Evolutionary Standards In Image Compression Along With Comparative Analysis Of Their: Fill & Download for Free

Contrary to some of the other answers to this question (from people who seem to have some expertise in conventional color theory) there is considerable benefit to adding ‘more colors’ to a conventional RGB display. It has been tried in the past, with Panasonic QuatreColor and Sharp Quattron without a lot of success, but on the other hand if you have a big screen OLED TV or a mobile phone with a ‘pentile’ display then chances are you are looking at a screen that has an extra ‘color’ already, but you probably don’t know it is there because there hasn’t been a huge advertising campaign to sell it as an exciting new technological advance. OLED TV screens produced by LG typically have 4 pixels rather than the conventional RGB. Its not particularly exciting because that extra ‘color’ is white. The LG screens are used by a number of other manufacturers, including Panasonic and Sony. If we look at the spectrum of light these screen produce we can easily see the light that this 4th pixel produces, which is quite distinct in the ‘yellow’ region of the spectrum.As we can see from the spectral power diagram of the Sony OLED display, not only do they have a separate white pixel but they also do something interesting with yellow. When the display produces yellow colors the red and green pixels are much brighter than when they produce red or green colors on their own.So, adding more colors is not only possible, but is actually already quite common, and it has been considerably more successful than ‘quadraphonic headphones’, which one of the answers from a technical expert suggest would be the fate of all attempts to add more colors to conventional RGB. This line of thinking is based on the observation that human color vision has 3 color sensor and therefore is trichromatic (ie. 3-colored). Birds with color vision generally have 4 color sensors and it is generally believed that their color vision is tetrachromatic (4-colored). With respect to audio this kind of thinking is something along the lines of we have 2 ears and therefore our perception of sound must be ‘stereo’. Except of course we know perfectly well that it isn’t. Our perception of sound is actually positional. We do indeed have only 2 ears, but our brain using a whole host of tricks that we do not really fully understand yet which translates the data it receives from two audio sensors into the perception of fully 3-dimensional positional sound. In theory, we have 2 ears and therefore two speakers should be all that is needed to reproduce sound. In practice, when the vast computational powers of our brain are applied to the sound coming from 2 speakers we tend to hear the sound exactly as it is presented to us; as coming from the spatial locations of two separate speakers. This has led to the development of ‘surround sound’, with increasingly many speakers. No upper bound has yet been found on the number of speakers needed to produce realistic positional audio that is sufficient to fool our ‘ears’. This has led to the development of positional audio, which codes sound not by specific speakers but by its position in 3 dimensional space. Quadraphonic headphones may not have been a commercial success, but headphones that claim to emulate 5.1 and 7.1 ‘surround sound’ are currently actively marketed and indeed are being supplanted by Dolby Atmos and DTS-X which advertise the ability to produce fully positional audio. With video we have not yet seen as much development as with audio. We are still at the stage of trying things without really understanding how they work.The addition of the white pixel for RGBW displays does not really improve color a great deal but it does show that adding additional colors is something that is feasible and practical. The reasons for doing so are not exactly clear from conventional color theory, and so its useful to have a look at the underlying principles. Conventional color theory says that when you mix colors between green and red that the results lie on a straight line. This means you don’t need all the intermediary colors, you can just take two primary colours and mix them by an arbitrary degree to produce all the colours in between. Yellow is on that straight line between red and green primaries and therefore there is no need for a yellow primary. Like ‘stereo’ sound, this is a convention produced by a lot of assumptions but it isn’t actually true. If you mix pure red and green primaries you don’t actually get yellow; rather you get something similar with stereo speakers. If conditions are not ‘perfect’ then the sound coming from the 2 speakers will sound exactly like what it actually is; separate sound coming from 2 speakers. That is, the sound will fail to perceptually integrate. Although it will appear to be ‘bad sound’ it is actually a sign of the perceptual system of your brain working correctly; it is not fooled by 2 speakers producing similar sounds. The same is true if you display an overlapping pure red circle and a pure green circle. What you will see is overlapping red and green circles rather than a separate yellow region where the two circles overlap. If you try the same thing with yellow and blue circles the overlapping region will be perceived very clearly as white. Of course this is not clear cut. In a laboratory setting with carefully controlled experimental conditions stereo sound produced by 2 speakers can be perceived as positional, and so too can red + green in ideal conditions appear yellow. So what exactly is going on?To help us understand, its a good idea to look at how our color sensors in our retina respond to light. In the diagram above we can see an approximation of how the human visual sensors respond to light superimposed on top of red and green primaries that are quite close to ideal (with 100% pure saturation being ideal). For a primary to be 100% pure it has to be very narrow, especially the green primary. We can see from the sensor functions that the red and green sensors have their strongest response in the yellow region of the spectrum. The green sensor has a peak response at about 550nm, which is why the green primary for many RGB systems is set to 550nm (usually fairly broad with a dominant wavelength of about 550nm). The red sensor has a peak response at about 600nm, so it makes sense to put the red primary there. If we have a broad green primary at about 550nm and a broad red primary at about 600nm then both red and green sensor will get fully activated. They will be spectrally adjacent and as a result the spectral distribution of green+red will approximate that of the yellows we find in nature. As a result this kind of approach will produce a strong yellows. However, when these primaries are used on their own they will produce a greenish yellow and an orange red, with both being poorly saturated. This leads to displays which have a mediocre color space, which is the state of affairs with current RGB color reproduction. Color standards for the future mandate much improved red and green primaries, similar to the spectrally narrow primaries shown in the figure above.We can see the conflict between broad primaries that produce good yellows and narrow primaries that produce more saturated colors in current display technology, as illustrated by the above figure. The HP DreamColor display has primaries that come close to matching the requirements for the future (Rec.2020) whereas the Apple MacBook Pro display focuses on producing good yellows, at the expense of color purity. Which approach is correct? To answer this question we can look at how color reproduction works in nature. The diagram below shows how sunflowers (renown for their purity of color) produce their yellows. Notable is the sharp transition from absorbing light to reflecting light at about 520nm. Light is reflected very broadly and very much equally all the way across the visible spectrum from 520nm and up.What sunflowers show us is that a lot of color in nature is broad spectrum and also highlights the importance of the reflected spectrum being flat (or equal energy). Of course sunflowers are always yellow and they can’t dynamically change color like a computer monitor can. There is some minor color variation between different varieties, but this is small. We can see this variation in the above diagram. If we measure with conventional techniques the wavelength that ‘dominates’ we find that that it is between 575 and 580nm. That is, if we compare a narrow spectrum light to the broad spectrum color of a sunflower we find a match between 575 and 580nm. Some flowers are capable of much more variety than sunflowers. A rose is capable of colors between pure yellows and deep reds, and it is also capable of producing white. The diagram below shows some of this variation.We can see from the rose that it produces color not by varying fixed primaries like an RGB display, but by varying the inflection point between absorption and reflection. When we compare the colors of a rose with narrow spectrum light we find that the colors of the rose are