A matrix representation of graphs and its spectrum as a graph invariant

We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the first two cases, we compute the spectrum explicitly and show that it is determined by the spectrum of the adjacency matrix of the original graph. We then show by computation that the isomorphism classes of many known families of strongly regular graphs (up to 64 vertices) are characterized by the spectrum of this matrix. We conjecture that this is always the case for strongly regular graphs and we show that the conjecture is not valid for general graphs. We verify that the smallest regular graphs which are not distinguished with our method are on 14 vertices.Comment: 14 page

Senior Recital, Simone Monroe, clarinet

The presentation of this senior recital will fulfill in part the requirements for the Bachelor of Music degree in Education. Simone Monroe studies clarinet with Dr. Tiffany Valvo

Co-evolution of networks and quantum dynamics: a generalization of preferential attachment

We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert model of preferential attachment and has a rich set of tunable parameters, such as the initial conditions of the dynamics or the interaction of the system with its environment. We show that the model produces networks with two-modal power-law degree distributions, super-hubs, finite clustering coefficient, small-world behaviour and non-trivial degree-degree correlations.Comment: 8 pages, 2 figure

Intermittent permeation of cylindrical nanopores by water

Molecular Dynamics simulations of water molecules in nanometre sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is {\emph{intermittent}} on a nanosecond timescale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulk-like. Its behaviour differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract into a highly layered structure inside the channel.Comment: 4 pages, 4 figure

Mercury's geochronology revised by applying Model Production Functions to Mariner 10 data: geological implications

Model Production Function chronology uses dynamic models of the Main Belt Asteroids (MBAs) and Near Earth Objects (NEOs) to derive the impactor flux to a target body. This is converted into the crater size-frequency-distribution for a specific planetary surface, and calibrated using the radiometric ages of different regions of the Moon's surface. This new approach has been applied to the crater counts on Mariner 10 images of the highlands and of several large impact basins on Mercury. MPF estimates for the plains show younger ages than those of previous chronologies. Assuming a variable uppermost layering of the Hermean crust, the age of the Caloris interior plains may be as young as 3.59 Ga, in agreement with MESSENGER results that imply that long-term volcanism overcame contractional tectonics. The MPF chronology also suggests a variable projectile flux through time, coherent with the MBAs for ancient periods and then gradually comparable also to the NEOs.Comment: Accepted by Journal Geophysical Research Letter

Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.Comment: 14 pages, 4 figure

Ion channel recordings on an injection-molded polymer chip

In this paper, we demonstrate recordings of the ion channel activity across the cell membrane in a biological cell by employing the so-called patch clamping technique on an injection-molded polymer microfluidic device. The findings will allow direct recordings of ion channel activity to be made using the cheapest materials and production platform to date and with the potential for very high throughput. The employment of cornered apertures for cell capture allowed the fabrication of devices without through holes and via a scheme comprising master origination by dry etching in a silicon substrate, electroplating in nickel and injection molding of the final part. The most critical device parameters were identified as the length of the patching capillary and the very low surface roughness on the inside of the capillary. The cross-sectional shape of the orifice was found to be less critical, as both rectangular and semicircular profiles seemed to have almost the same ability to form tight seals with cells with negligible leak currents. The devices were functionally tested using human embryonic kidney cells expressing voltage-gated sodium channels (Nav1.7) and benchmarked against a commercial state-of-the-art system for automated ion channel recordings. These experiments considered current–voltage (IV) relationships for activation and inactivation of the Nav1.7 channels and their sensitivity to a local anesthetic, lidocaine. Both IVs and lidocaine dose–response curves obtained from the injection-molded polymer device were in good agreement with data obtained from the commercial system

Right to Serve, Right to Lead: Lives and Legacies of the USCT

This is a catalog for an exhibit that follows the evolution of African-American participation in the Civil War, from slaves, to contrabands, to soldiers of the United States Colored Troops (USCT), as well as the lives of black veterans beyond the war, and their ultimate military and social legacy. Using a variety of period items, it creates a narrative that stretches from the Antebellum Period to the current day. In doing so, the exhibit shows how black sacrifice on the battlefield redefined the war\u27s purpose throughout the divided nation, how Jim Crowe suppressed the memory of black participation after Reconstruction, and how the illustrious African-American military tradition left by the USCT endures to this day in their modern heirs

Iron Status and Analysis of Efficacy and Safety of Ferric Carboxymaltose Treatment in Patients with Inflammatory Bowel Disease

Background and Aims:We analyzed iron deficiency and the therapeutic response following intravenous ferric carboxymaltose in a large single-center inflammatory bowel disease (IBD) cohort. Methods: 250 IBD patients were retrospectively analyzed for iron deficiency and iron deficiency anemia. A subgroup was analyzed regarding efficacy and side effects of iron supplementation with ferric carboxymaltose. Results: In the cohort (n = 250), 54.4% of the patients had serum iron levels 60 mu g/dl, 61.6% had ferritin >100 ng/ml, and 90.7% reached Hb >12/13 g/dl at follow-up (p < 0.0001 for all parameters vs. pretreatment values). The most frequent adverse event was a transient increase of liver enzymes with male gender as risk factor (p = 0.008, OR 8.62, 95% CI 1.74-41.66). Conclusions: Iron deficiency and anemia are frequent in IBD patients. Treatment with ferric carboxymaltose is efficious, safe and well tolerated in iron-deficient IBD patients. Copyright (C) 2011 S. Karger AG, Base