to implicate multiple other cortices as well. Some results are reflective of obsessive-compulsive (OC) symptoms of TS. Copious findings, however, drawn from structural magnetic resonance imaging (MRI), diffusion tensor imaging (DTI), magnetic resonance spectroscopy (MRS), resting-state functional magnetic resonance imaging (rsfMRI), task fMRI, and positron emission tomography (PET) implicate six of the eight cingulate subregions in TS. Gauged by MRI, cortical thinning and/or below-normal volume are seen in subgenual anterior cingulate cortex (sACC), pregenual anterior cingulate cortex (pACC), anterior middle cingulate cortex (aMCC), and posterior middle cingulate cortex (pMCC), correlating with tic severity in sACC, pACC, and aMCC. Moreover, in pMCC, dorsal posterior cingulate cortex (dPCC), and ventral posterior cingulate cortex (vPCC), cortical thickness is a candidate biomarker shared across siblings with TS. Loss of cortex may reflect excitotoxicity secondary to insufficient local GABAergic inhibition, a notion supported by the few relevant MRS and PET studies conducted to date, recommending continued development of GABAergic and glutamatergic pharmacologic agents to treat TS. Measurements of fractional anisotropy (FA) and apparent diffusion coefficient (ADC) obtained with DTI indicate that the white matter proximal to sACC, pACC, pMCC, and dPCC may also represent a seat of pathology in TS. rsfMRI reveals abnormal functional connectivity of pACC and dPCC with the globus pallidus internus, a favored target of therapeutic deep brain stimulation (DBS) for TS. In whole-brain network (graph theory) analysis, dPCC functional connectivity is related to the severity and complexity of tics. In task fMRI, in contrast, the pMCC seems to play a preeminent role in premonitory urges and preparation for tics as well as normal urges to urinate, swallow, and yawn. Strong monkey PET and EEG evidence ties vocal tics to spike discharges, α-activity, and regional blood flow in the pACC unleashed by failure of GABAergic inhibition in the ventral striatum. Tic suppression in fMRI scans is associated with increased blood oxygenation level-dependent activity in sACC, pACC, and aMCC, but decreased activity in pMCC and dPCC. Activity in the former three subregions may represent volitional effort, physical discomfort, and emotional distress that accompanies mounting tic urges; pMCC and dPCC may be more instrumental in amplifying than suppressing urges. Needs for future neuroimaging work in TS include longitudinal studies-particularly those striving to predict which individual pediatric patients will continue to suffer from TS as adults and studies of treatment response-particularly of behavioral therapies, which are as efficacious as pharmacology. Transcranial magnetic stimulation and related therapies such as cranial electrotherapy stimulation, which showed good efficacy in a recent trial, merit continued exploration. TS research using DTI, MRS, and PET will no doubt continue to benefit in coming years from technological advances such as ultrahigh-field scanners, multichannel head coils, and novel (including GABAergic and glutamatergic) ligands.