perceptually equal to that of very pure narrow spectrum light. What the rose is doing in effect is simply changing the dominant wavelength as it varies its colors between yellow and red. Furthermore, a rose is also capable of producing very good whites and the diagram above shows how this is achieved. White may be seen as a variation of yellow, simply extended into the lower wavelengths. White is, therefore, produced simply by reflecting all the visible wavelengths precisely equally all across the spectrum.How do we approximate the colors of the rose with fixed primaries? Both sunflowers and roses show that we need broad equal spectrum yellows. On the other hand, the colors between yellow and red are best produced by a spectral shift, which keeps the color pure. We can approximate this shift by using many spectrally adjacent narrow primaries, from pure green to deep red. The rose, therefore, suggests to us how we should be coding and reproducing color, and it is very much related to how positional audio codes and reproduces sound. We don’t code for each speaker to individually produce sound, instead we code where in 3-D space the sound should be and let the device work out how best to do it with the speakers it has available. In the same way, color really is just perceptual representation of a particular way to code light by wavelength. Our perceptual system assumes that what we see is a mix of narrow spectrum ‘color’ and broad spectrum ‘white’; dominant wavelength and saturation (in the jargon of color theory). Our visual system cannot do spectrum analysis and it has no inherent understanding of ‘wavelength’. What it does have is fixed reference points on the spectrum against which it can measure the light it is looking at. Those fixed reference points are the color sensors. If we have a narrow spectrum light, we can work out the wavelength of that light by using a sensor that has a flat response vs a sensor that has a linear response over the spectral range we want to measure. A sensor arrangement like this is known as an opponent pair, which is known to be fundamental in how our visual sensors measure light; they always do so with sensor pairs that oppose each other — black vs white, red vs green and blue vs yellow. With two opponent pairs it is easy to devise a general system which is capable of coding color across a broad range of the spectrum. What this kind of opponent system does is to code spectral distance from a known reference point. The primary colors of perception are these known reference points. The color that you actually see is the distance between two adjacent reference points. The colors that you see are therefore simply the end result of your visual system working out what the wavelength of the light that you are looking at is; that is, what the dominant wavelength of that light is. So, for example, if you see green at 520nm and you see blue at 460nm, you will see turquoise or cyan when shown light whose dominant wavelength is 490nm. Color naming might not be very precise, but if you measure these derived colors more formally as a mixture of primary colors, people will tell you that what they are seeing a mixture of blue and green at a ratio of 50:50. This estimation of a ratio of blue to green holds across the full range of colors between blue and green. People can accurately estimate the ratio to an accuracy of about 5% when shown pure fully saturated light. That means that people can look at light in a range of 60nm and estimate the wavelength of that light purely from the color that they are seeing to an accuracy of about 3nm. That is about the accuracy you would get with a mid-range spectrometer. When we look at difference between two colored lights we can tell the difference in color down to about 1nm. This indicates that what the human visual system is doing is exactly the same thing your spectrometer is doing — it is measuring the wavelength of the light being looking at. We don’t see numbers of course, which is what you get from your spectrometer. What you get instead is a proportioned difference from known reference points on the spectrum. That leads us to think that color is simply the visual representation of wavelength. What we see is the perceptual representation for how our visual system is coding wavelength. This code is very similar to how old style analog television signals used to code color or how image compression algorithms code colour.If color is simply how our visual system codes wavelength then to reproduce color it would be best to show wavelength as clearly and unambiguously as possible. Unlike our perception of sound, which has hardware capable of carrying out the equivalent of a Fourier transform, our visual system is not capable of true spectrum analysis. With sound we can disambiguate a wide variety of sounds all mixed together, but with color we can handle only a single color at a time. What our visual system is able to disambiguate is a mixture of color and white.Color should either be narrow spectrum or its broad spectrum equivalent (as illustrated by the rose). White should be full spectrum and as close to equal energy as possible. That this is true is suggested by our general dislike for fluorescent lighting, which as can be seen from the diagram below has a very ‘spiky’ spectrum. Color displays tend to produce a spike like spectrum in a similar way, with one sharp peak for each RGB primary. Illumination by natural sunlight by contrast is broad spectrum and relatively flat across the visible spectrum.So ideally, to reproduce color faithfully as we find it in nature we should have a large number of very narrow primaries, that together add up to a nice flat continuous spectrum; similar to what we see with a white rose. If we want colors that are above 99% saturation our primaries need to be about 5nm in spectral width. For a visible spectrum between 400 and 700nm that would mean 60 primaries. With that we could very closely approximate all the colors we are capable of seeing. That would be the equivalent of Dolby Atmos positional audio in your high end cinema. The key advantage that positional audio has is that it will work well with 100 speakers but you can also get very good results from just a handful of speakers; in your home for example where a 100 speaker system is unrealistic. A home system can therefore start with as few as 8 speakers and still use the same positional code that is used in the cinema. For display technology the number of colors we need to get a good approximation of all the colors we are capable of seeing is also about 8. This is a realistic number for a cinema because they currently use multiple projectors anyway (for 3-D presentations, or for increased brightness). With 2 projectors you have 6 colors and with 3 projectors you have 9 primaries.The figure below shows you what a system with 9 primaries would look like; that is, if we could tailor the light exactly as needed for each of the 9 primaries. They are designed to add up to a completely flat spectral power across the entire visible spectrum, which in this case is 415nm to 680nm. That is about as far into the lower and upper ranges of the visible spectrum that anyone can see. For people with exceptionally good color vision you might push this up to 400nm to 700nm but that would be an extreme high end option. This system has its primaries at 460nm for blue, 520nm for green, 580nm for yellow and 640nm at red — which means that the primary colors are spaced equidistantly on the spectrum at a distance of 60nm from each other. The human visual system sees the spectrum as circular and if the primaries are set 60nm apart on the visual spectrum then at the periphery there would be 30nm at the bottom of the spectrum and 30nm at the top of the spectrum (and at the point the meridian would be reached where bottom and top join). That would mean the human visual system can discriminate colors between 430nm and 470nm. The 9-primary system shown in the below comes quite close to this. The full range could be achieved by splitting the purple primary into two and extending the lower part slightly.The figure below shows how a display with 9 primaries would reproduce the white of a rose.The yellow of a sunflower can also be closely approximated, as shown by the figure below. The more primaries we have the more closely we can approximate the color. This idea is color reproduction by spectral approximation. Some people believe that this is the only way we can get really accurate color reproduction. We can do this with what is as a hyperspectral camera, which gives us the full spectrum for each pixel and then we code simply by approximating the spectral shape with the primaries we have available.While spectral approximation can produce really good color, unfortunately, color is not something outside in the environment but rather it is a product of our visual system. The human visual system is able to adapt to a wide variety of environmental conditions. One of the things that our visual system is able to do is to keep colors constant regardless of the conditions of the environment. The simplest element of