Motivic invariants of p-adic fields

We provide a complete analysis of the motivic Adams spectral sequences converging to the bigraded coefficients of the 2-complete algebraic Johnson-Wilson spectra BPGL over p-adic fields. These spectra interpolate between integral motivic cohomology (n=0), a connective version of algebraic K-theory (n=1), and the algebraic Brown-Peterson spectrum. We deduce that, over p-adic fields, the 2-complete BPGL split over 2-complete BPGL, implying that the slice spectral sequence for BPGL collapses. This is the first in a series of two papers investigating motivic invariants of p-adic fields, and it lays the groundwork for an understanding of the motivic Adams-Novikov spectral sequence over such base fields.Comment: 19 pages, 3 figures. Substantially updated from initial version to better reflect the version of the paper published a year ag

Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schr\"odinger Equations

We consider the existence and stability of real-valued, spatially antiperiodic standing wave solutions to a family of nonlinear Schr\"odinger equations with fractional dispersion and power-law nonlinearity. As a key technical result, we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations, i.e. that its kernel is generated by the translational and gauge symmetries of the governing evolution equation. In the process, we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional Schr\"odinger operators on $\mathbb{R}$ with real-valued, periodic potentials as well as a Sturm-Liouville type oscillation theory for the higher antiperiodic eigenfunctions.Comment: 46 pages, 2 figure

Student Privacy in Learning Analytics: An Information Ethics Perspective

In recent years, educational institutions have started using the tools of commercial data analytics in higher education. By gathering information about students as they navigate campus information systems, learning analytics “uses analytic techniques to help target instructional, curricular, and support resources” to examine student learning behaviors and change students’ learning environments. As a result, the information educators and educational institutions have at their disposal is no longer demarcated by course content and assessments, and old boundaries between information used for assessment and information about how students live and work are blurring. Our goal in this paper is to provide a systematic discussion of the ways in which privacy and learning analytics conflict and to provide a framework for understanding those conflicts. We argue that there are five crucial issues about student privacy that we must address in order to ensure that whatever the laudable goals and gains of learning analytics, they are commensurate with respecting students’ privacy and associated rights, including (but not limited to) autonomy interests. First, we argue that we must distinguish among different entities with respect to whom students have, or lack, privacy. Second, we argue that we need clear criteria for what information may justifiably be collected in the name of learning analytics. Third, we need to address whether purported consequences of learning analytics (e.g., better learning outcomes) are justified and what the distributions of those consequences are. Fourth, we argue that regardless of how robust the benefits of learning analytics turn out to be, students have important autonomy interests in how information about them is collected. Finally, we argue that it is an open question whether the goods that justify higher education are advanced by learning analytics, or whether collection of information actually runs counter to those goods

Advertising and Collusion in Retails Markets

We consider non-price advertising by retail firms that are privately informed as to their respective production costs. We first analyze a static model. We construct an advertising equilibrium, in which informed consumers use an advertising search rule whereby they buy from the highest-advertising firm. Consumers are rational in using the advertising search rule, since the lowest-cost firm advertises the most and also selects the lowest price. Even though the advertising equilibrium facilitates productive efficiency, we establish conditions under which firms enjoy higher expected profit when advertising is banned. Consumer welfare falls in this case, however. We next analyze a dynamic model in which privately informed firms interact repeatedly. In this setting, firms may achieve a collusive equilibrium in which they limit the use of advertising, and we establish conditions under which optimal collusion entails pooling at zero advertising. More generally, full or partial pooling is observed in optimal collusion. In summary, non-price advertising can promote product efficiency and raise consumer welfare; however, firms often have incentive to diminish advertising competition, whether through regulatory restrictions or collusion.non-price advertising, retail firms, advertising equilibrium

Two systems developed for purifying inert atmospheres

Two systems, one for helium and one for argon, are used for purifying inert atmospheres. The helium system uses an activated charcoal bed at liquid nitrogen temperature to remove oxygen and nitrogen. The argon system uses heated titanium sponge to remove nitrogen and copper wool beds to remove oxygen. Both use molecular sieves to remove water vapor