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### Connection structures

Loredana Biacino, Giangiacomo Gerla
1991 Notre Dame Journal of Formal Logic
Whitehead, presents an axiomatized calculus of individuals based on a primitive predicate "x is connected with y".  ...  To prove that, in a sense, the connection structure theory coincides with the orthocomplemented lattice theory, we associate with every connection structure (R, C) an algebraic structure (£,<, -) as follows  ...  The points in a connection structure A point of a connection structure (R, C) is defined by Clarke as a nonempty subset P of R such that (i) xeP,γEP=>xCy (ii) xEP,yEP 9 xθy =>XΛyEP (iii) xEP, y>x=*yeP  ...

### Structured Connectivity Augmentation [article]

Fedor V. Fomin, Petr A. Golovach, Dimitrios M. Thilikos
2017 arXiv   pre-print
We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H?  ...  For the unweighted variants of structured augmentation problems, i.e. the problems where the task is to identify whether there is a superposition of graphs of required connectivity, we provide necessary  ...  Structured k-Connectivity Augmentation Let us note that for k = 1 this is Structured Connectivity Augmentation and for k = 2 this is Structured 2-Connectivity Augmentation.  ...

### Structure equations of generalized connections

1982 Časopis pro pěstování matematiky
For a so-called homogeneous connection we obtain an interesting generalization of the classical structure equation of a principal connection.  ...  The structure equation of a homogeneous connection is (s) 8 £ ? -w, where o p (x) or £ f (x) is (9) d c co = -S Q (co,(o) + Q, where C is the associated connection.  ...

### Using structural connectivity to augment community structure in EEG functional connectivity

Katharina Glomb, Emeline Mullier, Margherita Carboni, Maria Rubega, Giannarita Iannotti, Sebastien Tourbier, Martin Seeber, Serge Vulliemoz, Patric Hagmann
2020 Network Neuroscience
Here, we investigate the relationship between white matter structural connectivity (SC) and large scale network structure encoded in EEG-FC.  ...  Thereby, FC between nearby, structurally connected brain regions increases while FC between non-connected regions remains unchanged, resulting in an increase in genuine, SC-mediated FC.  ...  RESULTS SC Provides Additional Predictive Power for EEG-FC Our goal is to use the structural connectivity matrix to boost functional connectivity that is mediated by white matter anatomical connections  ...

### Using structural connectivity to augment community structure in EEG functional connectivity [article]

Katharina Glomb, Emeline Mullier, Margherita Carboni, Maria Rubega, Giannarita Iannotti, Sebastien Tourbier, Martin Seeber, Serge Vulliemoz, Patric Hagmann
2019 bioRxiv   pre-print
Thereby, FC between nearby, structurally connected brain regions is increased while FC between non-connected regions remains unchanged.  ...  Here, we use information from white matter structural connectivity (SC) to attenuate the impact of volume conduction on EEG-FC.  ...  Finally, by identification of the ROIs connected by fibers , a graph is constructed and the structural connectivity matrices are estimated for each individual.  ...

### Connections with Symplectic Structures

A. K. M. Nazimuddin, Md. Showkat Ali
2016 American Journal of Computational Mathematics
In this article we review the basic notions with examples of symplectic structures and show the connections of symplectic geometry with the various branches of differential geometry using important theorems  ...  The following result was obtained using Seiberg-Witten theory: Theorem 4.2 (Taubes Theorem) The connected sum of an odd number of copies of 2  does not admit a symplectic structure (even though it admits  ...  In this work, we have developed a connection between various branches of differential geometry with symplectic geometry.  ...

### Connectivity of Turing structures [article]

Teemu Leppanen, Mikko Karttunen, R.A. Barrio, Kimmo Kaski
2003 arXiv   pre-print
., eutactic local structures. Also a mechanism for the observed "connectivity transition" is proposed.  ...  In the two-dimensional real space spotty structures we find some evidence of twin domain formation, of the kind seen in crystalline materials.  ...  [19, 20] ), while the issue of pattern structure and its connectivity has received less attention.  ...

