Pseudodeterminants and perfect square spanning tree counts

The pseudodeterminant $\textrm{pdet}(M)$ of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If $\partial$ is a symmetric or skew-symmetric matrix then $\textrm{pdet}(\partial\partial^t)=\textrm{pdet}(\partial)^2$. Whenever $\partial$ is the $k^{th}$ boundary map of a self-dual CW-complex $X$, this linear-algebraic identity implies that the torsion-weighted generating function for cellular $k$-trees in $X$ is a perfect square. In the case that $X$ is an \emph{antipodally} self-dual CW-sphere of odd dimension, the pseudodeterminant of its $k$th cellular boundary map can be interpreted directly as a torsion-weighted generating function both for $k$-trees and for $(k-1)$-trees, complementing the analogous result for even-dimensional spheres given by the second author. The argument relies on the topological fact that any self-dual even-dimensional CW-ball can be oriented so that its middle boundary map is skew-symmetric.Comment: Final version; minor revisions. To appear in Journal of Combinatoric

Sequential induction of NF-κB/Rel family proteins during B-cell terminal differentiation

The NF-kappa B/Rel family of at least five transcription factor polypeptides is thought to function both as a developmental regulator in B cells and as a rapid response system in all cells. To examine this notion in more detail, we determined the protein contents of both the inducible and constitutive NF-kappa B/Rel activities in a pre-B-cell line, 70Z/3, and a mature B-cell line, WEHI 231. NF-kappa B p50/p65 is the major inducible nuclear complex after lipopolysaccharide or phorbol myristate acetate treatment of 70Z/3 cells. The constitutive and inducible complexes in WEHI 231 cells are mainly composed of p50 and Rel. The constitutive or induced activities are all sensitive to I kappa B-alpha, but this inhibitor is very short-lived in WEHI 231 cells, suggesting that the balance between synthesis and degradation of I kappa B-alpha determines whether a particular cell lineage has constitutive activity. A patterned expression of the NF-kappa B/Rel activator proteins emerges from an analysis of other B-lineage cell lines and splenic B cells: mainly p50 and p65 in pre-B (and non-B) cells, a predominance of Rel and p50 in mature B cells, and expression of p52 and RelB in plasmacytoma lines. This ordered pattern of regulators may reflect the requirement for expression of different genes during terminal B-cell differentiation because different combinations of NF-kappa B/Rel family members preferentially activate distinct kappa B sites in reporter constructs

Still flat after all these years

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is amenable to measurement, through tests such as the determination of the angles of sufficiently large triangles. The angle subtended by the characteristic scale on the Cosmic Microwave sky provides a direct test, which has now been realised through a combination of exquisite results from a number of CMB experiments. After a long and detailed investigation, with many false clues, it seems that the mystery of the curvature of the Universe is now solved. It's an open and shut case: the Universe is flat.Comment: 7 pages, 2 figures, submitted to the Gravity Research Foundation Essay Competition for 200

Use of Alumni Advisory Board in Assessment of Achievement of Student Outcomes in Capstone Design

This paper discussed the use of the Alumni Advisory Board in assessment of capstone design projects. Since it is an ABET requirement that engineering programs obtain input from outside constituents on the continuous improvement processes for their programs, practically all engineering departments have established some form of external alumni advisory board which meets with the department administration and faculty on a regular basis, usually every semester. Since these boards are already in place, they can be used to assess the achievement of ABET student outcomes in the capstone design course. Specifically, the Alumni Advisory Board can be used to evaluate students’ oral presentations, if the schedule of their visit is aligned to coincide with the required presentations of the capstone design course. The Alumni Advisory Board members can also evaluate the final written project reports, which can be done anytime after the completion of the student projects, and so is not schedule dependent. At Bradley University we have conducted both of these assessments over the last ten years. An evaluation template has been developed for the final written reports that covers most of the ABET student outcomes a-k. A rubric has also been developed for evaluation of student poster presentations

DIRECT ESTIMATION OF ABOVEGROUND FOREST PRODUCTIVITY THROUGH HYPERSPECTRAL REMOTE SENSING OF CANOPY NITROGEN

The concentration of nitrogen in foliage has been related to rates of net photosynthesis across a wide range of plant species and functional groups and thus represents a simple and biologically meaningful link between terrestrial cycles of carbon and nitrogen. Although foliar N is used by ecosystem models to predict rates of leaf‐level photosynthesis, it has rarely been examined as a direct scalar to stand‐level carbon gain. Establishment of such relationships would greatly simplify the nature of forest C and N linkages, enhancing our ability to derive estimates of forest productivity at landscape to regional scales. Here, we report on a highly predictive relationship between whole‐canopy nitrogen concentration and aboveground forest productivity in diverse forested stands of varying age and species composition across the 360 000‐ha White Mountain National Forest, New Hampshire, USA. We also demonstrate that hyperspectral remote sensing can be used to estimate foliar N concentration, and hence forest production across a large number of contiguous images. Together these data suggest that canopy‐level N concentration is an important correlate of productivity in these forested systems, and that imaging spectrometry of canopy N can provide direct estimates of forest productivity across large landscapes

Chemistry in isolation: High CCH/HCO+ line ratio in the AMIGA galaxy CIG 638

Multi-molecule observations towards an increasing variety of galaxies have been showing that the relative molecular abundances are affected by the type of activity. However, these studies are biased towards bright active galaxies, which are typically in interaction. We study the molecular composition of one of the most isolated galaxies in the local Universe where the physical and chemical properties of their molecular clouds have been determined by intrinsic mechanisms. We present 3 mm broad band observations of the galaxy CIG 638, extracted from the AMIGA sample of isolated galaxies. The emission of the J=1-0 transitions of CCH, HCN, HCO+, and HNC are detected. Integrated intensity ratios between these line are compared with similar observations from the literature towards active galaxies including starburst galaxies (SB), active galactic nuclei (AGN), luminous infrared galaxies (LIRG), and GMCs in M33. A significantly high ratio of CCH with respect to HCN, HCO+, and HNC is found towards CIG 638 when compared with all other galaxies where these species have been detected. This points to either an overabundance of CCH or to a relative lack of dense molecular gas as supported by the low HCN/CO ratio, or both. The data suggest that the CIG 638 is naturally a less perturbed galaxy where a lower fraction of dense molecular gas, as well as a more even distribution could explain the measured ratios. In this scenario the dense gas tracers would be naturally dimmer, while the UV enhanced CCH, would be overproduced in a less shielded medium.Comment: Letter accepted for publication in A&

Solid-Phase Synthesis of Amine/Carboxyl Substituted Prolines and Proline Homologues: Scope and Limitations

A solid-phase procedure is used to synthesize racemic peptidomimetics based on the fundamental peptide unit. The peptidomimetics are constructed around proline or proline homologues variably substituted at the amine and carbonyl sites. The procedure expands the diversity of substituted peptidomimetic molecules available to the Distributed Drug Discovery (D3) project. Using a BAL-based solid-phase synthetic sequence the proline or proline homologue subunit is both constructed and incorporated into the peptidomimetic by an α-alkylation, hydrolysis and intramolecular cyclization sequence. Further transformations on solid-phase provide access to a variety of piperazine derivatives representing a class of molecules known to exhibit central nervous system activity. The procedure works well with proline cores, but with larger six- and seven-membered ring homologues the nature of the carboxylic acid acylating the cyclic amine can lead to side reactions and result in poor overall yields