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Integration by Parts: “Undoing” the Product Rule for Derivatives ∫x ln(x)dx Consider: We have no formula for this integral. Notice that x and ln(x) are not related by derivatives, so we cannot use the substitution method.

Integration by Parts: “Undoing” the Product Rule for Derivatives Integrating both sides, we get: ∫udv = ∫d (uv) −∫vdu Or ∫udv =uv−∫vdu ∫vdu should be simpler that the original ∫udv The integral If two functions are not related by derivatives (substitution does not apply), choose one function to be the u (to differentiate) and the other function to be the dv (to integrate)

Integration by Parts Every differentiation rule has a corresponding integration rule. For instance, the Substitution Rule for integration corresponds to the Chain Rule for differentiation. The rule that corresponds to the Product Rule for differentiation is called the rule for integration by parts. The Product Rule states that if f and g are differentiable functions, then [f (x)g (x)] = f (x)g (x) + g (x)f (x) 3

Comparison with other methods Recently, Tjong and Zhou (2007) developed a neural network method for predicting DNA-binding sites. In their method, for each surface residue, the PSSM and solvent accessibilities of the residue and its 14 neighbors were used as input to a neural network in the form of vectors. In their publication, Tjong and Zhou showed that their method achieved better performance than other previously published methods. In the current study, the 13 test proteins were obtained from the study of Tjong and Zhou. Thus, we can compare the method proposed in the current study with Tjong and Zhou’s neural network method using the 13 proteins. Figure 1. Tradeoff between coverage and accuracy In their publication, Tjong and Zhou also used coverage and accuracy to evaluate the predictions. However, they defined accuracy using a loosened criterion of “true positive” such that if a predicted interface residue is within four nearest neighbors of an actual interface residue, then it is counted as a true positive. Here, in the comparison of the two methods, the strict definition of true positive is used, i.e., a predicted interface residue is counted as true positive only when it is a true interface residue. The original data were obtained from table 1 of Tjong and Zhou (2007), the accuracy for the neural network method was recalculated using this strict definition (Table 3). The coverage of the neural network was directly taken from Tjong and Zhou (2007). For each protein, Tjong and Zhou’s method reported one coverage and one accuracy. In contrast, the method proposed this study allows the users to tradeoff between coverage and accuracy based on their actual need. For the purpose of comparison, for each test protein, topranking patches are included into the set of predicted interface residues one by one in the decreasing order of ranks until coverage is the same as or higher than the coverage that the neural network method achieved on that protein. Then the coverage and accuracy of the two methods are compared. On a test protein, method A is better than B, if accuracy(A)>accuracy(B) and coverage (A)≥coverage(B). Table 3 shows that the graph kernel method proposed in this study achieves better results than the neural network method on 7 proteins (in bold font in table 3). On 4 proteins (shown in gray shading in table 3), the neural network method is better than the graph kernel method. On the remaining 2 proteins (in italic font in table 3), conclusions can be drawn because the two conditions, accuracy(A)>accuracy(B) and coverage (A)≥coverage(B), never become true at the same time, i.e., when coverage (graph kernel)>coverage(neural network), we have accuracy(graph kernel)accuracy(neural network). Note that the coverage of the graph kernel method increases in a discontinuous fashion as we use more patches to predict DNA-binding sites. One these two proteins, we were not able to reach at a point where the two methods have identical coverage. Given these situations, we consider that the two methods tie on these 2 proteins. Thus, these comparisons show that the graph kernel method can achieves better results than the neural network on 7 of the 13 proteins (shown in bold font in Table 3). Additionally, on another 4 proteins (shown in Italic font in Table 3), the graph kernel method ties with the neural network method. When averaged over the 13 proteins, the coverage and accuracy for the graph kernel method are 59% and 64%. It is worth to point out that, in the current study, the predictions are made using the protein structures that are unbound with DNA. In contrast, the data we obtained from Tjong and Zhou’s study were obtained using proteins structures bound with DNA. In their study, Tjong and Zhou showed that when unbound structures were used, the average coverage decreased by 6.3% and average accuracy by 4.7% for the 14 proteins (but the data for each protein was not shown).

KU Group Consumers What to Share with Each KU Group Instrumental Use: Must Instrumental Use: Must demonstrate value of product demonstrate value of to end users (clinician or their product to end users via clients) via informational product packaging and literature, conference marketing efforts. presentations and marketing efforts. How to Reach Each Group Use sales representatives, product training sessions, news media (print, broadcast and internet based forms); product Use news media placement in stores. Offer Use email, phone calls (targeted print, product demonstrations at and web links to news broadcast and internet conferences and tradeshows. stories regarding the based forms); product Offer assessment tools that product. Report in formal placement in stores; help determine if a product is annual performance demonstration packages appropriate for a client, or the report. and trial use of product. ideal configuration, accessories, etc. for product. Provide demonstration packages and trial use of product. Anticipated Knowledge Translation Outcomes Clinicians Policy Makers Researchers Brokers Manufacturers Strategic Use: If public funds were used for product development, demonstrate return on investment (ROI). Conceptual Use: Provide information on path to market, barriers encountered and carriers used to overcome barriers to provide product development insights to other researchers. Conceptual Use: Demonstrate ROI (financial, university publicity, student training, etc.). Strategic Use: Demonstrate ROI and identify partnering opportunities with companies producing complementary products. Innovation Outputs. Consumers can use products, leading to a better QoL. Clinicians may use products directly or recommend products, leading to improved QoL. Present findings at research oriented conferences Use formal reports, (RESNA, etc.). Use email, phone calls and research papers and power face to face meetings. point presentations. Researchers will gain a greater appreciation and understanding of the Policy makers can share Knowledge to Axtion (KTA) ROI information with process, leading to an oversight organizations increased liklihood that new (ex. Office of Management research will be conducted and Budget). using the Need to Knowledge and KTA models. Brokers can use ROI information to justify future investments in similar products. Face to face meetings may be most effective. Seek out manufacturers at offices, conferences and tradeshows. Manufacturers can increase ROI by teaming up with companies selling complementary products.

Step 1 What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice? What do you notice?

Molecular Formula • Molecular formula is derived from empirical formula and molecular mass, which is obtained independently • Empirical formula = CxHyOz; molecular formula = (CxHyOz)n, where n = (molecular mass/empirical formula mass) • Example: A compound has an empirical formula C3H6O and its molecular formula is 116.2 u. What is the molecular formula? • Solution: Empirical formula mass = (2 x 12.01 u) + (6 x 1.008 u) + 16.00 u = 58.1 u Molecular formula = (C3H6O)n; where n = (116.2 u/58.1 u) = 2 Incorrect molecular formula = (C3H6O)2; • Correct molecular formula = C6H12O2

KU Group Consumers Clinicians Policy Makers Researchers Brokers Manufacturers What to Share with Each KU Group Strategic Use: Use business case and focus group/field test results to develop talking points to demonstrate how prototype could lead to product development and improved Quality of Life (QoL). Strategic Use: Use business case and focus group/field test results to demonstrate how prototype could lead to product development and improved QoL. Strategic Use: Use business case and focus group results to develop talking points that demonstrate how a product based upon the prototype design could lead to improved QoL and cost savings. Conceptual Use: Disseminate nonproprietary information regarding prototype to stimulate additional R. Instrumental Use: Develop full commercialization Instrumental Use: Develop full package including commercialization package information from initial need including information from initial assessment, valuability need assessment, valuability assessments, value assessments, value proposition, proposition, focus focus group/field test results, group/field test results, description of features and description of features and specifications and technical specifications and technical details of prototype.* details of prototype.* How to Reach Each KU Group Network with consumer advocacy organizations (CIL, Cerebral Palsy Association, AARP, etc.) and ask them to publish an article in their newsletter or have them email their constituents. Present at organizational meetings. Ask the organizations to have a link on their website to your website. Use fliers, emails, phone calls and face to face meetings. Present prototype/findings at clinician oriented conferences (AOTA, APTA, CSUN, ISS, etc.). Use research papers, power point presentations, mailings and emails. Presentations communicated to program directors, reply to invitations for comments or talk with elected officials. Use email, calls, face to face meetings and power point presentations. Present findings at research oriented conferences (RESNA, etc.). Use research papers and power point presentations. Conduct face to face meetings Face to face meetings with with individual manufacturers at University TTO may be their home offices or at most effective. conferences/tradeshows Commercialization package (Medtrade, ATIA, etc.). (soft or hard copies) and Commercialization package (soft power point presentations.* or hard copies), power point presentations and tailored emails.* Anticipated Knowledge Translation Outcomes Consumers can use talking points to contact politicians to advocate for reimbursement of potential devices, or contact manufacturers and distributors to stimulate product demand.* Clinicians can use talking points to contact politicians to advocate for reimbursement of potential devices, or contact manufacturers and distributors to stimulate product demand.* Policy makers can use talking points as basis for Researchers can use introducing and findings as basis for supporting legislation to additional research on provide reimbursement related topics.* for potential devices.* Invention outputs. Brokers can use a commercialization package to demonstrate the value of a product to manufacturers and encourage them to move to production.* Manufacturers can use a commercialization package to understand the value of a product, thereby encouraging them to move to production.*

2. RIEMANN SUMS 4 a. For the hypothetical function shown in the figures at right, approximate the integral: using a 5-term Riemann Sum with 5 (a) 3 f ( x)dx 0 2 * left-hand sampling points in figure (a), 1 * right-hand sampling points in figure (b). In each case, shade in the area that each Riemann Sum represents. 1 4 2 3 4 5 2 3 4 5 (b) 3 2 1 1 3. INTEGRATION AS AN AREA COMPUTATION a) For each integral below: i) make a sketch of the integrand, ii) shade in the total area represented by the integral, iii) identify which portions of the total area are positive or negative, iv) give the value of each integral based on your sketches. 2 x sin x dx ___ 3 dx ___ 2 b) A general rule based on the above illustrations is: "The integral of any function with ______ symmetry over limits that are ___________ with respect to the y-axis is always identically ________." c) For each integral below: i) make a sketch of the integrand, ii) shade in the total area represented by the integral, iii) identify which portions of the total area are positive or negative, iv) give an equivalent integral that is easier to evaluate 2 /2 2 ( 4 x ) dx cos x dx /2 2 -4-