Degree of the generalized Pl\"ucker embedding of a Quot scheme and Quantum cohomology

We compute the degree of the generalized Pl\"ucker embedding $\kappa$ of a Quot scheme $X$ over \PP^1. The space $X$ can also be considered as a compactification of the space of algebraic maps of a fixed degree from \PP^1 to the Grassmanian $\rm{Grass}(m,n)$. Then the degree of the embedded variety $\kappa (X)$ can be interpreted as an intersection product of pullbacks of cohomology classes from $\rm{Grass}(m,n)$ through the map $\psi$ that evaluates a map from \PP^1 at a point x\in \PP^1. We show that our formula for the degree verifies the formula for these intersection products predicted by physicists through Quantum cohomology~\cite{va92}~\cite{in91}~\cite{wi94}. We arrive at the degree by proving a version of the classical Pieri's formula on the variety $X$, using a cell decomposition of a space that lies in between $X$ and $\kappa (X)$.Comment: 18 pages, Latex documen

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.Comment: 28 page

Microwave remote sensing of soil moisture, volume 1

Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone

Multifrequency remote sensing of soil moisture

Multifrequency sensor data collected at Guymon, Oklahoma and Dalhart, Texas using NASA's C-130 aircraft were used to determine which of the all-weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. In comparison to other active and passive microwave sensors the L-band radiometer (1) was influenced least by ranges in surface roughness; (2) demonstrated the most sensitivity to soil moisture differences in terms of the range of return from the full range of soil moisture; and (3) was less sensitive to errors in measurement in relation to the range of sensor response. L-band emissivity related more strongly to soil moisture when moisture was expressed as percent of field capacity. The perpendicular vegetation index as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture

Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms, volume 2

Agricultural crop classification models using two or more spectral regions (visible through microwave) were developed and tested and biomass was estimated by including microwave with visible and infrared data. The study was conducted at Guymon, Oklahoma and Dalhart, Texas utilizing aircraft multispectral data and ground truth soil moisture and biomass information. Results indicate that inclusion of C, L, and P band active microwave data from look angles greater than 35 deg from nadir with visible and infrared data improved crop discrimination and biomass estimates compared to results using only visible and infrared data. The active microwave frequencies were sensitive to different biomass levels. In addition, two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass

Development of visible/infrared/microwave agriculture classification and biomass estimation algorithms

Agricultural crop classification models using two or more spectral regions (visible through microwave) are considered in an effort to estimate biomass at Guymon, Oklahoma Dalhart, Texas. Both grounds truth and aerial data were used. Results indicate that inclusion of C, L, and P band active microwave data, from look angles greater than 35 deg from nadir, with visible and infrared data improve crop discrimination and biomass estimates compared to results using only visible and infrared data. The microwave frequencies were sensitive to different biomass levels. The K and C band were sensitive to differences at low biomass levels, while P band was sensitive to differences at high biomass levels. Two indices, one using only active microwave data and the other using data from the middle and near infrared bands, were well correlated to total biomass. It is implied that inclusion of active microwave sensors with visible and infrared sensors on future satellites could aid in crop discrimination and biomass estimation

Thermal inactivation of Byssochlamys nivea in pineapple nectar combined with preliminary high pressure treatments

Byssochlamys nivea is a thermal resistant filamentous fungi and potential micotoxin producer. Recent studies have verified the presence of ascospores of such microorganism in samples of pineapple nectars. Although the majority of filamentous fungi have limited heat resistance and are easily destroyed by heat, Byssochlamys nivea ascospores have shown high thermal resistance. The aim of this work was to evaluate the application of linear and Weibull models on thermal inactivation (70, 80 and 90ºC) of Byssochlamys nivea ascospores in pineapple nectar after pretreatment with high pressure (550MPa or 650MPa during 15min). Following the treatments, survival curves were built up for each processing temperature and adjusted for both models. It was observed that survival curves at 90°C after high pressure pretreatment at 550 MPa/15 min did not fit well to linear and Weibull models. For all the other treatments, the Weibull model presented a better fit. At 90ºC without pressure treatment, the Weibull model also showed a better adjustment, having a larger R2 and a smaller RMSE. Regarding the process effectiveness, a 5-log reduction (t5), as recommended for pasteurization, was only achieved for Byssochlamys nivea ascospores presented in pineapple nectar at 90ºC/10.7 min with previous high pressure treatment of 650 MPa for 15 min. Considering the high intensity and energy demanding process with possibly product damage, other preventive and alternative treatments are being investigated