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A Process Algebraic Form to Represent Extensive Games 1
A Process Algebraic Form to Represent Extensive Games Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365-9415, Tehran, Iran Complex and Multi Agent System Lab Omid Gheibi∗, Rasoul Ramezaniany (alphabetical order) Abstract We present an agent-based display of extensive games inspired by concepts in process theory and process algebra. In games with lots of agents, it is a good strategy to explain the behavior of each agent individually by an adequate process (called process- game), and then obtain the whole of the game through parallel composition of these process-games. We propose a method based on agent-based display (introduced in this paper) to find the Nash equilibrium of extensive games in linear space complexity by deploying a revision of depth first search. Keywords: Extensive games, Nash equilibrium, process theory, process algebra 1 Introduction The word processes refers to behavior of a system (a game, a protocol, a machine, a software, and so on). The behavior of a system is the total of actions performed in the system and the order of their executions. The process theory [8] makes it possible to model the behavior of a system with enormous complexity through modeling the behavior of its components. Then using the process algebra [3] [9] [5] [7] [1] [15], we can code the process theory terms and definitions and take the advantage of the algebra such as automating calculations and running algorithms using parallel computing techniques. The process algebra has vast variety of applications in diverse fields such as performance evaluation [6], safety critical systems [13], network protocols [2] and biology [14]. -
Neuro-Developmental Treatment (NDT) and Neurological Disorders: the Latest Research and Resources for Ots and Pts
Neuro-Developmental Treatment (NDT) and Neurological Disorders: The Latest Research and Resources for OTs and PTs (2 CEs) Learning Objectives • Summarize foundational theories and treatment behind NDT. • Explain what NDT looks like as delivered through physical and occupational therapy practitioners. • Summarize current peer-reviewed NDT research. • Identify and describe NDT-appropriate neurological disorders outside of cerebral palsy (CP) and hemiplegia. • Identify updated resources for proper billing of NDT in specific practice settings. • Discuss current therapy resources for NDT to enhance the clinical practice. Introduction Neuro-developmental treatment (NDT) also referred to as the Bobath Concept or approach, has been around since the 1940s when it was first developed by Berta and Dr. Karel Bobath. Initially, the Bobaths introduced innovative therapeutic approaches for children with cerebral palsy and adults with hemiplegia. Today, NDT is widely used in the therapy realm for numerous neurological conditions and has revolutionized hands-on clinical work. Physical and occupational therapists working in various settings and capacities worldwide have incorporated NDT principles and practices into their patients’ treatment sessions. Like other theoretical and practical roots of physical therapy and occupational therapy, NDT’s foundations have aged; this, however, does not mean that NDT is less applicable or is out-of-date. As with other treatment theories, NDT was designed to evolve as clinicians learned more about the human function. In fact, the Bobaths insisted that NDT must be applied so that it could evolve over time in order to fully understand the recovery of function in neurological conditions (Runyan, 2006). As new treatments take the limelight, however, older treatment approaches are at risk of fading. -
Game Theory - Solution Set
1 Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1 Mathematics and Computing Grade 6 Math Circles Fall 2014 - October 28/29, 2014 Game Theory - Solution Set 1. Provide your own definition of Game Theory. Answers may vary. Game theory is the study of two or more people making decisions in a common situation to get the best outcome for themselves, an outcome that is affected by each person's decision. 2. Explain why the Nash Equilibrium is the best decision for both suspects in the \Prisoner's Dilemma". Answers may vary. The Nash Equilibrium is the best decision for both suspects in the \Pris- oner's Dilemma", because neither suspect could become better off, and leave the other person worse off, by individually changing their decision. 3. The game is defined as follows: • Two hunters go out to catch meat. • There are two rabbits in the range and one stag. The hunters can each bring the equip- ment necessary to catch one type of animal. • The stag has more meat than the rabbits combined, but both hunters must chase the stag to catch it. • Rabbit hunters can catch all of their prey by themselves. • The values in the table represent the amount of meat (in pounds) the hunters will get for each given outcome. 2 Hunter 2 Stag Rabbit Hunter 1 Stag 3,3 0,2 Rabbit 2,0 1,1 Using the Nash Equilibrium of this game, what is the best decision the hunters can make? If there is more than one best decision, explain the pros and cons of each. -
Games Due: Tuesday, October 30, at Beginning of Class Reading: Course Notes, Sections 4.1 and 4.2
