instruction:
In this task, you are given a paragraph (from a research paper) and your task is to classify each sentence of the paragraph (assume n sentence) into the following categories: Background, Purpose, Method, Finding/Contribution, or Other. Return the output in this format: 1 - category of sentence 1, 2 - category of sentence 2, ..., n - category of sentence n; where each number indicates the order of the sentence. The categories can be identified using the following questions: 
 Background: - Why is this problem important? - What relevant works have been done before? - What did the previous works miss? - What are the high-level research questions? - How might this help other researchers?
 Purpose: - What specific things do the researchers want to do? - What specific knowledge do the researchers want to know? - What specific hypothesis do the researchers want to test?
 Method: - How did the researchers do it or find it out? - What are the procedures and steps of this research?
 Finding/Contribution: - What did the researchers find out? Did the proposed methods work? - Did things behave as the researchers expected?
Other: put every text fragment that does not fit into any of the categories above here. Put a sentence here if its not in English, is not part of the article, contains numbers and dates, is a caption of a figure or a table, is a formatting error, or you are not sure about it.
question:
Define the space of probability distributions on the action space (0 ≤ a i ≤ 1) [0, 1] as ([0, 1]). A mixed strategy profile σ (·) is a function that maps the state s ∈ {0, 1} n to the space of probability distributions on the actions space, i.e., σ i : {0, 1} n → ([0, 1]). The definition of a mixed MMPE strategy profile σ * := {σ * i : {0, 1} n → [0, 1]} is a distribution on the action space that satisfies the following, for all t = 1, 2, . . . , and i ∈ N ,
answer:
1 - method, 2 - method, 3 - method, 4 - method, 5 - method, 6 - method


question:
A high proportion of dogs suffer from respiratory disease when they are placed in kennels for vacation or re-homing. The role of Mycoplasma cynos as an initiating agent in canine infectious respiratory disease was investigated by examining the serological response of dogs to this organism at the time of entry into a large re-homing kennel. Forty-two paired serum samples from dogs (21-day interval) were examined for antibody to M. cynos using Western blotting. The development of antibody in the serum was related to clinical disease recorded over the same period. Sixty seven per cent of the dogs showed a two-fold or greater rise in antibody to M. cynos during the first 3 weeks in the kennel. Reactivity with a 45 kDa antigen was dominant. Of those showing a positive serological reaction, 80% had recorded clinical respiratory disease while 20% remained healthy. The findings of this study show that an antibody response to M. cynos is common in dogs entering the re-homing kennel and is positively related to the development of clinical respiratory disease. #
answer:
1 - background, 2 - background, 3 - method, 4 - finding, 5 - finding, 6 - finding, 7 - finding, 8 - finding, 9 - finding, 10 - other


question:
Background: Respiratory viral infections can cause significant morbidity and mortality in immunocompromised patients. Conventional tests routinely available at most institutions are limited by the number of detectable pathogens, by a poor sensitivity and/or a long turnaround time. Objectives: To compare the performance of routine conventional testing with direct fluorescent antibody assays and viral culture to a customized TaqMan® array card (TAC) real-time PCR method, targeting 24 viruses, 8 bacteria and 2 fungi simultaneously. Study design: We collected 143 respiratory samples from 120 symptomatic immunocompromised patients. Samples for which conventional and TAC results were discordant underwent further verification testing. Results: The TAC assay identified viral pathogens in more samples than did conventional testing (77/143 versus 27/143; McNemar P < 0.0001), even when TAC results for viruses that could not be detected by conventional testing were excluded from analysis (59/143 versus 26/143; P < 0.0001). In addition, the TAC assay identified 18 samples with non-viral pathogens. Verification testing confirmed positive TAC results for 50 out of 55 samples for which conventional testing was negative. Two out of three samples with a positive conventional test but negative TAC result were confirmed positive. A viral and a total pathogen co-infection rate of 5.6% and 11.8% were found, respectively. Conclusions: The customized TAC assay resulted in a significantly increased identification of respiratory viruses. This study provides a practical real-life assessment of the performance of the TAC assay in a population for whom rapid and accurate diagnosis of viral and atypical pathogens is crucial for appropriate clinical management.
answer:

1 - background, 2 - background, 3 - background, 4 - purpose, 5 - purpose, 6 - method, 7 - method, 8 - finding, 9 - finding, 10 - finding, 11 - finding, 12 - finding, 13 - finding, 14 - finding, 15 - finding


