10,517 research outputs found
On the Computation Power of Name Parameterization in Higher-order Processes
Parameterization extends higher-order processes with the capability of
abstraction (akin to that in lambda-calculus), and is known to be able to
enhance the expressiveness. This paper focuses on the parameterization of
names, i.e. a construct that maps a name to a process, in the higher-order
setting. We provide two results concerning its computation capacity. First,
name parameterization brings up a complete model, in the sense that it can
express an elementary interactive model with built-in recursive functions.
Second, we compare name parameterization with the well-known pi-calculus, and
provide two encodings between them.Comment: In Proceedings ICE 2015, arXiv:1508.0459
Multicast Network Coding and Field Sizes
In an acyclic multicast network, it is well known that a linear network
coding solution over GF() exists when is sufficiently large. In
particular, for each prime power no smaller than the number of receivers, a
linear solution over GF() can be efficiently constructed. In this work, we
reveal that a linear solution over a given finite field does \emph{not}
necessarily imply the existence of a linear solution over all larger finite
fields. Specifically, we prove by construction that: (i) For every source
dimension no smaller than 3, there is a multicast network linearly solvable
over GF(7) but not over GF(8), and another multicast network linearly solvable
over GF(16) but not over GF(17); (ii) There is a multicast network linearly
solvable over GF(5) but not over such GF() that is a Mersenne prime
plus 1, which can be extremely large; (iii) A multicast network linearly
solvable over GF() and over GF() is \emph{not} necessarily
linearly solvable over GF(); (iv) There exists a class of
multicast networks with a set of receivers such that the minimum field size
for a linear solution over GF() is lower bounded by
, but not every larger field than GF() suffices to
yield a linear solution. The insight brought from this work is that not only
the field size, but also the order of subgroups in the multiplicative group of
a finite field affects the linear solvability of a multicast network
Nonparametric maximum likelihood approach to multiple change-point problems
In multiple change-point problems, different data segments often follow
different distributions, for which the changes may occur in the mean, scale or
the entire distribution from one segment to another. Without the need to know
the number of change-points in advance, we propose a nonparametric maximum
likelihood approach to detecting multiple change-points. Our method does not
impose any parametric assumption on the underlying distributions of the data
sequence, which is thus suitable for detection of any changes in the
distributions. The number of change-points is determined by the Bayesian
information criterion and the locations of the change-points can be estimated
via the dynamic programming algorithm and the use of the intrinsic order
structure of the likelihood function. Under some mild conditions, we show that
the new method provides consistent estimation with an optimal rate. We also
suggest a prescreening procedure to exclude most of the irrelevant points prior
to the implementation of the nonparametric likelihood method. Simulation
studies show that the proposed method has satisfactory performance of
identifying multiple change-points in terms of estimation accuracy and
computation time.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1210 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Throughput and Delay Scaling in Supportive Two-Tier Networks
Consider a wireless network that has two tiers with different priorities: a
primary tier vs. a secondary tier, which is an emerging network scenario with
the advancement of cognitive radio technologies. The primary tier consists of
randomly distributed legacy nodes of density , which have an absolute
priority to access the spectrum. The secondary tier consists of randomly
distributed cognitive nodes of density with , which
can only access the spectrum opportunistically to limit the interference to the
primary tier. Based on the assumption that the secondary tier is allowed to
route the packets for the primary tier, we investigate the throughput and delay
scaling laws of the two tiers in the following two scenarios: i) the primary
and secondary nodes are all static; ii) the primary nodes are static while the
secondary nodes are mobile. With the proposed protocols for the two tiers, we
show that the primary tier can achieve a per-node throughput scaling of
in the above two scenarios. In the associated
delay analysis for the first scenario, we show that the primary tier can
achieve a delay scaling of
with . In the second scenario, with two mobility
models considered for the secondary nodes: an i.i.d. mobility model and a
random walk model, we show that the primary tier can achieve delay scaling laws
of and , respectively, where is the random walk
step size. The throughput and delay scaling laws for the secondary tier are
also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC
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