University of Illinois Fall 2018 ECE 586BH: Problem Set 4: Problems and Solutions Extensive form (aka sequential) games Due: Tuesday, October 30, at beginning of class Reading: Course notes, Sections 4.1 and 4.2 1. [Variations of pirate game] Five pirates, A, B, C, D, E, in a boat at sea must decide how to allocate 100 gold coins among themselves. The pirates are lettered in order of seniority, with A being the most senior. The pirate protocol is that the most senior pirate proposes an allocation of coins to all pirates, with a nonnegative integer number of coins going to each pirate. Then all pirates, including the proposer, vote on the proposal. If a majority (meaning strictly more than half the number voting) approve the proposal, then the proposal is implemented and the game ends. Otherwise, the proposer is thrown overboard and votes no more, and the remaining pirates use the same protocol again, with the most senior remaining pirate being the next proposer, and so on. Pirates base decisions on four factors. First, each pirate prefers to not be thrown overboard, even if the pirate receives no coins. Second, given a pirate is not thrown overboard, the pirate prefers to have more coins. Third, if in any round the pirate would do as well to vote either way, the pirate will vote no in order to increase the chance the proposer is thrown overboard. Finally, pirates follow the protocol, but otherwise don't trust each other and so can't enter into binding side agreements with each other. -
Quorum Analysis for the “Pirate Game” Problem⋆
Quorum Analysis for the \Pirate Game" Problem? Ilya Chernov1 and Evgeny Ivashko1;2 1 Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences, Petrozavodsk, Russia 2 Petrozavodsk State University fchernov,[email protected] http://mathem.krc.karelia.ru/ Abstract. The \Pirate game" is a popular mathematical puzzle, the problem aimed at demonstration of backward induction. It is also a shin- ing example of non-cooperative behaviour of rational agents in mathe- matical game theory. A linearly ordered crew votes for the captain's sharing offer. The captain needs the approval by a given fraction of the crew called quorum at the minimal cost. In this paper, we present the comprehensive quorum analysis on strategies and payoffs for the \Pirate game" problem, for any crew size and any quorum. Keywords: Pirate Game · Puzzle for Pirates · Quorum Analysis · Non- Cooperative Game Theory 1 Introduction and Related Work The \Pirate game" (also known as the \Puzzle for pirates") is a well-known widely-used mathematical puzzle, which often stirs up disputes3. The first ap- pearing of the problem in scientific literature seems to be in the book by E. Mou- lin [6] as an example; we found no earlier publications of this problem. The \Pirate game" is the following4: There are five rational pirates (in strict order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them. The pirate world's rules of distribution say that the most senior pirate first proposes a plan of distribution. The pirates, including the proposer, then vote on whether to accept this distribution. -
Suit Therapy Adeli Suit
Suit Therapy Adeli Suit Alyssa Connifey Doug Eck Josh Egloff Sarah Kibiloski Maria King Sean McBride Background ● Developed in late 1960s/early 1970s by Russian space program for astronauts to maintain muscle tone in an anti- gravity environment ● Has been modified and used as an alternative treatment for patients with cerebral palsy and other neuromuscular disorders ● “Adeli” comes from the nickname of the prototype called the penguin suit, based on the Adeli Penguin Treatment ● Consists of a vest, shorts, knee pads, and shoes, connected by a series of adjustable, elastic bands ● Goal: maintain proper body alignment in order to restrict abnormal movement and ROM ● Provides immediate feedback to patient on normal movement patterns ● Suit is worn throughout intensive sessions to: ○ “retrain” the brain using correct muscle movements ○ improve body awareness ○ support weak muscles ○ improve gross motor skills and balance ○ provide normal proprioceptive input to the brain Rationale ● Research from the Pediatric Institute of the Russian Academy of Science showed that AST stimulates the restarting of the vestibular system’s development ● The vestibular system is a processing center for impulses from proprioceptors ○ The suit provides normal tactile and proprioceptive stimulation to normalize afferent vestibular-proprioceptive inputs to the vestibular system ○ Allows CNS to send out normal efferent signals ○ Muscle tone, balance, coordination, body awareness, and proprioception are influenced Treatment Sessions ● The original Russian protocol -
Effect of Modified Suit Therapy in Spastic Diplegic Cerebral Palsy - a Single Blinded Randomized Controlled Trial
