27 research outputs found
Network growth model with intrinsic vertex fitness
© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions
Програмне опрацювання гістологічних даних зрізів нервової тканини
In article the program designed for analysis of a brain sections is described. It allows to calculate the basic geometrical parameters of neuron’s bodies. The self-acting recognition of neurons is based on gradation of contrast and colour of cells bodies. The methods of building of digital templates conforming the actual photographic images and methods of approximation of the forms of neurons to more prime figures are described.Для морфометричного аналізу зразків мозку розроблено програму, яка дозволяє обраховувати основні геометричні параметри тіл нейронів. Автоматичне розпізнавання нейронів базується на градації контрасту та кольору клітинних тіл. Описано методи створення цифрових матриць, що відповідають реальним фотозображенням, і методи апроксимації форм нейронів до більш простих фігур. Для морфометричного аналізу зразків мозку розроблено програму, яка дозволяє обраховувати основні геометричні параметри тіл нейронів. Автоматичне розпізнавання нейронів базується на градації контрасту та кольору клітинних тіл. Описано методи створення цифрових матриць, що відповідають реальним фотозображенням, і методи апроксимації форм нейронів до більш простих фігур.
Quest for Rare Events in three-dimensional Mesoscopic Disordered Metals
The study reports on the first large statistics numerical experiment
searching for rare eigenstates of anomalously high amplitudes in
three-dimensional diffusive metallic conductors. Only a small fraction of a
huge number of investigated eigenfunctions generates the far asymptotic tail of
their amplitude distribution function. The relevance of the relationship
between disorder and spectral averaging, as well as of the quantum transport
properties of the investigated mesoscopic samples, for the numerical
exploration of eigenstate statistics is divulged. The quest provides exact
results to serve as a reference point in understanding the limits of
approximations employed in different analytical predictions, and thereby the
physics (quantum vs semiclassical) behind large deviations from the universal
predictions of random matrix theory.Comment: 5 pages, 3 embedded EPS figures, figure 3 replaced with new findings
on spectral vs disorder averagin
Statistics of Rare Events in Disordered Conductors
Asymptotic behavior of distribution functions of local quantities in
disordered conductors is studied in the weak disorder limit by means of an
optimal fluctuation method. It is argued that this method is more appropriate
for the study of seldom occurring events than the approaches based on nonlinear
-models because it is capable of correctly handling fluctuations of the
random potential with large amplitude as well as the short-scale structure of
the corresponding solutions of the Schr\"{o}dinger equation. For two- and
three-dimensional conductors new asymptotics of the distribution functions are
obtained which in some cases differ significantly from previously established
results.Comment: 17 pages, REVTeX 3.0 and 1 Postscript figur
Correlation Exponent and Anomalously Localized States at the Critical Point of the Anderson Transition
We study the box-measure correlation function of quantum states at the
Anderson transition point with taking care of anomalously localized states
(ALS). By eliminating ALS from the ensemble of critical wavefunctions, we
confirm, for the first time, the scaling relation z(q)=d+2tau(q)-tau(2q) for a
wide range of q, where q is the order of box-measure moments and z(q) and
tau(q) are the correlation and the mass exponents, respectively. The influence
of ALS to the calculation of z(q) is also discussed.Comment: 6 pages, 3 figure
A novel superconducting glass state in disordered thin films in Clogston limit
A theory of mesoscopic fluctuations in disordered thin superconducting films
in a parallel magnetic field is developed. At zero temperature, the
superconducting state undergoes a phase transition into a state characterized
by superfluid densities of random signs, instead of a spin polarized disordered
Fermi liquid phase. Consequently, the ground state belongs to the same
universality class as the 2D XY spin glass. As the magnetic field increases
further, mesoscopic pairing states are nucleated in an otherwise homogeneous
spin polarized disordered Fermi liquid. The statistics of these pairing states
is universal depending on the sheet conductance of the 2D film.Comment: Latex, 39 pages, 2 figures included; to appear in Int. J. Mod. Phys.
Kondo Temperature for the Two-Channel Kondo Models of Tunneling Centers
The possibility for a two-channel Kondo () non Fermi liquid state to
appear in a metal as a result of the interaction between electrons and movable
structural defects is revisited. As usual, the defect is modeled by a heavy
particle moving in an almost symmetric double-well potential (DWP). Taking into
account only the two lowest states in DWP is known to lead to a Kondo-like
Hamiltonian with rather low Kondo temperature, . We prove that, in
contrast to previous believes, the contribution of higher excited states in DWP
does not enhance . On the contrary, is reduced by three orders of
magnitude as compared with the two-level model: the prefactor in is
determined by the spacing between the second and the third levels in DWP rather
than by the electron Fermi energy. Moreover, , turns out to be
parametrically smaller than the splitting between the two lowest levels.
Therefore, there is no microscopic model of movable defects which may justify
non-Fermi liquid phenomenology.Comment: 5 pages, 4 .eps figure
Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations
We reveal a general explicit relation between the statistics of delay times
in one-channel reflection from a mesoscopic sample of any spatial dimension and
the statistics of the eigenfunction intensities in its closed counterpart. This
opens a possibility to use experimentally measurable delay times as a sensitive
probe of eigenfunction fluctuations. For the particular case of quasi-one
dimensional geometry of the sample we use an alternative technique to derive
the probability density of partial delay times for any number of open channels.Comment: 12 pages; published version with updated reference
Real roots of Random Polynomials: Universality close to accumulation points
We identify the scaling region of a width O(n^{-1}) in the vicinity of the
accumulation points of the real roots of a random Kac-like polynomial
of large degree n. We argue that the density of the real roots in this region
tends to a universal form shared by all polynomials with independent,
identically distributed coefficients c_i, as long as the second moment
\sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to
the previously reported abrupt) and quite nontrivial suppression of the number
of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled
as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been
removed. 10 pages, 12 eps figures. This version contains all updates, clearer
pictures and some more thorough explanation
Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions
We consider Dirac fermions interacting with a disordered non-Abelian vector
potential. The exact solution is obtained through a special type of conformal
field theory including logarithmic correlators, without resorting to the
replica or supersymmetry approaches. It is shown that the proper treatment of
the conformal theory leads to a different multifractal scaling behaviour than
initially expected. Moreover, the previous replica solution is found to be
incorrect at the level of higher correlation functions.Comment: 4 pages, no figure