Descent c-Wilf Equivalence

Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of left-to-right minima of $\sigma$. For any sequence of statistics $\mathrm{stat}_1, \ldots \mathrm{stat}_k$ on permutations, we say two permutations $\alpha$ and $\beta$ in $S_j$ are $(\mathrm{stat}_1, \ldots \mathrm{stat}_k)$-c-Wilf equivalent if the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\alpha$ equals the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\beta$. We give many examples of pairs of permutations $\alpha$ and $\beta$ in $S_j$ which are $\mathrm{des}$-c-Wilf equivalent, $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent, and $(\mathrm{des},\mathrm{inv},\mathrm{LRmin})$-c-Wilf equivalent. For example, we will show that if $\alpha$ and $\beta$ are minimally overlapping permutations in $S_j$ which start with 1 and end with the same element and $\mathrm{des}(\alpha) = \mathrm{des}(\beta)$ and $\mathrm{inv}(\alpha) = \mathrm{inv}(\beta)$, then $\alpha$ and $\beta$ are $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent.Comment: arXiv admin note: text overlap with arXiv:1510.0431

Agricultural Arbitrage, Adjustment Costs, and the Intensive Margin

Farmland and capital are an important and rapidly expanding component of the agricultural economy, and empirical evidence suggests that these assets are quasi-fixed in that adjustment costs are incurred when holdings are altered. Increased interest in the rate of return for investing in farmland suggests that an important consideration is the effect of adjustment costs on this return. A novel theoretical model is developed that ties together contributions from the farmland pricing and adjustment cost literatures, and the first order conditions for a utility maximizing decision maker are rearranged into intertemporal arbitrage equations that are similar in spirit to traditional finance models. The common assumptions that land and capital are quasi-fixed assets, and that production is characterized by constant returns to scale are tested and the evidence supports these assumptions. An empirical application of the arbitrage equations provides evidence that risk aversion and adjustment costs are jointly significant components of agricultural production, and that adjustment costs generate significant changes in the rate of return to farmland. The results have important policy implications as sluggish supply response due to quasi-fixity can lead to dramatically inflated commodity prices, and an accurate measure of the farmland return can help determine how far the extensive margin will expand or contract in response to a variety of policy scenarios, such as the subsidization of corn for ethanol, an increase in the variety of subsidized crop insurance products, or the introduction of new revenue support programs such as ACRE.Arbitrage, Adjustment Costs, Farmland, Asset Pricing, Capital, Cost Function, Risk, Production, Agricultural Finance, Consumer/Household Economics, Crop Production/Industries, Farm Management, Financial Economics, Land Economics/Use, Production Economics, Risk and Uncertainty,

The Middle Class Parent Penalty: Child Benefits in the U.S. Tax Code

Low-income families with children receive large tax benefits from the Earned Income Tax Credit, while high income taxpayers receive large tax benefits from dependent exemptions (whose value is greater to those in higher tax brackets). In contrast, middle-income parents receive substantially smaller tax benefits associated with children. This U-shaped pattern of benefits by income, which we call the middle-class parent penalty,' not only raises issues of fairness; it also generates marginal tax rates and marriage penalties for moderate income families that are as high or higher than those facing more well-to-do taxpayers. This paper documents how the tax benefits of children vary with income, and illustrates their impact on marginal tax rates and marriage penalties. It then examines five options for reducing or eliminating the middle-class parent penalty and the high marginal tax rates and marriage penalties it produces.

Australian Fathers\u27 Study: What influences paternal engagement with antenatal care?

This mixed-methods study explores factors associated with and levels of engagement of fathers in antenatal care. One hundred expectant fathers were recruited from antenatal clinics and community settings in Western Australia. They completed validated questionnaires. Eighty-three percent of expectant fathers reported a lack of engagement with antenatal care. Factors significantly associated with lack of engagement in multivariate analysis were working more than 40 hours a week and lack of adequate consultation by antenatal care staff. In qualitative analysis, 6 themes emerged in association with a lack of engagement. They were role in decision making, time pressures, the observer effect, lack of knowledge, barriers to attendance, and feeling unprepared or anxious. Care providers should involve fathers in consultations to improve paternal engagement

Polyetheretherketone as a Biomaterial for Spinal Applications

Threaded lumbar interbody spinal fusion devices (TIBFD) made from titanium have been reported to be 90% effective for single-level lumbar interbody fusion, although radiographic determination of fusion has been intensely debated in the literature. Using blinded radiographic, biomechanic, histologic, and statistical measures, we evaluated a radiolucent polyetheretherketone (PEEK)-threaded interbody fusion device packed with autograft or rhBMP-2 on an absorbable collagen sponge in 13 sheep at 6 months. Radiographic fusion, increased spinal level biomechanical stiffness, and histologic fusion were demonstrated for the PEEK cages filled with autograft or rhBMP-2 on a collagen sponge. No device degradation or wear debris was observed. Only mild chronic inflammation consisting of a few macrophages was observed in peri-implant tissues. Based on these results, the polymeric biomaterial PEEK may be a useful biomaterial for interbody fusion cages due to the polymer\u27s increased radiolucency and decreased stiffness

Band Gap and Edge Engineering via Ferroic Distortion and Anisotropic Strain: The Case of SrTiO3_{3}

The effects of ferroic distortion and biaxial strain on the band gap and band edges of SrTiO$_{3}$ (STO) are calculated using density functional theory and many-body perturbation theory. Anisotropic strains are shown to reduce the gap by breaking degeneracies at the band edges. Ferroic distortions are shown to widen the gap by allowing new band edge orbital mixings. Compressive biaxial strains raise band edge energies, while tensile strains lower them. To reduce the STO gap, one must lower the symmetry from cubic while suppressing ferroic distortions. Our calculations indicate that for engineered orientation of the growth direction along [111], the STO gap can be controllably and considerably reduced at room temperature.Comment: 5 pages, 5 figures. To be published in Phys. Rev. Let