Online Journal of Health and Allied Sciences Peer Reviewed, Open Access, Free Online Journal Published Quarterly : Mangalore, South India : ISSN 0972-5997 This work is licensed under a Volume 9, Issue 4; Oct-Dec 2010 Creative Commons Attribution- No Derivative Works 2.5 India License Short Report: Effect of Modified Suit Therapy in Spastic Diplegic Cerebral Palsy - A Single Blinded Randomized Controlled Trial Jagatheesan Alagesan, Associate Professor, KJ Pandya College of Physiotherapy, Sumandeep University, Vadodara, Angelina Shetty, Senior Physiotherapist, Mobility India, Bangalore. Address For Correspondence: Dr. A. Jagatheesan, Associate Professor, KJ Pandya College of Physiotherapy, Sumandeep Vidyapeeth, Piparia, Waghodia, Vadodara, India - 391760. E-mail: [email protected] Citation: Alagesan J, Shetty A. Effect of Modified Suit Therapy in Spastic Diplegic Cerebral Palsy - A Single Blinded Randomized Controlled Trial. Online J Health Allied Scs. 2010;9(4):14 URL: http://www.ojhas.org/issue36/2010-4-14.htm Open Access Archives: http://cogprints.org/view/subjects/OJHAS.html and http://openmed.nic.in/view/subjects/ojhas.html Submitted: Jul 26, 2010; Accepted: Nov 2, 2010; Published: Jan 20, 2011 Abstract: Treatment program is use of specific sets of exercise to work Background & Objective: Development of gross motor towards 3 important goals, preventing the weakening or deteri- function in children with cerebral palsy has been a primary goal oration of muscles that can follow disuse, avoiding contractures of physical therapists for decades. Suit therapy has been and to improve the child’s motor development. It also includes proposed as an adjunct to conventional physiotherapy to treat activities and education to improve flexibility, strength, mobil- the impairments associated with cerebral palsy. -
Designing a Virtual Reality Game for the Pediatric Patient-Player Experience
Navigating the Pixelated Waters of Voxel Bay: Designing a Virtual Reality Game for the Pediatric Patient-Player Experience Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Fine Arts in the Graduate School of The Ohio State University By Alice Grishchenko Graduate Program in Design Ohio State University 2017 Thesis Committee: Alan Price Maria Palazzi Jeremy Patterson Copyright by Alice Grishchenko ©2017 All Rights Reserved Abstract Voxel Bay is a virtual reality game created in collaboration with Nationwide Children’s Hospital to distract pediatric hemophilia patients from the anxiety related to the prophylaxis infusion procedure they must undergo regularly. This paper documents answers to the question when designing a game to serve as a pain management distraction technique for pediatric patients, what factors should be considered for the overall experience of the patient-player, clinicians and caregivers, and what may be unique or different from conventional approaches to game development? The answers to the research question are presented in context to the development of Voxel Bay. They are a list of factors to be considered and a documentation of my contribution to the project. The game design concepts discussed include spatial level design for virtual reality and ways to world build without cut scenes. This paper also mentions the hardware configuration used to create an entertaining hands-free system without sacrificing the integrity of the player’s medical experience. After an exploration of these concepts, the paper describes the novel processes used to realize them. The design choices and process documentation are supported by a review of research precedents regarding virtual reality as a distraction tool for medical settings as well as games designed to be used with breathing peripherals, games that use a networked system with different user roles and games that directly inspired the design of Voxel Bay. -
By Margaret Bukola, Fatudimu
IMPACT OF MOTOR DEVELOPMENT IN CHILDREN WITH CEREBRAL PALSY ON THE QUALITY OF LIFE AND GENERAL HEALTH STATUS OF CAREGIVERS BY MARGARET BUKOLA, FATUDIMU B. Physiotherapy (Ib), M.Sc (Neuro-physiotherapy) Ib. A Thesis in the Department of Physiotherapy Submitted to the Faculty of Clinical Sciences, College of Medicine in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY (NEURO-PHYSIOTHERAPY) of the UNIVERSITY OF IBADAN NOVEMBER 2011 ABSTRACT Cerebral Palsy (CP) is a neuropaediatric condition which occurs as a result of damage to an immature brain resulting in abnormal motor development requiring special care. Caring for children with CP may affect the quality of life and/or impact on the general health status of their caregivers. There is paucity of longitudinal studies exploring this inter-relationship. The relationship between motor development of Children With Cerebral Palsy (CWCP) and impact of caring on each of Quality of Life (QoL) and General Health Status (GHS) of caregivers of CWCP was therefore evaluated. Participants in this longitudinal study comprised of consecutively recruited 107 CWCP and 107 Caregivers of CWCP (CCWCP) from four specialist hospitals in southwest Nigeria. Ninety eight caregivers of normally developing children were also recruited to constitute the Control Group (CG). The CCWCP and CG were matched for age and socio-economic status. However 67 participants in each of the CWCP, CCWCP, and 87 in the CG completed the study. Gross motor function of the CWCP was assessed in the clinic and their respective homes using the Gross Motor Function Measure (GMFM)(scored 0 to 100) at baseline and monthly for eight consecutive months in order to assess the likely influence of the home and the clinic environments on their motor function. -
Complementary and Alternative Methods in Cerebral Palsy
