Beating the Generator-Enumeration Bound for pp-Group Isomorphism

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime dividing the order of the group) has been the best worst-case result for general groups. In this work, we show the first improvement over the generator-enumeration bound for p-groups, which are believed to be the hard case of the group isomorphism problem. We start by giving a Turing reduction from group isomorphism to n^((1 / 2) log_p n + O(1)) instances of p-group composition-series isomorphism. By showing a Karp reduction from p-group composition-series isomorphism to testing isomorphism of graphs of degree at most p + O(1) and applying algorithms for testing isomorphism of graphs of bounded degree, we obtain an n^(O(p)) time algorithm for p-group composition-series isomorphism. Combining these two results yields an algorithm for p-group isomorphism that takes at most n^((1 / 2) log_p n + O(p)) time. This algorithm is faster than generator-enumeration when p is small and slower when p is large. Choosing the faster algorithm based on p and n yields an upper bound of n^((1 / 2 + o(1)) log n) for p-group isomorphism.Comment: 15 pages. This is an updated and improved version of the results for p-groups in arXiv:1205.0642 and TR11-052 in ECC

Never Again: Lessons from Louisiana's Gustav Evacuation

A report by STAND, a grassroots project of NOWCRJ, that exposes the impact of Lousiana's unjust and inequitable evacuation policy during the Hurricane Gustav on the state's poorest evacuees, based on hundreds of interviews with evacuees.This report exposes Louisiana's differential treatment sheltering policy which directs that in disasters, the state shall segregate evacuees relying on city/ state transportation in state-run warehouse shelters separate from evacuees using their own cars. Pursuant to this policy, the state advisory system directs self-transporting evacuees to separate parish, Red Cross, and church shelters with better conditions. Those who evacuate by bus are primarily the residents who do not have the economic means (or the cars) to self-evacuate, including homeless residents, public housing residents, low-wage workers, low-income renters, and their families -- almost all African American.This report's findings are based on assessments of the state-run warehouse shelters and extensive interviews of hundreds of affected residents. The findings expose startling inequity. In the Gustav evacuation, the state's differential treatment policy subjected the most vulnerable state residents to extremely inhumane shelter conditions. In each of the four state-run warehouse shelters, over a thousand evacuees were housed in a single large one-room space. Women, infants, children, the elderly, the sick, and the disabled were all using the same space, without privacy, and sharing the same bathrooms -- outdoor portable toilets. They had no access to running water inside the facilities. The only showers -- until close to the end of the evacuations -- were the portable toilets outside, in which mothers were washing themselves and their babies with bottled water. Residents had limited access to medical care, and no access to counselors or to news from the state about the hurricane and its aftermath

FAME, a microprocessor based front-end analysis and modeling environment

Higher order software (HOS) is a methodology for the specification and verification of large scale, complex, real time systems. The HOS methodology was implemented as FAME (front end analysis and modeling environment), a microprocessor based system for interactively developing, analyzing, and displaying system models in a low cost user-friendly environment. The nature of the model is such that when completed it can be the basis for projection to a variety of forms such as structured design diagrams, Petri-nets, data flow diagrams, and PSL/PSA source code. The user's interface with the analyzer is easily recognized by any current user of a structured modeling approach; therefore extensive training is unnecessary. Furthermore, when all the system capabilities are used one can check on proper usage of data types, functions, and control structures thereby adding a new dimension to the design process that will lead to better and more easily verified software designs

The Cost of Caring for Young Children

This study examines the "cost burden" of child care, defined as day care expenses divided by after-tax income. Data are from the wave 10 core and child care topical modules to the 1996 Survey of Income and Program Participation. We estimate that the average child under six years of age lives in a family that spends 4.9 percent of after-tax income on day care. However, this conceals wide variation: 63 percent of such children reside in families with no child care expenses and 10 percent are in families where the cost burden exceeds 16 percent. The burden is typically greater in single-parent than married-couple families but is not systematically related to a measure of socioeconomic status that we construct. One reason for this is that disadvantaged families use lower cost modes and pay less per hour for given types of care. The cost burden would be much less equal without low cost (presumably subsidized) formal care focused on needy families, as well as government tax and transfer policies that redistribute income towards them.

Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity

We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual $\star$-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.Comment: 13 page

Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization

We introduce normal coordinates on the infinite dimensional group $G$ introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincar\'e lemma, given a closed left invariant 1-form on $G$. For the special case of the ladder primitives, we find a second description that relates them to the Hopf algebra of functionals on power series with the usual product. Either approach shows that the ladder primitives are given by the Schur polynomials. The relevance of the lower central series of the dual Lie algebra in the process of renormalization is also discussed, leading to a natural concept of $k$-primitiveness, which is shown to be equivalent to the one already in the literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy