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In the penultimate paragraph of the paper, Hiltner listed a number of conditions that must be met to explain the presence of polarization in distant stars, namely 1 the mechanism must be independent of wavelength, 2 the mechanism must be operating over a large distance stars within a small area on the sky exhibit polarization of different amounts but with the same position angle, 3 a positive colour excess is necessary but not suf cient and 4 the plane of polarization is associated with the galactic plane, i e, stars of low galactic latitude tend to provide the electric vector maximum which is approximately parallel to the galactic plane Finally, Hiltner surmised:

// Read 32-bit integer LSB first public int ReadInt32( ref byte[] aBuffer, int aStartPos) { int retVal = aBuffer[aStartPos] | aBuffer[aStartPos+1]<<8 ; retval = retval | aBuffer[aStartPos+2]<<16 | aBuffer[aStartPos+3]<<24; return retVal; } ... try { ISCBALDeviceService service = mDevice.Services["ectcpadapter"]; System.Console.WriteLine("Ectcpadapter found - version {0} Address {1} Port {2}", service.Version, service.IPAddress, service.Port); ISCBALSequentialStream myStream = service.StartServiceOnStream(); byte[] message = new byte[40]; // Zeroed by default message[4] = (byte)'E'; message[5] = (byte)'C'; message[6] = (byte)'H'; message[7] = (byte)'O'; message[8] = (byte)'C'; message[9] = (byte)'S'; // Operation and version left at zero int retval = myStream.Write(message); byte[] response = new byte[40]; object oResponse = response; retval = myStream.Read(4, out oResponse); response = (byte[])oResponse; int responseCode = ReadInt32(ref response, 0); System.Console.WriteLine("session response {0} with {1} bytes read", responseCode, retval); } catch { }

an nx -dimensional binary-valued problem is transformed into a smaller 4-dimensional continuous-valued problem

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if the polarization is a consequence of scattering by interstellar particles, it follows that these particles must be unsymmetrical, that is, elongated, and that these particles are subject to some alignment force This force may take the form of magnetic elds,

The binary DE (binDE) borrows concepts from the binary particle swarm optimizer (binPSO), developed by Kennedy and Eberhart [450] (also refer to Section 1657) As with DE, particle swarm optimization (PSO; refer to 16) uses vector algebra to calculate new search positions, and was therefore developed for continuous-valued problems In PSO, a velocity vector represents the mutation step sizes as stochastically weighted di erence vectors (ie the social and cognitive components) The binPSO does not interpret the velocity as a step size vector Rather, each component of the velocity vector is used to compute the probability that the corresponding component of the solution vector is bit 0 or bit 1

This mixin de nes the methods which a concrete command class must implement It is created with a message, and the command is then responsible for the memory of this message A pointer to the client socket is also passed as a parameter in the constructor It can process more than one message Member Methods virtual void ExecuteLD () = 0 Executes the command, called by the client socket when the command has been created, or after a persistent command has captured a message virtual void SendErrorMessage (TUint aErrorCode) = 0 This method sends an error message to the remote client aErrorCode the error code to send to the remote client virtual TBool NewMessageReceived (MMessage* aMessage) = 0 This method is called by the client socket when a receive operation has completed.

In a similar way, the binDE uses the oating-point DE individuals to determine a probability for each component These probabilities are then used to generate a bitstring solution from the oating-point vector This bitstring is used by the tness function to determine its quality The resulting tness is then associated with the oating-point representation of the individual Let xi (t) represent a DE individual, with each xij (t) (j = 1, , nx , where nx is the dimension of the binary-valued problem) oating-point number Then, the corresponding bitstring solution, yi (t), is calcualted using yij = where f is the sigmoid function, f (x) = 1 1 + e x (1330) 0 1 if f (xij (t)) 05 if f (xij (t)) < 05 (1329)

Hiltner and Hall continued to make measurements, both producing catalogues (Hiltner, 1951, 1954; Hall, 1958) which mapped the variations of interstellar polarization around the Galaxy, a task which was made more complete by Mathewson & Ford (1970) (see Figure 14)

The tness of the individual xi (t) is then simply the tness obtained using the binary representation, yi (t) The binDE algorithm is summarized in Algorithm 1310 Algorithm 1310 Binary Di erential Evolution Algorithm Initialize a population and set control parameter values; t = 0; while stopping condition(s) not true do t = t + 1; Select parent xi (t); Select individuals for reproduction; Produce one o spring, x (t); yi (t) = generated bitstring from xi (t); yi (t) = generated bitstring from xi (t); if f (yi (t)) is better than f (xi (t)) then Replace parent, xi (t), with o spring, xi (t); end else Retain parent, xi (t); end end

The discussions in the previous sections considered application of DE to unconstrained, single-objective optimization problems, where the tness landscape remains static This section provides a compact overview of adaptations to the DE such that di erent types of optimization problems as summarized in Appendix A can be solved using DE

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