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3.7: Exercises(Concepts)


  1. Consider the weighted voting system ([q: 7, 3, 1])
    1. Which values of (q) result in a dictator (list all possible values)
    2. What is the smallest value for (q) that results in exactly one player with veto power but no dictators?
    3. What is the smallest value for (q) that results in exactly two players with veto power?
  2. Consider the weighted voting system ([q: 9, 4, 2])
    1. Which values of (q) result in a dictator (list all possible values)
    2. What is the smallest value for (q) that results in exactly one player with veto power?
    3. What is the smallest value for (q) that results in exactly two players with veto power?
  3. Using the Shapley-Shubik method, is it possible for a dummy to be pivotal?
  4. If a specific weighted voting system requires a unanimous vote for a motion to pass:
    1. Which player will be pivotal in any sequential coalition?
    2. How many winning coalitions will there be?
  5. Consider a weighted voting system with three players. If Player 1 is the only player with veto power, there are no dictators, and there are no dummies:
    1. Find the Banzhaf power distribution.
    2. Find the Shapley-Shubik power distribution
  6. Consider a weighted voting system with three players. If Players 1 and 2 have veto power but are not dictators, and Player 3 is a dummy:
    1. Find the Banzhaf power distribution.
    2. Find the Shapley-Shubik power distribution
  7. An executive board consists of a president (P) and three vice-presidents (left(mathrm{V}_{1}, mathrm{V}_{2}, mathrm{V}_{3} ight)). For a motion to pass it must have three yes votes, one of which must be the president's. Find a weighted voting system to represent this situation.
  8. On a college’s basketball team, the decision of whether a student is allowed to play is made by four people: the head coach and the three assistant coaches. To be allowed to play, the student needs approval from the head coach and at least one assistant coach. Find a weighted voting system to represent this situation.
  9. In a corporation, the shareholders receive 1 vote for each share of stock they hold, which is usually based on the amount of money the invested in the company. Suppose a small corporation has two people who invested $30,000 each, two people who invested $20,000 each, and one person who invested $10,000. If they receive one share of stock for each $1000 invested, and any decisions require a majority vote, set up a weighted voting system to represent this corporation’s shareholder votes.
  10. A contract negotiations group consists of 4 workers and 3 managers. For a proposal to be accepted, a majority of workers and a majority of managers must approve of it. Calculate the Banzhaf power distribution for this situation. Who has more power: a worker or a manager?
  11. The United Nations Security Council consists of 15 members, 10 of which are elected, and 5 of which are permanent members. For a resolution to pass, 9 members must support it, which must include all 5 of the permanent members. Set up a weighted voting system to represent the UN Security Council and calculate the Banzhaf power distribution.

Data Mining: Concepts and Techniques provides the concepts and techniques in processing gathered data or information, which will be used in various applications. Specifically, it explains data mining and the tools used in discovering knowledge from the collected data. This book is referred as the knowledge discovery from data (KDD). It focuses on the feasibility, usefulness, effectiveness, and scalability of techniques of large data sets. After describing data mining, this edition explains the methods of knowing, preprocessing, processing, and warehousing data. It then presents information about data warehouses, online analytical processing (OLAP), and data cube technology. Then, the methods involved in mining frequent patterns, associations, and correlations for large data sets are described. The book details the methods for data classification and introduces the concepts and methods for data clustering. The remaining chapters discuss the outlier detection and the trends, applications, and research frontiers in data mining.

This book is intended for Computer Science students, application developers, business professionals, and researchers who seek information on data mining.

  • Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects
  • Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields
  • Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of your data

Surrounding Yourself With Critical Thinkers

One of the best things you can do to improve your critical thinking isn't really an exercise it's an environmental change. If you're surrounded with critical thinkers who freely express their thoughts and share their opinions, you'll be exposed to more sources of knowledge and perspective, and will have access to much better ideas--whether they're yours or someone else's. If you're in a position to hire or build a team, look for people who show strong signs of critical thinking. If not, try to seek critical thinkers elsewhere, in a peer group or in a class outside of work.


Single Leg Balance Exercises For Kids

Once you are ready for single leg balance exercises there is so much that you can do. Single leg standing is the basis of most exercises and components can be added from there.

Single leg standing reaching outside of the base of support is one fun way to work on this gross motor skill. To make this balance exercise more challenging don’t allow the foot to touch the ground in between taps of the toe.


Balbharati solutions for Mathematics 2 Geometry 9th Standard Maharashtra State Board chapter 1 (Basic Concepts in Geometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics 2 Geometry 9th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics 2 Geometry 9th Standard Maharashtra State Board chapter 1 Basic Concepts in Geometry are Basic Concept in Geometry, Co-ordinates of Points and Distance, Basic concept of segment, ray and line, Conditional Statements and Converse, Proofs.

Using Balbharati 9th Standard solutions Basic Concepts in Geometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 9th Standard prefer Balbharati Textbook Solutions to score more in exam.


