2,619 research outputs found
High frequency sampling of a continuous-time ARMA process
Continuous-time autoregressive moving average (CARMA) processes have recently
been used widely in the modeling of non-uniformly spaced data and as a tool for
dealing with high-frequency data of the form , where
is small and positive. Such data occur in many fields of application,
particularly in finance and the study of turbulence. This paper is concerned
with the characteristics of the process (Y_{n\Delta})_{n\in\bbz}, when
is small and the underlying continuous-time process (Y_t)_{t\in\bbr}
is a specified CARMA process.Comment: 13 pages, submitte
The phase transition in the configuration model
Let be a random graph with a given degree sequence , such as a
random -regular graph where is fixed and . We study
the percolation phase transition on such graphs , i.e., the emergence as
increases of a unique giant component in the random subgraph obtained by
keeping edges independently with probability . More generally, we study the
emergence of a giant component in itself as varies. We show that a
single method can be used to prove very precise results below, inside and above
the `scaling window' of the phase transition, matching many of the known
results for the much simpler model . This method is a natural extension
of that used by Bollobas and the author to study , itself based on work
of Aldous and of Nachmias and Peres; the calculations are significantly more
involved in the present setting.Comment: 37 page
A surprising property of the least eigenvalue of a graph
AbstractLet λ(G) be the least eigenvalue of a graph G. A real number r has the induced subgraph property provided λ(G)<r implies G has an induced subgraph H with λ(H)=r. It is shown that the only numbers with the induced subgraph property are 0, −1, −2, and −2
Small Scale Retrodigitization
summary:The digitization of papers born in the print-only era is vital for the health of the mathematical record. Many large scale retrodigitization projects are underway and, at this point, probably more that half of the mathematical history has been finished. Many smaller journals and books remain to be done. This paper gives a framework within which these may also be completed. It uses the digitization of the Canadian Journal of Mathematics (53,000 pages), completed as a one-man project over a few months, as the working example. The project described herein not only may be used as a model for similar efforts but also indicates some interesting problems yet to be solved
Social Stratification and Political Behavior: An Emphasis upon Structural Dynamics
The interrelationship of social stratification factors (Social stratification is the relative position of ranks, and their distribution found within a society.) and political institutions is a frequent problem of interest to social scientists. In studies of the relationship between political behavior and social stratification, there are numerous analyses of location or rank. in the stratification system and their effects on political behavior. There also are studies on the relationship between social mobility, status crystallization, (Social mobility for the purposes of this study concerns the comparative social rank between a father and his son.) and political behavior. The interaction between mobility, crystallization, and politics has been alluded to throughout the literature, but there appear to be few systematic propositions or theories about this area. We can examine this problem in the works of learned men of many disciplines.
Status crystallization is an individual\u27s consistency in rank for several status dimensions, specifically occupation, education, ethnicity, religion, and income
Social Stratification and Political Behavior: An Emphasis upon Structural Dynamics
The interrelationship of social stratification factors (Social stratification is the relative position of ranks, and their distribution found within a society.) and political institutions is a frequent problem of interest to social scientists. In studies of the relationship between political behavior and social stratification, there are numerous analyses of location or rank. in the stratification system and their effects on political behavior. There also are studies on the relationship between social mobility, status crystallization, (Social mobility for the purposes of this study concerns the comparative social rank between a father and his son.) and political behavior. The interaction between mobility, crystallization, and politics has been alluded to throughout the literature, but there appear to be few systematic propositions or theories about this area. We can examine this problem in the works of learned men of many disciplines.
Status crystallization is an individual\u27s consistency in rank for several status dimensions, specifically occupation, education, ethnicity, religion, and income
Deformed Gaussian Orthogonal Ensemble description of Small-World networks
The study of spectral behavior of networks has gained enthusiasm over the
last few years. In particular, Random Matrix Theory (RMT) concepts have proven
to be useful. In discussing transition from regular behavior to fully chaotic
behavior it has been found that an extrapolation formula of the Brody type can
be used. In the present paper we analyze the regular to chaotic behavior of
Small World (SW) networks using an extension of the Gaussian Orthogonal
Ensemble. This RMT ensemble, coined the Deformed Gaussian Orthogonal Ensemble
(DGOE), supplies a natural foundation of the Brody formula. SW networks follow
GOE statistics till certain range of eigenvalues correlations depending upon
the strength of random connections. We show that for these regimes of SW
networks where spectral correlations do not follow GOE beyond certain range,
DGOE statistics models the correlations very well. The analysis performed in
this paper proves the utility of the DGOE in network physics, as much as it has
been useful in other physical systems.Comment: Replaced with the revised version, accepted for publication in Phys.
Rev.
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