Types of Linkage of Quadratic Pfister Forms

Given a field $F$ of positive characteristic $p$, $\theta \in H_p^{n-1}(F)$ and $\beta,\gamma \in F^\times$, we prove that if the symbols $\theta \wedge \frac{d \beta}{\beta}$ and $\theta \wedge \frac{d \gamma}{\gamma}$ in $H_p^n(F)$ share the same factors in $H_p^1(F)$ then the symbol $\theta \wedge \frac{d \beta}{\beta} \wedge \frac{d \gamma}{\gamma}$ in $H_p^{n+1}(F)$ is trivial. We conclude that when $p=2$, every two totally separably $(n-1)$-linked $n$-fold quadratic Pfister forms are inseparably $(n-1)$-linked. We also describe how to construct non-isomorphic $n$-fold Pfister forms which are totally separably (or inseparably) $(n-1)$-linked, i.e. share all common $(n-1)$-fold quadratic (or bilinear) Pfister factors

Economics of Disability Research Report #4: Estimates of the Prevalence of Disability, Employment Rates, and Median Household Size-Adjusted Income for People with Disabilities Aged 18 though 64 in the United States by State, 1980 through 2000

This report replicates Economics of Disability Reports 1, 2, and 3, with some minor changes. These reports contain the prevalence of a disability, employment rates, and median household size-adjusted income between states over the 1980s and 1990s. In response to the requests of state officials to generate statistics that reflect the population they serve, this report includes people aged 18 through 64 rather than people aged 25 through 61. The new age group is more likely to include those who enter the labor force after high school, during college, and post-college as well as those people who have decided not to take early retirement. In addition, at the request of state officials, the statistics in this report are not separated by gender because most government agencies do not make a strong distinction between men and women, even though men and women face different labor market conditions. This report uses data from the March Current Population Survey to estimate the prevalence of a disability, employment rate, and median household size-adjusted income among the non-institutionalized working-age (aged 18 through 64) civilian population in the United States, and for each state and the District of Columbia for the survey years 1981 through 2000 and income/employment years 1980 through 1999. Two definitions of disability that are commonly used in the literature—work limitation and work disability—are utilized. The prevalence of a work limitation and work disability varies greatly across states and over time. The employment rate of persons with work limitations relative to that of persons without a disability varies greatly across states. However, over the last 20 years the relative employment rate of those with work limitations dramatically declined overall and in most states. Consequently, the decrease in the relative employment rate for persons with work limitations induced the growth in the median household size-adjusted income of those with work limitations

Acoustic metafluids made from three acoustic fluids

Significant reduction in target strength and radiation signature can be achieved by surrounding an object with multiple concentric layers comprised of three acoustic fluids. The idea is to make a finely layered shell with the thickness of each layer defined by a unique transformation rule. The shell has the effect of steering incident acoustic energy around the structure, and conversely, reducing the radiation strength. The overall effectiveness and the precise form of the layering depends upon the densities and compressibilities of the three fluids. Nearly optimal results are obtained if one fluid has density equal to the background fluid, while the other two densities are much greater and much less than the background values. Optimal choices for the compressibilities are also found. Simulations in 2D and 3D illustrate effectiveness of the three fluid shell. The limited range of acoustic metafluids that are possible using only two fluid constituents is also discussed.Comment: 12 pages, 11 figure

Total linkage of quaternion algebras and Pfister forms in characteristic two

We study the subfields of quaternion algebras that are quadratic extensions of their center in characteristic 2. We provide examples of the following: two non-isomorphic quaternion algebras that share all their quadratic subfields, two quaternion algebras that share all their inseparable but not all their separable quadratic subfields and two algebras that share all their separable but not all their inseparable quadratic subfields. We also discuss quaternion algebras over global fields and fields of Laurent series over a perfect field of characteristic 2 and show that the quaternion algebras over these fields are determined by their separable quadratic subfields. Throughout, these linkage questions are treated in the more general setting by considering the linkage of Pfister forms.Comment: 16 page

Amplitude analysis of resonant production in three pions

We present some results on the analysis of three pion resonances. The analyses are motivated by the recent release of the largest data set on diffractively produced three pions by the COMPASS collaboration. We construct reaction amplitudes that satisfy fundamental $S$-matrix principles, which allows the use of models that have physical constraints to be used in fitting data. The models are motivated by the isobar model that satisfy unitarity constraints. The model consist of a Deck production amplitude with which final state interactions are constrained by unitarity. We employ the isobar model where two of the pions form a quasi-stable particle. The analysis is performed in the high-energy, single Regge limit. We specifically discuss the examples of the three pion $J^{PC}=2^{-+}$ resonance in the $\rho\pi$ and $f_2\pi$ channels.Comment: 4 pages, 1 figure, proceedings of the "14th International Workshop on Meson Production, Properties and Interaction" (MESON2016), Krak\'ow, Poland, June 02-07, 201

Root Mean Square Error of Neural Spike Train Sequence Matching with Optogenetics

Optogenetics is an emerging field of neuroscience where neurons are genetically modified to express light-sensitive receptors that enable external control over when the neurons fire. Given the prominence of neuronal signaling within the brain and throughout the body, optogenetics has significant potential to improve the understanding of the nervous system and to develop treatments for neurological diseases. This paper uses a simple optogenetic model to compare the timing distortion between a randomly-generated target spike sequence and an externally-stimulated neuron spike sequence. The distortion is measured by filtering each sequence and finding the root mean square error between the two filter outputs. The expected distortion is derived in closed form when the target sequence generation rate is sufficiently low. Derivations are verified via simulations.Comment: 6 pages, 5 figures. Will be presented at IEEE Global Communications Conference (IEEE GLOBECOM 2017) in December 201