The Figure of Speech Exercise – 6

Here are the sentences in the figure of speech exercise with answers. Identify and name them.
  1. O world! Oh, Life! O Time! On Whose last steps I climb.
  2. Why, man, if the river were dry I am able to fill it with tears.
  3. James, I was the wisest fool.
  4. But patient, to prevent That murmur, soon replies
  5. I hear lake water lapping with low sounds by the shore.
  6. So like a shattered column lay the king?
  7. I wandered lonely as a cloud.

Check Your Answers

Now check your answers with the section given below.
  1. Apostrophe
  2. Hyperbole
  3. Oxymoron
  4. Onomatopoeia
  5. Onomatopoeia
  6. Simile
  7. Simile

Rotator cuff repair: post-operative rehabilitation concepts

Purpose of review: With improvements in surgical techniques and increased knowledge of rotator cuff healing, there was a need to identify a safe progression after rotator cuff repair. The rehabilitation specialist plays an integral role in the care of these patients, and by implementing an evidence and criteria-based model, patients may be able to return to their prior levels of function sooner with fewer complications.

Recent findings: Timing of progression for rotator cuff patients should align not only with healing but also potential strain on the involved tissue. Recent electromyography studies have identified exercises which elicit highest level of muscle activation for individual dynamic stabilizers. The physical therapist should also be aware of potential complications and be prepared to manage appropriately if they should arise. During rehabilitation after rotator cuff repair, there should be constant communication with the surgical team. Awareness of complication management, healing potential of the repaired tendon, and anatomy of the shoulder complex are critical. During the early stages, reducing pain and inflammation should be prioritized followed by progressive restoration of range of motion. When advancing range of motion, progression from passive, active assisted, and active movements allow for gradual introduction of stress to the healing construct. Even though time frames are not used for progression, it is important not to place excessive stress on the shoulder for up to 12 weeks to allow for proper tendon-to-bone healing. As exercises are progressed, scapular muscle activation is initiated, followed by isometric and lastly isotonic rotator cuff exercises. When treating overhead athletes, advanced strengthening in the overhead position is performed, followed by plyometric training. Advanced strengthening is initiated when all preceding criteria have been met. It is important that patients are educated early in the rehabilitation process so that they can manage their expectations to realistic time frames.

Keywords: Post-operative rehabilitation Rotator cuff Shoulder.

Conflict of interest statement

Conflict of interest

Both authors declare that they have no conflict of interest.

Human and animal rights and informed consent

This article does not contain any studies with human or animal subjects performed by any of the authors.


Evolution in Action

The Chromosome 18 InversionNot all structural rearrangements of chromosomes produce nonviable, impaired, or infertile individuals. In rare instances, such a change can result in the evolution of a new species. In fact, an inversion in chromosome 18 appears to have contributed to the evolution of humans. This inversion is not present in our closest genetic relatives, the chimpanzees.

The chromosome 18 inversion is believed to have occurred in early humans following their divergence from a common ancestor with chimpanzees approximately five million years ago. Researchers have suggested that a long stretch of DNA was duplicated on chromosome 18 of an ancestor to humans, but that during the duplication it was inverted (inserted into the chromosome in reverse orientation.

A comparison of human and chimpanzee genes in the region of this inversion indicates that two genes—ROCK1 and USP14—are farther apart on human chromosome 18 than they are on the corresponding chimpanzee chromosome. This suggests that one of the inversion breakpoints occurred between these two genes. Interestingly, humans and chimpanzees express USP14 at distinct levels in specific cell types, including cortical cells and fibroblasts. Perhaps the chromosome 18 inversion in an ancestral human repositioned specific genes and reset their expression levels in a useful way. Because both ROCK1 and USP14 code for enzymes, a change in their expression could alter cellular function. It is not known how this inversion contributed to hominid evolution, but it appears to be a significant factor in the divergence of humans from other primates. 1

A translocation occurs when a segment of a chromosome dissociates and reattaches to a different, nonhomologous chromosome. Translocations can be benign or have devastating effects, depending on how the positions of genes are altered with respect to regulatory sequences. Notably, specific translocations have been associated with several cancers and with schizophrenia. Reciprocal translocations result from the exchange of chromosome segments between two nonhomologous chromosomes such that there is no gain or loss of genetic information (Figure 7.12).

Figure 7.12 An (a) inversion occurs when a chromosome segment breaks from the chromosome, reverses its orientation, and then reattaches in the original position. A (b) reciprocal translocation occurs between two nonhomologous chromosomes and does not cause any genetic information to be lost or duplicated. (credit: modification of work by National Human Genome Research Institute (USA)


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Request Exercise Support

Learn how to receive support for design, development, conduct, and evaluation support for individual exercises through the National Exercise Program.

Exercise and Preparedness Tools

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About the National Level Exercise

Learn about the nation’s cornerstone biennial exercise that helps validate national capabilities to prepare for and respond to catastrophic events.

About the Homeland Security Exercise and Evaluation Program

Learn how organizations can use HSEEP to run their own effective exercise and evaluation programs.


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