Integration

Integration may refer to:

Sociology and economy

Mathematics

Autoregressive integrated moving average

In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. These models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting). They are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the "integrated" part of the model) can be applied to reduce the non-stationarity.

Non-seasonal ARIMA models are generally denoted where parameters p, d, and q are non-negative integers, is the order of the Autoregressive model, is the degree of differencing, and is the order of the Moving-average model. Seasonal ARIMA models are usually denoted , where refers to the number of periods in each season, and the uppercase refer to the autoregressive, differencing, and moving average terms for the seasonal part of the ARIMA model. ARIMA models form an important part of the Box-Jenkins approach to time-series modelling.

Helix

A helix (pl: helixes or helices) is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helices are coil springs and the handrails of spiral staircases. A "filled-in" helix – for example, a spiral ramp – is called a helicoid. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word helix comes from the Greek word ἕλιξ, "twisted, curved".

Types

Helices can be either right-handed or left-handed. With the line of sight along the helix's axis, if a clockwise screwing motion moves the helix away from the observer, then it is called a right-handed helix; if towards the observer, then it is a left-handed helix. Handedness (or chirality) is a property of the helix, not of the perspective: a right-handed helix cannot be turned to look like a left-handed one unless it is viewed in a mirror, and vice versa.

Helix (band)

Helix is a Canadian hard rock/heavy metal band. They formed in 1974, and are best known for their 1984 single "Rock You". The original lineup was formed by drummer Bruce Arnold, and consisted of lead vocalist Brian Vollmer, guitarists Ron Watson and Rick "Minstrel" Trembley, keyboardist Don Simmons, and bassist Keith "Bert" Zurbrigg. However, their most well known lineup, and the one that recorded "Rock You", was the 80s version of the band: Vollmer on vocals, accompanied by guitarists Brent "The Doctor" Doerner and Paul Hackman, bassist Daryl Gray, and drummer Greg "Fritz" Hinz. The history of the band has been marked by many lineup changes, with Vollmer being the sole constant member and only remaining member of the original lineup. Although Hackman was killed in a tour bus accident in 1992, the surviving members of the 80s lineup reunited in 2009 for an album and have continued to tour since 2011.

Helix have toured with bands such as Kiss, Aerosmith, Rush, Mötley Crüe, Alice Cooper, Whitesnake, Night Ranger, Heart, Quiet Riot, W.A.S.P., Ian Gillan and Motörhead among others.

Phelix

Phelix is a high-speed stream cipher with a built-in single-pass message authentication code (MAC) functionality, submitted in 2004 to the eSTREAM contest by Doug Whiting, Bruce Schneier, Stefan Lucks, and Frédéric Muller. The cipher uses only the operations of addition modulo 2³², exclusive or, and rotation by a fixed number of bits. Phelix uses a 256-bit key and a 128-bit nonce, claiming a design strength of 128 bits. Concerns have been raised over the ability to recover the secret key if the cipher is used incorrectly.

Performance

Phelix is optimised for 32-bit platforms. The authors state that it can achieve up to eight cycles per byte on modern x86-based processors.

FPGA Hardware performance figures published in the paper "Review of stream cipher candidates from a low resource hardware perspective" are as follows:

Helix

Phelix is a slightly modified form of an earlier cipher, Helix, published in 2003 by Niels Ferguson, Doug Whiting, Bruce Schneier, John Kelsey, Stefan Lucks, and Tadayoshi Kohno; Phelix adds 128 bits to the internal state.