Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension

Algorithmic mechanism design (AMD) studies the delicate interplay between computational efficiency, truthfulness, and optimality. We focus on AMD's paradigmatic problem: combinatorial auctions. We present a new generalization of the VC dimension to multivalued collections of functions, which encompasses the classical VC dimension, Natarajan dimension, and Steele dimension. We present a corresponding generalization of the Sauer-Shelah Lemma and harness this VC machinery to establish inapproximability results for deterministic truthful mechanisms. Our results essentially unify all inapproximability results for deterministic truthful mechanisms for combinatorial auctions to date and establish new separation gaps between truthful and non-truthful algorithms

Unavoidable Multicoloured Families of Configurations

Balogh and Bollob\'as [{\em Combinatorica 25, 2005}] prove that for any $k$ there is a constant $f(k)$ such that any set system with at least $f(k)$ sets reduces to a $k$-star, an $k$-costar or an $k$-chain. They proved $f(k)<(2k)^{2^k}$. Here we improve it to $f(k)<2^{ck^2}$ for some constant $c>0$. This is a special case of the following result on the multi-coloured forbidden configurations at 2 colours. Let $r$ be given. Then there exists a constant $c_r$ so that a matrix with entries drawn from $\{0,1,...,r-1\}$ with at least $2^{c_rk^2}$ different columns will have a $k\times k$ submatrix that can have its rows and columns permuted so that in the resulting matrix will be either $I_k(a,b)$ or $T_k(a,b)$ (for some $a\ne b\in \{0,1,..., r-1\}$), where $I_k(a,b)$ is the $k\times k$ matrix with $a$'s on the diagonal and $b$'s else where, $T_k(a,b)$ the $k\times k$ matrix with $a$'s below the diagonal and $b$'s elsewhere. We also extend to considering the bound on the number of distinct columns, given that the number of rows is $m$, when avoiding a $t k\times k$ matrix obtained by taking any one of the $k \times k$ matrices above and repeating each column $t$ times. We use Ramsey Theory.Comment: 16 pages, add two application

Impacts of social networks, technology adoption and market participation on smallholder household welfare in Northern Ghana

Abstract Food insecurity remains a major challenge in many parts of sub-Saharan Africa, despite the increased access to improved agricultural technologies and markets in the past few decades. Several attempts have been made to understand the factors accounting for the low uptake of improved agricultural technologies and smallholder market engagement, and their implications on household income, food security and nutrition in the sub-region. Social networks have been recognized as playing important roles in influencing household production decisions in many developing countries. However, not much has been done, in the empirical literature, on how heterogeneities in social learning about both benefits and production techniques of improved technologies, social networks structures and smallholder market orientation affect smallholder production decisions and welfare. This study, therefore, contributes to these strands of literature by examining the role of social networks on smallholder adoption of improved soybean varieties, and the impacts of smallholder adoption and market orientation on household welfare in Northern Ghana. Specifically, the study first examines the impacts of peer adoption of two improved and competing soybean varieties on smallholders’ adoption decisions of these varieties using spatial autoregressive multinomial probit model to account for interdependence across varieties. Second, random-effects complementary log-log hazard model was used to investigate the role of social learning, network transitivity, centrality and modularity on the diffusion of these improved varieties. Third, the study examines the effects of own and peer adoption of the improved varieties on household soybean yield, food security and nutrition using the marginal treatment effects. It also explores the effects of policies that either increase affordability or access to improved seeds on adoption and the outcomes using the policy relevant treatment effects. Finally, the study employed an ordered probit selection model to examine the impacts of smallholder market-orientation on household food security and nutrition. The results show that a farmer’s adoption decision of a given improved variety is positively influenced by the adopting peers of this variety, but negatively by the adopting peers of the competing improved variety. Furthermore, when the relative share of adopting peers are equal, farmers are more likely to wait and not to switch from the old variety. In addition, the results show that both learning about benefits and production process are important in accelerating adoption, although the effects of learning about production process are higher when sufficient peers adopt the improved varieties. Also, the role of transitivity in the learning and diffusion processes is stronger, compared to centrality, although modularity tends to slow down the diffusion process, and also constrains the effects of both transitivity and centrality. The results further show that own and peer adoption of the improved varieties significantly increase smallholder yield and food consumption, and that adoption tend to make less endowed households to catchup with more endowed households. Similarly, policies that increase either affordability or accessibility significantly increase adoption, yield and consumption, but increasing accessibility appears to deliver somewhat higher food consumption than the affordability-oriented policies. The estimates also reveal substantial heterogeneity in consumption gains across market orientations and suggest the need for transition targeted and sensitive policies in promoting smallholder food security and nutrition through crop commercialization. Similarly, the findings on adoption suggest the need for policymakers to focus promotion efforts on demonstrating the relative benefits and production process of improved varieties to farmers. Also, interventions, such as self-help groups, farmer field-days and training workshops aimed at promoting smallholder interactions, and enhancing exchange can increase the effectiveness of social networks in promoting adoption and household welfare

Meeting Review: Airborne Aerosol Inlet Workshop

Proceedings from the Airborne Aerosol Inlet Workshop are presented. The two central topics of discussion were the role of aerosols in atmospheric processes and the difficulties in characterizing aerosols. The following topics were discussed during the working sessions: airborne observations to date; identification of inlet design issues; inlet modeling needs and directions; objectives for aircraft experiments; and future laboratory and wind tunnel studies

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation