Motivic Steenrod operations in characteristic pp

Using the recent work of Frankland and Spitzweck, we define Steenrod operations $P^{n}$ on the mod $p$ motivic cohomology of smooth varieties defined over a base field of characteristic $p$. We show that $P^{n}$ is the $p$th power on $H^{2n,n}(-,\mathbb{F}_{p})\cong CH^{n}(-)/p$ and prove an instability result for the operations. Restricted to mod $p$ Chow groups, we show that the operations satisfy the expected Adem relations and Cartan formula. For $p=2$, we use the new Steenrod squares to obtain new results on quadratic forms over a base field of characteristic $2$.Comment: 26 pages; v2: added result on base change of operations, added result on compatibility of Steenrod operations with specialization maps on Chow groups, added more applications to quadratic forms in characteristic 2, other minor changes and correction

Estimating expected first passage times using multilevel Monte Carlo algorithm

In this paper we devise a method of numerically estimating the expected first passage times of stochastic processes. We use Monte Carlo path simulations with Milstein discretisation scheme to approximate the solutions of scalar stochastic differential equations. To further reduce the variance of the estimated expected stopping time and improve computational efficiency, we use the multi-level Monte Carlo algorithm, recently developed by Giles (2008a), and other variance-reduction techniques. Our numerical results show significant improvements over conventional Monte Carlo techniques

Homogeneous Groups and Covers

This paper is my 2014 Cornell Senior Thesis, written under the supervision of R. Keith Dennis. It contains results on homogeneous covers and generating sequences of finite groups.Comment: 11 page

Motivic cohomology and infinitesimal group schemes

For $k$ a perfect field of characteristic $p>0$ and $G/k$ a split reductive group with $p$ a non-torsion prime for $G,$ we compute the mod $p$ motivic cohomology of the geometric classifying space $BG_{(r)}$, where $G_{(r)}$ is the $r$th Frobenius kernel of $G.$ Our main tool is a motivic version of the Eilenberg-Moore spectral sequence, due to Krishna. For a flat affine group scheme $G/k$ of finite type, we define a cycle class map from the mod $p$ motivic cohomology of the classifying space $BG$ to the mod $p$ \'etale motivic cohomology of the classifying stack $\mathcal{B}G.$ This also gives a cycle class map into the Hodge cohomology of $\mathcal{B}G.$ We study the cycle class map for some examples, including Frobenius kernels.Comment: 20 pages, comments welcom

WHAT DOES A SUCCESSFUL UNIVERSITY LOOK LIKE? - THE STUDENTS' VIEW

"There is a lot more that is necessary for a successful university: for example, ensuring proper financing would be a very basic condition. I also did not discuss about research or about institutional autonomy and academic freedom, which are also building blocs of a successful university. As the whole list would take much more than the space I was allocated for this article, I have focused on what I would perceive as the most important points of a l l - the ones that are crucial to ensure that a university truly is a community of teachers and students." -

Strategies for developing lentil protein stabilized canola oil in water nanoemulsions

