On a Tree and a Path with no Geometric Simultaneous Embedding

Two graphs $G_1=(V,E_1)$ and $G_2=(V,E_2)$ admit a geometric simultaneous embedding if there exists a set of points P and a bijection M: P -> V that induce planar straight-line embeddings both for $G_1$ and for $G_2$. While it is known that two caterpillars always admit a geometric simultaneous embedding and that two trees not always admit one, the question about a tree and a path is still open and is often regarded as the most prominent open problem in this area. We answer this question in the negative by providing a counterexample. Additionally, since the counterexample uses disjoint edge sets for the two graphs, we also negatively answer another open question, that is, whether it is possible to simultaneously embed two edge-disjoint trees. As a final result, we study the same problem when some constraints on the tree are imposed. Namely, we show that a tree of depth 2 and a path always admit a geometric simultaneous embedding. In fact, such a strong constraint is not so far from closing the gap with the instances not admitting any solution, as the tree used in our counterexample has depth 4.Comment: 42 pages, 33 figure

Recognition and Belonging: Engaging First Generation Students

This paper is based on a reflective journey taken by project members which offers insight into the unique challenges that first generation students face and considers the institutional responses needed to enhance their engagement and experience. The student as academic partner’s project was developed to further explore issues of recognition, belonging and engagement for first generation students - who are the first in their families to attend higher education. Whilst this group of students should be celebrated as pioneers of higher education they are more likely than their counterparts to drop out of their studies or have a difficult transition to higher education because they lack the required social capital. In the face of widening participation and increasing access to university for students from diverse backgrounds the paper will consider the tension between the need for students to adapt in order to fit the university and the university’s need to adapt in order to fit the students. We will highlight small developments that can have the largest impact on both the university and the student population. Through this research, we believe that being a first generation student is not a barrier but a real and ongoing achievement

Bone marrow transplantation alters the tremor phenotype in the murine model of globoid-cell leukodystrophy

Tremor is a prominent phenotype of the twitcher mouse, an authentic genetic model of Globoid-Cell Leukodystrophy (GLD, Krabbe’s disease). In the current study, the tremor was quantified using a force-plate actometer designed to accommodate low-weight mice. The actometer records the force oscillations caused by a mouse’s movements, and the rhythmic structure of the force variations can be revealed. Results showed that twitcher mice had significantly increased power across a broad band of higher frequencies compared to wildtype mice. Bone marrow transplantation (BMT), the only available therapy for GLD, worsened the tremor in the twitcher mice and induced a measureable alteration of movement phenotype in the wildtype mice. These data highlight the damaging effects of conditioning radiation and BMT in the neonatal period. The behavioral methodology used herein provides a quantitative approach for assessing the efficacy of potential therapeutic interventions for Krabbe’s disease

Cosmic ray tables - Asymptotic directions, variational coefficients and cut-off rigidities IQSY instruction manual no. 10

Cosmic ray deflections in geomagnetic field, variational coefficients, and diurnal intensity variations - table

Fluid-crystal coexistence for proteins and inorganic nanocolloids: dependence on ionic strength

We investigate theoretically the fluid-crystal coexistence of solutions of globular charged nanoparticles like proteins and inorganic colloids. The thermodynamic properties of the fluid phase are computed via the optimized Baxter model. This is done specifically for lysozyme and silicotungstates for which the bare adhesion parameters are evaluated via the experimental second virial coefficients. The electrostatic free energy of the crystal is approximated by supposing the cavities in the interstitial phase between the particles are spherical in form. In the salt-free case a Poisson-Boltzmann equation is solved to calculate the effective charge on a particle and a Donnan approximation is used to derive the chemical potential and osmotic pressure in the presence of salt. The coexistence data of lysozyme and silicotungstates are analyzed within this scheme, especially with regard to the ionic-strength dependence of the chemical potentials. The latter agree within the two phases provided some upward adjustment of the effective charge is allowed for.Comment: 15 pages, 9 figure

Proper Sanitization of Broiler and Pullet Houses.

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Degenerate Fermi gas perturbations at standard background cosmology

The hypothesis of a tiny fraction of the cosmic inventory evolving cosmologically as a degenerate Fermi gas test fluid at some dominant cosmological background is investigated. Our analytical results allow for performing preliminary computations to the evolution of perturbations for relativistic and non-relativistic test fluids. The density fluctuation, $\delta$, the fluid velocity divergence, $\theta$, and an explicit expression for the dynamics of the shear stress, $\sigma$, are obtained for a degenerate Fermi gas in the background regime of radiation. Extensions to the dominance of matter and to the $\Lambda$CDM cosmological background are also investigated and lessons concerning the formation of large structures of degenerate Fermi gas are depicted.Comment: 20 pages, 4 figure

Exactly solvable extended Hubbard model

In this work, we introduce long range version of the extended Hubbard model. The system is defined on a non-uniform lattice. We show that the system is integrable. The ground state, the ground state energies, the energy spectrum are also found for the system. Another long range version of the extended Hubbard model is also introduced on a uniform lattice, and this system is proven to be integrable.Comment: 10 pages, Latex. Typoes are fixed in this revised versio

The development of biofilm architecture

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al. (2011 Proc. R. Soc. A 467, 1449–1467 (doi:10.1098/rspa.2010.0327)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures