216 research outputs found
Limit laws for distorted return time processes for infinite measure preserving transformations
We consider conservative ergodic measure preserving transformations on
infinite measure spaces and investigate the asymptotic behaviour of distorted
return time processes with respect to sets satisfying a type of Darling-Kac
condition. We identify two critical cases for which we prove uniform
distribution laws. For this we introduce the notion of uniformly returning sets
and discuss some of their properties.Comment: 18 pages, 2 figure
Sign-time distribution for a random walker with a drifting boundary
We present a derivation of the exact sign-time distribution for a random
walker in the presence of a boundary moving with constant velocity.Comment: 5 page
Twin‐engined diagnosis of discrete‐event systems
Diagnosis of discrete-event systems (DESs) is computationally complex. This is why a variety of knowledge compilation techniques have been proposed, the most notable of them rely on a diagnoser. However, the construction of a diagnoser requires the generation of the whole system space, thereby making the approach impractical even for DESs of moderate size. To avoid total knowledge compilation while preserving efficiency, a twin-engined diagnosis technique is proposed in this paper, which is inspired by the two operational modes of the human mind. If the symptom of the DES is part of the knowledge or experience of the diagnosis engine, then Engine 1 allows for efficient diagnosis. If, instead, the symptom is unknown, then Engine 2 comes into play, which is far less efficient than Engine 1. Still, the experience acquired by Engine 2 is then integrated into the symptom dictionary of the DES. This way, if the same diagnosis problem arises anew, then it will be solved by Engine 1 in linear time. The symptom dic- tionary can also be extended by specialized knowledge coming from scenarios, which are the most critical/probable behavioral patterns of the DES, which need to be diagnosed quickly
Critical dimensions of the diffusion equation
We study the evolution of a random initial field under pure diffusion in
various space dimensions. From numerical calculations we find that the
persistence properties of the system show sharp transitions at critical
dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the
persistence exponents for low dimensions.Comment: 4 pages, 5 figure
Superprocesses as models for information dissemination in the Future Internet
Future Internet will be composed by a tremendous number of potentially
interconnected people and devices, offering a variety of services, applications
and communication opportunities. In particular, short-range wireless
communications, which are available on almost all portable devices, will enable
the formation of the largest cloud of interconnected, smart computing devices
mankind has ever dreamed about: the Proximate Internet. In this paper, we
consider superprocesses, more specifically super Brownian motion, as a suitable
mathematical model to analyse a basic problem of information dissemination
arising in the context of Proximate Internet. The proposed model provides a
promising analytical framework to both study theoretical properties related to
the information dissemination process and to devise efficient and reliable
simulation schemes for very large systems
A stochastic network with mobile users in heavy traffic
We consider a stochastic network with mobile users in a heavy-traffic regime.
We derive the scaling limit of the multi-dimensional queue length process and
prove a form of spatial state space collapse. The proof exploits a recent
result by Lambert and Simatos which provides a general principle to establish
scaling limits of regenerative processes based on the convergence of their
excursions. We also prove weak convergence of the sequences of stationary joint
queue length distributions and stationary sojourn times.Comment: Final version accepted for publication in Queueing Systems, Theory
and Application
On Kaluza's sign criterion for reciprocal power series
T. Kaluza has given a criterion for the signs of the power series of a
function that is the reciprocal of another power series. In this note the
sharpness of this condition is explored and various examples in terms of the
Gaussian hypergeometric series are given. A criterion for the monotonicity of
the quotient of two power series due to M. Biernacki and J. Krzy\.z is applied.Comment: 13 page
Operator renewal theory and mixing rates for dynamical systems with infinite measure
We develop a theory of operator renewal sequences in the context of infinite
ergodic theory. For large classes of dynamical systems preserving an infinite
measure, we determine the asymptotic behaviour of iterates of the
transfer operator. This was previously an intractable problem.
Examples of systems covered by our results include (i) parabolic rational
maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly
expanding interval maps with indifferent fixed points.
In addition, we give a particularly simple proof of pointwise dual ergodicity
(asymptotic behaviour of ) for the class of systems under
consideration.
In certain situations, including Pomeau-Manneville intermittency maps, we
obtain higher order expansions for and rates of mixing. Also, we obtain
error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a
minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated
version includes minor corrections in Sections 10 and 11, and corresponding
modifications of certain statements in Section 1. All main results are
unaffected. In particular, Sections 2-9 are unchanged from the published
versio
Investigating Cold Dust Properties of 12 Nearby Dwarf Irregular Galaxies by Hierarchical Bayesian Spectral Energy Distribution Fitting
Combining infrared and submillimeter observations and applying a two-temperature modified blackbody (TMBB) model with a hierarchical Bayesian technique, we model the spectral energy distribution of 12 nearby dwarf irregular (dIrr) galaxies. We aim to probe potential submillimeter excess emission at 350, 500, and 850 μm and investigate the properties of cold dust parameters. Based on the TMBB model with cold dust emissivity index (βc) fixed to 2, one galaxy shows 500 μm excess emission and nine galaxies show excess at 850 μm (five of them still show 850 μm excess in the case of free βc). We find that the 850 μm excess emission is easily detected in the dIrr galaxies with low star formation activity. The 850 μm excess is more frequent and more prominent in dIrr galaxies with low molecular hydrogen gas mass fraction or low ratios between cold dust mass and gas mass. As galaxies evolve, the ratios between atomic hydrogen gas mass and stellar mass decrease and the 850 μm excess emission tends to decrease or even disappear. Our results suggest that the cold dust temperature may increase, as the dIrr galaxies have more intense star formation or richer metallicity. There is a weak anticorrelation between the cold dust-to-stellar mass ratio and the specific star formation rate for our galaxies
Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System
Limit theorems for the time average of some observation functions in an
infinite measure dynamical system are studied. It is known that intermittent
phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky
reaction, are described by infinite measure dynamical systems.We show that the
time average of the observation function which is not the function,
whose average with respect to the invariant measure is finite, converges to
the generalized arcsine distribution. This result leads to the novel view that
the correlation function is intrinsically random and does not decay. Moreover,
it is also numerically shown that the time average of the observation function
converges to the stable distribution when the observation function has the
infinite mean.Comment: 8 pages, 8 figure
- …