On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

Prospectus, October 22, 1980

INTERNATIONAL STUDENTS CELEBRATE TODAY; Letters to the Editors: Student has questions for Schumacher, Co-editor apologizes to runners, Student supports Schumacher\u27s view; PACT discusses day care; Food, beer, fun planned for Oktoberfest; Seniors to tour Parkland next week; Stories of America will be presented October 29-Nov 1; Two-hundred help celebrate: Parkland students celebrate International Students Day today; State rep. candidates express their views; PC drama department presents its fall production; PC offers Pharmacy Technician program; Fall means football... and football means Homecoming; Handle your $$ properly; Learn to take care of you car: enroll in PC\u27s car care course; Leardship is not shout, flout, and clout; Compunds from marine animals could cure cancer; U of I\u27s John Dickel will talk; Reaching Out ; Jeff Beck gives a hot, jazzy show; Marcel Marceau: the Master isn\u27t up to par; IM football winds down: teams available for volleyball, b-ball; Career center needs guides; X-country third in invitational; PC to offer EMT refresher; Arts showcase scheduled for next week; PC Datebook; Cobras can tie for championship; Freddy\u27s record looking better; Bench Warmer: Women\u27s b-ball team looking for balance; Fast Freddy Contesthttps://spark.parkland.edu/prospectus_1980/1016/thumbnail.jp

Genetic Variants of Milk Proteins - Relevance to Milk Composition and Cheese Production.

End of Project ReportObjectives: (i) to develop rapid screening procedures for the determination of milk protein polymorphism (genetic variants) (ii) to determine the frequency distribution of milk protein genetic variants in a large population of Irish Holstein-Friesians and to determine if there was an association between κ-casein variant and milk yield and composition in this group of animals, and (iii) to make Cheddar and low-moisture part-skim Mozzarella cheese from different κ-casein genetic variant milks and to assess any effect on cheese yield, composition and functional characteristics. Conclusions:Analysis of 6,007 individual Irish Holstein-Friesian milks showed that the phenotype distribution of the κ-casein BB variant was very low at 1.98% compared to 53.07% for κ-casein AA and 44.95% for κ-casein AB. While no statistically significant associations were observed between κ-casein variant and milk yield and composition, κ-casein BB variant milks had superior rennet coagulation properties to that of the AA or AB variants. Generally, κ-casein variant had little effect on compositional attributes of cheese apart from FDM (fat in dry matter) which was significantly higher in cheeses from κ-casein BB milk than in those from κ-casein AA milk. Generally, κ-casein variant had no significant effects on either primary or secondary proteolysis, or on the sensory and/or textural characteristics of Cheddar or Mozzarella cheese throughout ripening; or on the functional characteristics (e.g. flow and stretch) of baked Mozzarella on storage for 90 days at 4°C. However, κ-casein BB variant milk gave significantly higher actual, and moisture adjusted yields of Cheddar and Mozzarella cheese than either κ-casein AB or AA variant milks. For example, the moisture adjusted Cheddar yield from κ-casein BB milk was 8.2% higher than from κ-casein AA milk. In the case of Mozzarella, the moisture adjusted yield was 12% higher. Based on the results, it is estimated that the actual yield of cheese in a plant producing 20,000 tonnes per year from κ-casein AA milk would increase to approximately 21,180 tonnes of Cheddar, or 21,780 tonnes of Mozzarella if made from κ-casein BB milk. Where κ-casein AB milk is used instead of κ-casein BB milk, the estimated yield of Mozzarella would increase to 21,580 tonnes.Department of Agriculture, Food and the Marin

Prospectus, February 20, 1980

JOURN, BROADCAST STUDENTS TOUR SOUTHLAND; University Ave. to receive facelift, lights; Week in Review: World, Nation, State, Local; New bus shelter for MTD riders; Cancelled; Faculty Focus: You were conned, Mr. Novak! ; DSC aids handicapped; Parkland horse program breeds interest; Many careers in agriculture are available; Dates to live by; English 100 testing goes through studies; Letters to the Editor: They can\u27t change; Radio programs on health information; PC Women\u27s Forum; Between the Tracks: Another oh so boring Best of the Year; Soap operas grab student attention in television lounge; Steve\u27s \u27shoes\u27 funny; Up against The Wall ; Classifieds; Pratt, Dunson add sparkle; Women cagers up two more; Equine Club makes horse sense; Bench Warmer: Coaches, faculty put stress on winning; Cobras split in B-ball; PC\u27s Cox, Clark, win; Hoop Express, Pacers take leadhttps://spark.parkland.edu/prospectus_1980/1037/thumbnail.jp

Prospectus, May 7, 1980

STAERKEL ANNOUNCES ADDITIONS, CHANGES TO TAKE PLACE BEFORE FALL; Inflation plan announced; Interest-gathering accounts: big financial changes for U.S.; Walsh, Wienke to be 1980-81 co-editors; Resolution is just a suggestion; Youngersters voicing opinions on candidates; Trikes: the new mode of transportation; Special Olympics teaches student; Spring fever in college; Krannert events are listed; Letters to the Editor; REO still favorite in the Midwest; Dates to live by; Movie tells of anti-war movement in \u2760s; Rec students provide overnight camp-out; The sky\u27s the limit; Classifieds; C-U \u27turned upside down\u27 by punch of Journey and Ramones; Training for women; Trackmen win Region, smash state records; Parkland bows out of Section, prepares for conference tourney; Cobras lose at State; Complete Parkland Statisticshttps://spark.parkland.edu/prospectus_1980/1027/thumbnail.jp