Explain why the following algorithm that decides LCM does not run in polynomial time:

Given two numbers a and b, the least common multiple (lcm) of a and b is the smallest number m such that both a and b are factors of m. For example, lcm(15, 21) = 105 because it is the smallest number that has both 15 and 21 as factors.Formally, we will work with the following decision problem: LCM = {a, b, m | lcm(a, b) = m}(a) Explain why the following algorithm that decides LCM does not run in polynomial time: a) Check if m is a multiple of a and b; if not reject a, b, m b) For i = 1, 2, . . . , m ? 1 do: i. If i is a multiple of a and b, a multiple smaller than m was found. Reject a, b, m. c) If it reached the end of the loop without finding a multiple less than m, accept a, b, m.(b) Prove that LCM ? P.

Evaluate the employment of psychoactive drugs in the treatment of disorders over the lifespan from both an ethical and risk-benefits perspective.

Prior to beginning work on this discussion, read the required chapters from the text and review the required articles for this week. Over the course of the past weeks, we have considered the use of medications in the treatment of various psychological disorders. This discussion will provide you with an opportunity to give an informed appraisal on the use of drugs to treat disorders and defend your stance based on your judgment of the literature. In your initial post, describe what you believe are the greatest strengths and weaknesses of using the medications to treat psychological disorders. Evaluate the employment of psychoactive drugs in the treatment of disorders over the lifespan from both an ethical and risk-benefits perspective. Summarize the theories of psychiatric disease and the scientific rationale behind its treatment through the employment of drug therapies. Explain what you believe to be the greatest challenges in the use of psychoactive medications over the next several years. Support your statements with references and logical arguments.

Describe briefly how you will work to engage each stakeholder and move them to where you would like them to be within the engagement matrix.

One of the key aspects of developing your project plan is understanding who is involved with this project and their role as it impacts the project. Once you have identified your stakeholders, it is also important look at how often and in what way you should be communicating with these individuals.Review Exhibits 5.4 and 5.11 from the text before beginning this assignment.Stakeholder Assessment – Identify the stakeholders for your project and complete a Stakeholder Identification and Prioritization Matrix (exhibit 5.4) for your project as well as stakeholder engagement assessment matrix. Describe briefly how you will work to engage each stakeholder and move them to where you would like them to be within the engagement matrix.Communication Plan – Create your Communications Matrix (exhibit 5.11) using your identified stakeholders.

The risks of an unhealthy lifestyle (relate to common medical conditions).

You need to design a single poster or infographic (electronic image containing written facts and/or statistical information) to communicate the benefits of a healthy lifestyle and the risks of obesity and an unhealthy lifestyle. The poster is targeted at people who are considering making changes to their lifestyle but who are still not fully committed.The type and level of information conveyed should be appropriate for the target group. You should use a combination of images, statistical data and bullet-point text to describe the following:The message• The health risks of being overweight or obese.• The current prevalence of obesity in the UK.• The benefits of a healthy lifestyle.• The risks of an unhealthy lifestyle (relate to common medical conditions).You must include sources of evidence-based, credible health and well-being information.

Use descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated the relationship between geographic location and depression. A sample of 60 individuals, all in reasonably good health, was selected; 20 individuals were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. Each of the individuals sampled was given a standardized test to measure depression. The data collected follow; higher test scores indicate higher levels of depression. These data are contained in the file Medical1.A second part of the study considered the relationship between geographic location and depression for individuals 65 years of age or older who had a chronic health condition such as arthritis, hypertension, and/or heart ailment. A sample of 60 individuals with such conditions was identified. Again, 20 were residents of Florida, 20 were residents of New York, and 20 were residents of North Carolina. The levels of depression recorded for this study follow. These data are contained in the file Medical2. Managerial ReportUse descriptive statistics to summarize the data from the two studies. What are your preliminary observations about the depression scores?Use analysis of variance on both data sets. State the hypotheses being tested in each case. What are your conclusions?Use inferences about individual treatment means where appropriate. What are your conclusions? DiscussionInitial post prompt: Your Managerial Report serves as your initial post to the discussion forum. After responding to the requirements posed by the Managerial Report, also provide an example in your career in which you believe one of the lessons learned from the Case has been/could be applicable. Alternatively, if you don’t have/foresee direct experience relevant to your current position, what type of scenario can you anticipate occurring where you can utilize one of the lessons learned from examining this case?Response post prompt: Consider Managerial Reports posted by two of your peers. One or both of your responses may be to Managerial Reports for a case problem different from your own. Think critically and ask open-ended questions. If you agree, consider their position and expand upon their ideas. Provide an additional perspective. If you disagree, provide your reasoning. Always be professional and courteous in your responses.

How do you stay current on special education issues and policies?

Special education teachers have a professional responsibility to be a self-directed learner and seek information related to current issues and policies within the district and state where they work. An understanding of legislation, policies, and procedures will guide compliance with regulations and improve interaction with other staff, families, and students. Allocate at least 2 hours in the field to support this field experience.Interview two of the following about current special education issues and policies:Certified K-12 special education administratorSpecial education chairAn individual in a certified special education leadership role Your interviews should address the following:How do you stay current on special education issues and policies?Do you attend regular board meetings or professional conferences? If so, which and why?Do you have an affiliation with any professional organizations outside of the school district? What are the benefits of participating in a professional organization that promotes special education?How do you relay current special education issues and policies to school employees?What are the challenges in keeping all employees up-to-date regarding current special education issues and policies?What are some of the ramifications you have experienced when current special education policies are not followed?What was the best advice you received to help you become better in your field/position?What professional advice do you have for future special education teachers? In 250-500 words, summarize and reflect upon your interview and describe how foundational knowledge and current issues will influence your future professional practice. Discuss the similarities and differences of roles and responsibilities based on your feedback from the interviews. In addition, provide any additional insight the interviewees provided you may not have realized until now.

Do you think that the process of discovering WHY things don’t work is as important as the results that they do not work?

Thomas Edison said, “Results?…I have gotten lots of results. I know several thousand things that won’t work!”Based on your preliminary understanding and reading this week, react to this quotation! Six sigma is a methodology that can be used (among other things) validate business cases, improve process efficiencies, mitigate risk, and reduce wastes. How important do you think understanding things that don’t work is to six sigma and operations management? Do you think that the process of discovering WHY things don’t work is as important as the results that they do not work? Do you think we are able to replicate some of the creativity and innovation that Edison is famous for in today’s modern business environment?