113,076 research outputs found
KRONECKER GRAPHS
No full textDiplomsko delo se osredotoča na preučevanje Kroneckerjevih grafov. Najprej je predstavljena motivacija za vpeljavo in študij Kroneckerjevih grafov. V nadaljevanju je definiran Kroneckerjev ali tenzorski produkt matrik ter Kroneckerjev produkt grafov in njune osnovne lastnosti. V naslednjih poglavjih se pozornost nameni lastnostim Kroneckerjevih in stohastičnih Kroneckerjevih grafov. Predstavljen je porazdelitveni zakon stopnje posameznih vozlišč teh grafov. Dokazana sta zgostitveni potenčni zakon med številom vozlišč in številom povezav ter ohranjanje efektivnega premera glede na začetni graf. Pri stohastičnih Kroneckerjevih grafih so podani potrebni in zadostni pogoji za povezanost ter obstoj velike povezane komponente tega grafa. Dokazano je tudi, če je graf povezan, je premer v tem grafu konstanten. Na koncu so prikazani primeri praktične uporabe teorije, predstavljene skozi vso diplomsko nalogo.This graduation thesis focuses on the study of Kronecker graphs. First the motivation for introduction and investigation of Kronecker graphs is presented. Next are the definitions of the Kronecker or tensor product of matrices and the Kronecker product of graphs, introduced together with their basic properties. In the following chapters the focus is oriented to the study of the properties of Kronecker and stochastic Kronecker graphs. One of the important properties is the behaviour of the degree distribution. This result is folowed by the proof of the densification power law between the number of edges and the number of nodes and the proof of the conservation of the size of the effective diameter regarding the initiator graph. Next, necessary and sufficient conditions are proven for the connectivity and the existance of a giant component in the stochastic Kronecker graphs. From this follows that: under the parameters that the graph is connected, it also has a constant diameter. For conclusion examples for practical use of the theory presented throughout the thesis are given
Extensions of Functors From Set to V-cat
No full textWe show that for a commutative quantale V every functor from Set to V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric
Chronique des Églises orientales
No full textLacombe J., Grégoire V., O. E., G P., Balan J., V E. Chronique des Églises orientales. In: Échos d'Orient, tome 20, n°121, 1921. pp. 86-111
Chronique des Églises orientales
No full textLacombe J., Grégoire V., O. E., G P., Balan J., V E. Chronique des Églises orientales. In: Échos d'Orient, tome 20, n°121, 1921. pp. 86-111
Extending Set Functors to Generalised Metric Spaces
No full textFor a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor TV on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.
Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we study how their solutions (that is, the final coalgebras) are related via change of base.
Mathematically, the heart of the matter is to show that, for any commutative quantale V, the “discrete functor Set → V-cat from sets to categories enriched over V is V-cat-dense and has a density presentation that allows us to compute left-Kan extensions along D
Morphological and genetic variation in populations of Sitana marudhamneydhal and the validity of Sitana attenboroughii
No full textBalan, A., Jude, D., Narayanan, Surya, Varma, Sandeep, Deepak, V. (2021): Morphological and genetic variation in populations of Sitana marudhamneydhal and the validity of Sitana attenboroughii. Zootaxa 4964 (3): 523-540, DOI: https://doi.org/10.11646/zootaxa.4964.3.
author-bios-SRD-19-0063.R1 – Supplemental material for The Network Structure of Police Misconduct
No full textSupplemental material, author-bios-SRD-19-0063.R1 for The Network Structure of Police Misconduct by George Wood, Daria Roithmayr and Andrew V. Papachristos in Socius</p
On-line simulation and rule based control applied in control of technological processes
No full textElectrical Engineering Research Report EER
On-line simulation and rule based control applied in control of non-linear processes
No full textElectrical Engineering Research Repor
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