On set systems with restricted intersections modulo p and p-ary t-designs

We consider bounds on the size of families ℱ of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections. We improve the known bound when ℱ is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families ℱ holds with equality, then ℱ is the set of blocks of what we call a p-ary t-design for certain values of t. This motivates us to make a few observations about p-ary t-designs for their own sake

CSR, Contracting and Socially Responsible Investment : Opportunities for Pakistani Firms

The purpose of our paper is to explore two ways in which Pakistani firms can take advantage of the growing corporate social responsibility movement so as to improve their own economic performance. First, the presence of MNCs in Pakistan, the vast majority of which have made significant CSR undertakings, means that Pakistani firms seeking to do business with them will often have to meet CSR tests themselves. Second, the increasing financial clout of so-called Socially Responsible Investement (SRI) funds means that Pakistani firms have an incentive to comply with CSR standards so as to become eligible investment instruments. We begin by canvassing briefly the history of CSR movement and what are by now relatively well-known CSR principles and standards. We then explore some examples of how Pakistan-based multinationals as well local firms are currently engaging in CSR practices. We argue that Pakistan can and should acquire the reputation for being a leader in this domain.corporate social responsibility movement, economic performance, CSR

Technology Prizes for Climate Change Mitigation

We analyze whether technology inducement prizes could be a useful complement to standard research grants and contracts in developing climate change mitigation technologies. We find that there are important conceptual advantages to using inducement prizes in certain circumstances. These conceptual inferences are borne out by an examination of the track record of prizes inducing research into public goods, including relevant energy technologies. However, we also find that the prizes’ successes are contingent on their proper design. We analyze how several important design elements could influence the effectiveness of a climate technology prize.inducement prize, research and development, climate change, technology, policy

Spanning trees of graphs on surfaces and the intensity of loop-erased random walk on planar graphs

We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "intensity" of the loop-erased random walk in ${\mathbb Z}^2$, that is, the probability that the walk from (0,0) to infinity passes through a given vertex or edge. For example, the probability that it passes through (1,0) is 5/16; this confirms a conjecture from 1994 about the stationary sandpile density on ${\mathbb Z}^2$. We do the analogous computation for the triangular lattice, honeycomb lattice and ${\mathbb Z} \times {\mathbb R}$, for which the probabilities are 5/18, 13/36, and $1/4-1/\pi^2$ respectively.Comment: 45 pages, many figures. v2 has an expanded introduction, a revised section on the LERW intensity, and an expanded appendix on the annular matri

Boundary Partitions in Trees and Dimers

Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of the different possible node connections in a grove. These probabilities only depend on boundary measurements of the graph and not on the actual graph structure, i.e., the probabilities can be expressed as functions of the pairwise electrical resistances between the nodes, or equivalently, as functions of the Dirichlet-to-Neumann operator (or response matrix) on the nodes. These formulae can be likened to generalizations (for spanning forests) of Cardy's percolation crossing probabilities, and generalize Kirchhoff's formula for the electrical resistance. Remarkably, when appropriately normalized, the connection probabilities are in fact integer-coefficient polynomials in the matrix entries, where the coefficients have a natural algebraic interpretation and can be computed combinatorially. A similar phenomenon holds in the so-called double-dimer model: connection probabilities of boundary nodes are polynomial functions of certain boundary measurements, and as formal polynomials, they are specializations of the grove polynomials. Upon taking scaling limits, we show that the double-dimer connection probabilities coincide with those of the contour lines in the Gaussian free field with certain natural boundary conditions. These results have direct application to connection probabilities for multiple-strand SLE_2, SLE_8, and SLE_4.Comment: 46 pages, 12 figures. v4 has additional diagrams and other minor change

Projected Red Pine Yields from Aldrin-Treated and Untreated Stands Damaged by White Grubs and Other Agents

(excerpt) Young red pines, Pinus resinosa Ait., during the first few years after planting in the Lake States, are vulnerable to several injurious agents, including white grubs, the larvae of May beetles, Phyllophaga spp. (Kittredge, 1929; Craighead, 1950). The pesticide aldrin3 has frequently been applied at planting time to protect seedlings from white grubs. More than 12,000 acres of national forest land were treated with aldrin from 1960 to 1967 in the Lake States; almost 10,000 of these were on the Hiawatha National Forest (Fowler, 1973)