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🔗 Statistics

In probability theory, the Chinese restaurant process is a discrete-time stochastic process, analogous to seating customers at tables in a Chinese restaurant. Imagine a Chinese restaurant with an infinite number of circular tables, each with infinite capacity. Customer 1 sits at the first table. The next customer either sits at the same table as customer 1, or the next table. This continues, with each customer choosing to either sit at an occupied table with a probability proportional to the number of customers already there (i.e., they are more likely to sit at a table with many customers than few), or an unoccupied table. At time n, the n customers have been partitioned among m ≤ n tables (or blocks of the partition). The results of this process are exchangeable, meaning the order in which the customers sit does not affect the probability of the final distribution. This property greatly simplifies a number of problems in population genetics, linguistic analysis, and image recognition.

David J. Aldous attributes the restaurant analogy to Jim Pitman and Lester Dubins in his 1983 book.

🔗 Computer science

In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space ${\displaystyle \Omega }$ on which a sensible kernel function (measuring similarity between elements of ${\displaystyle \Omega }$) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in ${\displaystyle \mathbb {R} ^{d}}$, discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song , Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in.

The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings.

Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages:

1. Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables
2. Intermediate density estimation is not needed
3. Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel)
4. If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations
5. Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven.
6. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods

Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms.

🔗 Computing 🔗 Systems 🔗 Business 🔗 Engineering 🔗 Systems/Systems engineering

Parkinson's law of triviality is C. Northcote Parkinson's 1957 argument that members of an organization give disproportionate weight to trivial issues. Parkinson provides the example of a fictional committee whose job was to approve the plans for a nuclear power plant spending the majority of its time on discussions about relatively minor but easy-to-grasp issues, such as what materials to use for the staff bike shed, while neglecting the proposed design of the plant itself, which is far more important and a far more difficult and complex task.

The law has been applied to software development and other activities. The terms bicycle-shed effect, bike-shed effect, and bike-shedding were coined as metaphors to illuminate the law of triviality; it was popularised in the Berkeley Software Distribution community by the Danish software developer Poul-Henning Kamp in 1999 and has spread from there to the whole software industry.

🔗 Spaceflight 🔗 Physics 🔗 Alternative Views

A quantum vacuum thruster (QVT or Q-thruster) is a theoretical system hypothesized to use the same principles and equations of motion that a conventional plasma thruster would use, namely magnetohydrodynamics (MHD), to make predictions about the behavior of the propellant. However, rather than using a conventional plasma as a propellant, a QVT would interact with quantum vacuum fluctuations of the zero-point field.

The concept is controversial and generally not considered physically possible. However, if QVT systems were possible they could eliminate the need to carry propellant, being limited only by the availability of energy.

🔗 United States 🔗 Crime 🔗 Statistics

In September 2013, the incarceration rate of the United States of America was the highest in the world at 716 per 100,000 of the national population. While the United States represents about 4.4 percent of the world's population, it houses around 22 percent of the world's prisoners. Corrections (which includes prisons, jails, probation, and parole) cost around $74 billion in 2007 according to the U.S. Bureau of Justice Statistics.

At the end of 2016, the Prison Policy Initiative estimated that in the United States, about 2,298,300 people were incarcerated out of a population of 324.2 million. This means that 0.7% of the population was behind bars. Of those who were incarcerated, about 1,316,000 people were in state prison, 615,000 in local jails, 225,000 in federal prisons, 48,000 in youth correctional facilities, 34,000 in immigration detention camps, 22,000 in involuntary commitment, 11,000 in territorial prisons, 2,500 in Indian Country jails, and 1,300 in United States military prisons.

🔗 Computer science 🔗 Databases 🔗 Databases/Computer science

R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both theoretical and applied contexts. A common real-world usage for an R-tree might be to store spatial objects such as restaurant locations or the polygons that typical maps are made of: streets, buildings, outlines of lakes, coastlines, etc. and then find answers quickly to queries such as "Find all museums within 2 km of my current location", "retrieve all road segments within 2 km of my location" (to display them in a navigation system) or "find the nearest gas station" (although not taking roads into account). The R-tree can also accelerate nearest neighbor search for various distance metrics, including great-circle distance.

🔗 Mathematics

Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series. Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.

🔗 Computing 🔗 Computing/Early computers

Lehmer sieves are mechanical devices that implement sieves in number theory. Lehmer sieves are named for Derrick Norman Lehmer and his son Derrick Henry Lehmer. The father was a professor of mathematics at the University of California, Berkeley at the time, and his son followed in his footsteps as a number theorist and professor at Berkeley.

A sieve in general is intended to find the numbers which are remainders when a set of numbers are divided by a second set. Generally, they are used in finding solutions of Diophantine equations or to factor numbers. A Lehmer sieve will signal that such solutions are found in a variety of ways depending on the particular construction.

🔗 Architecture 🔗 Japan

Gate Tower Building (ゲートタワービル, gēto tawā biru) is a 16 floor office building in Fukushima-ku, Osaka, Japan. It is notable for the highway offramp at Umeda Exit that passes through the building.