Fetch is a pet game where an object, such as a stick or ball, is thrown a moderate distance away from the animal, and it is the animal's objective to grab and retrieve ("fetch") it. Many times, the owner of the animal will say "Fetch" to the animal before or after throwing the object. The game is usually played with a dog, but, in rare instances, cats (especially kittens) have been known to engage in fetch behavior.
Arizona State psychology professor Michael McBeath has proposed a simple model to explain how dogs play fetch. By mounting a camera on the head of a dog, he found that the dog changed its speed and direction in order to keep the frisbee's image in a constant position on its retina. This approach, called the linear optical trajectory, makes the frisbee appear to move in a linear path at a constant speed. McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls. [1]
Tim Pennings, [2] a mathematics professor at Hope College, has found that dogs are somehow able to calculate the optimal path to a ball thrown in the water. While playing Fetch with his Welsh Corgi, he noticed that the dog ran along the beach for a certain distance before jumping into the water. Because the dog is faster on land, this technique minimizes the total retrieval time. He showed that the dog is able to calculate the optimal point to jump into the water, a problem Pennings must resort to calculus to solve.
Perruchet and Gallego [3] have demonstrated a method for calculating this optimal path using calculus in a different way. They propose that the dog optimizes its behaviour on a moment-to-moment basis, choosing at each moment the path that allows it to maximize its speed of approach to the ball. This requires the dog to be able to accurately estimate its speed on both land and water, but does not rely on the premise that the dog plans the entire route in advance. [4]
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming.
A sheepdog trial – also herding event, stock dog trial or simply dog trial — is a competition or test of the working abilities of dogs of herding breeds. It is a type of dog sport that emerged in the 1860s in New Zealand. By the 1870s regular trials were also being held in Australia and in the United Kingdom, and by the end of the twentieth century the sport had spread to many countries of the world. In competition, dogs demonstrate basic herding management skills assessed by the judge. These events are organised by international and national cynological and sports organisations and by associations of sheep- and cattle-breeders. Usually sheep are to be herded; other animals including ducks or cows may also be used.
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function.
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because it starts with the effects and then calculates the causes. It is the inverse of a forward problem, which starts with the causes and then calculates the effects.
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.
Disc dog is a dog sport. In disc dog competitions, dogs and their human flying disc throwers compete in events such as distance catching and somewhat choreographed freestyle catching. The sport celebrates the bond between handler and dog, by allowing them to work together. The term "disc" is preferred because "Frisbee" is a trademark for a brand of flying disc.
Dog intelligence or dog cognition is the process in dogs of acquiring information and conceptual skills, and storing them in memory, retrieving, combining and comparing them, and using them in new situations.
Clicker training is a positive reinforcement animal training method based on a bridging stimulus in operant conditioning. The system uses conditioned reinforcers, which a trainer can deliver more quickly and more precisely than primary reinforcers such as food. The term "clicker" comes from a small metal cricket noisemaker adapted from a child's toy that the trainer uses to precisely mark the desired behavior. When training a new behavior, the clicker helps the animal to quickly identify the precise behavior that results in the treat. The technique is popular with dog trainers, but can be used for all kinds of domestic and wild animals.
The Smith–Waterman algorithm performs local sequence alignment; that is, for determining similar regions between two strings of nucleic acid sequences or protein sequences. Instead of looking at the entire sequence, the Smith–Waterman algorithm compares segments of all possible lengths and optimizes the similarity measure.
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital A, B, E, Z, H, I, K, M, N, O, P, T, Y, X. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o and u. Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used.
Trajectory optimization is the process of designing a trajectory that minimizes some measure of performance while satisfying a set of constraints. Generally speaking, trajectory optimization is a technique for computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop solution is not required, impractical or impossible. If a trajectory optimization problem can be solved at a rate given by the inverse of the Lipschitz constant, then it can be used iteratively to generate a closed-loop solution in the sense of Caratheodory. If only the first step of the trajectory is executed for an infinite-horizon problem, then this is known as Model Predictive Control (MPC).
Human–animal communication is the communication observed between humans and other animals, ranging from non-verbal cues and vocalizations to the use of language.
In optics, a caustic or caustic network is the envelope of light rays which have been reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light. In some cases caustics can be seen as patches of light or their bright edges, shapes which often have cusp singularities.
In mathematical optimization and computer science, heuristic is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Betsy is a black and white longhaired Border Collie, credited with being one of the world's most intelligent dogs.
Waboba is an international outdoor toy and sporting goods brand headquartered in Stockholm, Sweden with offices in Atlanta, Georgia and Guangzhou, China. Waboba is most known for its invention of balls that bounce on water, the high bouncing Moon Ball, and the Wingman silicone flying disc. The company specializes in beach and backyard toys and games. The slogan used in advertising is Keep Life Fun. The name Waboba is a registered trademark and many of its products are internationally patented.
Heuristics are simple strategies for decision making that are used to achieve a specific goal quickly and efficiently, and are commonly implemented in sports. Many sports require the ability to make fast decisions under time pressure, and the proper use of heuristics is essential for many of these decisions.
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