Numerical Experiments for Darcy Flow on a Surface Using Mixed Exterior Calculus Methods

There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus. However, we are not aware of any numerical experiments where mixed finite elements derived from discretizations of exterior calculus are used for a surface domain. This short note shows results of our preliminary experiments using mixed methods for Darcy flow (hence scalar Poisson's equation in mixed form) on surfaces. We demonstrate two numerical methods. One is derived from the primal-dual Discrete Exterior Calculus and the other from lowest order finite element exterior calculus. The programming was done in the language Python, using the PyDEC package which makes the code very short and easy to read. The qualitative convergence studies seem to be promising.Comment: 14 pages, 11 figure

Least Squares Ranking on Graphs

Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise the comparison data. The basic idea is very simple and old: come up with values on vertices such that their differences match the given edge data. Since an exact match will usually be impossible, one settles for matching in a least squares sense. This formulation was first described by Leake in 1976 for rankingfootball teams and appears as an example in Professor Gilbert Strang's classic linear algebra textbook. If one is willing to look into the residual a little further, then the problem really comes alive, as shown effectively by the remarkable recent paper of Jiang et al. With or without this twist, the humble least squares problem on graphs has far-reaching connections with many current areas ofresearch. These connections are to theoretical computer science (spectral graph theory, and multilevel methods for graph Laplacian systems); numerical analysis (algebraic multigrid, and finite element exterior calculus); other mathematics (Hodge decomposition, and random clique complexes); and applications (arbitrage, and ranking of sports teams). Not all of these connections are explored in this paper, but many are. The underlying ideas are easy to explain, requiring only the four fundamental subspaces from elementary linear algebra. One of our aims is to explain these basic ideas and connections, to get researchers in many fields interested in this topic. Another aim is to use our numerical experiments for guidance on selecting methods and exposing the need for further development.Comment: Added missing references, comparison of linear solvers overhauled, conclusion section added, some new figures adde

Magnonic spin-transfer torque MRAM with low power, high speed, and error-free switching

A new class of spin-transfer torque magnetic random access memory (STT-MRAM) is discussed, in which writing is achieved using thermally initiated magnonic current pulses as an alternative to conventional electric current pulses. The magnonic pulses are used to destabilize the magnetic free layer from its initial direction, and are followed immediately by a bipolar electric current exerting conventional spin-transfer torque on the free layer. The combination of thermal and electric currents greatly reduces switching errors, and simultaneously reduces the electric switching current density by more than an order of magnitude as compared to conventional STT-MRAM. The energy efficiency of several possible electro-thermal circuit designs have been analyzed numerically. As compared to STT-MRAM with perpendicular magnetic anisotropy, magnonic STT-MRAM reduces the overall switching energy by almost 80%. Furthermore, the lower electric current density allows the use of thicker tunnel barriers, which should result in higher tunneling magneto-resistance and improved tunnel barrier reliability. The combination of lower power, improved reliability, higher integration density, and larger read margin make magnonic STT-MRAM a promising choice for future non-volatile storage.Comment: 9 Pages, 11 Figure

Sequential Innovation in Mobile App Development

PROBLEM DEFINITION: In today’s highly dynamic and competitive app markets, a significant portion of development takes place after the initial product launch via the addition of new features and the enhancement of existing products. In managing the sequential innovation process in mobile app development, two key operational questions arise. (i) What features and attributes should be added to existing products in successive versions? (ii) How should these features and attributes be implemented for greater market success? We investigate the implications of three different types of mobile app development activities on market performance. ACADEMIC/PRACTICAL RELEVANCE: Our study contributes to the operations management literature by providing an empirically based understanding of sequential innovation and its market performance implications in mobile app development, an important industry in terms of size, scope and potential. METHODOLOGY: Using a novel data set of mobile apps in the Productivity category, we leverage text-mining and information retrieval techniques to study the rich information in the release notes of apps. We then characterize product development activities at each version release and link these activities with app performance in a dynamic estimation model. We also incorporate an instrumental variables analysis to substantiate our findings. RESULTS: We find that greater update dissimilarity (i.e., dissimilarity of the features and attributes of a new update from those of previous updates) is associated with higher performance, especially in mature apps. We also find that the greater the product update market orientation (i.e., the greater the similarity of the focal firm’s new features and attributes with respect to the recent additions of its competitors), the higher is the market performance. This finding suggests that the market rewards those developers who have a responsive policy to their competitors’ product innovation efforts. Our results also suggest that a rapid introduction of updates dampens the potential market benefits that the mobile app developers might gain from market orientation. We find no evidence of a beneficial effect of product update scope (i.e., incorporating features and attributes from other product subcategories) on market performance. MANAGERIAL IMPLICATIONS: Our study offers managerial insights into mobile app development by exploring the sequential innovation characteristics that are associated with greater market success in pursuing and implementing new features and attributes

PNA Targeting the PBS and A-Loop Sequences of HIV-1 Genome Destabilizes Packaged tRNA3Lys in the Virions and Inhibits HIV-1 Replication

AbstractDuring assembly of the HIV-1 virions, cellular tRNALys3 is packaged into the virion particles and is utilized as a primer for the initiation of reverse transcription. The 3′-terminal 18 nucleotides of the cellular tRNALys3 are complementary to nucleotides 183–201 of the viral RNA genome, referred to as the primer binding sequence (PBS). Additional sequences (A-Loop) upstream of the PBS are essential for tRNA primer selection. We report here that a PNA targeted to PBS and A-Loop sequence (PNAPBS) exhibits high specificity for its target sequence and prevents tRNALys3 priming on the viral genome. We also demonstrate that PNAPBS is able to invade the duplex region of the tRNALys3–viral RNA complex and destabilize the priming process, thereby inhibiting the in vitro initiation of reverse transcription. The endogenously packaged tRNALys3 bound to the PBS region of the viral RNA genome in the HIV-1 virion is efficiently competed out by PNAPBS, resulting in near complete inhibition of initiation of endogenous reverse transcription. Examination of the effect of PNAPBS on HIV-1 production in CEM cells infected with pseudotyped HIV-1 virions carrying luciferase reporter exhibited dramatic reduction of HIV-1 replication by nearly 99%. Analysis of the mechanism of PNAPBS-mediated inhibition indicated that PNAPBS interferes at the step of reverse transcription. These findings suggest the antiviral efficacy of PNAPBS in blocking the process of HIV-1 replication

Delaunay Hodge Star

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for DEC and is a diagonal matrix with the ratio of primal and dual volumes along the diagonal. A correct definition requires that all entries be positive. DEC is a framework for numerically solving differential equations on meshes and for geometry processing tasks and has had considerable impact in computer graphics and scientific computing. Our result allows the use of DEC with a much larger class of meshes than was previously considered possible.Comment: Corrected error in Figure 1 (columns 3 and 4) and Figure 6 and a formula error in Section 2. All mathematical statements (theorems and lemmas) are unchanged. The previous arXiv version v3 (minus the Appendix) appeared in the journal Computer-Aided Desig

Coherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit

The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.Comment: Change in the format from aps to iop since we decided to submit it to NJP; Minor changes in tex