P-matrices and signed digraphs

We associate a signed digraph with a list of matrices whose dimensions permit them to be multiplied, and whose product is square. Cycles in this graph have a parity, that is, they are either even (termed e-cycles) or odd (termed o-cycles). The absence of e-cycles in the graph is shown to imply that the matrix product is a P0-matrix, i.e., all of its principal minors are nonnegative. Conversely, the presence of an e-cycle is shown to imply that there exists a list of matrices associated with the graph whose product fails to be a P0-matrix. The results generalise a number of previous results relating P- and P0-matrices to graphs

HOMFLY-PT polynomial and normal rulings of Legendrian solid torus links

We show that for any Legendrian link $L$ in the $1$-jet space of $S^1$ the $2$-graded ruling polynomial, $R^2_L(z)$, is determined by the Thurston-Bennequin number and the HOMFLY-PT polynomial. Specifically, we recover $R^2_L(z)$ as a coefficient of a particular specialization of the HOMFLY-PT polynomial. Furthermore, we show that this specialization may be interpreted as the standard inner product on the algebra of symmetric functions that is often identified with a certain subalgebra of the HOMFLY-PT skein module of the solid torus. In contrast to the $2$-graded case, we are able to use $0$-graded ruling polynomials to distinguish many homotopically non-trivial Legendrian links with identical classical invariants.Comment: 30 pages, 9 figure

The Bennequin number, Kauffman polynomial, and ruling invariants of a Legendrian link: the Fuchs conjecture and beyond

We show that the ungraded ruling invariants of a Legendrian link can be realized as certain coefficients of the Kauffman polynomial which are non-vanishing if and only if the upper bound for the Bennequin number given by the Kauffman polynomial is sharp. This resolves positively a conjecture of Fuchs. Using similar methods a result involving the upper bound given by the HOMFLY polynomial and 2-graded rulings is proved.Comment: 17 pages, 9 figure

An Illustrated Key to the Pupae of Six Species of \u3ci\u3eHydropsyche\u3c/i\u3e (Trichoptera: Hydropsychidae) Common in Southern Ontario Streams

I present a key for the identification of pupae and pupal exuviae of six species of Hydropsyche that are widely distributed throughout northeastern North America and that are particularly abundant in the streams of southern Ontario. Use of the pupal key requires less manipulation of a specimen than either removing larval sclerites from the pupal case or attempting to discern the adult genitalia through the pupal integument

Investigations into feline (Felis catus) palatability : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Nutritional Science at Massey University

Due to the finicky nature of the domestic cats' feeding habits, palatability is a highly complex area of feline nutrition, but one which is vitally important, with pet owners today selecting a brand based on palatability rather than nutritional value (Trivedi and Benning 1999). To date there is little published literature about the specific compounds and ingredients responsible for the palatability of cat foods, however, some animal by-products, particularly fish offals have been reported as being highly palatable to the cat (MacDonald et al. 1984). There is much interest in the use of synthetic diets for palatability testing because these diets can be easily manipulated to control specific properties of the diet. The aims of this study, using the domestic cat as the test species were to: (1) test the efficacy of using synthetic diets in palatability trials, (2) determine the palatability of various fish by-products when included in synthetic and commercially canned diets, (3) develop a method suitable for fractionating fish by-products and fractionate selected by-products. (4) determine the palatability of the fish by-product fractions obtained and (5) determine the palatability of various pure compounds when dissolved in pet milk. All palatability trials carried out used the two bowl free choice testing method. The freeze dried forms of hoki, mussel, salmon and jack mackerel by-products were included in a synthetic diet and compared to an un-supplemented synthetic diet. Hoki, mussel, salmon and barracouta by-products and the three fish by-product fractions (salmon oil, salmon water and barracouta water) were included fresh in commercially made canned diets and compared to a common commercial diet (control). Finally various pure compounds (amino acids, malic acid, salts, urea, creatinine, creatine, etc.) were dissolved in pet milk and compared to un-supplemented pet milk (control). Feed intakes were recorded daily for all of the trials. The test animals used were domestic short haired cats obtained from the Centre for Feline Nutrition (Massey University, Palmerston North, New Zealand) and all were in excellent health before testing began. The panels of cats used were either all castrated males aged three to nine years old, or a mixture of castrated males, entire females and entire males aged two to eleven years old. The feed intake data collected during the trials were analysed using t tests, and repeat measures ANOVA. Feed intakes were low overall during the synthetic trial due to the un-supplemented control diet itself not being very palatable. These low feed intakes resulted in weight losses in the cats and the study had to be abandoned prematurely. Therefore, the results are only based on a sample size of two and are of limited value as such. The other three trials were highly successful, with all cats remaining healthy, apart from two which were taken from the milk trial due to health reasons unrelated to these trials. Salmon and jack mackerel by-products were both significantly (P0.05) from the control when they were included in synthetic diets. When the fish by-products were included in commercial diets, the salmon and mussel by-products were the most palatable of the test diets, however, the salmon, mussel and barracouta by-products were not significantly different (P>0.05) from the control in terms of palatability. The hoki by-product was significantly (P0.05) different from the control in terms of palatability. Lastly, the trials involving the testing of pure compounds highlighted that at the 0.3% dose proline, lysine (lysine hydrochloride), histidine, cysteine (cysteine hydrochloride), glycine and sodium dihydrogen phosphate were all significantly (P0.05) than the control at this inclusion level. In conclusion, salmon by-product was liked and hoki by-product was disliked by the cats when included in both synthetic and commercial diets. Mussel by-product was palatable when included in the commercial diets, but was no more palatable than the control when tested in the synthetic diet. Jack mackerel by-product was palatable in the synthetic diet and barracouta by-product was no more palatable than the control in the commercial diet. Salmon oil and the compounds proline, lysine hydrochloride, histidine, glycine, cysteine hydrochloride and sodium dihydrogen phosphate were highly palatable to the cat.If future work with synthetic diets occurs it needs to be aimed at pre-weaned kittens as it would be easier to wean young inexperienced kittens onto a synthetic diet than older cats which are used to receiving a commercially made diet. The fish by-products tested here, along with other New Zealand fish species need to be further investigated. It may also be of use to test the fish by-products and their fractions in a different type of base diet in order to determine how this affects their palatability. The dose dependency of the compounds found palatable in the milk trials also needs to be established, in order to find an optimum dose for them to be used as palatability enhancers

Bearing witness: working with clients who have experienced trauma - considerations for a person-centered approach to counseling

This paper explores traumatic experience from both a cultural and neurophysiological perspective. An argument is developed to support and challenge the person-centered approach in working with clients who have experienced trauma. Through a case study, elements of theory are illustrated. Drawing from the increased knowledge base in neurophysiology, this paper aims to strengthen confidence in wider empathic attunement and brings attention to safety for both client

Mountains in the Sea: Journey to the Unknown

In this activity, students will experience the excitement of discovery and problem-solving to learn what organisms could live in extreme environments in the deep ocean. Students will also understand the importance of ocean exploration. In addition to following National Science Education Standards, this hands-on, inquiry-based activity includes focus questions, background information for teachers, links to interesting websites, and extensions. Educational levels: Intermediate elementary, Middle school

The Battle of Passchendale: The Experiences of Lieutenant Tom Rutherford, 4th Battalion, Canadian Mounted Rifles

For a man who experienced many battles, 26 October 1917 was a pivotal day for Lieutenant Tom Rutherford. Destined to have a long and distinguished career, his experience that day, in many ways, would shape his military character and strengthen his resolve in defeating the German enemy