7,374 research outputs found
Upper bound for the height of S-integral points on elliptic curves
We establish new upper bounds for the height of the S-integral points of an
elliptic curve. This bound is explicitly given in terms of the set S of places
of the number field K involved, but also in terms of the degree of K, as well
as the rank, the regulator and the height of a basis of the Mordell-Weil group
of the curve. The proof uses the elliptic analogue of Baker's method, based on
lower bounds for linear forms in elliptic logarithms.Comment: 17 pages. arXiv admin note: substantial text overlap with
arXiv:1203.386
Distortion Exponent in MIMO Channels with Feedback
The transmission of a Gaussian source over a block-fading multiple antenna
channel in the presence of a feedback link is considered. The feedback link is
assumed to be an error and delay free link of capacity 1 bit per channel use.
Under the short-term power constraint, the optimal exponential behavior of the
end-to-end average distortion is characterized for all source-channel bandwidth
ratios. It is shown that the optimal transmission strategy is successive
refinement source coding followed by progressive transmission over the channel,
in which the channel block is allocated dynamically among the layers based on
the channel state using the feedback link as an instantaneous automatic repeat
request (ARQ) signal.Comment: Presented at the IEEE Information Theory Workshop (ITW), Taormina,
Italy, Oct. 200
Diversity-Multiplexing Tradeoffs in MIMO Relay Channels
A multi-hop relay channel with multiple antenna terminals in a quasi-static
slow fading environment is considered. For both full-duplex and half-duplex
relays the fundamental diversity-multiplexing tradeoff (DMT) is analyzed. It is
shown that, while decode-and-forward (DF) relaying achieves the optimal DMT in
the full-duplex relay scenario, the dynamic decode-and-forward (DDF) protocol
is needed to achieve the optimal DMT if the relay is constrained to half-duplex
operation. For the latter case, static protocols are considered as well, and
the corresponding achievable DMT performance is characterized.Comment: To appear at IEEE Global Communications Conf. (Globecom), New
Orleans, LA, Nov. 200
Minimum Sparsity of Unobservable Power Network Attacks
Physical security of power networks under power injection attacks that alter
generation and loads is studied. The system operator employs Phasor Measurement
Units (PMUs) for detecting such attacks, while attackers devise attacks that
are unobservable by such PMU networks. It is shown that, given the PMU
locations, the solution to finding the sparsest unobservable attacks has a
simple form with probability one, namely, , where
is defined as the vulnerable vertex connectivity of an augmented
graph. The constructive proof allows one to find the entire set of the sparsest
unobservable attacks in polynomial time. Furthermore, a notion of the potential
impact of unobservable attacks is introduced. With optimized PMU deployment,
the sparsest unobservable attacks and their potential impact as functions of
the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and
300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed
that, as more PMUs are added, the maximum potential impact among all the
sparsest unobservable attacks drops quickly until it reaches the minimum
sparsity.Comment: submitted to IEEE Transactions on Automatic Contro
Protective Factors Among Postsecondary Students Enrolled in a First-Generation Program
For generations, researchers have examined attributes that contribute to the adaptability of low socioeconomic youth. Attributes that help one become resilient are known as protective factors. The purpose of this descriptive study was to explore the protective factor(s) that contributed to the enrollment of first-generation, low-socioeconomic status (SES) students at a southern land-grant university. The population consisted of postsecondary students in a First Scholars program during the 2015-2016 academic year. The authors examine the existing literature on the effects of low SES on postsecondary education in order to explore what assists these students in maintaining a steadfast behavior. Recommendations are made for the recruitment of students who display a higher resiliency to be successful at the postsecondary level and for the First Scholars program on how to further enhance the program
The Multi-way Relay Channel
The multiuser communication channel, in which multiple users exchange
information with the help of a relay terminal, termed the multi-way relay
channel (mRC), is introduced. In this model, multiple interfering clusters of
users communicate simultaneously, where the users within the same cluster wish
to exchange messages among themselves. It is assumed that the users cannot
