S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

Electroolfactogram (EOG) Recording in the Mouse Main Olfactory Epithelium

Olfactory sensory neurons in the main olfactory epithelium (MOE) are responsible for detecting odorants and EOG recording is a reliable approach to analyze the peripheral olfactory function. However, recently we revealed that rodent MOE can also detect the air pressure caused by airflow. The sensation of airflow pressure and odorants may function in synergy to facilitate odorant perception during sniffing. We have reported that the pressure-sensitive response in the MOE can also be assayed by EOG recording. Here we describe procedures for pressure-sensitive as well as odorant-stimulated EOG measurement in the mouse MOE. The major difference between the pressure-sensitive EOG response and the odorant-stimulated response was whether to use pure air puff or use an odorized air puff

Assessing the Economic Impact of Sports Facilities on Residential Property Values: A Spatial Hedonic Approach

This paper estimates the intangible benefits of a two sports facilities in Columbus, Ohio on residential property values. We estimate a spatial hedonic model that avoids biased and inconsistent estimates in the presence of uncorrected spatial autocorrelation. The results suggest that the presence of sports facilities in Columbus have a significant positive distance-decaying effect on surrounding house values, supporting the idea that professional sports facilities generate important intangible benefits in the local economy. OLS overestimates the hedonic model parameters compared with Maximum Likelihood and Spatial Two Stage-Least-Squares.Economic Impact, Residential Property Values, Sports Facilities, Hedonic Model, Spatial Dependence, Spatial Hedonic Model

Stimulation of electro-olfactogram responses in the main olfactory epithelia by airflow depends on the type 3 adenylyl cyclase

Cilia of olfactory sensory neurons are the primary sensory organelles for olfaction. The detection of odorants by the main olfactory epithelium (MOE) depends on coupling of odorant receptors to the type 3 adenylyl cyclase (AC3) in olfactory cilia. We monitored the effect of airflow on electro-olfactogram (EOG) responses and found that the MOE of mice can sense mechanical forces generated by airflow. The airflow-sensitive EOG response in the MOE was attenuated when cAMP was increased by odorants or by forskolin suggesting a common mechanism for airflow and odorant detection. In addition, the sensitivity to airflow was significantly impaired in the MOE from AC3−/− mice. We conclude that AC3 in the MOE is required for detecting the mechanical force of airflow, which in turn may regulate odorant perception during sniffing

Coronal rain in magnetic arcades: Rebound shocks, Limit cycles, and Shear flows

We extend our earlier multidimensional, magnetohydrodynamic simulations of coronal rain occurring in magnetic arcades with higher resolution, grid-adaptive computations covering a much longer ($>6$ hour) timespan. We quantify how in-situ forming blob-like condensations grow along and across field lines and show that rain showers can occur in limit cycles, here demonstrated for the first time in 2.5D setups. We discuss dynamical, multi-dimensional aspects of the rebound shocks generated by the siphon inflows and quantify the thermodynamics of a prominence-corona-transition-region like structure surrounding the blobs. We point out the correlation between condensation rates and the cross-sectional size of loop systems where catastrophic cooling takes place. We also study the variations of the typical number density, kinetic energy and temperature while blobs descend, impact and sink into the transition region. In addition, we explain the mechanisms leading to concurrent upflows while the blobs descend. As a result, there are plenty of shear flows generated with relative velocity difference around 80 km s$^{-1}$ in our simulations. These shear flows are siphon flows set up by multiple blob dynamics and they in turn affect the deformation of the falling blobs. In particular, we show how shear flows can break apart blobs into smaller fragments, within minutes

Rheology of the gel formed in the California Mastitis Test

The California Mastitis Test has previously been adapted for use in an inline, cow-side sensor and relies on the fact that the viscosity of the gel formed during the test is proportional to the somatic cell concentration. In this paper, the use of capillary and rotational viscometry was compared in light of the expected rheology of the gel formed during the test. It was found that the gel is non-Newtonian, but the initial phase of viscosity increase was not due to shear dependence, but rather due to the gelation reaction. The maximum apparent viscosity of the gel was shear dependent while the time it took to reach the maximum was not truly shear dependent, but was rather dependent on the degree of mixing during gelation. This was confirmed by introducing a delay time prior to viscosity measurement, in both capillary and rotational viscometry. It was found that by mixing the reagent and infected milk, then delaying viscosity measurement for 30 s, shortened the time it took to reach maximum viscosity by more than 60 s. The maximum apparent viscosity, however, was unaffected. It was found that capillary viscometry worked well to correlate relative viscosity with somatic cell count, but that it was sensitive to the reagent concentration. It can therefore be deduced that the rheology of the gel is complicated not only by it being non-Newtonian, but also by the strong dependence on test conditions. These make designing a successful sensor much more challenging

Simulating coronal condensation dynamics in 3D

We present numerical simulations in 3D settings where coronal rain phenomena take place in a magnetic configuration of a quadrupolar arcade system. Our simulation is a magnetohydrodynamic simulation including anisotropic thermal conduction, optically thin radiative losses, and parametrised heating as main thermodynamical features to construct a realistic arcade configuration from chromospheric to coronal heights. The plasma evaporation from chromospheric and transition region heights eventually causes localised runaway condensation events and we witness the formation of plasma blobs due to thermal instability, that evolve dynamically in the heated arcade part and move gradually downwards due to interchange type dynamics. Unlike earlier 2.5D simulations, in this case there is no large scale prominence formation observed, but a continuous coronal rain develops which shows clear indications of Rayleigh-Taylor or interchange instability, that causes the denser plasma located above the transition region to fall down, as the system moves towards a more stable state. Linear stability analysis is used in the non-linear regime for gaining insight and giving a prediction of the system's evolution. After the plasma blobs descend through interchange, they follow the magnetic field topology more closely in the lower coronal regions, where they are guided by the magnetic dips.Comment: 47 pages, 59 figure