A Stochastic-Geometry Approach to Coverage in Cellular Networks with Multi-Cell Cooperation

Multi-cell cooperation is a promising approach for mitigating inter-cell interference in dense cellular networks. Quantifying the performance of multi-cell cooperation is challenging as it integrates physical-layer techniques and network topologies. For tractability, existing work typically relies on the over-simplified Wyner-type models. In this paper, we propose a new stochastic-geometry model for a cellular network with multi-cell cooperation, which accounts for practical factors including the irregular locations of base stations (BSs) and the resultant path-losses. In particular, the proposed network-topology model has three key features: i) the cells are modeled using a Poisson random tessellation generated by Poisson distributed BSs, ii) multi-antenna BSs are clustered using a hexagonal lattice and BSs in the same cluster mitigate mutual interference by spatial interference avoidance, iii) BSs near cluster edges access a different sub-channel from that by other BSs, shielding cluster-edge mobiles from strong interference. Using this model and assuming sparse scattering, we analyze the shapes of the outage probabilities of mobiles served by cluster-interior BSs as the average number $K$ of BSs per cluster increases. The outage probability of a mobile near a cluster center is shown to be proportional to $e^{-c(2-\sqrt{\nu})^2K}$ where $\nu$ is the fraction of BSs lying in the interior of clusters and $c$ is a constant. Moreover, the outage probability of a typical mobile is proved to scale proportionally with $e^{-c' (1-\sqrt{\nu})^2K}$ where $c'$ is a constant.Comment: 5 page

WIC Contract Spillover Effects

The infant formula rebate program of the Special Nutrition Program for Women, Infants, and Children (WIC) requires each state to hold an auction where the low-bidder among the three major manufacturers of infant formula became the sole provider of formula to the state, which issues WIC voucher to low-income WIC participants. Using these WIC vouchers the WIC consumers can get contract brand infant formula for free from participating grocery stores or directly from the state. The WIC agencies then reimburse the retailers for the full retail price of the formula purchased by WIC consumers. Since the rebate program started, the wholesale prices of infant formula have increased markedly. The infant formula industry is highly concentrated, with three firms accounting for more than 90% of market share. Since the start of the rebate program, Congress has been concerned with the program's effects on non-WIC consumers. Congress mandated several studies of this issue by the GAO and USDA. Despite these government and other academic studies, there is no consensus on a theory as to how the rebate program affects non-WIC consumers. Empirical studies have not resolved this issue due to a lack of data. The goal of this study is two-fold. First, in contrast to earlier studies that describe firms' behavior as price discrimination, we present a theoretical model based on spillover effects. We refer to increases in non-WIC demand for the WIC brand due to its WIC brand status as a spillover effect. A firm will submit an extremely low bid because the WIC contract winner brand gains substantial additional sales and becomes the dominant player in the non-WIC market. The resulting differential between the WIC and non-WIC price may exceed that of the pure price-discrimination model. Second, we use widely available scanner data to test our hypothesis and estimate the magnitude of the spillover effect. Methodology Our theory is based on three important characteristics of this market. First, the wholesale prices do not change substantially before and after a firm wins the WIC contract in a state. Second, all three major firms set a national wholesales price annually. Third, the share of the WIC contract winner increases dramatically after a it takes over a contract. Hence, a price discrimination model where firms set wholesales prices to each retailer or state and adjust wholesale prices with every contract change is not consistent with these stylized facts. We solve for the oligopolistic equilibrium uniform prices (in the absence of a WIC rebate program) and compare those to the equilibrium prices under WIC if the firms could price discriminate or where they cannot price discriminate and there are spillover effects. Possible channel of spillover could be simply change in shelf space allocation in grocery stores. We show that with a large spillover effect, a firm is willing to bid more aggressively so as to be able to charge higher prices to the non-WIC market. As a result, the differential between the WIC and non-WIC price may exceed that of the price discrimination model. We estimate the magnitude of the spillover effects. It would be straightforward to investigate spillover effects if we had data that distinguishes WIC and non-WIC sales. However, such data are not available. Therefore to identify the spillover effect, we explore the variation over time in states where the WIC contract has changed between firms during our sample period. Our empirical strategy is based the following rationale. After the WIC contract change between brands, WIC participants, who receive the current WIC brand for free, immediately switch from the loser to the winner brand. Consequently, stores must provide more shelf-space to the contract winning brand. Non-WIC consumers may be influenced by shelf-space allocation and are more likely to choose the contract winning brand as a result. However, parents do not like switching brands for fear that their babies will reject the new brand. Thus, only new non-WIC consumers are influenced by the shelf-space allocation. Consequently, the non-WIC spillover effect occurs slowly over time as parents with new babies enter the market and those with older babies exit. Are idea, then, is to identify the non-WIC spillover effect through a gradual adjustment pattern following a contract change. The panel structure of our data also allows us to exploit the variation in share changes when different firms win or lose the contracts in various cities. Using IRI scanner data from year 1997 to year 1999 from 11 cities in 7 states where WIC contract change occurred during the period, we estimate a multinomial logit model with dependent variables being the shares of the WIC contract winner, loser and the remaining brands, and independent variable are the time elapsed since the contract change, state birth rates, and firm and state fixed effects. We confirm that there is an instantaneous switch in shares after the contract change followed by a spillover effect that gradually increase over time until it too is substantial. Potential for generating discussion The WIC program provides formula to half of all U.S. infants. Despite the importance of this rebate program, no consensus exists on how this program affects non-WIC consumers, either theoretically or empirically. For example, the U.S. GAO (1998) argued based on simulations that spillover effects could not be substantial in the WIC infant formula market. Thus our theory and confirming empirical evidence contrast substantially with earlier studies. Reference: U.S. General Accounting Office. 1998. Food Assistance: Information on WIC Sole-Source Rebates and Infant Formula Prices, Report to the Chairman, Committee on the Budget, House of Representatives, GAO/RCED-98-146.Food Consumption/Nutrition/Food Safety,

