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Information Theory and Fitts’ Law
Published in Richard J. Jagacinski, John M. Flach, Control Theory for Humans, 2018
Richard J. Jagacinski, John M. Flach
A choice reaction time task is a task where several possible signals are each assigned a different response. For example, the possible stimuli could be the numbers 1 to 5 and the possible responses could be pressing a key under each of the 5 fingers of one hand. Thus, if the number 1 is presented, press the key under the thumb, whereas if the number 3 is presented, press the key under the middle finger. Merkel (1885, cited in Keele, 1973) found that as the number of equally likely possible alternatives increased from 1 (i.e., 1 number and 1 key; this is called simple reaction time) to 10 (i.e., 10 numbers and 10 keys), the reaction time increased. The relation between reaction time (RT) and number of alternatives found by Merkel showed that, for every doubling of the number of alternatives, there was a roughly constant increase in RT. These results are plotted in Fig. 3.1. Figure 3.1(a) shows reaction time as a function of the number of alternatives and Fig. 3.1(b) shows reaction time as a function of the base two logarithm of the number of alternatives. [The base two logarithm of a number is the number expressed in terms of powers of two. For example, the log2 (1) = 0, because 20 = 1; the log2 (2) = 1; the log2 (4) = 2; the log2 (8) = 3; and the log2 (64) = 6, because 26 = 64.]
Digital audio principles
Published in Francis Rumsey, Desktop Audio Technology, 2003
In the decimal number system each digit of a number represents a power of ten. In a binary system each digit or bit represents a power of two (see Figure 2.4). It is possible to calculate the decimal equivalent of a binary integer (whole number) by using the method shown. A number made up of more than one bit is called a binary ‘word’, and an 8-bit word is called a ‘byte’ (from ‘by eight’). Four bits is called a ‘nibble’. The more bits there are in a word the larger the number of states it can represent, with 8 bits allowing 256 (28) states and 16 bits allowing 65 536 (216). The bit with the lowest weight (20) is called the least significant bit or LSB and that with the greatest weight is called the most significant bit or MSB. The term kilobyte or Kbyte is used to mean 1024 or 210 bytes and the term megabyte or Mbyte represents 1024 Kbytes.
Audio Waveform
Published in Alexander U. Case, Sound FX, 2012
Note that the equation changes a little. Instead of multiplying the logarithm by 10, sound pressure statements require multiplication by 20. This is a result of the physical relationship between acoustic power and sound pressure. Power is proportional to pressure squared. The sound power terms within Equation 1.17 become sound pressure squared instead. It is a property of logarithms that this power of two within the logarithm may be converted to multiplication by two outside the logarithm. Hence the 10 becomes 20 for decibel calculations related to pressure. Likewise, we can use decibels to describe the voltage in our gear. Electrical power is proportional to voltage squared, so again we use a 20 instead of a 10 in the decibel calculations for voltage.
Testing different supervised machine learning architectures for the classification of liquid crystals
Published in Liquid Crystals, 2023
Ingo Dierking, Jason Dominguez, James Harbon, Joshua Heaton
The Keras deep learning framework [42] in Python was used to implement deep learning models. In all these models, real-time preprocessing was done via Keras. Images were converted to greyscale. This was done because texture, rather than colour, determines the phase and because computational time can be saved. Images were further resized to 256 × 256 to obtain square images of dimensions that are powers of two. Both of these scalings are common practices with CNNs [32]. Further, this image size was small enough to reduce the computation time for working with standard personal computers, without obscuring texture details. Finally, the image’s grayscales were rescaled by 1/255, so that pixel values were between 0 and 1, a requirement for CNNs to work correctly [32].