Decorated Feynman Categories

In [KW14], the new concept of Feynman categories was introduced to simplify the discussion of operad--like objects. In this present paper, we demonstrate the usefulness of this approach, by introducing the concept of decorated Feynman categories. The procedure takes a Feynman category $\mathfrak F$ and a functor $\mathcal O$ to a monoidal category to produce a new Feynman category ${\mathfrak F}_{dec {\mathcal O}}$. This in one swat explains the existence of non--sigma operads, non--sigma cyclic operads, and the non--sigma--modular operads of Markl as well as all the usual candidates simply from the category $\mathfrak G$, which is a full subcategory of the category of graphs of [BM08]. Moreover, we explain the appearance of terminal objects noted in [Mar15]. We can then easily extend this for instance to the dihedral case. Furthermore, we obtain graph complexes and all other known operadic type notions from decorating and restricting the basic Feynman category $\mathfrak G$ of aggregates of corollas. We additionally show that the construction is functorial. There are further geometric and number theoretic applications, which will follow in a separate preprint.Comment: Updated version from 6/8/16 to appear in J. of Noncommutative Geometr

Helical Fields and Filamentary Molecular Clouds II - Axisymmetric Stability and Fragmentation

In Paper I (Fiege & Pudritz, 1999), we constructed models of filamentary molecular clouds that are truncated by a realistic external pressure and contain a rather general helical magnetic field. We address the stability of our models to gravitational fragmentation and axisymmetric MHD-driven instabilities. By calculating the dominant modes of axisymmetric instability, we determine the dominant length scales and growth rates for fragmentation. We find that the role of pressure truncation is to decrease the growth rate of gravitational instabilities by decreasing the self-gravitating mass per unit length. Purely poloidal and toroidal fields also help to stabilize filamentary clouds against fragmentation. The overall effect of helical fields is to stabilize gravity-driven modes, so that the growth rates are significantly reduced below what is expected for unmagnetized clouds. However, MHD ``sausage'' instabilities are triggered in models whose toroidal flux to mass ratio exceeds the poloidal flux to mass ratio by more than a factor of $\sim 2$. We find that observed filaments appear to lie in a physical regime where the growth rates of both gravitational fragmentation and axisymmetric MHD-driven modes are at a minimum.Comment: 16 pages with 18 eps figures. Submitted to MNRA

Helical Fields and Filamentary Molecular Clouds

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first derive a new virial equation appropriate for magnetized filamentary clouds, which includes the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds. We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We also examine the effects of the equation of state by comparing ``isothermal'' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state. We perform a Monte Carlo exploration of our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r^{-1.8} to r^{-2}, while logatropes have density profiles that range from r^{-1} to r^{-1.8}. We find that purely poloidal fields produce filaments with steep density gradients that not allowed by the observations.Comment: 21 pages, 8 eps figures, submitted to MNRAS. Significant streamlining of tex

Enhancement of Cohesion and Engagement through Motivational Factors in the Multi-Generational Workforce

Leaders in all corporations will have to answer the multi-generational challenges in the workplace to motivate their employees by maintaining cohesion and engagement (Ahmad & Ibrahim, 2015; Lazaroiu, 2015). A gap in the literature exists to understand how leaders can create group cohesion and engagement by possessing the instruction and tools necessary to adequately lead the multi-generational diverse workforce to long-term success of the medical device division (Cote, 2019; Dwyer & Azevedo, 2016; Lewis & Wescott, 2017; Stegaroiu & Talal, 2014; Wesolowski, 2014). The central research questions in this qualitative case study addressed the understanding of how leaders use motivational factors, as perceived by the generational groups of (a) Baby Boomers, (b) Generation X, and (c) Millennials, to enhance group engagement and collaboration of the new generationally diverse workplace bounded in a medical device company and how motivational factors influence enhanced engagement and collaboration to lead in the long-term success in the medical device industry as perceived per the generational groups of (a) Baby Boomers, (b) Generation X, and (c) Millennials. Fourteen major themes were found to support the knowledge to answer the research questions. Conceptual frameworks were created to summarize the findings and use for implementation training to relate the subthemes per major themes per generational cohort

Tracking interacting dust: comparison of tracking and state estimation techniques for dusty plasmas

When tracking a target particle that is interacting with nearest neighbors in a known way, positional data of the neighbors can be used to improve the state estimate. Effects of the accuracy of such positional data on the target track accuracy are investigated in this paper, in the context of dusty plasmas. In kinematic simulations, notable improvement in the target track accuracy was found when including all nearest neighbors in the state estimation filter and tracking algorithm, whereas the track accuracy was not significantly improved by higher-accuracy measurement techniques. The state estimation algorithm, involving an extended Kalman filter, was shown to either remove or significantly reduce errors due to "pixel locking". It is concluded that the significant extra complexity and computational expense to achieve these relatively small improvements are likely to be unwarranted for many situations. For the purposes of determining the precise particle locations, it is concluded that the simplified state estimation algorithm can be a viable alternative to using more computationally-intensive measurement techniques.Comment: 11 pages, 6 figures, Conference paper: Signal and Data Processing of Small Targets 2010 (SPIE