46 research outputs found
Identifying statistical dependence in genomic sequences via mutual information estimates
Questions of understanding and quantifying the representation and amount of
information in organisms have become a central part of biological research, as
they potentially hold the key to fundamental advances. In this paper, we
demonstrate the use of information-theoretic tools for the task of identifying
segments of biomolecules (DNA or RNA) that are statistically correlated. We
develop a precise and reliable methodology, based on the notion of mutual
information, for finding and extracting statistical as well as structural
dependencies. A simple threshold function is defined, and its use in
quantifying the level of significance of dependencies between biological
segments is explored. These tools are used in two specific applications. First,
for the identification of correlations between different parts of the maize
zmSRp32 gene. There, we find significant dependencies between the 5'
untranslated region in zmSRp32 and its alternatively spliced exons. This
observation may indicate the presence of as-yet unknown alternative splicing
mechanisms or structural scaffolds. Second, using data from the FBI's Combined
DNA Index System (CODIS), we demonstrate that our approach is particularly well
suited for the problem of discovering short tandem repeats, an application of
importance in genetic profiling.Comment: Preliminary version. Final version in EURASIP Journal on
Bioinformatics and Systems Biology. See http://www.hindawi.com/journals/bsb
Adaptive policies for spatial Reuse ring networks
A slotted ring that allows simultaneous transmissions of messages by different users is considered. Such a ring network is commonly called ring with spatial resue. It can achieve significantly higher throughtput than standard token rings but it also can lead to unfairness problems. Policies that operate in cycles and quarantee that a certain number (quota) of packets will be transmitted by every node in every cycle have been considered before to alleviate the unfairness. We consider here the problem of designing a policy that will result in a stable system whenever the arrival rates are whitin the stability region of a ring with spatial reuse (the stability region is defined as the set of node arrival rates for which there is a policy that makes the ring stable). We provide such a policy. No knowledge of arrival rates or message destination probabilities are required. The policy is an adaptive version of the quota policies and can be implemented with the same distributed mechanism. We shall use Lyapunov test function techniques together with the regenerative approach to derive our main results
Leadership Statistics in Random Structures
The largest component (``the leader'') in evolving random structures often
exhibits universal statistical properties. This phenomenon is demonstrated
analytically for two ubiquitous structures: random trees and random graphs. In
both cases, lead changes are rare as the average number of lead changes
increases quadratically with logarithm of the system size. As a function of
time, the number of lead changes is self-similar. Additionally, the probability
that no lead change ever occurs decays exponentially with the average number of
lead changes.Comment: 5 pages, 3 figure
Scaled penalization of Brownian motion with drift and the Brownian ascent
We study a scaled version of a two-parameter Brownian penalization model
introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model
penalizes Brownian motion with drift by the weight process
where and
is the running maximum of the Brownian motion. It was
shown there that the resulting penalized process exhibits three distinct phases
corresponding to different regions of the -plane. In this paper, we
investigate the effect of penalizing the Brownian motion concurrently with
scaling and identify the limit process. This extends a result of Roynette-Yor
for the case to the whole parameter plane and reveals two
additional "critical" phases occurring at the boundaries between the parameter
regions. One of these novel phases is Brownian motion conditioned to end at its
maximum, a process we call the Brownian ascent. We then relate the Brownian
ascent to some well-known Brownian path fragments and to a random scaling
transformation of Brownian motion recently studied by Rosenbaum-Yor.Comment: 32 pages; made additions to Section
Stability Analysis of Frame Slotted Aloha Protocol
Frame Slotted Aloha (FSA) protocol has been widely applied in Radio Frequency
Identification (RFID) systems as the de facto standard in tag identification.
However, very limited work has been done on the stability of FSA despite its
fundamental importance both on the theoretical characterisation of FSA
performance and its effective operation in practical systems. In order to
bridge this gap, we devote this paper to investigating the stability properties
of FSA by focusing on two physical layer models of practical importance, the
models with single packet reception and multipacket reception capabilities.
Technically, we model the FSA system backlog as a Markov chain with its states
being backlog size at the beginning of each frame. The objective is to analyze
the ergodicity of the Markov chain and demonstrate its properties in different
regions, particularly the instability region. By employing drift analysis, we
obtain the closed-form conditions for the stability of FSA and show that the
stability region is maximised when the frame length equals the backlog size in
the single packet reception model and when the ratio of the backlog size to
frame length equals in order of magnitude the maximum multipacket reception
capacity in the multipacket reception model. Furthermore, to characterise
system behavior in the instability region, we mathematically demonstrate the
existence of transience of the backlog Markov chain.Comment: 14 pages, submitted to IEEE Transaction on Information Theor
Statistical dependence in biological sequences
We demonstrate the use of information-theoretic tools for the task of identifying segments of hiomolecules (DNA or RNA) that are statistically correlated. We develop a precise and reliable methodology, based on the notion of mutual information, for finding and extracting statistical as well as structural dependencies. A simple threshold function is defined, and its use in quantifying the level of significance of dependencies between biological segments is explored. These tools are used in two specific applications. First, for the identification of correlations between different parts of the maize zmSRp32 gene. There, we find significant dependencies between the 5' untranslated region and its alternatively spliced exons. This observation may indicate the presence of as-yet unknown alternative splicing mechanisms or structural scaffolds. Second, using data from CODIS, we demonstrate that our approach is well suited for the problem of discovering short tandem repeals (STRs). ©2007 IEEE