Analogies between the crossing number and the tangle crossing number

Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tanglegram is the minimum crossing number over all such drawings and is related to biologically relevant quantities, such as the number of times a parasite switched hosts. Our main results for tanglegrams which parallel known theorems for crossing numbers are as follows. The removal of a single matching edge in a tanglegram with $n$ leaves decreases the tangle crossing number by at most $n-3$, and this is sharp. Additionally, if $\gamma(n)$ is the maximum tangle crossing number of a tanglegram with $n$ leaves, we prove $\frac{1}{2}\binom{n}{2}(1-o(1))\le\gamma(n)<\frac{1}{2}\binom{n}{2}$. Further, we provide an algorithm for computing non-trivial lower bounds on the tangle crossing number in $O(n^4)$ time. This lower bound may be tight, even for tanglegrams with tangle crossing number $\Theta(n^2)$.Comment: 13 pages, 6 figure

Enhancing 1α-Hydroxylase Activity with the 25-Hydroxyvitamin D-1α-Hydroxylase Gene in Cultured Human Keratinocytes and Mouse Skin

1α,25-Dihydroxyvitamin D3 (1α,25(OH)2D3) and its analogs are used to treat psoriasis because of their potent antiproliferative activity. They have the potential for causing hypercalcemia, however, and patients often become resistant to the drug. We examined the feasibility of enhancing the cutaneous production of 1α,25(OH)2D3 using a human 25-hydroxyvitamin D-1α-hydroxylase (1α-OHase) plasmid. The 1α-OHase gene was fused to the green fluorescent protein gene (1α-OHase-GFP) driven by the cytomegalovirus promoter. Transfection of cultured normal human keratinocytes with the 1α-OHase-GFP plasmid resulted in a marked increase in the expression of 1α-OHase-GFP in the mitochondria. Transfection of keratinocytes with 1α-OHase-GFP or 1α-OHase plasmids in vitro enhanced the 1α-OHase activity substantially and increased the sensitivity of the keratinocytes to the antiproliferative effect of 25(OH)D3. The 1α-OHase-GFP plasmid was topically applied to shaved C57/BL6 mice. Twenty-four hours after topical application, immunohistochemical analysis of the skin for 1α-OHase-GFP revealed the presence of 1α-OHase-GFP in the epidermis and epidermal appendages including the hair follicles. The results from this study offer a unique new approach for the topical treatment of hyperproliferative disorders such as psoriasis and skin cancer using the 1α-OHase gene that could locally increase the production of 1α,25(OH)2D3 without causing hypercalcemia or resistance

The colonial ascidian \u3cem\u3eDidemnum\u3c/em\u3e sp. A: Current distribution, basic biology and potential threat to marine communities of the northeast and west coasts of North America

Didemnum sp. A is a colonial ascidian with rapidly expanding populations on the east and west coasts of North America. The origin of Didemum sp. A is unknown. Populations were first observed on the northeast coast of the U.S. in the late 1980s and on the west coast during the 1990s. It is currently undergoing a massive population explosion and is now a dominant member of many subtidal communities on both coasts. To determine Didemnum sp. A\u27s current distribution, we conducted surveys from Maine to Virginia on the east coast and from British Columbia to southern California on the west coast of the U.S. between 1998 and 2005. In nearshore locations Didemnum sp. A currently ranges from Eastport, Maine to Shinnecock Bay, New York on the east coast. On the west coast it has been recorded from Humboldt Bay to Port San Luis in California, several sites in Puget Sound, Washington, including a heavily fouled mussel culture facility, and several sites in southwestern British Columbia on and adjacent to oyster and mussel farms. The species also occurs at deeper subtidal sites (up to 81 m) off New England, including Georges, Stellwagen and Tillies Banks. On Georges Bank numerous sites within a 230 km2 area are 50–90% covered by Didemnum sp. A; large colonies cement the pebble gravel into nearly solid mats that may smother infaunal organisms. These observations suggest that Didemnum sp. A has the potential to alter marine communities and affect economically important activities such as fishing and aquaculture

