Using Geometry of the Set of Symmetric Positive Semidefinite Matrices to Classify Structural Brain Networks

2018 ◽  
pp. 257-267
Author(s):  
Mikhail Belyaev ◽  
Yulia Dodonova ◽  
Daria Belyaeva ◽  
Egor Krivov ◽  
Boris Gutman ◽  
...  
Keyword(s):  
Brain Networks ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Structural Brain

scholarly journals Intergenerational transmission of the patterns of functional and structural brain networks

iScience ◽  
2021 ◽  
pp. 102708
Author(s):  
Yu Takagi ◽  
Naohiro Okada ◽  
Shuntaro Ando ◽  
Noriaki Yahata ◽  
Kentaro Morita ◽  
...  
Keyword(s):  
Intergenerational Transmission ◽  
Brain Networks ◽  
Structural Brain

scholarly journals Association between age of cannabis initiation and gray matter covariance networks in recent onset psychosis

2021 ◽  
Author(s):  
Nora Penzel ◽  
◽  
Linda A. Antonucci ◽  
Linda T. Betz ◽  
Rachele Sanfelici ◽  
...  
Keyword(s):  
Gray Matter ◽  
Inferior Frontal Gyrus ◽  
Brain Networks ◽  
Developmental Trajectory ◽  
Cannabis Use ◽  
Brain Maturation ◽  
Confounding Factors ◽  
Recent Onset ◽  
Increased Risk ◽  
Structural Brain

AbstractCannabis use during adolescence is associated with an increased risk of developing psychosis. According to a current hypothesis, this results from detrimental effects of early cannabis use on brain maturation during this vulnerable period. However, studies investigating the interaction between early cannabis use and brain structural alterations hitherto reported inconclusive findings. We investigated effects of age of cannabis initiation on psychosis using data from the multicentric Personalized Prognostic Tools for Early Psychosis Management (PRONIA) and the Cannabis Induced Psychosis (CIP) studies, yielding a total sample of 102 clinically-relevant cannabis users with recent onset psychosis. GM covariance underlies shared maturational processes. Therefore, we performed source-based morphometry analysis with spatial constraints on structural brain networks showing significant alterations in schizophrenia in a previous multisite study, thus testing associations of these networks with the age of cannabis initiation and with confounding factors. Earlier cannabis initiation was associated with more severe positive symptoms in our cohort. Greater gray matter volume (GMV) in the previously identified cerebellar schizophrenia-related network had a significant association with early cannabis use, independent of several possibly confounding factors. Moreover, GMV in the cerebellar network was associated with lower volume in another network previously associated with schizophrenia, comprising the insula, superior temporal, and inferior frontal gyrus. These findings are in line with previous investigations in healthy cannabis users, and suggest that early initiation of cannabis perturbs the developmental trajectory of certain structural brain networks in a manner imparting risk for psychosis later in life.

scholarly journals A trace bound for integer-diagonal positive semidefinite matrices

2020 ◽  
Vol 8 (1) ◽  
pp. 14-16
Author(s):  
Lon Mitchell
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrix ◽  
Positive Semidefinite Matrices ◽  
Semidefinite Matrix

AbstractWe prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.

scholarly journals Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Benju Wang ◽  
Yun Zhang
Keyword(s):  
Singular Values ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Fischer’S Inequality ◽  
New Inequalities

In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.

scholarly journals A Characterization of Polynomial Density on Curves via Matrix Algebra

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1231
Author(s):  
Carmen Escribano ◽  
Raquel Gonzalo ◽  
Emilio Torrano
Keyword(s):  
Matrix Algebra ◽  
Optimization Problems ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Alternative Proof ◽  
General Context ◽  
Positive Semidefinite Matrices ◽  
Jordan Curves ◽  
Point Evaluations

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L 2 ( μ ) , with μ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure μ . To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, γ ( M ) and λ ( M ) , associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index γ and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index γ that will allow us to give an alternative proof of Thomson’s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.

scholarly journals A class of positive semidefinite matrices

1987 ◽  
Vol 93 ◽  
pp. 121-126
Author(s):  
A.M. Russell ◽  
C.J.F. Upton
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrices

scholarly journals Altered Structural Brain Networks in Tuberous Sclerosis Complex

2015 ◽  
Vol 26 (5) ◽  
pp. 2046-2058 ◽  
Author(s):  
Kiho Im ◽  
Banu Ahtam ◽  
Daniel Haehn ◽  
Jurriaan M. Peters ◽  
Simon K. Warfield ◽  
...  
Keyword(s):  
Tuberous Sclerosis ◽  
Tuberous Sclerosis Complex ◽  
Brain Networks ◽  
Structural Brain
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