Keyed Non-Parametric Hypothesis Tests

The recent popularity of machine learning calls for a deeper understanding of AI security. Amongst the numerous AI threats published so far, poisoning attacks currently attract considerable attention. In a poisoning attack the opponent partially tampers the dataset used for learning to mislead the classifier during the testing phase. This paper proposes a new protection strategy against poisoning attacks. The technique relies on a new primitive called keyed non-parametric hypothesis tests allowing to evaluate under adversarial conditions the training input's conformance with a previously learned distribution $\mathfrak{D}$. To do so we use a secret key $\kappa$ unknown to the opponent. Keyed non-parametric hypothesis tests differs from classical tests in that the secrecy of $\kappa$ prevents the opponent from misleading the keyed test into concluding that a (significantly) tampered dataset belongs to $\mathfrak{D}$.Comment: Paper published in NSS 201

Fitness of Crop-Wild Hybrid Sunflower under Competitive Conditions: Implications for Crop-to-Wild Introgression

Understanding the likelihood and extent of introgression of novel alleles in hybrid zones requires comparison of lifetime fitness of parents and hybrid progeny. However, fitness differences among cross types can vary depending on biotic conditions, thereby influencing introgression patterns. Based on past work, we predicted that increased competition would enhance introgression between cultivated and wild sunflower (Helianthus annuus) by reducing fitness advantages of wild plants. To test this prediction, we established a factorial field experiment in Kansas, USA where we monitored the fitness of four cross types (Wild, F1, F2, and BCw hybrids) under different levels of interspecific and intraspecific competition. Intraspecific manipulations consisted both of density of competitors and of frequency of crop-wild hybrids. We recorded emergence of overwintered seeds, survival to reproduction, and numbers of seeds produced per reproductive plant. We also calculated two compound fitness measures: seeds produced per emerged seedling and seeds produced per planted seed. Cross type and intraspecific competition affected emergence and survival to reproduction, respectively. Further, cross type interacted with competitive treatments to influence all other fitness traits. More intense competition treatments, especially related to density of intraspecific competitors, repeatedly reduced the fitness advantage of wild plants when considering seeds produced per reproductive plant and per emerged seedling, and F2 plants often became indistinguishable from the wilds. Wild fitness remained superior when seedling emergence was also considered as part of fitness, but the fitness of F2 hybrids relative to wild plants more than quadrupled with the addition of interspecific competitors and high densities of intraspecific competitors. Meanwhile, contrary to prediction, lower hybrid frequency reduced wild fitness advantage. These results emphasize the importance of taking a full life cycle perspective. Additionally, due to effects of exogenous selection, a given hybrid generation may be especially well-suited to hastening introgression under particular environmental conditions.The study was conducted at and partially supported by the University of Kansas Field Station, a research unit of the Kansas Biological Survey and the University of Kansas. It was also supported by Biotechnology Risk Assessment Grant Program competitive grant no. 2006-39454-17438 to AAS, KLM, and HMA from the United States Department of Agriculture, National Institute of Food and Agriculture; www.nifa.usda.gov. Salaries and research support also provided by State and Federal funds appropriated to the Ohio Agricultural Research and Development Center, Ohio State University: manuscript no. HCS-14-07. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

An elementary proof of uniqueness of the particle trajectories for solutions of a class of shear-thinning non-Newtonian 2D fluids

We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories