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, $\kappa(G^M) + 1$, where $\kappa(G^M)$ 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