DEVELOPMENTAL MEDICINE & CHILD NEUROLOGY REVIEW Complementary and alternative methods in cerebral palsy WILLIAM L OPPENHEIM MD Margaret Holden Jones Kaanar Professor, David Geffen School of Medicine at UCLA, Los Angeles, CA 90095, USA. Correspondence to William L Oppenheim at UCLA ⁄ Orthopaedic Hospital Center for Cerebral Palsy, Box 956902, Geffen School of Medicine, Los Angeles, CA, USA. E-mail: [email protected] LIST OF ABBREVIATIONS There are no published studies specifically addressing complementary and AHRQ Agency for Healthcare Research and alternative treatments in adults with cerebral palsy (CP). However, national Quality surveys of adults with chronic disabilities document that a majority of them AST Adeli suit treatment use such treatments, that they are willing to pay out of pocket, if necessary, CAM Complementary and alternative and that they believe that pursuing such treatment relieves pain, reduces stress methods and anxiety, and leads to improved feelings of fitness and well-being. FES Functional electrical stimulation HBOT Hyperbaric oxygen therapy Individuals enjoy taking charge of their own health care decisions, and NCCAM frequently feel more in control with these therapies than with more traditional National Center for Complementary methods. In contrast to adults, there is some information on complementary and Alternative Medicine and alternative methods (CAM) in children with CP. This article discusses some NMES Neuromuscular electrical stimulation of the CAM used in children that may be carried over into adulthood, as well as TES Threshold electrical stimulation the pitfalls for patients and conventional physicians as they try to sort out what might be helpful and what might be harmful in this arena. -
Suit Therapy
Cigna Medical Coverage Policy Effective Date ............................ 4/15/2014 Next Review Date ...................... 4/15/2015 Coverage Policy Number ................. 0353 Subject Suit Therapy Table of Contents Hyperlink to Related Coverage Policies Coverage Policy .................................................. 1 Occupational Therapy General Background ........................................... 1 Physical Therapy Coding/Billing Information ................................... 3 References .......................................................... 4 INSTRUCTIONS FOR USE The following Coverage Policy applies to health benefit plans administered by Cigna companies. Coverage Policies are intended to provide guidance in interpreting certain standard Cigna benefit plans. Please note, the terms of a customer’s particular benefit plan document [Group Service Agreement, Evidence of Coverage, Certificate of Coverage, Summary Plan Description (SPD) or similar plan document] may differ significantly from the standard benefit plans upon which these Coverage Policies are based. For example, a customer’s benefit plan document may contain a specific exclusion related to a topic addressed in a Coverage Policy. In the event of a conflict, a customer’s benefit plan document always supersedes the information in the Coverage Policies. In the absence of a controlling federal or state coverage mandate, benefits are ultimately determined by the terms of the applicable benefit plan document. Coverage determinations in each specific instance require consideration of 1) the terms of the applicable benefit plan document in effect on the date of service; 2) any applicable laws/regulations; 3) any relevant collateral source materials including Coverage Policies and; 4) the specific facts of the particular situation. Coverage Policies relate exclusively to the administration of health benefit plans. Coverage Policies are not recommendations for treatment and should never be used as treatment guidelines. -
1. Characteristics of an Oligopoly, Which Can Be Demonstrated by Game Theory, Include Which of the Following? I
1. Characteristics of an oligopoly, which can be demonstrated by game theory, include which of the following? I. Collusion can increase oligopolists’ profits. II. Oligopolistic firms are interdependent. III. Few barriers to entry exist. a. I only b. II only c. III only d. I and II only e. I, II, and III 2. Which of the following is true of a cartel? a. Customers substitute away from the good when the price increases. b. Individual cartel members are tempted to cheat on the agreement. c. Although the total gain to cartel members is positive, all members lose when everyone sticks to the agreement. d. Some firms will reduce output in an effort to lower costs of production. e. Oligopolistic behavior is generally predictable as production occurs where MC=MR. Questions 3 and 4 refer to Royal’s Fast Food this payoff matrix: High price Low price High price 120, 85 150, 120 Brewer’s Fast Food Low price 65, 100 50, 80 3. Based on the payoff matrix above, which of the following statements is true? a. Brewer’s has a dominant strategy to choose high prices. b. Brewer’s has a dominant strategy to choose low prices. c. Royal’s has a dominant strategy to choose high prices. d. Royal’s has a dominant strategy to choose low prices. e. Neither restaurant has a dominant strategy. 4. What is the Nash equilibrium in the game above? a. Both fast food restaurants choose high prices. b. Both fast food restaurants choose low prices. c. Brewer’s chooses high and Royal’s chooses low.