Injection of FGD Grout to Abate Acid Mine Drainage in Underground Coal Mines

Acid Mine Drainage (AMD) from abandoned underground coal mines in Ohio is a concern for both residents and regulatory agencies. Effluent from these mines is typically characterized by low pH and high iron and sulfate concentrations and may contaminate local drinking-water supplies and streams. The objective of this project is to demonstrate the technical feasibility of injecting cementitious alkaline materials, such as Flue Gas Desulfurization (FGD) material to mitigate current adverse environmental impacts associated with AMD in a small, abandoned deep mine in Coshocton County Ohio. The Flue Gas Desulfurization material will be provided from American Electric Power`s (AEP) Conesville Plant. It will be injected as a grout mix that will use Fixated Flue Gas Desulfurization material and water. The subject site for this study is located on the border of Coshocton and Muskingum Counties, Ohio, approximately 1.5 miles south-southwest of the town of Wills Creek. The study will be performed at an underground mine designated as Mm-127 in the Ohio Department of Natural Resources register, also known as the Roberts-Dawson Mine. The mine operated in the mid-1950s, during which approximately 2 million cubic feet of coal was removed. Effluent discharging from the abandoned mine entrances has low pH in the range of 2.8-3.0 that drains directly into Wills Creek Lake. The mine covers approximately 14.6 acres. It is estimated that 26,000 tons of FGD material will be provided from AEP`s Conesville Power Plant located approximately 3 miles northwest of the subject site

The colonial ascidian Didemnum sp. A: Current distribution, basic biology and potential threat to marine communities of the northeast and west coasts of North America

Author Posting. © The Author(s), 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Experimental Marine Biology and Ecology 342 (2007): 99-108, doi:10.1016/j.jembe.2006.10.020.Didemnum sp. A is a colonial ascidian with rapidly expanding populations on the east and west coasts of North America. The origin of Didemum sp. A is unknown. Populations were first observed on the northeast coast of the U.S. in the late 1980s and on the west coast during the 1990s. It is currently undergoing a massive population explosion and is now a dominant member of many subtidal communities on both coasts. To determine Didemnum sp. A’s current distribution, we conducted surveys from Maine to Virginia on the east coast and from British Columbia to southern California on the west coast of the U.S. between 1998 and 2005. In nearshore locations Didemnum sp. A currently ranges from Eastport, Maine to Shinnecock Bay, New York on the east coast. On the west coast it has been recorded from Humboldt Bay to Port San Luis in California, several sites in Puget Sound, Washington, including a heavily fouled mussel culture facility, and several sites in southwestern British Columbia on and adjacent to oyster and mussel farms. The species also occurs at deeper subtidal sites (up to 81 m) off New England, including Georges, Stellwagen and Tillies Banks. On Georges Bank numerous sites within a 147 km2 area are 50-90% covered by Didemnum sp. A; large colonies cement the pebble gravel into nearly solid mats that may smother infaunal organisms. These observations suggest that Didemnum sp. A has the potential to alter marine communities and affect economically important activities such as fishing and aquaculture.Funding for this project was provided by EPA (STAR) grant GZ1910464 to R.B. Whitlatch, NSF-DGE 0114432 to J. Byrnes, NSF-OCE 0117839 to R. Etter and R.J. Miller, MIT Sea Grant NA86RG0074 and USEPA Grant GX83055701-0 to J. Pederson. RI Sea Grant NA07R90363 to J.S. Collie. Funding for A.N. Cohen and G. Lambert was provided by Mass. Sea Grant, U.S. EPA, Smithsonian Envl. Research Center Invasions Lab, Natl. Geographic Soc., San Francisco Bay-Delta Science Consortium and CALFED Science Program, Calif. Coastal Conservancy and the Rose Foundation. Additional funding and support was provided by the Stellwagen Bank National Marine Sanctuary

Mutual Altruism: Evidence from Alzheimer Patients and Their Spouse Caregivers

Background: Preferences of both Alzheimer patients and their spouse caregivers are related to a willingness-to-pay (WTP) measure which is used to test for the presence of mutual (rather than conventional unilateral) altruism. Methods: Contingent valuation experiments were conducted in 2000 – 2002, involving 126 Alzheimer patients and their caregiving spouses living in the Zurich metropolitan area (Switzerland). WTP values for three hypothetical treatments of the demented patient were elicited. The treatment Stabilization prevents the worsening of the disease, bringing dementia to a standstill. Cure restores patient health to its original level. In No burden, dementia takes its normal course while caregiver’s burden is reduced to its level before the disease. Results: The three different types of therapies are reflected in different WTP values of both caregivers and patients, suggesting that moderate levels of Alzheimer’s disease still permit clear expression of preference. According to the WTP values found, patients do not rank Cure higher than No burden, implying that their preferences are entirely altruistic. Caregiving spouses rank Cure before Burden, reflecting less than perfect altruism which accounts for some 40 percent of their to-tal WTP. Still, this constitutes evidence of mutual altruism. Conclusions: The evidence suggests that WTP values reflect individuals’ preferences even in Alzheimer patients. The values found suggest that an economically successful treatment should provide relief to caregivers, with its curative benefits being of secondary importance