The overall goal of this research is to utilize the lentil protein isolate (LPI), prepared with isoelectric precipitation by POS Bio-Sciences (Saskatoon, SK, Canada), in the development of canola oil-in-water nanoemulsions. The effect of LPI concentration and the effect of high-pressure treatment of LPI on the formation, stability and rheological behaviour of canola oil-in-water nanoemulsions was investigated. According to a previous study of coarse emulsions, LPI showed the best emulsifying properties at pH 3; therefore, all nanoemulsions were prepared at this pH. In the first study, nanoemulsions were prepared by adding 5 wt% canola oil to the LPI solutions at various concentrations (0.5 – 5 wt% LPI) in a citric acid buffer at pH 3 and homogenized at 20,000 psi pressure. The storage stability of the nanoemulsions was recorded for 28 days. All nanoemulsions showed bimodal droplet size distribution, where the smaller peak was attributed to the oil droplets while the larger peak was attributed to unadsorbed protein aggregates in the continuous phase which grew in the size with increasing LPI concentration. The protein aggregation was also confirmed with confocal microscopy. Concentration of 0.5 wt% LPI was not sufficient for long term stabilization of oil droplets therefore the nanoemulsion separated out over the 28 days. The best stability of the nanoemulsions was observed with 1, 1.5 and 2 wt% LPI, confirmed by a photocentrifuge, which evaluates oil droplet movement and hence emulsion stability under accelerated gravitational force. Nanoemulsions stabilized with 3 and 5 wt% LPI transformed to a thick gel, most likely due to a network formation between the oil droplets and free proteins in the continuous phase. The viscosity and the gel strength of nanoemulsions increased with increasing protein concentration because of increased aggregation of free proteins in the continuous phase of the nanoemulsions. In the second study, the effect of high-pressure homogenization of LPI on the formation and stability of the nanoemulsions were investigated. The most stable and flowable nanoemulsions at 1, 1.5 and 2 wt% LPI concentrations were chosen based on the previous results. Prior to nanoemulsion formation, LPI solutions (1 -2 wt% LPI) were homogenized at 5,000 and 15,000 psi pressure for six cycles. Nanoemulsions were then prepared by adding 5 wt% canola oil to 95 wt% pre-treated LPI solutions at pH 3 and homogenized at 20,000 psi pressure. High-pressure homogenization of LPI significantly improved long term stability of the nanoemulsions by decreasing the large protein particles into small ones, which was confirmed by particle size distribution, light microscopy and photocentrifuge dispersion analysis. Small particles improved migration of proteins to the oil-water interface and facilitated formation of oil droplets and resulted in a decrease in the average oil droplet size from ~ 250 nm to less than 200 nm. No significant difference was observed between 5,000 and 15,000 psi pressure indicating that 5,000 psi homogenization of LPI solution was sufficient to brake large protein particles into small ones. High-pressure homgenization of LPI solutions also decreased protein aggregation in the continuous phase of the nanoemulsions which was confirmed with the confocal microscopic imaging and this might be due to the lower surface hydrophobicity created by high-pressure homogenization of LPI. Results from the interfacial rheology indicated that weaker interfacial film was formed by the high-pressure homogenized LPI solutions compared to un-homogenized proteins. Storage stability of the nanoemulsions prepared with high-pressure homogenized LPI solutions was significantly improved compare to the nanoemulsions prepared without high-pressure treated LPI due to a smaller droplet size and less protein aggregation in the continuous phase. Lipid digestibility showed an increase for nanoemulsions prepared with high-pressure homogenized LPI solutions (1 wt%) due to a smaller droplet size and weaker interfacial film, however no significant difference was observed for 1.5 and 2 wt% LPI homogenized solutions. This might be due to a higher LPI concentration covering the oil droplet surface and preventing digestive enzymes to access the oil. Overall, high-pressure homogenization improved emulsification properties of LPI and shelf life and lipid digestibility of the prepared nanoemulsions thereby increasing the nutritional value of the product. Lentil protein-stabilized nanoemulsions containing low oil volume fractions have many applications in the development of beverage type products due to their increased stability, flowability and longer shelf life

Effective Communication and Collaboration in Project Management: a Study of the Use of Document Version Control in Higher Education

Facilities planning in higher education necessitates collaborative efforts from various stakeholders working as a cohesive team. This study emphasizes the significance of implementing document version control to attain communication that is both effective and efficient while establishing a collaborative approach. The study advocates for Document Management Systems that allow for document sharing and should be a standardized tool for group document collaboration

Proteinase-catalyzed Hydrolysis of Casein at Atmospheric Pressure and in Supercritical Media

In the presented work, reaction parameters for hydrolysis of casein, catalyzed by Carica papaya latex at atmospheric and high pressure, were optimized. Casein is a remarkably efficient nutrient, supplying not only essential amino acids, but also some carbohydrates, calcium, phosphorus and therefore is very important for the food industry. Different reaction parameters such as temperature, stirring rate, casein and enzyme concentration were studied to found the optimal conditions for the reaction. Reactions were performed at atmospheric pressure; an influence of temperature/pressure on the casein hydrolysis in supercritical carbon dioxide (SC CO2) was also investigated to improve the reaction rates. Higher conversions were achieved when the reactions were performed in SC CO2, even though casein was not soluble in this medium

Facial soft tissue changes during the pre-pubertal and pubertal growth phase: a mixed longitudinal laser-scanning study

BACKGROUND/OBJECTIVES: Facial soft tissues changes during growth roughly tend to mimic the underlying hard tissues, but not completely. The aim of this mixed longitudinal study was to assess facial growth among pre-pubertal and pubertal subjects without malocclusion using a non-invasive three-dimensional laser scanning system. SUBJECTS/METHODS: Fifty-nine subjects (30 females and 29 males) aged at baseline 5.4-8.9 years with normal occlusion were clustered into the younger, older pre-pubertal, and pubertal groups according to age and the absence/presence of a standing height growth spurt. Three-dimensional facial images were obtained using laser scanners for five consecutive years. Several transversal, sagittal, and vertical parameters were assessed for between and within group comparisons. RESULTS: Significant overall changes of almost all parameters were seen within each group (P 0.05). The younger pre-pubertal group showed greater annual growth rates of lip prominence; both pre-pubertal groups showed greater rates in facial middle third height. The pubertal group showed greater annual rates in facial profile angle changes during the growth peak. LIMITATIONS: A high standing height increment (7cm) was used as the threshold for subject allocation in the pubertal group. CONCLUSIONS: Soft tissue facial growth has generally similar amounts and rates irrespective of the pubertal growth spurt. Pre-pubertal subjects show greater annual rates of facial middle third height changes while pubertal subjects show greater annual rates of chin protrusion