Search results for "Graph theory"
showing 10 items of 784 documents
Ultrametric Vs. Quantum Query Algorithms
2014
Ultrametric algorithms are similar to probabilistic algorithms but they describe the degree of indeterminism by p-adic numbers instead of real numbers. This paper introduces the notion of ultrametric query algorithms and shows an example of advantages of ultrametric query algorithms over deterministic, probabilistic and quantum query algorithms.
One-loop results for the quark-gluon vertex in arbitrary dimension
2000
Results on the one-loop quark-gluon vertex with massive quarks are reviewed, in an arbitrary covariant gauge and in arbitrary space-time dimension. We show how it is possible to get on-shell results from the general off-shell expressions. The corresponding Ward-Slavnov-Taylor identity is discussed.
Structure of eigenvectors of random regular digraphs
2018
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we study the structure of the kernel of submatrices of $M-z\,{\rm Id}$, formed by removing a subset of rows. We show that with large probability the kernel consists of two non-intersecting types of vectors, which we call very steep and gradual with many levels. As a corollary, we show, in particular, that every eigenvector of $M$, except for constant multiples of $(1,1,\dots,1)$, possesses a weak delocalization property: its level sets have cardin…
Growth, percolation, and correlations in disordered fiber networks
1997
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
Spatial graphs and Convolutive Models
2020
In the last two decades, many complex systems have benefited from the use of graph theory, and these approaches have shown robust applicability in the field of finance, computer circuits and in biological systems. Large scale models of brain systems make also a great use of random graph models. Graph theory can be instrumental in modeling the connectivity and spatial distribution of neurons, through a characterization of the relative topological properties. However, all approaches in studying brain function have been so far limited to use experimental constraints obtained at a macroscopic level (e.g. fMRI, EEG, MEG, DTI, DSI). In this contribution, we present a microscopic use (i.e. at the …
Conformations of Star-Branched Polyelectrolytes
1996
Scaling theory describing the conformations of weakly charged star-branched polyelectrolytes in dilute and semi-dilute salt-free solutions is developed. The dependence of the star size on the number of branches as well as on the solution concentration is analyzed. It is shown that the star size increases with an increase in the number of branches, f, at small f and tends to a constant value at large f. An increase in the concentration of stars in a solution results in a decrease in the star size R according to the power low : R ∼ c -1/3 in the range of a moderate concentration and R ∼ c -1/4 at larger concentration. For stars with a small number of branches the behavior R ∼ c -1/2 in a cert…
Fields of values of odd-degree irreducible characters
2019
Abstract In this paper we clarify the quadratic irrationalities that can be admitted by an odd-degree complex irreducible character χ of an arbitrary finite group. Write Q ( χ ) to denote the field generated over the rational numbers by the values of χ, and let d > 1 be a square-free integer. We prove that if Q ( χ ) = Q ( d ) then d ≡ 1 (mod 4) and if Q ( χ ) = Q ( − d ) , then d ≡ 3 (mod 4). This follows from the main result of this paper: either i ∈ Q ( χ ) or Q ( χ ) ⊆ Q ( exp ( 2 π i / m ) ) for some odd integer m ≥ 1 .
Left-star order structure of Rickart *-rings
2015
Janowitz proved in 1983 that the initial segments of a Rickart *-ring with the star order are orthomodular posets. In this paper, the same result is proved for the left-star order , which was introduced by Marovtet al., by finding an orthogonality which corresponds to in a certain way and then applying a result proved by Cīrulis which states that the initial segments of any quasi-orthomodular set are orthomodular.
Daži trīssakarīgi grafi un to saimes bez Hamiltona cikliem
2013
These manuscripts (in Latvian) contain examples of graphs without Hamiltonian cycles. See the flower snark J5 on the page 13. The date here 1.6.78.
Pulsations in the late-type Be star HD 50 209 detected by CoRoT
2009
The presence of pulsations in late-type Be stars is still a matter of controversy. It constitutes an important issue to establish the relationship between non-radial pulsations and the mass-loss mechanism in Be stars. To contribute to this discussion, we analyse the photometric time series of the B8IVe star HD 50209 observed by the CoRoT mission in the seismology field. We use standard Fourier techniques and linear and non-linear least squares fitting methods to analyse the CoRoT light curve. In addition, we applied detailed modelling of high-resolution spectra to obtain the fundamental physical parameters of the star. We have found four frequencies which correspond to gravity modes with az…