EFICAz²: enzyme function inference by a combined approach enhanced by machine learning

©2009 Arakaki et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2105/10/107doi:10.1186/1471-2105-10-107Background: We previously developed EFICAz, an enzyme function inference approach that combines predictions from non-completely overlapping component methods. Two of the four components in the original EFICAz are based on the detection of functionally discriminating residues (FDRs). FDRs distinguish between member of an enzyme family that are homofunctional (classified under the EC number of interest) or heterofunctional (annotated with another EC number or lacking enzymatic activity). Each of the two FDR-based components is associated to one of two specific kinds of enzyme families. EFICAz exhibits high precision performance, except when the maximal test to training sequence identity (MTTSI) is lower than 30%. To improve EFICAz's performance in this regime, we: i) increased the number of predictive components and ii) took advantage of consensual information from the different components to make the final EC number assignment. Results: We have developed two new EFICAz components, analogs to the two FDR-based components, where the discrimination between homo and heterofunctional members is based on the evaluation, via Support Vector Machine models, of all the aligned positions between the query sequence and the multiple sequence alignments associated to the enzyme families. Benchmark results indicate that: i) the new SVM-based components outperform their FDR-based counterparts, and ii) both SVM-based and FDR-based components generate unique predictions. We developed classification tree models to optimally combine the results from the six EFICAz components into a final EC number prediction. The new implementation of our approach, EFICAz², exhibits a highly improved prediction precision at MTTSI < 30% compared to the original EFICAz, with only a slight decrease in prediction recall. A comparative analysis of enzyme function annotation of the human proteome by EFICAz² and KEGG shows that: i) when both sources make EC number assignments for the same protein sequence, the assignments tend to be consistent and ii) EFICAz² generates considerably more unique assignments than KEGG. Conclusion: Performance benchmarks and the comparison with KEGG demonstrate that EFICAz² is a powerful and precise tool for enzyme function annotation, with multiple applications in genome analysis and metabolic pathway reconstruction. The EFICAz² web service is available at: http://cssb.biology.gatech.edu/skolnick/webservice/EFICAz2/index.htm

Space Division Multiple Access with a Sum Feedback Rate Constraint

On a multi-antenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper-bounded by a constant. This design consists of algorithms for CSI quantization, threshold based CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded.Comment: 29 pages; submitted to IEEE Transactions on Signal Processin