VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Crosstalk and the Dynamical Modularity of Feed-Forward Loops in Transcriptional Regulatory Networks

Network motifs, such as the feed-forward loop (FFL), introduce a range of complex behaviors to transcriptional regulatory networks, yet such properties are typically determined from their isolated study. We characterize the effects of crosstalk on FFL dynamics by modeling the cross regulation between two different FFLs and evaluate the extent to which these patterns occur in vivo. Analytical modeling suggests that crosstalk should overwhelmingly affect individual protein-expression dynamics. Counter to this expectation we find that entire FFLs are more likely than expected to resist the effects of crosstalk (approximate to 20% for one crosstalk interaction) and remain dynamically modular. The likelihood that cross-linked FFLs are dynamically correlated increases monotonically with additional crosstalk, but is independent of the specific regulation type or connectivity of the interactions. Just one additional regulatory interaction is sufficient to drive the FFL dynamics to a statistically different state. Despite the potential for modularity between sparsely connected network motifs, Escherichia coli (E. coli) appears to favor crosstalk wherein at least one of the cross-linked FFLs remains modular. A gene ontology analysis reveals that stress response processes are significantly overrepresented in the cross-linked motifs found within E. coli. Although the daunting complexity of biological networks affects the dynamical properties of individual network motifs, some resist and remain modular, seemingly insulated from extrinsic perturbations-an intriguing possibility for nature to consistently and reliably provide certain network functionalities wherever the need arise

Thermodynamical Properties of Hall Systems

We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the presence of an electromagnetic field and quantum statistical mechanically investigate its basic features. Solving the eigenvalue equation, we analytically derive the energy levels and the corresponding wavefunctions. These will be used, at low temperature and weak electric field, to determine the thermodynamical potential \Omega^{nc} and related physical quantities. Varying \Omega^{nc} with respect to the non-commutativity parameter \theta, we define a new function that can be interpreted as a \Omega^{nc} density. Evaluating the particle number, we show that the Hall conductivity of the system is \theta-dependent. This allows us to make contact with quantum Hall effect by offering different interpretations. We study the high temperature regime and discuss the magnetism of the system. We finally show that at \theta=2l_B^2, the system is sharing some common features with the Laughlin theory.Comment: 20 pages, misprints correcte

Examining the terminology of race issues in assessments for international exchange students

This study examined assignments by students from a university in Scotland and a university in the USA, and explored the terminology used by student when referring to race issues in assignments linked to practice. The findings suggest the terminology of race issues in assessments may be inappropriate for students because they allow racism to be marginalized from practice or presented in a way that conveys little analysis

Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics

We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of $i=\sqrt{-1}$ times a pseudo-Hermitian matrix, and determine the structure of the Lie groups consisting of pseudo-unitary matrices. In particular, we present a thorough treatment of $2\times 2$ pseudo-unitary matrices and discuss an example of a quantum system with a $2\times 2$ pseudo-unitary dynamical group. As other applications of our general results we give a proof of the spectral theorem for symplectic transformations of classical mechanics, demonstrate the coincidence of the symplectic group $Sp(2n)$ with the real subgroup of a matrix group that is isomorphic to the pseudo-unitary group U(n,n), and elaborate on an approach to second quantization that makes use of the underlying pseudo-unitary dynamical groups.Comment: Revised and expanded version, includes an application to symplectic transformations and groups, accepted for publication in J. Math. Phy

Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page