Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)

We show that Khovanov homology (and its sl(3) variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of 2-representations of categorified quantum sl(m) via categorical skew Howe duality. Utilizing Cautis-Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of Jones-Wenzl projectors and their sl(3) analogs purely from the higher representation theory of categorified quantum groups. In the sl(2) case, this work reveals the importance of a modified class of foams introduced by Christian Blanchet which in turn suggest a similar modified version of the sl(3) foam category introduced here.Comment: 75 pages, tikz and xypic figure

Animal experimentation and its relevance to man.

The problem of quantitatively estimating human cancer risk based upon animal carcinogenesis studies is reviewed. Mathematical functions for dose-response relationships are discussed with particular emphasis on multistage models. These models are based upon a single cell somatic mutation theory for the carcinogenesis process. It is shown that the multistage model and others which incorporate background additively are well approximated in low dose region by a linear function. The relationship between time-to-tumor and the multistage model is indicated. This relationship is important when dealing with less than life time exposure such as with data from many occupational studies. Design of bioassay experiments and its impact on risk estimation is noted. Finally, the problem of species-to-species extrapolation is considered

Statistical approaches to toxicological data.

Statistical techniques as applied to toxicological data are discussed. Issues concerning statistical hypothesis testing and combining studies are considered as well as design of experiments. The problems surrounding risk assessment are also mentioned

Radiation risk estimation models.

Cancer risk models and their relationship to ionizing radiation are discussed. There are many model assumptions and risk factors that have a large quantitative impact on the cancer risk estimates. Other health end points such as mental retardation may be an even more serious risk than cancer for those with in utero exposures

Ionizing radiation and cancer prevention.

Ionizing radiation long has been recognized as a cause of cancer. Among environmental cancer risks, radiation is unique in the variety of organs and tissues that it can affect. Numerous epidemiological studies with good dosimetry provide the basis for cancer risk estimation, including quantitative information derived from observed dose-response relationships. The amount of cancer attributable to ionizing radiation is difficult to estimate, but numbers such as 1 to 3% have been suggested. Some radiation-induced cancers attributable to naturally occurring exposures, such as cosmic and terrestrial radiation, are not preventable. The major natural radiation exposure, radon, can often be reduced, especially in the home, but not entirely eliminated. Medical use of radiation constitutes the other main category of exposure; because of the importance of its benefits to one's health, the appropriate prevention strategy is to simply work to minimize exposures

Cancer risk models for ionizing radiation.

Risk estimation in radiation carcinogenesis depends primarily on epidemiological data and hazard rate models. The A-bomb survivors follow-up provides information on the complexity of this process. Several hazard rate models are briefly discussed and illustrated using the A-bomb experience

Use of historical controls for animal experiments.

Statistical methods for the use of historical control data in testing for a trend in proportions in carcinogenicity rodent bioassays are reviewed. Asymptotic properties of the Hoel-Yanagawa exact conditional tests are developed and compared with the Tarone test. It is indicated that the Hoel-Yanagawa test is more powerful than the Tarone test. These tests depend on the beta-binomial parameters which are estimated from historical data. The goodness of fit of beta-binomial distributions to historical data is illustrated by application to the historical control database in the National Toxicology Program. Finally, sensitivities of the exact conditional test to the historical information is discussed and a conservative use of the test is considered

Nonlinearity of dose-response functions for carcinogenicity.

Carcinogenesis data for 315 chemicals were obtained from the National Cancer Institute-National Toxicology Program (NCI-NTP) bioassay programs and were analyzed to examine the shape of carcinogenesis dose-response curves. Tumor site data were more often consistent with a quadratic response than with a linear response, suggesting that the routine use of linear dose-response models will often overestimate risk. Information from in vivo short-term mutagenicity and genotoxicity assays was also obtained for most of these rodent bioassays. It was found that there were no clear relationships between the shape of the carcinogenesis dose-response curve and the result of the short-term test. These observations argue against the concept that carcinogens that are positive in a short-term assay be regulated using a linear dose-response curve and those that are negative be regulated using a sublinear dose-response curve or a safety factor approach

Metabolite-based internal doses used in a risk assessment of benzene.

Risk assessments of benzene have been based upon both human and animal studies. In this paper, metabolite information is used to construct an internal dose (a surrogate of the biologically effective dose) for a given administered dose. The relationship between the administered dose and this internal dose is nonlinear and is well described by a Michaelis-Menten function. The administered doses from the National Toxicology Program's rodent carcinogenicity study of benzene are transformed into internal doses, and these internal doses are used in conjunction with a multistage model to compare previous estimated virtually safe doses (VSD) associated with small added health risks. The ratio of VSD for the administered dose risk assessment to the VSD from the internal dose risk assessment was approximately 1.0 for the F344/N rats and ranged from 2.5 to 5.0 for B6C3F1 mice in the National Toxicology Program study. For an occupational exposure of 1 ppm, a risk estimate of 0.7 excess cancers/1000 exposed with an upper bound of 3.5/1000 was obtained for a total metabolite internal dose risk assessment. Risk estimates based upon internal doses constructed from levels of the toxic metabolites of benzene are also presented. The implication of a dose-rate study of benzene metabolism for risk assessment is discussed, and finally, suggestions for better characterization of the dose-response function for benzene are provided

Using mortality data to estimate radiation effects on breast cancer incidence.

In this paper we combine Japanese data on radiation exposure and cancer mortality with U.S. data on cancer incidence and lethality to estimate the effects of ionizing radiation on cancer incidence. The analysis is based on the mathematical relationship between the mortality rate and the incidence and lethality rates, as well as on statistical models that relate Japanese incidence rates to U.S. incidence rates and radiation risk factors. Our approach assumes that the risk of death from causes other than the cancer does not depend on whether or not the cancer is present, and among individuals with the cancer, the risk of death attributable to the cancer is the same in Japan and the U.S. and is not affected by radiation exposure. In particular, we focus on the incidence of breast cancer in Japanese women and how this incidence is affected by radiation risk factors. The analysis uses Japanese exposure and mortality data from the Radiation Effects Research Foundation study of atomic bomb survivors and U.S. incidence and lethality data from the Surveillance, Epidemiology, and End Results Registry. Even without Japanese incidence data, we obtain reasonable estimates of the incidence of breast cancer in unexposed Japanese women and identify the radiation risk factors that affect this incidence. Our analysis demonstrates that the age at exposure is an important risk factor, but that the incidence of breast cancer is not affected by the city of residence (Nagasaki versus Hiroshima) or the time since exposure