Higher commutativity and nilpotency in finite groups

We consider ordered tuples in finite groups generating nilpotent subgroups. Given an integer $q$ we consider the poset of nilpotent subgroups of class less than $q$ and its corresponding coset poset. These posets give rise to a family of finite Dirichlet series parametrized by the nilpotency class of the subgroups, which in turn reflect probabilistic and topological invariants determined by these subgroups. Connections of these series to filtrations of classifying spaces of a group are discussed.Comment: 16 pages. Preliminary versio

Challenging Party Hegemony: Identity Work in China’s Emerging Virreal Places

The Chinese Communist Party has chosen to base the legitimacy of its rule on its performance as leading national power. Since national identity is based on shared imaginations of and directly tied to territory – hence place, this paper analyses both heterodox models for identification on the national and potentially competing place-based collective identities on the local level. This analysis, based on communication within a number of popular communication forums and on observation of behavior in the physical reality of today’s urban China, shows that communication within the virtual and behavior in the real world are not separated realities but form a new virreal spatial continuum consisting of imagined places both online and offline. I argue that ties to place are stronger and identities constructed on shared imaginations of place are more salient the more direct the experience of place is – be the place real, virtual or virreal. Hence in China challenges to one-party rule will probably accrue from competing localized collective identities rather than from heterodox nationalism.to explore the variety and complexity of functional antagonisms in the social subsystems.China, Internet, political power, collective identity, nationalism, place, bulletin, board system, online communication, online community

Perturbative operator approach to high-precision light-pulse atom interferometry

Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like magnetic stray fields or blackbody radiation. Pushing the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here, we present a systematic operator expansion to obtain phase shifts and contrast analytically in powers of the perturbation. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects

Fundamental Groups of Commuting Elements in Lie Groups

We compute the fundamental group of the spaces of ordered commuting $n$-tuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the computation of the mod-2 cohomology of the components of these spaces is also obtained

Should I Bug You? Identifying Domain Experts in Software Projects Using Code Complexity Metrics

In any sufficiently complex software system there are experts, having a deeper understanding of parts of the system than others. However, it is not always clear who these experts are and which particular parts of the system they can provide help with. We propose a framework to elicit the expertise of developers and recommend experts by analyzing complexity measures over time. Furthermore, teams can detect those parts of the software for which currently no, or only few experts exist and take preventive actions to keep the collective code knowledge and ownership high. We employed the developed approach at a medium-sized company. The results were evaluated with a survey, comparing the perceived and the computed expertise of developers. We show that aggregated code metrics can be used to identify experts for different software components. The identified experts were rated as acceptable candidates by developers in over 90% of all cases

Using Technology as a Vehicle to Appropriately Integrate Mathematics and Science Instruction for the Middle School

At the College of William and Mary, pre-service middle school science and mathematics teachers enroll in their respective methods courses taught in the same time period. Both instructors emphasize the importance of the content pedagogy unique to their disciplines in their individual courses such as strategies for teaching problem solving, computation, proportional reasoning, algebraic and geometric thinking in mathematics, and strategies for teaching students how to investigate or design and conduct experiments in science. However, the two classes come together for sessions in which they examine the relationship of the two disciplines and the proper role of technology, both graphing calculator and computer, in their instruction Starting with resources such as Science in Seconds for Kids by Jean Potter [1], the science students collaborate with the math students to design and conduct brief experiments. The data generated is analyzed using spreadsheets and later graphing calculators. Various classes of mathematical curves are examined using data generated by sensors/probes and CBLs. Through this experience the pre-service teachers learn to work collaboratively with their colleagues on meaningful tasks, strengthening the effectiveness of all participants

A New Keynesian Model with Endogenous Frictions

We develop a New Keynesian model that incorporates rigidities in the ability of households and firms to adjust their utility-efficient / profit-efficient resource allocation in response to shocks. These rigidities reflect the fact that households and firms enter into commitments for several periods of time regarding the allocation of resources limiting their ability to flexibly respond to unforeseen shocks. We show that these rigidities can adversely impact the productivity of firms and households' utility and result in the appearance of higher statistical moments in the demand and supply curves which are not exogenously constant but system-endogenous. As a result, we will derive the appearance of an inflation bias which exists even in the case of an efficient natural output and which cannot be removed by a rule-based monetary policy. Further, we show that monetary policy faces an additional trade-off in managing the friction losses due to inflation uncertainty and output uncertainty.