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Apple Inc. (formerly Apple Computer, Inc.) is an American multinational corporation and technology company headquartered in Cupertino, California, in Silicon Valley.It designs, develops, and sells consumer electronics, computer software, and online services.Devices include the iPhone, iPad, Mac, Apple Watch, Vision Pro, and Apple TV; operating systems include iOS, iPadOS, and macOS; and ...
Apple Daily (Chinese: 蘋果日報; pinyin: Píngguǒ Rìbào; Pe h-ōe-jī: Pîn-kó Ji t-pò) was a Chinese-language tabloid published in Taiwan, known for its sensational headlines, paparazzi photographs, and animated news videos.
The iPhone is a line of smartphones produced by Apple that use Apple's own iOS mobile operating system. The first-generation iPhone was announced by then–Apple CEO Steve Jobs on January 9, 2007. Since then, Apple has annually released new iPhone models and iOS updates. As of November 1, 2018, more than 2.2 billion iPhones had been sold.
Pyrus dioica Moench. An apple is a round, edible fruit produced by an apple tree ( Malus spp., among them the domestic or orchard apple; Malus domestica ). Apple trees are cultivated worldwide and are the most widely grown species in the genus Malus. The tree originated in Central Asia, where its wild ancestor, Malus sieversii, is still found.
- Overview
- Application
- Computational Costs
- History
- Definitions
- Applications
- Use in Mathematics
Monte Carlo methods vary, but tend to follow a particular pattern: 1. Define a domain of possible inputs 2. Generate inputs randomly from a probability distributionover the domain 3. Perform a deterministiccomputation of the outputs 4. Aggregate the results For example, consider a quadrant (circular sector) inscribed in a unit square. Given that th...
Monte Carlo methods are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo met...
Despite its conceptual and algorithmic simplicity, the computational cost associated with a Monte Carlo simulation can be staggeringly high. In general the method requires many samples to get a good approximation, which may incur an arbitrarily large total runtime if the processing time of a single sample is high. Although this is a severe limitati...
Before the Monte Carlo method was developed, simulations tested a previously understood deterministic problem, and statistical sampling was used to estimate uncertainties in the simulations. Monte Carlo simulations invert this approach, solving deterministic problems using probabilistic metaheuristics (see simulated annealing). An early variant of ...
There is no consensus on how Monte Carlo should be defined. For example, Ripley defines most probabilistic modeling as stochastic simulation, with Monte Carlo being reserved for Monte Carlo integration and Monte Carlo statistical tests. Sawilowsky distinguishes between a simulation, a Monte Carlo method, and a Monte Carlo simulation: a simulation i...
Monte Carlo methods are especially useful for simulating phenomena with significant uncertainty in inputs and systems with many coupleddegrees of freedom. Areas of application include:
In general, the Monte Carlo methods are used in mathematics to solve various problems by generating suitable random numbers (see also Random number generation) and observing that fraction of the numbers that obeys some property or properties. The method is useful for obtaining numerical solutions to problems too complicated to solve analytically. T...
Pearson correlation coefficient. Several sets of ( x , y) points, with the correlation coefficient of x and y for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom).
Principal component analysis ( PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing . The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
