Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise

The problem of nonlinear filtering of a random field observed in the presence of a noise, modeled by a persistent fractional Brownian sheet of Hurst index $(H_1,H_2)$ with $0.5<H_1,H_2<1$, is studied and a suitable version of the Bayes' formula for the optimal filter is obtained. Two types of spatial "fractional" analogues of the Duncan-Mortensen-Zakai equation are also derived: one tracks evolution of the unnormalized optimal filter along an arbitrary "monotone increasing" (in the sense of partial ordering in $\mathbb{R}^2$) one-dimensional curve in the plane, while the other describes dynamics of the filter along the paths that are truly two-dimensional. Although the paper deals with the two-dimensional parameter space, the presented approach and results extend to $d$-parameter random fields with arbitrary $d\geq 3$.Comment: 24 page

The impact of increased turbidity, as a result of global climate change, on the stress and alarm signaling in the crayfish, Orconectes virilis.

Undergraduate Research ExperienceThe objective of this study was to investigate the influence potential increasing suspended sediment loads due to global climate change could have on Orconectes virilis chemical communication. Experiments were designed to determine if suspended sediment triggers an increase in the quantity of chemical stress signals that crayfish release voluntarily under stressful environments. As well as determine if crayfish behavior is altered when exposed to chemical stress signals and damage-induced signals under turbid water conditions. In order to determine if suspended sediment triggers an increase in urine quantity crayfish were catheterized and exposed to clear water as well as turbid water in separate treatments. The influence of suspended sediment on the behavior of conspecifics exposed to both stress signals and alarm signals was determined by monitoring behavior in a Y-maze experimental stream. This Y-maze consisted of two separated arms to allow for the simultaneous input of clear and turbid with holding tanks for conspecifics to release chemical signals. First, crayfish exposed to turbid water conditions released urine quantities that were similar to that of crayfish exposed to clear water conditions. The behavior of conspecifics exposed to damage-induced alarm signals in turbid water showed no difference from the behavior of conspecifics exposed to these chemicals in clear water conditions. This indicates that Orconectes virilis disturbance chemical communication is tolerant to turbid water conditions for at least short durations of time.http://deepblue.lib.umich.edu/bitstream/2027.42/88216/1/Linn_Matthew_2011_REU.pd

Risk and Return in Equity and Options Markets.

While theory can tell us about the relationship between prices of risk in options and equity markets within the context of a specific model, what we observe in the data rarely fits any single option pricing model with perfect precision. There seems to be little consensus on a single option pricing model with superior performance above all others. The purpose of this thesis is to empirically investigate the risk-return relation in options markets directly, without resorting to the use of option pricing models based upon relative pricing of options in terms of their underlying. Options markets provide a rich cross-section of data with which to study how investors price assets because they vary across firms, strikes and maturity. As a result, options data provides additional and complimentary information beyond the information contained in stocks. Using these facts, in this thesis I empirically investigate the risk-return relationship across stock option, index option and equity markets. In Chapter I of the thesis I empirically show how to use options data to better estimate the cross-sectional price of market-wide volatility risk. I furthermore compare the price of volatility implicit in the cross-section of stock returns with the price implicit in the cross-section of option returns. In the same chapter I exploit the fact that options can be used to study the term structure properties of risk and return by examining the volatility risk and return tradeoff in options of different times to maturity. In Chapter II, based upon the paper "Pricing Kernel Monotonicity and Conditional Information," co-authored with Sophie Shive and Tyler Shumway, I use data on index options and the underlying index to extract estimates of stochastic discount factors. We propose a new method for non-parametrically estimating the stochastic discount factor. Our method improves upon existing methods by aligning information sets available to investors at each time in our sample and taking these into consideration in our estimation scheme. Empirical results suggest that this may be the solution to a well known anomaly in the literature whereby non-parametric estimates of the pricing kernel tend to be non-monotonic in market returns.PhDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113552/1/linnm_1.pd

Impact of Intercollegiate Athletics on Undergraduate Enrollment at a Small, Faith-Based Institution

Based on previous research, it is apparent many National Collegiate Athletic Association (NCAA) Division I institutions benefit from the existence of and success in intercollegiate athletics. However, few studies have researched the impact of intercollegiate athletics at National Association of Intercollegiate Athletics (NAIA) institutions. Therefore, the purpose of this study was to investigate the effect of intercollegiate athletics at a small, faith-based institution affiliated with the NAIA. More specifically, does success in or the existence of intercollegiate athletics have an effect on students’ decisions to enroll at this institution? Findings indicate the majority of freshmen student participants, including many intercollegiate athletes, were not considerably influenced by the existence of intercollegiate athletics or the existence of successful intercollegiate athletics when deciding to attend the institution. These findings indicate the need for similar institutions to reevaluate the importance placed on and benefits derived from intercollegiate athletics

Difference in Preparedness: Do School Staff Feel Prepared for an Active Shooter or Attack?

The 2020 Texas Educators’ Needs Assessment Regarding School Safety and Victims Services included responses from educators across the state of Texas regarding school safety. This needs assessment generated data that provided researchers with the unique opportunity to analyze the school safety issues in Texas (Fuller et al, 2020). The purpose of the study was to evaluate Texas K-12 educators responses to their school’s preparedness for an active attack or shooter using data from that needs assessment. To build a strong analysis, the results were separated into three categories: educator role; Texas school regions; and urbanicity. Pearson chi square statistical analysis was used to create an understanding of the data. The results of this analysis revealed a trend that a majority of K-12 educators felt prepared for an active attack or shooter

Interactive robot control system and method of use

A robotic system includes a robot having joints, actuators, and sensors, and a distributed controller. The controller includes command-level controller, embedded joint-level controllers each controlling a respective joint, and a joint coordination-level controller coordinating motion of the joints. A central data library (CDL) centralizes all control and feedback data, and a user interface displays a status of each joint, actuator, and sensor using the CDL. A parameterized action sequence has a hierarchy of linked events, and allows the control data to be modified in real time. A method of controlling the robot includes transmitting control data through the various levels of the controller, routing all control and feedback data to the CDL, and displaying status and operation of the robot using the CDL. The parameterized action sequences are generated for execution by the robot, and a hierarchy of linked events is created within the sequence

Investigation of the Young’s modulus and thermal expansion of amorphous titania-doped tantala films

The current generation of advanced gravitational wave detectors utilize titania-doped tantala/silica multilayer stacks for their mirror coatings. The properties of the low-refractive-index silica are well known; however, in the absence of detailed direct measurements, the material parameters of Young’s modulus and coefficient of thermal expansion (CTE) of the high refractive index material, titania-doped tantala, have been assumed to be equal to values measured for pure tantala coatings. In order to ascertain the true values necessary for thermal noise calculations, we have undertaken measurements of Young’s modulus and CTE through the use of nanoindentation and thermal-bending measurements. The measurements were designed to assess the effects of titania-doping concentration and post-deposition heat-treatment on the measured values in order to evaluate the possibility of optimizing material parameters to further improve thermal noise in the detector. Young’s modulus measurements on pure tantala and 25% and 55% titania-doped tantala show a wide range of values, from 132 to 177 GPa, which are dependent on both titania concentration and heat-treatment. Measurements of CTE give values of (3.9±0.1)×10^(−6)  K^(−1) and (4.9±0.3)×10^(−6)  K^(−1) for 25% and 55% titania-doped tantala, respectively, without dependence on post-deposition heat-treatment