Explicit convex and concave envelopes through polyhedral subdivisions with Unstable Equilibria

In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of concave-extendable supermodular functions and the convex envelopes of disjunctive convex functions.

Internet Versus Mailed Questionnaires: A Randomized Comparison (2)

BACKGROUND Low response rates among surgeons can threaten the validity of surveys. Internet technologies may reduce the time, effort, and financial resources needed to conduct surveys. OBJECTIVE We investigated whether using Web-based technology could increase the response rates to an international survey. METHODS We solicited opinions from the 442 surgeon–members of the Orthopaedic Trauma Association regarding the treatment of femoral neck fractures. We developed a self-administered questionnaire after conducting a literature review, focus groups, and key informant interviews, for which we used sampling to redundancy techniques. We administered an Internet version of the questionnaire on a Web site, as well as a paper version, which looked similar to the Internet version and which had identical content. Only those in our sample could access the Web site. We alternately assigned the participants to receive the survey by mail (n=221) or an email invitation to participate on the Internet (n=221). Non-respondents in the mail arm received up to three additional copies of the survey, while non-respondents in the Internet arm received up to three additional requests, including a final mailed copy. All participants in the Internet arm had an opportunity to request an emailed Portable Document Format (PDF) version. RESULTS The Internet arm demonstrated a lower response rate (99/221, 45%) than the mail questionnaire arm (129/221, 58%) (absolute difference 13%, 95% confidence interval 4%-22%, P<0.01). CONCLUSIONS. Our Internet-based survey to surgeons resulted in a significantly lower response rate than a traditional mailed survey. Researchers should not assume that the widespread availability and potential ease of Internet-based surveys will translate into higher response rates.Department of Surgery, McMaster University, Hamilton, Ontario, Canad

Applying asymptotic methods to synthetic biology: modelling the reaction kinetics of the mevalonate pathway

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class of organic compounds. This pathway has been successfully introduced to Escherichia coli, enabling a biosynthetic production route for many isoprenoids. In this paper, we develop and solve a mathematical model for the concentration of metabolites in the mevalonate pathway over time, accounting for the loss of acetyl-CoA to other metabolic pathways. Additionally, we successfully test our theoretical predictions experimentally by introducing part of the pathway into Cupriavidus necator. In our model, we exploit the natural separation of time scales as well as of metabolite concentrations to make significant asymptotic progress in understanding the system. We confirm that our asymptotic results agree well with numerical simulations, the former enabling us to predict the most important reactions to increase isopentenyl diphosphate production whilst minimizing the levels of HMG-CoA, which inhibits cell growth. Thus, our mathematical model allows us to recommend the upregulation of certain combinations of enzymes to improve production through the mevalonate pathway

Particle-Hole Asymmetry in Doped Mott Insulators: Implications for Tunneling and Photoemission Spectroscopies

In a system with strong local repulsive interactions it should be more difficult to add an electron than to extract one. We make this idea precise by deriving various exact sum rules for the one-particle spectral function independent of the details of the Hamiltonian describing the system and of the nature of the ground state. We extend these results using a variational ansatz for the superconducting ground state and low lying excitations. Our results shed light on the striking asymmetry in the tunneling spectra of high Tc superconductors and should also be useful in estimating the local doping variations in inhomogeneous materials.Comment: 4 pages, no figure

Fermions in 3D Optical Lattices: Cooling Protocol to Obtain Antiferromagnetism

A major challenge in realizing antiferromagnetic (AF) and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling, but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an AF Mott phase.Comment: 4 pages; 5 figures; also see supplementary material in 2 pages with 1 figur

Verification and Validation of Semantic Annotations

In this paper, we propose a framework to perform verification and validation of semantically annotated data. The annotations, extracted from websites, are verified against the schema.org vocabulary and Domain Specifications to ensure the syntactic correctness and completeness of the annotations. The Domain Specifications allow checking the compliance of annotations against corresponding domain-specific constraints. The validation mechanism will detect errors and inconsistencies between the content of the analyzed schema.org annotations and the content of the web pages where the annotations were found.Comment: Accepted for the A.P. Ershov Informatics Conference 2019(the PSI Conference Series, 12th edition) proceedin

Viscosity of strongly interacting quantum fluids: spectral functions and sum rules

The viscosity of strongly interacting systems is a topic of great interest in diverse fields. We focus here on the bulk and shear viscosities of \emph{non-relativistic} quantum fluids, with particular emphasis on strongly interacting ultracold Fermi gases. We use Kubo formulas for the bulk and shear viscosity spectral functions, $\zeta(\omega)$ and $\eta(\omega)$ respectively, to derive exact, non-perturbative results. Our results include: a microscopic connection between the shear viscosity $\eta$ and the normal fluid density $\rho_n$; sum rules for $\zeta(\omega)$ and $\eta(\omega)$ and their evolution through the BCS-BEC crossover; universal high-frequency tails for $\eta(\omega)$ and the dynamic structure factor $S({\bf q}, \omega)$. We use our sum rules to show that, at unitarity, $\zeta(\omega)$ is identically zero and thus relate $\eta(\omega)$ to density-density correlations. We predict that frequency-dependent shear viscosity $\eta(\omega)$ of the unitary Fermi gas can be experimentally measured using Bragg spectroscopy.Comment: Published versio

Suspension Assembly of BAJA ATV

In the modern day and age where automobiles are an essential part of our day to day life, the requirements of each are different. Some demand for a high-performance machine whereas others require a comfortable ride. The modern engineering helps in achieving all the aspects of a safe, reliable and fast vehicle. With the change in time, the need for an all-terrain vehicle has gradually increased. The research paper includes the optimisation of wheel assembly for better stability, comfort ride along with better handling. The analysis and simulation are done to obtain a better wheel assembly which can provide the best in class arrangements for the customer. The research mainly focused on the wheel hub, wishbones and knuckle. The designs provide the sturdiness and durability which is the primary requirement for an all-terrain vehicle. The key focus is given to material selection which provides durability and comfort. The material is inexpensive which presents an edge for the market competition as well as is value for money for the customer point of view. The Static load on wheel hub is calculated and analysed for elucidating the characteristics. The material EN-24 provides better machinability and welding applications making it more suitable for mass production

Effective Lagrangians for BCS Superconductors at T=0

We show that the low frequency, long wavelength dynamics of the phase of the pair field for a BCS-type s-wave superconductor at T=0 is equivalent to that of a time-dependent non-linear Schr\"odinger Lagrangian (TDNLSL), when terms required by Galilean invariance are included. If the modulus of the pair field is also allowed to vary, the system is equivalent to two coupled TDNLSL's. We also refer the interested reader to our earlier paper, `Nonlinear Schrodinger equation for superconductors' [cond-mat/9312099], for a different line of derivationComment: Latex, 13 page