### Connectivity Structure of Systems [article]

Remco Bras
2011 arXiv   pre-print
In this paper, we consider to what degree the structure of a linear system is determined by the system's input/output behavior.  ...  First, we show that for a number of parameterizations, we can characterize when two systems have the same structure.  ...  Systems, graph structure and equivalent structures In this section, we recall the definition of a discrete-time LTI system and its associated graph structure.  ...

### Structure connectivity and substructure connectivity of twisted hypercubes [article]

Dong Li, Xiaolan Hu, Huiqing Liu
2018 arXiv   pre-print
The T-structure connectivity κ(G; T) (or resp., T-substructure connectivity κ^s(G; T)) of G is the minimum number of a set of subgraphs F={T_1, T_2, ..., T_m} (or resp., F={T^'_1, T^'_2, ..., T^'_m}) such  ...  Let G be a graph and T a certain connected subgraph of G.  ...  However, determining the K 1,r -structure connectivity and K 1,r -substructure connectivity of H n with r ≥ 5 remain open.  ...

### Inference of functional connectivity from structural brain connectivity

Fani Deligianni, Emma C. Robinson, Christian F. Beckmann, David Sharp, A. David Edwards, Daniel Rueckert
2010 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro
Here, we predict functional connectivity from structural connectivity, explicitly, by utilizing a predictive model based on PCA and CCA.  ...  Studies that examine the relationship of functional and structural connectivity are tremendously important in interpreting neurophysiological data.  ...  Fig. 2 . 2 Inference of functional connectivity from structural connectivity. a) The original functional connectivity matrix, b) The structural connectivity matrix, c) The predicted functional connectivity  ...

### Contribution of structural connectivity to MEG functional connectivity [article]

Anirudh Wodeyar, Ramesh Srinivasan
2019 bioRxiv   pre-print
of structural connectivity to functional connectivity.  ...  Structural connectivity by axonal fiber bundles provides the substrate for transmission of action potentials across the brain.  ...  structural connectivity model.  ...

### Projective structures and ρ-connections [article]

2016 arXiv   pre-print
Thomas's approach to the projective structures, over the complex analytic category, by involving the ρ-connections.  ...  control of the projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold P is endowed with a complex projective structure  ...  the projective space is the only Fano manifold which admits a projective structure (compare [7, (5. 3)] , [6] , [10] ). j are the local connection forms of a connection on M .  ...

### Higher Complex Structures and Flat Connections [article]

Alexander Thomas
2021 arXiv   pre-print
We show that higher complex structures can be deformed to flat connections.  ...  More precisely we show that the cotangent bundle of the moduli space of higher complex structures can be included into a 1-parameter family of spaces of flat connections.  ...  Find an isomorphism χ and a hermitian structure h such that C(λ) = λΦ + A + λ −1 Φ * h is a flat connection where A is the Chern connection.  ...

### Domination structure in 3-connected graphs [article]

Misa Nakanishi
2019 arXiv   pre-print
From a recent perspective, the structure of a 3-connected graph is studied in this paper. It stipulates the minimum dominating set of a 3-connected graph.  ...  Also, we count the number of structures, as a consequence, the upper bound is obtained. By it, the minimum dominating set of a 3-connected graph is determined in polynomial time.  ...  That is to say, a 3-connected graph is explained only by this structure to have a minimum dominating set. Especially, we call the structure that attains a d-set the domination structure.  ...

### Pre-symplectic structures on the space of connections [article]

Tosiaki Kori
2019 arXiv   pre-print
We shall describe (i) a pre-symplectic structure on the space of connections of the trivial SU(n)-bundle over X that comes from the canonical symplectic structure on the cotangent bundle of the connection  ...  space, and (ii) a pre-symplectic structure on the space of flat connections of the trivial SU(n)-bundle over M that have null charge.  ...  Hence the pre-symplectic structure (0.1) on A(X) descends to the moduli space of flat connections M ♭ (X) = A ♭ (X)/G 0 (X).  ...
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