receive each other's signals directly, and hence the relay terminal in this
model is the enabler of communication. In particular, restricted encoders,
which ignore the received channel output and use only the corresponding
messages for generating the channel input, are considered. Achievable rate
regions and an outer bound are characterized for the Gaussian mRC, and their
comparison is presented in terms of exchange rates in a symmetric Gaussian
network scenario. It is shown that the compress-and-forward (CF) protocol
achieves exchange rates within a constant bit offset of the exchange capacity
independent of the power constraints of the terminals in the network. A finite
bit gap between the exchange rates achieved by the CF and the
amplify-and-forward (AF) protocols is also shown. The two special cases of the
mRC, the full data exchange model, in which every user wants to receive
messages of all other users, and the pairwise data exchange model which
consists of multiple two-way relay channels, are investigated in detail. In
particular for the pairwise data exchange model, in addition to the proposed
random coding based achievable schemes, a nested lattice coding based scheme is
also presented and is shown to achieve exchange rates within a constant bit gap
of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information
Theor
Joint Source-Channel Cooperative Transmission over Relay-Broadcast Networks
Reliable transmission of a discrete memoryless source over a multiple-relay
relay-broadcast network is considered. Motivated by sensor network
applications, it is assumed that the relays and the destinations all have
access to side information correlated with the underlying source signal. Joint
source-channel cooperative transmission is studied in which the relays help the
transmission of the source signal to the destinations by using both their
overheard signals, as in the classical channel cooperation scenario, as well as
the available correlated side information. Decode-and-forward (DF) based
cooperative transmission is considered in a network of multiple relay terminals
and two different achievability schemes are proposed: i) a regular encoding and
sliding-window decoding scheme without explicit source binning at the encoder,
and ii) a semi-regular encoding and backward decoding scheme with binning based
on the side information statistics. It is shown that both of these schemes lead
to the same source-channel code rate, which is shown to be the "source-channel
capacity" in the case of i) a physically degraded relay network in which the
side information signals are also degraded in the same order as the channel;
and ii) a relay-broadcast network in which all the terminals want to
reconstruct the source reliably, while at most one of them can act as a relay.Comment: Submitted to IEEE Transactions on Information Theory, 201
Lossy Source Transmission over the Relay Channel
Lossy transmission over a relay channel in which the relay has access to
correlated side information is considered. First, a joint source-channel
decode-and-forward scheme is proposed for general discrete memoryless sources
and channels. Then the Gaussian relay channel where the source and the side
information are jointly Gaussian is analyzed. For this Gaussian model, several
new source-channel cooperation schemes are introduced and analyzed in terms of
the squared-error distortion at the destination. A comparison of the proposed
upper bounds with the cut-set lower bound is given, and it is seen that joint
source-channel cooperation improves the reconstruction quality significantly.
Moreover, the performance of the joint code is close to the lower bound on
distortion for a wide range of source and channel parameters.Comment: Proceedings of the 2008 IEEE International Symposium on Information
Theory, Toronto, ON, Canada, July 6 - 11, 200
Distribution System Outage Detection using Consumer Load and Line Flow Measurements
An outage detection framework for power distribution networks is proposed.
Given the tree structure of the distribution system, a method is developed
combining the use of real-time power flow measurements on edges of the tree
with load forecasts at the nodes of the tree. A maximum a posteriori detector
{\color{black} (MAP)} is formulated for arbitrary number and location of
outages on trees which is shown to have an efficient detector. A framework
relying on the maximum missed detection probability is used for optimal sensor
placement and is solved for tree networks. Finally, a set of case studies is
considered using feeder data from the Pacific Northwest National Laboratories.
We show that a 10\% loss in mean detection reliability network wide reduces the
required sensor density by 60 \% for a typical feeder if efficient use of
measurements is performed.Comment: Complete rework of result
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