this is to correct for spectral imbalance in the light that is illuminating the environment. A much more sophisticated element is the ability to adjust its primaries dynamically depending on the colors of the environment. What this means is that, for example, we know that bananas should be yellow and grass should be green so our visual system tries to use these known objects to establish reference points for its primaries. So if you are in an environment that has lots of grass in it, that grass may have a dominant wavelength of up to 560nm. Yellow bananas on the other hand can have a dominant wavelength of 570nm. That means that all the colors from yellow to green are squeezed into the 10nm between red and green. If you then introduce a sunflower and a green car whose dominant wavelength is 520nm then your visual system recalibrates to the standard model presented so far. What this means perceptually is that a yellow banana can suddenly appear quite greenish and some leaves of grass can appear quite yellowish. While our visual system works hard to keep colors constant, colors do change depending on the state of our perceptual system. Spectral approximation ignores this important factor. A hyperspectral camera is therefore not especially useful. It is more important for a camera to know when grass is pure green and when it is rather yellowish. In the presence of sunflowers the camera should code bananas as slightly green but in the supermarket they should be coded as pure yellow. We can do this not by knowing anything about complex objects such as bananas and grass are but by adjusting the primaries dynamically. So the sensors might show the leaves of a tree to be fairly dark and to have a dominant wavelength of 555nm, but the camera would choose to code the color as pure green (520nm). When it comes to displaying the color of the tree leaves, the display might be calibrated to a specific user who sees pure green at 530nm, and as a result it would shift the primary to that spectral position. This illustrates the importance of coding color abstractly, as suggested by the way flowers reproduce color. How exactly this coding system works is best left for future.While 9 primaries is desirable and can readily be achieved with current projection technology it is only practical in large space which can host an array of projectors. It is difficult to achieve with handheld devices or within a single monitor. Perhaps in the future OLED displays which layer pixels will be designed, making many primaries possible on individual devices. Currently, the maximum number of primaries that are practical is 4. This is because there currently are devices with 4 primaries. What should that 4′th primary look like? It most certainly should not look like the white primary in the LG OLED displays (see first 2 figures of Panasonic and Sony displays). The blue of the white primary is exactly identical to that of the blue primary. A white primary without the blue component used with the blue primary would achieve the exact same white as the white primary. There is no point in duplicating the light from primaries we already have. What duplicating the blue component shows is that the blue primary is more or less correct. It is centered more or less on the human visual systems blue sensor and it produces a perceptually correct blue which is well saturated. It is the red and green primaries that are incorrect. To achieve pure red and green colors the primaries need to be narrow and spectrally far apart (at 520nm and 640nm, which is 120nm apart). In that case, the most pressing need is to fill that gap between green and red. That would be where a 4′th primary would be most effective.All of this is fairly straight forward and largely consistent with current color theory. Yet there is a thread of work in color theory that fundamentally disagrees with this approach. This is from people who have laboriously constructed what are known as color appearance models. They are almost religiously wedded to the idea that human color vision is trichromatic, that our vision is based on 3 sensors and therefore that 3 primary colors is all you will ever need. In their view, all that we need to do is tweak the current system a bit and then we will have perceptually predictable and reliable color. They have been tweaking for 50 years, with what it must be said to be fairly mediocre results; results which most people involved in actual practical color reproduction can’t use and which as a result is largely ignored. To understand where they have gone wrong you have to understand a little bit of basic math.The figure above shows what are called color matching functions (CMF) in the jargon of color theory. They were standardized almost a century ago by the CIE (Commission Internationale de l'Éclairage, which is French for International Illumination Commission). These 3 functions approximate how the 3 color sensors of the human visual system respond to light. By convention the functions are called X, Y and Z (rather than Red, Green and Blue). If we had 4 color sensors equally distributed along the visual spectrum, like birds have, we can just subtract the opponent sensor pairs (blue-yellow and red-green) and this will map any color nicely and neatly into a circular color space with 4-poles (in practice its a bit more complicated, but that is basically how it works). With 3 sensors there is no way we can do that. Instead, standard color theory says that what our visual system is doing is taking a ratio of the 3 sensor values and from this we produce a two dimensional color coordinate (x,y). This is a very simple calculation: [math]x = \frac{X}{X+Y+Z}[/math] and [math]y = \frac{Y}{X+Y+Z}[/math]. The (x,y) coordinate is known as a chromaticity coordinate. The good thing about this is that we can produce a graph from these coordinates which maps all the colors we can see into an easy to understand 2-dimensional diagram. If we do this for all the colors we can see, we get something like what is shown in the figure below.Chromaticity diagrams often confuse people, but they are actually quite simple. All of the pure colors are shown by the small blue circles that are closely adjacent to each other. We can see this as a kind of boundary, on which are all the colors we are capable of seeing. The figure above is slightly more useful than what is shown conventionally because we can count exactly where we are on the visual spectrum nanometer by nanometer; with each small blue circle representing 1 nm. As we shall find out below, knowing where we are on this outer boundary is really important. Although this boundary is not really closed we can imagine it is by drawing a line from the circle representing the lowest visible wavelength to the highest (which is called the line of purple). With the line of purple we can now imagine an enclosed space which has a triangular elliptical shape. Inside this space are all the colors that are a mix of a pure color and white. In the center of the space is pure white. This is all there is to chromaticity. An important property of chromaticity is that if we take any 2 coordinates we can draw a line between the two points and all the colors that lie on that line can be produced by proportionally mixing the two colors. This is what makes systematic color reproduction with as few as 3 primaries possible. For any display, the area enclosed by 3 or more primaries is called the chromaticity space (or color gammut) of that display. Ideally, the chromaticity space of a display should be the same as the space bounded by the chromaticity diagram. In the figure above is shown the actual chromaticity space of the RGB primaries of the LG OLED display panel used in the Sony display we started this answer with. We can see that the color space of this display is far from having the ability to display all the colors we can see, despite it being the latest in display technology, which is advertised for its ability to produce life-like colors.Once you understand the idea of a chromaticity space you can see why some people are so wedded to it. It is a nicely elegant and simple way to represent color. We can see that any RGB display will have a triangular chromaticity space and overall the entire chromaticity space for human color vision is roughly triangular. Unfortunately, its not entirely triangular. A lot of effort has gone into tweaking the chromaticity functions to make the chromaticity space more triangular. It also has other problems like having some perceptual irregularities (where perceived color does not match predicted color). Overall though, these problems are generally considered fairly minor and it is thought that they will eventually be ironed out with enough modelling of color appearance.The current state of affairs with color theory is similar to the problem physicists had with the unexplained anomalies in the orbit of the planet Mercury. Newtonian mechanics worked perfectly for all the planets except for Mercury, where there was a small anomaly with the orbit of Mercury that could not be explained. Newtonian mechanics provided a nice, neat and simple explanation for gravity, which stood the test of time and almost all physicists at the time were supremely confident that it was right. Except of course Newtonian mechanics was wrong. Eventually someone came up with a very strange complicated theory that at first no one could understand but which eventually was shown to be right (or at least more right).The problem with the standard CIE chromaticity space is that you can say it is approximately triangular but you can also say that it is approximately circular. It has some areas which are linear, which is consistent with a triangle. But it also has some areas that are very much circular. Because no one has made the triangular system work we can easily suppose that maybe the triangular hypothesis is incorrect. Maybe the human visual system is not actually trichromatic. But how could this be? We only have 3 color sensors.In fact what is known as the standard CIE observer is based on quite limited data, and it is known that the people who did the initial studies fudged the data a bit. They also used people who did not really have very good color vision. We can actually produce color functions for an individual person, and if you do that you will find that people with poor color vision will have a more triangular color space and people with good color vision will have a more circular color space. The standard CIE observer is based on an average of a small group of people. In this case an average is not a very useful measure, as it will be wrong for both groups.Researchers also tend to stick quite dogmatically to trying to measure how the human visual sensors work. This is actually quite difficult, as human color sensors uses all kinds of complex tricks, most of which we don’t yet understand. Rather than painstakingly measure the actual sensors we can try to understand the underlying principles. If the objective of color sensors is to enable the measurement of wavelength then it makes sense to have sensors with a more systematic arrangement. The figure below shows a set of 3 sensors that have a linear response over their entire spectral range. They are simply copies of the same sensor, simply spectrally shifted by 60nm from each other.When we calculate the color space for the sensors in the figure above we get the chromaticity space in the diagram below. What is interesting about this space is that it is fully enclosed, which means it can see all the colors in its range. There is no purple gap like in the standard CIE color space where colors are undefined. What is even more interesting is that the color space is approximately square, with 4 distinct corners. These corners are the inherent primaries for this color system. To reproduce all the colors for a system like this we would need 4 lights, each precisely at the corner of the square (which would be at 460nm, 520nm, 580nm and 640nm). That makes this a tetrachromatic system.While the chromaticity space in the diagram above is interesting, it is quite different from how the human visual system works. But it demonstrates an important principle; that we don’t need 4 color sensors for tetrachromacy, we can make due with 3 sensors. This suggests that trichromacy is just a wrong idea. In fact we know that our distant ancestors (as far back as the dinosaurs) had 4 color sensors just like birds do. As our ancestors evolved into small creatures that scurried about in the dark we lost two of those color sensors. Like an old style TV that had two wires in the back to carry color information, one of those wires stopped working. In fact most mammals that live today can see only blue-yellow colors. The underlying circuitry though has not stopped working. If you plug the red-green wire back in then full color vision is restored. Someone has actually done that work with monkeys, restoring color vision that was lost millions of years ago by plugging in the lost color sensors. Some types of monkeys have redeveloped full color vision on their own though, and this includes apes (which is us). If you look at the sensor functions for human color vision you will see that it is basically a 2 sensor design, with a blue sensor and a yellow sensor. Relatively recently in our evolutionary history the yellow sensor split into two separate sensors; a green and a red sensor. The two sensors are very similar though; quite close to each other on the spectrum. In fact, there is a lot of variation in these 2 sensors in humans, so much so that in some people these sensors are too close to each other and this leads to anomalous color vision (often called color blindness). The closer the 2 sensors are to each other the more color blind you will be.That is probably more detail than you want to know. Nevertheless, if you want to build a camera that is capable of recording all the colors that we can see then understanding chromaticity is essential. The final piece of the puzzle that we have to know is how to calculate the dominant wavelength from chromaticity coordinates. For a display with 3 primaries color is mapped directly into the chromaticity space enclosed by those primaries. The multi-primary display presented above works differently. One or two of the narrow primaries will be used to approximate the dominant wavelength of the color (sometimes called the hue) and all the other primaries will together produce the amount of white (which determines how saturated the color is). This means that cameras must code color not as RGB values but by the actual color that the display should produce. That means the camera must calculate the dominant wavelength and saturation from its raw sensor values. This is an area much neglected by conventional color theory. If, for example, we want to calculate the dominant wavelengths for the primaries of the Sony A1 display (shown in the chromaticity diagram above) we place our ruler on the white point and on the primary and extend that line until we reach the outer chromaticity boundary. The location where the line intersects tells us what the dominant wavelength is. The green primary for example intersects about half way between 543nm and 544nm. The dominant wavelength is therefore 543.5nm. The distance from the white point is 82.5% to the outer boundary, and this is how saturated the primary is. We can graph this out by hand, but what is surprising is there is no way to do it automatically. That is, the standard CIE color space is not computable. You can of course do it by brute force (like a look-up table) but there is no simple formula that solves the problem for us. What we need is something simple that given an x and y value produces for us the dominant wavelength (and the amount of white). For converting matter into energy we have [math]e=mc^2[/math] which might need big numbers but can be readily calculated. That is the kind of thing we need. Not everything can be calculated though. If a function (or a color space) is irregular then it can’t be calculated (or computed) — other than by approximation or in some case by brute force methods. That is ok if you need to calculate just 1 pixel. But a camera (or the neural circuitry in your retina) has to calculate millions of pixels every few milliseconds and this means you have to do the calculation in hardware (and in real time), and you can only implement the hardware if you have a computable function — preferably an easily computable function.Because it is not computable, this makes the standard CIE chromaticity space not very useful. The neural circuitry that sit behind the retina is able to do this calculation with just a few layers of neurons. It is quite likely, therefore, that the actual color space used by the human visual system is computable. If the human visual system can do it then a camera can to do it as well. We just have to work out what that color space is that the human visual system actually uses. The square color space shown above is I think a step in that direction. Its not entirely regular, but fairly close. With a few tweaks to the sensor function it may be possible to produce an entirely regular color space.So that, in summary, is why RGB is insufficient and we need displays with more colors. The easy answer is that we can just approximate how colors are made in nature. We can get pretty good color with just 4 primary colors, but we will have some gaps in the spectrum. People with excellent color vision will be able to notice those gaps. With 9 primary colours we can produce colors that are indistinguishable to those found in nature for almost all people. We can add a few more colors for good measure, but realistically 9 is about the maximum that we will ever need. We have the technology to do it today, but we are being held back by people who still believe in things like Newtonian mechanics and the aether. Once the theory is clear we can get to work on designing multi-primary displays. But displays are the easy part. Designing cameras to correctly see color is the hard part. Its easy if we can do spectral analysis for each pixel, but that's unlikely ever to be practical. A basic mid-range spectrum analyzer has about 90 sensors covering the visual spectrum. That is very different from having 3 or 4 sensors. But we know from birds, that 4 sensors is all we need. Birds probably have the most refined color vision that we know of and they have spent 100 million years working out how best to do it. The answer from studying color vision in birds is that you don’t need more than 4 sensors to achieve really good color vision. If a bird has no need for more sensors then its unlikely that a camera producing images for human use will need more than 4 sensors.

