Farming in Alaska.

An analysis of commercial farming in Alaska has long been needed. This report may supply helpful information. It spans the yea rs from 1949 to 1954, a time of rapid development and growth. T he study analyzes detailed information supplied by 75 to 85 farmers in the Matanuska Valley and by 15 to 30 others in the Tanana Valley. In 1952, records were also obtained from 19 farmers in the Kenai Peninsula. These record s are estimated to cover about 60 per cent of all commercial farming activity in these particular areas during the period. Information on farming in areas outside the Kenai Peninsula and the Railbelt was gathered from mailed questionnaires supplemented by personal observations. Data for 1949 and 1950 were collected by Clarence A. Moore and were first summarized in his Mimeographed Circular 1, Alaska Farms : Organization and Practices in 1949, and Bulletin 14, Farming in the Matanuska and Tanana Valleys of A laska, both published by the Alaska Agricultural Experiment Station. The authors are grateful to the farmers, agencies and others whose help made this work possible

Age Disparities in Unemployment and Reemployment During the Great Recession and Recovery

Analyzes patterns in the percentage of workers unemployed at any point between May 2008 and March 2011, number of months they were unemployed, wage losses at reemployment, and likelihood of workers leaving the labor force by age group

How Much Might Automatic IRAs Improve Retirement Security for Low- and Moderate-Wage Workers?

Estimates the extent to which requiring employers with no retirement plan to set up individual retirement accounts and automatically deposit a portion of pay would improve low- and moderate-wage workers' retirement security. Outlines policy implications

Subgraphs and Colourability of Locatable Graphs

We study a game of pursuit and evasion introduced by Seager in 2012, in which a cop searches the robber from outside the graph, using distance queries. A graph on which the cop wins is called locatable. In her original paper, Seager asked whether there exists a characterisation of the graph property of locatable graphs by either forbidden or forbidden induced subgraphs, both of which we answer in the negative. We then proceed to show that such a characterisation does exist for graphs of diameter at most 2, stating it explicitly, and note that this is not true for higher diameter. Exploring a different direction of topic, we also start research in the direction of colourability of locatable graphs, we also show that every locatable graph is 4-colourable, but not necessarily 3-colourable.Comment: 25 page

Locally Complete Path Independent Choice Functions and Their Lattices

The concept of path independence (PI) was first introduced by Arrow (1963) as a defense of his requirement that collective choices be rationalized by a weak ordering. Plott (1973) highlighted the dynamic aspects of PI implicit in Arrow's initial discussion. Throughout these investigations two questions, both initially raised by Plott, remained unanswered. What are the precise mathematical foundations for path independence? How can PI choice functions be constructed? We give complete answers to both these questions for finite domains and provide necessary conditions for infinite domains. We introduce a lattice associated with each PI function. For finite domains these lattices coincide with locally lower distributive or meet-distributive lattices and uniquely characterize PI functions. We also present an algorithm, effective and exhaustive for finite domains, for the construction of PI choice functions and hence for all finite locally lower distributive lattices. For finite domains, a PI function is rationalizable if and only if the lattice is distributive. The lattices associated with PI functions that satisfy the stronger condition of the weak axiom of revealed preference are chains of Boolean algebras and conversely. Those that satisfy the strong axiom of revealed preference are chains and conversely.

Locating a robber with multiple probes

We consider a game in which a cop searches for a moving robber on a connected graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any $n$-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m\geq n$. The present authors showed that, for all but a few small values of $n$, this bound may be improved to $m\geq n/2$, which is best possible. In this paper we consider the natural extension in which the cop probes a set of $k$ vertices, rather than a single vertex, at each turn. We consider the relationship between the value of $k$ required to ensure victory on the original graph and the length of subdivisions required to ensure victory with $k=1$. We give an asymptotically best-possible linear bound in one direction, but show that in the other direction no subexponential bound holds. We also give a bound on the value of $k$ for which the cop has a winning strategy on any (possibly infinite) connected graph of maximum degree $\Delta$, which is best possible up to a factor of $(1-o(1))$.Comment: 16 pages, 2 figures. Updated to show that Theorem 2 also applies to infinite graphs. Accepted for publication in Discrete Mathematic

Subdivisions in the Robber Locating Game

We consider a game in which a cop searches for a moving robber on a graph using distance probes, which is a slight variation on one introduced by Seager. Carragher, Choi, Delcourt, Erickson and West showed that for any n-vertex graph $G$ there is a winning strategy for the cop on the graph $G^{1/m}$ obtained by replacing each edge of $G$ by a path of length $m$, if $m \geqslant n$. They conjectured that this bound was best possible for complete graphs, but the present authors showed that in fact the cop wins on $K^{1/m}$ if and only if $m \geqslant n/2$, for all but a few small values of $n$. In this paper we extend this result to general graphs by proving that the cop has a winning strategy on $G^{1/m}$ provided $m \geqslant n/2$ for all but a few small values of $n$; this bound is best possible. We also consider replacing the edges of $G$ with paths of varying lengths.Comment: 13 Page

The Potential Impact of the Great Recession on Future Retirement Incomes

Estimates the effects of job loss, slower wage growth, and withdrawals from retirement savings during the 2007-09 recession on retirement incomes at age 70, including decline in income by age group and number of those likely to live in poverty at 70