Pursuit–evasion | Game theory | Calculus of variations | Recreational mathematics | Multivariable calculus

Homicidal chauffeur problem

In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor vehicle, which is much faster but far less maneuverable, who is attempting to run him down. Both runner and driver are assumed to never tire. The question to be solved is: under what circumstances, and with what strategy, can the driver of the car guarantee that he can always catch the pedestrian, or the pedestrian guarantee that he can indefinitely elude the car? The problem is often used as an unclassified proxy for missile defence and other military targeting, allowing scientists to publish on it without security implications. The problem was proposed by Rufus Isaacs in a 1951 report for the RAND Corporation, and in the book Differential Games. The homicidal chauffeur problem is a classic example of a differential game played in continuous time in a continuous state space. The calculus of variations and level set methods can be used as a mathematical framework for investigating solutions of the problem. Although the problem is phrased as a recreational problem, it is an important for mathematics used in a number of real-world applications. A discrete version of the problem was described by Martin Gardner (in his book Mathematical Carnival, chapter 16), where a squad car of speed 2 chases a crook of speed 1 on a rectangular grid, where the squad car but not the crook is constrained not to make left-hand turns or U-turns. (Wikipedia).

Video thumbnail

Underactive thyroid.mov

An general explanation of the underactive thyroid.

From playlist For Patients

Video thumbnail

Obtsructive jaundice

In today's video we take a look at the common causes of obstructive jaundice and how you should go about investigating these patients.

From playlist Let's talk Surgery

Video thumbnail

Equilateral Triangles Problem

GeoGebra Link: https://www.geogebra.org/m/f5zgupmz

From playlist Geometry: Challenge Problems

Video thumbnail

Hypothyroidism Part 2 Causes and Subclinical Hypothyroidism.mov

A list of causes of hypothyroidism and a short discussion on subclinical hypothyroidism.

From playlist Surgery Intermediate Exam Masterclass

Video thumbnail

Why You Think You Might Have ADHD

Most people experience many symptoms of ADHD to some degree, and one of the most well known is the inability to stay focused. However, there are other less common symptoms of ADHD that people often struggle with. In this episode on ADHD, Julian describes these other symptoms and how they c

From playlist Seeker+

Video thumbnail

Joan Walker: "Travel Behavior Implications of Autonomous Vehicles"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop IV: Social Dynamics beyond Vehicle Autonomy "Travel Behavior Implications of Autonomous Vehicles" Joan Walker - University of California, Berkeley Institute for Pure and Applied Mathematics, UCLA December 1,

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

Video thumbnail

Dominique MANCHON - On Multiple Zeta Values and their q-analogues

Multiple zeta values are real numbers which appeared in depth one and two in the work of L. Euler in the Eighteenth century. They first appear as a whole in the work of J. Ecalle in 1981, as infinite nested sums. A systematic study starts one decade later with M. Hoffman, D. Zagier and M.

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Video thumbnail

Relativity & Gravity - The Complete History

Einstein (and his friends) came to some pretty crazy conclusions about gravity. By the end of this video, you'll have no choice but to come to the same conclusions. We'll start with a little background though: From Galileo in 1632 all the way to Einstein in 1905 and 1915. _________________

From playlist Einstein's Relativity

Video thumbnail

Shopping Cart Truck Mishap

I guess this is what happens when you don't put anything up to keep the shopping carts from falling out of the truck.

From playlist Inertia

Video thumbnail

Concave Quadrilateral Craziness! (GoGeometry Action 80)

Link: https://www.geogebra.org/m/T4axJRwY

From playlist Geometry: Challenge Problems

Video thumbnail

What Kind of Gun Laws Work? Guns and Public Health Part 4

Let’s be honest. The real controversy around the issue of guns is… what might we do about it? It’s the potential firearms policy changes that make people squirrelly. But guns have been regulated in the United States, we can see what happened, and we can use that to inform what we might do.

From playlist Healthcare Triage

Video thumbnail

Lagrange Multipliers

Some problems using Lagrange Multipliers for optimization. In this video there are some technical problems beginning at about 9:10. The first problem is worked entirely, but the 2nd problem is interrupted.

From playlist Calc3Exam3Fall2013

Video thumbnail

Steven Pinker: Are guns to blame for America’s homicide rate? | Big Think

Steven Pinker: Are guns to blame for America’s homicide rate? New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- One of t

From playlist Steven Pinker | Big Think

Video thumbnail

Wolfram Burgard: "(Self-)Supervised Learning for Perception Tasks in Automated Driving"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop I: Individual Vehicle Autonomy: Perception and Control "(Self-)Supervised Learning for Perception Tasks in Automated Driving" Wolfram Burgard - Toyota Research Institute Abstract: At the Toyota Research Insti

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

Video thumbnail

Dominique Manchon - Hopf-Algebraic Renormalization of Multiple Zeta Values and their q-analogues

After a brief introductory account, I’ll explain how a quasi-shuffle compatible definition (by no means unique) of multiple zeta values can be given for integer arguments of any sign, through Connes-Kreimer’s Hopf-algebraic renormalization. Finally, I’ll introduce the Ohno-Okuda-Zudilin mo

From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020

Video thumbnail

15. Crime and the Law

Early Modern England: Politics, Religion, and Society under the Tudors and Stuarts (HIST 251) In this lecture Professor Wrightson examines the problem of order in early modern society, focusing on crimes of violence and upon property crime. In examining violence, he notes the existence

From playlist Early Modern England with Keith E. Wrightson

Video thumbnail

Rebuilding Trust: The City That Sat Down With The Police (Crime Documentary) | Real Stories

Determined to seek justice for her son’s death, a woman single-handedly changes the relationship between local families and the police for the better. A timely and important film about gun violence, homicide and police-community relations. The film tells the story of how one Black woman,

From playlist Crime Documentaries

Video thumbnail

Market Structure and Extortion: Evidence from 50,000 Extortion Payments in El Salvador

How do gangs compete for extortion? Using detailed data on individual extortion payments to gangs and sales from a leading wholesale distributor of consumer goods and pharmaceuticals in El Salvador, Professor Sviatschi and her co-authors document evidence on the determinants of extortion p

From playlist Refugee Program Seminars

Related pages

Level-set method | Level set | Differential game | Martin Gardner | Game theory | Calculus of variations | State space | Angel problem