SYLLABUS FOR ICAR’S ALL INDIA ENTRANCE EXAMINATION FOR ADMISSION TO BACHELOR DEGREE PROGRAMMES PHYSICSINSTRUCTIONYou can access the syllabus in two ways:Open the link clicking on the web address given below;Web address: https://www.icar.org.in/sites/default/files/Syllabus%20UG%20-2019_1.pdf#overlay-context=content/syllabus-aieea-ug-aieea-pg-and-aice-jrfsrfpgs-20192. If you find any difficulty with the above method, you can copy what I have copied and pasted below. A few units I have arranged, you can copy and paste to a word document and arrange in the same fashion as I have arranged Unit-1 to Unit-12.NOTE: Since method two involve distortion during copying and pasting (for your benefit), it is likely that some information is deleted/distorted.ALL THE BEST …!Unit-1:Physical World and Measurement Physics scope and excitement; nature of physical laws; Physics, technology and society. Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures. Dimensions of physical quantities, dimensional analysis and its applications.Unit-2: Kinematics Frame of reference. Motion in a straight line: Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion: velocity-time graph, positiontime graphs, relations for uniformly accelerated motion (graphical treatment). Elementary concepts of differentiation and integration for describing motion. Scalar and vector quantities: Position and displacement vectors, general vectors and notation, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane - rectangular components. Motion in a plane. Cases of uniform velocity and uniform acceleration-projectile motion. Uniform circular motion. Motion of objects in three dimensional space. Motion of objects in three dimensional space.Unit-3: Laws of Motion Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road).Unit-4: Work, Energy and Power Scalar product of vectors. Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: elastic and inelastic collisions in one and two dimensions.Unit-5: Motion of System of Particles and Rigid Body Centre of mass of a two-particle system, momentum conversation and centre of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod. Vector product of vectors; moment of a force, torque, angular momentum, conservation of angular momentum with some examples. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects. Statement of parallel and perpendicular axes theorems and their applications.Unit-6: Gravitation Keplar’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.Unit-7: Properties of Bulk Matter Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure. Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Bernoulli’s theorem and its applications. Surface energy and surface tension, angle of contact, application of surface tension ideas to drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat - calorimetry; change of state - latent heat. Heat transferconduction, convection and radiation, thermal conductivity, Newton’s law of cooling.Unit-8: Thermodynamics Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Heat engines and refrigerators.Unit-9: Behaviour of Perfect Gas and Kinetic Theory Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application to specific heats of gases; concept of mean free path, Avogadro’s number.Unit-10: Oscillations and Waves Periodic motion - period, frequency, displacement as a function of time. Periodic functions. Simple Harmonic Motion (S.H.M) and its equation; phase; oscillations of a spring–restoring force and force constant; energy in S.H.M.- kinetic and potential energies; simple pendulum– derivation of expression for its time period; free, forced and damped oscillations, resonance. Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.Unit-11: Electrostatics Electric Charges; Conservation of charge, Coulomb’s law - force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.Unit-12: Current Electricity Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V - I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchoff’s laws and simple applications. Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell. Unit-13: Magnetic Effects of Current and Magnetism Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets. Unit-14: Electromagnetic Induction and Alternating Currents Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Need for displacement current. Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer. Unit-15: Electromagnetic waves Displacement current, Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses. Unit-16: Optics Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of light through a prism. Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia, hypermetropia, presbyopia and astigmatism) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. Wave optics: wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids. Unit-17: Dual Nature of Matter and Radiation Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment. Unit-18: Atoms & Nuclei Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear reactor, nuclear fusion. Unit-19: Electronic Devices Semiconductors; semiconductor diode – I -V characteristics in forward and reverse bias, diode as a rectifier; I - V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch. Unit-20: Communication Systems Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave. CHEMISTRY Unit-1: Some Basic Concepts of Chemistry General Introduction: Importance and scope of chemistry. Historical approach to particulate nature of matter, laws of chemical combination. Dalton’s atomic theory: concept of elements, atoms and molecules. Atomic and molecular masses mole concept and molar mass: percentage composition, empirical and molecular formula chemical reactions, stoichiometry and calculations based on stoichiometry. Unit-2: Solid State Classification of solids based on different binding forces: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Unit-3: Solutions Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapour pressure, elevation of Boiling Point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass. Unit-4: Structure of Atom Discovery of electron, proton and neutron; atomic number, isotopes and isobars. Thomson’s model and its limitations, Rutherford’s model and its limitations. Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals - Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals. Unit-5: Classification of Elements and Periodicity in Properties Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii. Ionization enthalpy, electron gain enthalpy, electro negativity, valence. Unit-6: Chemical Bonding and Molecular Structure Valence electrons, ionic bond, covalent bond: bond parameters. Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR (Valence shell electron pair repulsion) theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital; theory of homonuclear diatomic molecules (qualitative idea only), hydrogen bond. Unit-7: States of Matter: Gases and Liquids Three states of matter. Intermolecular interactions, type of bonding, melting and boiling points. Role of gas laws in elucidating the concept of the molecule, Boyle’s law. Charles law, Gay Lussac’s law, Avogadro’s law. Ideal behaviour, empirical derivation of gas equation, Avogadro’s number. Ideal gas equation. Derivation from ideal behaviour, liquefaction of gases, critical temperature. Liquid State - Vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations). Unit-8: Thermodynamics Concepts of System, types of systems, surroundings. Work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics - internal energy and enthalpy, heat capacity and specific heat, measurement of DU and DH, Hess’s law of constant heat summation, enthalpy of: bond dissociation, combustion, formation, atomization, sublimation. Phase transformation, ionization, and solution. Introduction of entropy as a state function, free energy change for spontaneous and non-spontaneous processes, criteria for equilibrium. Unit-9: Equilibrium Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium - Le Chatelier’s principle; ionic equilibrium - ionization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts. Buffer solutions, solubility product, common ion effect. Unit-10: Redox Reactions Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions. Unit-11: Hydrogen Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides - ionic, covalent and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxide-preparation, properties and structure; hydrogen as a fuel. Unit-12: s-Block Elements (Alkali and Alkaline earth metals) Group 1 and Group 2 elements General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses. Unit-13: Preparation and properties of some important compounds Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of sodium and potassium. CaO, CaCO3 and industrial use of lime and limestone, biological importance of Mg and Ca Unit-14: Some p-Block Elements General Introduction to p-Block Elements: Group 13 elements General introduction, electronic configuration, occurrence. Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron- physical and chemical properties, some important compounds: borax, boric acids, boron hydrides. Aluminum: uses, reactions with acids and alkalies. Unit-15: Group 14 elements General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behavior of first element, Carbon - catenation, allotropic forms, physical and chemical properties; uses of some important compounds: oxides. Important compounds of silicon and a few uses: silicon tetrachloride, silicones, silicates and zeolites. Unit-16: Organic Chemistry Some Basic Principles and Techniques General introduction, methods of qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds, Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions Unit-17: Hydrocarbons Classification of hydrocarbons Alkanes - Nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis. Alkenes - Nomenclature, structure of double bond (ethene) geometrical isomerism, physical properties, methods of preparation; chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition. Alkynes - Nomenclature, structure of triple bond (ethyne), physical properties. Methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of - hydrogen, halogens, hydrogen halides and water. Aromatic hydrocarbons: Introduction, IUPAC nomenclature; benzene: resonance, aromaticity; chemical properties: mechanism of electrophilic substitution. – nitration, sulphonation, halogenation, Friedel-Craft’s alkylation and acylation: directive influence of functional group in mono-substituted benzene; carcinogenicity and toxicity. Unit-18: Electrochemistry Conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea), dry cell – electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion. Unit-19: Chemical Kinetics Rate of a reaction (average and instantaneous), factors affecting rate of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment) Unit-20: Surface Chemistry Adsorption – physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis : homogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions; lyophilic, lyophobic, multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion – types of emulsions. Unit-21: General Principles and Processes of Isolation of Elements Principles and methods of extraction - concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron. Unit-22: p-Block Elements Group 15 elements General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen - preparation, properties and uses; compounds of nitrogen: preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); Phosphorous-allotropic forms; compounds of phosphorous: preparation and properties of phosphine, halides (PCl3, PCl5) and oxoacids Unit-23: Group 16 elements General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: preparation, properties and uses; simple oxides; Ozone. Sulphur - allotropic forms; compounds of sulphur: preparation, properties and uses of sulphur dioxide; sulphuric acid: industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only). Unit-24: Group 17 elements General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structures only). Unit-25: Group 18 elements General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses. Unit-26: d and f Block Elements General introduction ,electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour catalytic property, magnetic properties, interstitial compounds, alloy formation preparation and properties of K2Cr2O7 and KMnO4. Lanthanoids - electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction. Actinoids - Electronic configuration, oxidation states. Unit-27: Coordination Compounds Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. bonding; isomerism, importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems). Unit-28: Haloalkanes and Haloarenes Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions. Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only) Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT. Unit-29: Alcohols, Phenols and Ethers Alcohols Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol. Phenols : Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols. Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses. Unit-30: Aldehydes, Ketones and Carboxylic Acids Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses. Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses. Unit-31: Organic compounds containing Nitrogen Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines. Cyanides and Isocyanides - will be mentioned at relevant places in context. Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry. Unit-32: Biomolecules Carbohydrates- Classification (aldoses and ketoses), monosaccharide (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance. Proteins - Elementary idea of á-amino acids, peptide bond, polypeptides, proteins, structure of amines-primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Vitamins - Classification and functions. Nucleic Acids: DNA and RNA . Unit-33: Polymers Classification - natural and synthetic, methods of polymerization (addition and condensation), copolymerization. Some important polymers: natural and synthetic like polythene, nylon, polyesters, Bakelite, rubber. Unit-34: Environmental Chemistry Environmental pollution - air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming - pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution. Unit-35: Chemistry in Everyday life 1. Chemicals in medicines - analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines. 2. Chemicals in food - preservatives, artificial sweetening agents. 3. Cleansing agents - soaps and detergents, cleansing action. BIOLOGY (BOTANY AND ZOOLOGY) Unit : 1 The Living World Nature and scope of Biology. Methods of Biology. Our place in the universe. Laws that govern the universe and life. Level of organization. Cause and effect relationship. Being alive. What does it mean? Present approaches to understand life processes, molecular approach; life as an expression of energy; steady state and homeostasis; self duplication and survival; adaptation; death as a positive part of life. Origin of life and its maintenance. Origin and diversity of life. Physical and chemical principles that maintain life processes. The living crust and interdependence. The positive and negative aspects of progress in biological sciences. The future of the living world, identification of human responsibility in shaping our future. Unit : 2 Unit of Life Cell as a unit of life. Small biomolecules; water, minerals, mono and oligosaccharides, lipids, amino acids, nucleotides and their chemistry, cellular location and function. Macromolecules in cells - their chemistry, cellular location and functional significance. Polysaccharides, proteins and nucleic acids. Enzymes; chemical nature, classification, mechanism in action-enzyme complex, allosteric modulation (brief), irreversible activation. Biomembranes; Fluid mosaic model of membrane, role in transport, recognition of external information (brief). Structural organization of the cell; light and electron microscopic views of cell, its organelles and their functions; nucleus mitochondria, chloroplasts, endoplasmic reticulum. Golgi complex, lysosomes, microtubules, cell wall, cilia and flagella, vacuoles, cell inclusions. A general account of cellular respiration. Fermentation, biological oxidation (A cycle outline), mitochondrial electron transport chain, high energy bonds and oxidative phosphorylation, cell reproduction; Process of mitosis and meiosis. Unit : 3 Diversity of Life Introduction. The enormous variety of living things, the need for classification to cope with this variety; taxonomy and phylogeny; shortcomings of a two kingdom classification as plants and animals; the five kingdom classification, Monera, Protista, Plantae, Fungi and Animalia; the basic features of five kingdom classification. modes of obtaining nutrition-autotrophs and heterotrophs. Life style producers, consumers and decomposers. Unicellularity and multicellularity, phylogenetic relationships. Concepts of species, taxon and categories - hierarchical levels of classification; binomial nomenclature; principles of classification and nomenclature; identification and nature of viruses and bacteriophages; kingdom Monera-archeabacteria - life in extreme environments; Bacteria, Actinomycetes, Cyanobacteria. Examples & illustration of autotrophic and heterotrophic life; mineralizes-nitrogen fixers; Monera in cycling matter; symbiotic forms; disease producers. Kingdom Protista-Eukaryotic unicellular organisms, development of flagella and cilia; beginning of mitosis; syngamy and sex. Various life styles shown in the major phyla. Evolutionary precursors of complex life forms. Diatoms, dinoflagellates, slime moulds, protozons; symbiotic