Multi-latin squares

A multi-latin square of order $n$ and index $k$ is an $n\times n$ array of multisets, each of cardinality $k$, such that each symbol from a fixed set of size $n$ occurs $k$ times in each row and $k$ times in each column. A multi-latin square of index $k$ is also referred to as a $k$-latin square. A $1$-latin square is equivalent to a latin square, so a multi-latin square can be thought of as a generalization of a latin square. In this note we show that any partially filled-in $k$-latin square of order $m$ embeds in a $k$-latin square of order $n$, for each $n\geq 2m$, thus generalizing Evans' Theorem. Exploiting this result, we show that there exist non-separable $k$-latin squares of order $n$ for each $n\geq k+2$. We also show that for each $n\geq 1$, there exists some finite value $g(n)$ such that for all $k\geq g(n)$, every $k$-latin square of order $n$ is separable. We discuss the connection between $k$-latin squares and related combinatorial objects such as orthogonal arrays, latin parallelepipeds, semi-latin squares and $k$-latin trades. We also enumerate and classify $k$-latin squares of small orders.Comment: Final version as sent to journa

Furthering Entomological Outreach and Education for High School Aged Students with Madagascar Hissing Cockroaches

This project was designed and conducted as an entomological educational outreach program for high school students. I was given access to an environmental science class at Kaiserslautern High School (KHS) under the guidance and supervision of a licensed teacher. Environmental Science is an elective class that fulfills the course requirement at the school for a science course with a laboratory component. I was given three groups of students, and I taught four classes to each of these groups. Each class had students in their freshman, sophomore, and junior years. During these class periods, I composed a food preference experiment that involved Madagascar hissing cockroaches (MHCs). This experiment drew heavily on my own experiences during my studies (i.e., ENTO 115 at the University of Nebraska, Lincoln). This project aimed to increase entomological education at this school. Lastly, I highlighted the use of technology in the classroom to better assist the instructor. My name is Robert Guy Lefevre, and I am currently in my 17th year of active-duty service in the United States Army. I have served as an artilleryman, a transportation coordinator, and a bandsman. I am currently serving as a guitarist in the U.S. Army Europe Band and Chorus garrisoned at Sembach, Germany, and I am currently a Staff Sergeant. I hold a Bachelor of Arts in History from California State University at San Bernardino. I was accepted into the Master of Science in Entomology program at UNL in 2015. I can attest that crossing over from the arts side to the science side of campus was a particularly arduous undertaking. In this paper, I further expand on how my experiences as a soldier and an academic greatly facilitated my connection with the students in such a short timeframe. My sponsor teacher was Ms. Nancy Hoehn. Ms. Hoehn holds a Bachelor of Science in Food Science from Purdue University and a Master of Arts in Human Relations from the University of Oklahoma. She is credentialed in Texas as a licensed physical science teacher and is currently employed by the Department of Defense Education Activity (DoDEA) as an environmental science and physics teacher. Ms. Hoehn has been recognized as a National Geographic Certified Educator, a NASA Solar System Ambassador Master Teacher, and is a Google Certified Educator (Level 1). It cannot be expressed how her experience and education aided this project, particularly her Google certification. Kaiserslautern High School is a secondary education facility that is in the Kaiserslautern military community. It is located on the United States Army Garrison Rheinland-Pfalz, Vogelweh. Vogelweh, as it is colloquially known, serves the greater Ramstein Airbase community. This area of Germany has approximately 30,000 American uniformed personnel and their families. Kaiserslautern High School is one of two DoDEA high schools. Kaiserslautern High School has a student body population of approximately 550 students. It is the newest school to be built in the DoDEA Europe area

Selection genetique sur la reponse au stress et stress a l'abattage: consequences sur le proteome musculaire et lien avec la qualite de la chair chez la truite arc-en-ciel.

L'origine génétique des animaux est un des facteurs déterminants des caractéristiques des poissons en élevage (croissance, morphologie…) et de la qualité de leur chair. Une sélection divergente, basée sur la réponse individuelle de truite, en terme de niveau plasmatique de cortisol, suite à un stress aigu de confinement, a permis de montrer que ce paramètre est héritable, et d'obtenir des familles de truites présentant des niveaux de réponse à un stress aigu bien distincts (Pottinger et Carrick, 1999). Les animaux de ces familles divergentes ont été caractérisés pour leur croissance, qui s'avère meilleure pour les poissons répondant faiblement au stress, leur morphologie, et la qualité de leur chair. Les poissons répondant faiblement au stress présentent une chair moins lumineuse, plus jaune, et une résistance mécanique moindre associée à des fibres musculaires plus grosses et une teneur en lipides plus importante (Lefèvre et al., 2008a). Un stress au moment de l'abattage modifie le métabolisme post-mortem et conduit, la plupart du temps chez les salmonidés, à une chair moins ferme et plus pale (Lefèvre et al., 2008b). Un tel effet a été confirmé dans cette expérimentation de façon similaire pour les deux souches sélectionnées. Les protéines permettant d’expliquer potentiellement ces différences de qualité ne sont pas connues. L'objectif de ce travail était d'identifier les protéines différentiellement exprimées entre les deux souches sélectionnées et ayant subies ou non un stress de confinement juste avant l'abattage et de faire le lien avec les paramètres de qualité déjà mesurés