12,120 research outputs found
Effective equidistribution of primitive rational points on expanding horospheres
We prove an effective version of a result due to Einsiedler, Mozes, Shah and
Shapira who established the equidistribution of primitive rational points on
expanding horospheres in the space of unimodular lattices in at least
dimensions. Their proof uses techniques from homogeneous dynamics and relies in
particular on measure-classification theorems --- an approach which does not
lend itself to effective bounds. We implement a strategy based on spectral
theory, Fourier analysis and Weil's bound for Kloosterman sums in order to
quantify the rate of equidistribution for a specific horospherical subgroup in
any dimension. We apply our result to provide a rate of convergence to the
limiting distribution for the appropriately rescaled diameters of random
circulant graphs.Comment: 21 pages, incorporates the referee's comments and correction
On a conjecture of Dekking : The sum of digits of even numbers
Let and denote by the sum-of-digits function in base . For
consider # \{0 \le n < N : \;\;s_q(2n) \equiv j \pmod q \}.
In 1983, F. M. Dekking conjectured that this quantity is greater than
and, respectively, less than for infinitely many , thereby claiming an
absence of a drift (or Newman) phenomenon. In this paper we prove his
conjecture.Comment: 6 pages, accepted by JTN
First-principle calculation of monovacancy and divacancy interactions with atomic oxygen in nickel: thermal expansion effects
The insertion and diffusion energies of oxygen in presence of vacancies in nickel are studied by using the first-principle projector augmented waves (PAW). When the oxygen atom is located in a substitution site, the formation of a vacancy-oxygen pair is observed. Furthermore, we show that the formation of divacancies allows the oxygen atom to migrate more easily in the metal. A model for the migration process of the three-defect system is proposed. Finally, thermal expansion effects are included in our study; it is shown that
temperature effects emphasize the diffusion
Forever Young: Aging Control For Smartphones In Hybrid Networks
The demand for Internet services that require frequent updates through small
messages, such as microblogging, has tremendously grown in the past few years.
Although the use of such applications by domestic users is usually free, their
access from mobile devices is subject to fees and consumes energy from limited
batteries. If a user activates his mobile device and is in range of a service
provider, a content update is received at the expense of monetary and energy
costs. Thus, users face a tradeoff between such costs and their messages aging.
The goal of this paper is to show how to cope with such a tradeoff, by devising
\emph{aging control policies}. An aging control policy consists of deciding,
based on the current utility of the last message received, whether to activate
the mobile device, and if so, which technology to use (WiFi or 3G). We present
a model that yields the optimal aging control policy. Our model is based on a
Markov Decision Process in which states correspond to message ages. Using our
model, we show the existence of an optimal strategy in the class of threshold
strategies, wherein users activate their mobile devices if the age of their
messages surpasses a given threshold and remain inactive otherwise. We then
consider strategic content providers (publishers) that offer \emph{bonus
packages} to users, so as to incent them to download updates of advertisement
campaigns. We provide simple algorithms for publishers to determine optimal
bonus levels, leveraging the fact that users adopt their optimal aging control
strategies. The accuracy of our model is validated against traces from the
UMass DieselNet bus network.Comment: See also http://www-net.cs.umass.edu/~sadoc/agecontrol
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