forms. Plant kingdom-complex autotrophs, red brown and green algae; conquest of land, bryophytes, ferns, gymnosperms and angiosperms. Vascularization; development of flower, fruit and seed. Kingdom fungi-lower fungi (Zygomycetes), higher fungi (Ascomycetes and Basidiomycetes); the importance of fungi. Decomposers; parasitic forms; lichens and mycorrhizae. Animal kingdom-animal body pattern and symmetry. The development of body cavity in invertebrate vertebrate physia. Salient features with reference to habitat and example of phylum porifera, coelenterata, helminthis, annelids, mollusca, arthropoda, echinoderms; chordata - (classes-fishes, amphibians, reptiles, birds and mammals) highlighting major characters. Unit : 4 Organisms and Environment Species: Origin and concept of species population, interaction between environment and population community. Biotic community, interaction between different species, biotic stability. Changes in the community. Succession. Ecosystem; interaction between biotic and abiotic components; major ecosystems, manmade ecosystem- Agro ecosystem. Biosphere; flow of energy, trapping of solar energy, energy pathway, food chain, food web, biogeochemical cycles, calcium and sulphur, ecological imbalance and its consequences. Conservation of natural resources; renewable and non-renewable (in brief). Water and land management, wasteland development. Wild life and forest conservation; causes for the extinction of some wild life, steps taken to conserve the remaining species, concept of endangered species-Indian examples, conservation of forests; Indian forests, importance of forests, hazards of deforestation, concept of afforestation. Environmental pollution; air and water pollution, sources, major pollutants of big cities of our country, their effects and methods of control, pollution due to nuclear fallout and waste disposal, effect and control, noise pollution; sources and effects. Unit : 5 Multicellularity : Structure and Function - Plant Life Form and function. Tissue system in flowering plants; meristematic and permanent. Mineral nutrition-essential elements, major functions of different elements, passive and active uptake of minerals. Modes of nutrition, transport of solutes and water in plants. Photosynthesis; photochemical and biosynthetic phases, diversity in photosynthetic pathways, photosynthetic electron transport and photophosphorylation, photorespiration. Transpiration and exchange of gases. Stomatal mechanism. Osmoregulation in plants: water relations in plant cells, water potential. Reproduction and development in Angiosperms; asexual and sexual reproduction. Structure and functions of flower: development of male and female gametophytes in angiosperms, pollination, fertilization and development of endosperm, embryo seed and fruit. Differentiation and organ formation. Plant hormones and growth regulation; action of plant hormones in relation to seed dormancy and germination, apical dominance, senescence and abscission. Applications of synthetic growth regulators. A brief account of growth and movement in plants. Unit : 6 Multicellularity : Structure and Function - Animal Life Animal tissues, epithelial, connective, muscular, nerve. Animal nutrition, organs of digestion and digestive process, nutritional requirements for carbohydrates, proteins, fats, minerals and vitamins; nutritional imbalances and deficiency diseases. Gas exchange and transport: Pulmonary gas exchange and organs involved, transport of gases in blood, gas exchange in aqueous media circulation: closed and open vascular systems, structure and pumping action of heart, arterial blood pressure, lymph. Excretion and osomoregulation. Ammonotelism, Ureotelism, urecotelism, excretion of water and urea with special reference to man. Role of kidney in regulation of plasma, osmolarity on the basis of nephron structure, skin and lungs in excretion. Hormonal coordination; hormones of mammals, role of hormones as messengers and regulators. Nervous coordination, central autonomic and peripheral nervous systems, receptors, effectors, reflex action, basic physiology of special senses, integrative control by neuroendocrinal systems. Locomotion: joints, muscle movements, types of skeletal muscles according to types of movement, basic aspects of human skeleton. Reproduction; human reproduction, female reproductive cycles. Embryonic development in mammals (upto three germs layers), growth, repair and ageing. Unit : 7 Continuity of Life Heredity and variation: Introduction, Mendel’s experiments with peas and concepts of factors. Mendel’s laws of inheritance. Genes: Packaging of heredity material in prokaryotes-bacterial chromosome and plasmid; and eukaryote chromosomes. Extranuclear genes, viral genes. Linkage (genetic) maps. Sex determination and sex linkage. Genetic material and its replication, gene manipulation. Gene expression; genetic code, transcription, translation, gene regulation. Molecular basis of differentiation. Unit : 8 Origin and Evolution of Life Origin of life: living and non-living, chemical evolution, organic evolution; Oparin ideas, Miller-Urey experiments. Interrelationship among living organisms and evidences of evolution: fossil records including geological scale, Morphological evidence - hematology, vestigeal organs, embryological similarities and biogeographical evidence. Darwin’s two major contributions. Common origin of living organisms and recombination as source of variability, selection and variation, adaptation (Lederberg’s replica plating experiment for indirect selection of bacterial mutants), reproductive isolation, speciation. Role of selection, change and drift in determining composition of population. Selected examples: industrial melanism; drug resistance, mimicry, malaria in relation to G-6-PD deficiency and sickle cell disease. Human evolution: Palcontological evidence, man’s place among mammals. Brief idea of Dryopithecus, Australopithecus, Homo erectus, H.neanderthlensis, Cro-Magnon man and Homo sapiens. Human chromosomes, similarity in different racial groups. Comparison with chromosomes of nonhuman primates to indicate common origin; Cultural vs. biological evolution. Mutation: origin and types of mutation, their role in speciation. Unit : 9 Application of Biology Introduction, role of biology, in the amelioration of human problems. Domestication of plant- a historical account, improvement of crop plants; Principles of plant breeding and plant introduction. Use of fertilizers, their economic and ecological aspects. Use of pesticides: advantages and hazards. Biological methods of pest control. Crops today. Current concerns, gene pools and genetic conservation. Underutilized crops with potential uses of oilseeds, medicines, beverages, spices, fodder, New crops-Leucaena (Subabul), Jojoba, Guayule, winged bean, etc. Biofertilizers - green manure, crop residues and nitrogen fixation (symbiotic, non symbiotic). Applications of tissue culture and genetic engineering in crops. Domestication and introduction of animals. Livestock, poultry, fisheries (fresh water, marine, aquaculture). Improvement of animals: principles of animal breeding. Major animal diseases and their control. Insects and their products (silk, honey, wax and lac). Bioenergy-biomass, wood (combustion; gasification, ethanol). Cow dung cakes, gobar gas, plants as sources of hydrocarbons for producing petroleum, ethanol from starch and lignocellulose. Biotechnology, application in health and agriculture, genetically modified (GM) organisms, bio-safety issues. A brief historical account-manufacture of cheese. yoghurt, alcohol, yeast, vitamins, organic acids, antibiotics, steroids, dextrins. Scaling up laboratory findings to Industrial production, sewage treatment. Production of insulin, human growth hormones, interferon. Communicable diseases including STD and diseases spread through ‘blood transfusion (hepatitis, AIDS, etc) Immune response, vaccine and antisera. Allergies and Inflammation. Inherited diseases and dysfunctions, sex-linked diseases, genetic incompatibilities, and genetic counseling. Cancer-major types, causes, diagnosis and treatment. Tissue and organ transplantation. Community health services and measures; blood banks; mental health, smoking, alcoholism and drug addiction-physiological symptoms and control measures. Industrial wastes, toxicology, pollution-related diseases. Biomedical engineering - spare parts for man, instruments for diagnosis of diseases and care. Human population related diseases. Human population, growth, problems and control, inequality between sexes, control measures; test-tube babies aminocentesis. Future of Biology. MATHEMATICS Unit-1: Sets and Functions 1. Sets : Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets, Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. 2. Relations & Functions: Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of relation, Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations, Pictorial representation of a function, domain. Co-domain and range of a relation. Function as a special kind of relation from one set to another. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions. 3. Trigonometric Functions: Positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x=1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x+y) and cos (x+y) in terms of sinx, siny, cosx&cosy. Deducing the identities like the following: Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sin è ?= sin á, cos è ?= cos á ?and tan è ?= tan á. Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Properties of triangles, including centroid, incentre, circum-centre and orthocentre, Solution of triangles. Heights and Distances. Unit-2: Algebra 1. Principle of Mathematical Induction: Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications. 2. Complex Numbers and Quadratic Equations: Need for complex numbers, especially -1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. 3. Linear Inequalities: Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables- graphically. 4. Permutations & Combinations: Fundamental principle of counting. Factorial n. (n!). Permutations and combinations, derivation of formulae and their connections, simple applications. 5. Binomial Theorem: History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications. 6. Sequence and Series: Sequence and Series. Arithmetic progression (A. P.). arithmetic mean (A.M.) Geometric progression (G.P.), general term of a G.P., sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G.M. Sum to n terms of the special series Ón, Ón2 and Ón3. 7. Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists. 8. Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. Unit-3: Coordinate Geometry 1. Straight Lines:Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line. Distance of a point from a line. 2. Conic Sections: Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle. 3. Introduction to Three-dimensional Geometry: Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Unit-4: Calculus 1. Limits and Derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions. 2. Continuity and Differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations. 3. Applications of Derivatives: Applications of derivatives: rate of change, increasing/decreasing functions, tangents &normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems. 4. Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts; only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 5. Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves. 6. Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: + = , where p and q are functions of x. Unit-5: Vectors and Three-Dimensional Geometry 1. Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors. 2. Three-dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane. Unit-6: Linear Programming Linear Programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). Unit-7: Mathematical Reasoning Mathematical Reasoning: Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words, difference between contradiction, converse and contrapositive. Unit-8: Statistics & Probability 1. Statistics: Measures of central tendency,mean, median and mode from ungrouped/grouped data. Measures of dispersion, mean deviation, variance and standard deviation from ungrouped/grouped data. Correlation, regression lines. 2. Probability: Random experiments: outcomes, sample spaces (set representation). Events: occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability, Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events. Multiplication theorem on probability. Conditional probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of stochastic variable. Repeated independent (Bernoulli) trials and Binomial distribution. Unit-9: Statics Introduction, basic concepts and basic laws of mechanics, force, resultant of forces acting at a point, parallelogram law of forces, resolved parts of a force, Equilibrium of a particle under three concurrent forces. Triangle law of forces and its converse, Lami’s theorem and its converse, Two Parallel forces, like and unlike parallel forces, couple and its moment. Unit-10: Dynamics Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant of two velocities. Motion of a particle along a line, moving with constant acceleration. Motion under gravity. Laws of motion, Projectile motion. AGRICULTURE Unit-1: Agrometeorology, Genetics and Plant Breeding, Biochemistry and Microbiology Agrometerology: Elements of Weather-rainfall, temperature, humidity, wind velocity, Sunshine weather forecasting, climate change in relation to crop production. Genetics & Plant Breeding : (a) Cell and its structure, cell division-mitosis and meiosis and their significance (b) Organisation of the genetic materials in chromosomes, DNA and RNA (c) Mendel’s laws of inheritance. Reasons for the success of Mendel in his experiments, Absence of linkage in Mendel’s experiments. (d) Quantitative inheritance, continuous and discontinuous variation in plants. (e) Monogenic and polygenic inheritance. (f) Role of Genetics in Plant breeding, self and cross-pollinated crops, methods of breeding in field crops-introduction, selection, hybridization, mutation and polyploidy, tissue and cell culture. (g) Plant Biotechnology-definition and scope in crop production. Biochemistry: pH and buffers,Classification and nomenclature of carbohydrates; proteins; lipids; vitamins and enzymes. Microbiology: Microbial cell structure,Micro-organisms- Algae, Bacteria, Fungi, Actinomycetes, Protozoa and Viruses. Role of micro-organisms in respiration, fermentation and organic matter decomposition Unit-2: Livestock Production Scope and importance : (a) Importance of livestock in agriculture and industry, White revolution in India. (b) Important breeds Indian and exotic, distribution of cows, buffaloes and poultry in India. Care and management : (a) Systems of cattle and poultry housing (b) Principles of feeding, feeding practices. (c) Balanced ration-definition and ingredients. (d) Management of calves, bullocks, pregnant and milch animals as well as chicks crockrels and layers, poultry. (e) Signs of sick animals, symptoms of common diseases in cattle and poultry, Rinderpest, black quarter, foot and mouth, mastitis and haemorrhagicsepticaemiacoccidiosis, Fowl pox and Ranikhet disease, their prevention and control. Artificial Insemination : Reproductive organs, collection, dilution and preservation of semen and artificial insemination, role of artificial insemination in cattle improvement. Livestock Products: Processing and marketing of milk and Milk products. Unit-3: Crop Production Introduction : (a) Targets and achievements in foodgrain production in India since independence and its future projections, sustainable crop production, commercialization of agriculture and its scope in India. (b) Classification of field crops based on their utility-cereals, pulses, oils seeds, fibre, sugar and forage crops. Soil, Soil fertility, Fertilizers and Manures: (a) Soil, soil pH, Soil texture, soil structure, soil organisms, soil tilth, soil fertility and soil health. (b) Essential plant nutrients, their functions and deficiency symptoms. (c) Soil types of India and their characteristics. (d) Organic manure, common fertilizers including straight, complex, fertilizer mixtures and biofertilizers; integrated nutrient management system. Irrigation and Drainage: (a) Sources of irrigation (rain, canals, tanks, rivers, wells, tubewells). (b) Scheduling of irrigation based on critical stages of growth, time interval, soil moisture content and weather parameters. (c) Water requirement of crops. (d) Methods of irrigation and drainage. (e) Watershed management Weed Control : Principles of weed control, methods of weed control (cultural, mechanical, chemical, biological and Integrated weed management). Crops: Seed bed preparation, seed treatment, time and method of sowing/planting, seed rate; dose, method and time of fertilizer application, irrigation, interculture and weed control; common pests and diseases, caused by bacteria, fungi virus and nematode and their control, integrated pest management, harvesting, threshing, post harvest technology: storage, processing and marketing of major field crops-Rice, wheat, maize, sorghum, pearl millet, groundnut, mustard, pigeon-pea, gram, sugarcane, cotton and berseem. Unit-4: Horticulture (a) Importance of fruits and vegetables in human diet, Crop diversification & processing Industry. (b) Orchardlocation and layout, ornamental gardening and kitchen garden. (c) Planting system, training, pruning, intercropping, protection from frost and sunburn. (d) Trees, shrubs, climbers, annuals, perennials-definition and examples. Propagation by seed, cutting, budding, layering and grafting. (e) Cultivation practices, processing and marketing of: (i) Fruits - mango, papaya, banana, guava, citrus, grapes. (ii) Vegetables - Radish, carrot, potato, onion, cauliflower, brinjal, tomato, spinach and cabbage. (iii) Flowers - Gladiolus, canna, chrysanthemums, roses and marigold. (f) Principles and methods of fruit and vegetable preservation. (g) Preparation of jellies, jams, ketchup, chips and their packing. Note: Besides above syllabi, any other question of scientific and educational importance may be asked.