Any-angle path planning

Any-angle path planning algorithms search for paths on a cell decomposition of a continuous configuration space (such as a two-dimensional terrain).

Motivation

Consider, for example, a uniform grid with blocked and unblocked cells. Searching the corresponding visibility graph finds a shortest path from a given start vertex to a given goal vertex but is typically very slow since the number of edges can grow quadratically in the number of vertices. Searching the corresponding grid graph typically finds suboptimal paths (since, for example, the heading changes of the resulting path are constrained to multiples of 45 degrees on an eight-neighbor grid graph) but is fast since the number of edges grows no faster than linearly in the number of vertices. Optimizing the path after the search typically shortens the path but does not change the topology of the path. It does not find a shortest path, for example, if the path found by the search algorithm passes a blocked cell on the left but the shortest path passes the same blocked cell on the right. Thus, there is an advantage to interleaving the search and the optimization. Any-angle path planning algorithms propagate information along grid edges (to search fast) without constraining their paths to grid edges (to find short paths). Thus, the heading changes of their paths are not constrained to specific angles, which explains their name.

Greeks (finance)

In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities,risk measures or hedge parameters.

Use of the Greeks

The Greeks are vital tools in risk management. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure; see for example delta hedging.

The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. For this reason, those Greeks which are particularly useful for hedging—such as delta, theta, and vega—are well-defined for measuring changes in Price, Time and Volatility. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.

Theta (disambiguation)

Theta is the eighth Greek letter, written Θ (uppercase) or θ (lowercase).

Theta also refers to:

Places

Science and mathematics

Business

Organizations

Guilt

Guilt may refer to:

Music

Film and television

See also

Guilt (2009 film)

Guilt (Greek: "Ενοχή" 2009) is a feature Greek - Cypriot film, directed by the Greek director - writer and producer Vassilis Mazomenos. It was awarded in 2012 with the Best Screenwriting and Best Photography award in London Greek Film Festival (U.K.) and was official selection in Montreal World Film Festival, Cairo International Film Festival, International Film Festival of India, Tallinn Black Nights Film Festival, Fantasporto and opening film in the Panorama of European Cinema in Athens. In 2010 was Nominated for the best film from the Hellenic Film Academy. In 2010 the film received the Best Soundtrack (George Andreou) for Greek movies of the year. As Vrasidas Karalis wrote in the History of Greek cinema: "His later films Remembrance (2002) Words and Sins (2004) and Guilt (2010) received many positive reviews and international recognition; especially the last in which Mazomenos explored narrative cinema through a nightmarish and confronting story."

References

External links

Guilt (1931 film)

Guilt is a 1931 British romance film directed by Reginald Fogwell and starring James Carew, Anne Grey, Harold Huth and James Fenton. In the film, the wife of a playwright has an affair with an actor.

Cast

References

External links