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Stellar polarimetry appeared as a green shoot in astrophysical diagnostic practice some 60 years ago Following the early nineteenth-century discoveries of polarimetric phenomena in the physics and chemistry laboratories, and the establishment of the understanding of the transverse nature of the oscillatory disturbances within electromagnetic radiation, polarimetry lay dormant for over 100 years in its application to stars Its dawning on the stellar scene awaited the combination of a prediction by Chandrasekhar (1946) related to the outcome of radiative transfer studies for early-type stellar atmospheres, and the simultaneous development of detector technology suf cient to make an observational response to the challenge set by theory With a degree of interpretive licence, the introduction of polarimetry to Astronomy may be set to an earlier millennium Much of the early history of astronomy is bound up with application of celestial observations to determinations of local time and geographical position It has been suggested that a navigational tool, or medieval GPS, in the form of the natural crystal (cordierite) with polarization properties, was used as an astrolabe by the Vikings as early as ad 1000 (see Walker, 1978) With such a device the position of the Sun, hidden by a cloud, or below the horizon, could have been determined to within 3 It might be claimed, therefore, that polarimetry was utilised within Astronomy well in advance of the more readily appreciated diagnostic tool of spectroscopy! The concept of polarimetry as applied to the pursuit of physical understanding of the heavens did not emerge, however, until the turn of the nineteenth century, with application particularly to the Solar System, running hand in hand with the development of the subject in the optical laboratory The history of polarimetry within the physical sciences can be followed in a variety of optical texts and will not be expounded in detail here A benchmark in its study was the discovery in 1669 of the birefringence of Iceland Spar by Erasmus Bartholinus (1669) 1) This phenomenon was investigated by Huyghens (1690) 2) and.

Computational Intelligence: An Introduction, Second Edition AP Engelbrecht c 2007 John Wiley & Sons, Ltd

Once you have your custom server on the smartphone, you need to get ectcpadapter to load it. This is not dif cult. You need to open a stream to communicate with ectcpadapter (which is always started when a connection is active) and send a command in the right format. The format is as follows: Session Request Message

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Figure 31 illustrates a standard feedforward neural network (FFNN), consisting of three layers: an input layer (note that some literature on NNs do not count the input layer as a layer), a hidden layer and an output layer While this gure illustrates only one hidden layer, a FFNN can have more than one hidden layer However, it has been proved that FFNNs with monotonically increasing di erentiable functions can approximate any continuous function with one hidden layer, provided that the hidden layer has enough hidden neurons [383] A FFNN can also have direct (linear) connections between the input layer and the output layer

1) An excerpt from this work, translated into English, can be found in Swindell (1975) 2) Again, relevant excerpts from Huygens Trait de la Lumi re can be found in Swindell (1975)

Figure 31 Feedforward Neural Network The output of a FFNN for any given input pattern zp is calculated with a single forward pass through the network For each output unit ok , we have (assuming no direct connections between the input and output layers), ok,p = fok (netok,p ) = fok = fok

wkj fyj (netyj,p ) vji zi,p (31)

Stellar Polarimetry David Clarke Copyright 2010 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 978-3-527-40895-5

Length: 40 bytes Data Format:

hidden unit yj ; wkj is the weight between output unit ok and hidden unit yj ; zi,p is the value of input unit zi of input pattern zp ; the (I + 1)-th input unit and the (J + 1)-th hidden unit are bias units representing the threshold values of neurons in the next layer Note that each activation function can be a di erent function It is not necessary that all activation functions be the same Also, each input unit can implement an activation function It is usually assumed that input units have linear activation functions

The history of the serendipitous discovery that interstellar dust imposes polarization on starlight passing through it has been sketched out by Struve & Zebergs (1962) They comment that:

In functional link neural networks (FLNN) input units do implement activation functions (or rather, transformation functions) A FLNN is simply a FFNN with the input layer expanded into a layer of functional higher-order units [314, 401] The input layer, with dimension I, is therefore expanded to functional units h1 , h2 , , hL , where L is the total number of functional units, and each functional unit hl is a function of the input parameter vector (z1 , , zI ), ie hl (z1 , , zI ) (see Figure 32) The weight matrix U between the input layer and the layer of functional units is de ned as uli = 1 if functional unit hl is dependent of zi 0 otherwise (32)

Op (4 bytes) Operation Code. 0 00000000 (Start Session) is the only supported value N (32 characters) Custom Server Name. The name of the custom server as an ASCII string (not Unicode) without the le extension and with the remainder of the string padded with zeros Maj (1 byte) Major Version Number Min (1 byte) Minor Version Number Bld (2 bytes) Build Number In response to this message, ectcpadapter will return a response message. Session Response Message

Calculation of the activation of each output unit ok occurs in the same manner as for FFNNs, except that the additional layer of functional units is taken into account: ok,p = fok

The detection of interstellar polarization always will remain one of the most striking examples of purely accidental discovery, such as Wilhelm R ntgen s discovery of X-rays in 1885

vjl hl (zp )

(33)

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