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In simplest terms, information is what allows one mind to influence another. Information can be measured and compared using a measurement called entropy.

We can describe exactly how much using a unit called the bit, a measure of surprise.

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A bit is linked to a very simple idea. The answer to a yes or no question.

Žmogaus kalbos ir alfabeto raidos istorija. Paskaitos: 1 Origins of written language2 History of the alphabet Somewhere around 50, years ago there was a sudden explosion of diverse cultural artifacts, including instruments for making music, new tools, and other forms of creative expression At the time, the universal written language was art Our ancestors use natural materials to create pictorial representations of their reality.

A common theme among these ancient paintings are animal forms, as well as the human hand. Pictograms a simplified drawing that resembles the physical object it represents are an important step in the evolution of writing. C Ideogram - a conceptual picture of an abstract idea Ancient Mesopotamia is home to some of the oldest written documents ever found, some dating before 3, B. The Rebus Principle - Sound plus sound equals new meaning it has nothing to do with the individual symbols A great example of this was found in Egypt along the Nile River.

Dated to around 3, B. Messages are formed by arranging symbols in specific patterns. The symbols have two categories: word signs - symbols that represent a single meaningful concept sound signs - these symbols btc 1 semestro egzamino data chunks of sound. The total number of different symbols in common use was over 1, At the time, the medium used to store the symbols was primarily rock.

Mobility was not a main concern when communicating messages in this way. However, a new physical medium for storing symbols was emerging at the time - Papyrus.

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This medium was ideal for sending messages across greater spaces. This lead to a cursive script, known as Hieratic. These symbols were based on Hieroglyphics, however the pictures were simplified to match the swiftness of writing in ancient shorthand. Also, the number of common symbols in use began to shrink down to around A marked increase in writing by hand lead to a new writing system called Demotic around BC.

The new simplicity meant that achildren could be tught to write at a young age. When it was adapted by the Akkadians and fitted to their language, they reduced the number of symbols to aroundand they did this again by moving towards sound signs.

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When sounded out correctly, the letters would produce words in ancient Semitic. The secret power - it did not need Semitic speech in order to work. This was the source of the Greek and later Roman alphabet forms we know today. Šaltinio informacijos kodavimas ir vaizdo telegrafo veikimas.

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Paskaitos: 1 Source encoding 2 Visual telegraphs Turime paprastą kanalą laidą - triukšmas leidžia perduoti tik paprasčiausius signalus Reikia užkoduoti skaičių, išmestą dviem kauliukais Paprasčiausia - tiek signalų, kiek akučių iškrenta Kanalo riba pardavimo greitis - 2 signalai per sekundę jei daugiau - sunku suprasti Tam, kad perdavimas būtų efektyvesnis, akučių skaičius surikiuojamas pagal išmetimo tikimybę Priskiriamas mažiausias signalų skaičius tikėtiniausiam akučių skaičiui Tai - optimaliausias kodavimas tokiam metodui Btc 1 semestro egzamino data signal fire - one difference, two states.

Polybius was a Greek historian born in BC. The limitation of a signal fire was clear to him.

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A fire signal is great when the space of possible messages is small. However, when the message space, which is the total number of possible messages, grows there was a need to communicate many differences.

Aeneas Tacticus, one of the earliest Greek writers on the art of war from the fourth century, BC, developed the equal water vessel communication method. First, sender and receiver raises the torch to indicate message start Then, the sender lowers the torch and opens his vessel The receiver opens his vessel when he sees the torch lowered When the water stops, the level of water means a specific greek alphabet letter Polybius square, works as follows: Two people separated by a distance each have 10 torches separated into two groups of five.

To begin, the sender raises a torch and waits for the receiver to respond. Then the sender lights a certain number from each group of torches and raises them. The receiver then counts the number of torches lit in the first group.

This number defines the row position in an alphabetic grid they share. And the second group of torches signifies the column position in this grid. The intersection of the row and column number defines the letter btc turtai. Realize that given N yes or no questions, there are two to the power of N possible answer sequences.

With six shutters we have six questions, open or closed?

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Providing us with two to the power of six, or 64 differences. With a telescope it was now possible to send letters at an incredible distance between beacons.

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Elektrostatinio ir elektromagnetinio telegrafo veikimas. Morzės abėcėlė. Paskaitos: 1 Electrostatic telegraphs 2 The battery and electromagnetism pirkti bitcoin didmeninė prekyba Morse code BC - Thales of Miletus widely regarded as the first Greek philosopher - discovers that amber attracts small particles when rubbed to fur.

Benjamin Franklin, who in set out to prove that there is a connection between lightning and these tiny shocks due to friction. In a famously dangerous experiment done alone with his son, he let a kite into a thunderstorm and near the bottom where the thread was wet, he tied an iron key and after some time he brought his knuckle up to the key experienced the series of small shocks identical to the ones created by contact with fur. It was found that conductors such as copper wire would transmit this pulling effect over a distance.

In French inventor George Louis Le Sage sent messages through an array of 26 wires each wire representing a letter of the alphabet. When a discharge occurred at one end the pith ball would move at the other. The trouble with this telegraph was that it only extended between the two rooms of his house. The power the deflection was small and difficult to work with. Alessandro Volta invented the Leyden jar a capacitor or charge storing device.

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And when he chained many jars together he found he could increase the capacity even more and release deadly volt of electricity.

Over the next 50 years people tried to design systems for sending sparks across greater distances using longer wires and more powerful discharges. However sending electrostatic discharges as a communication method seemed clumsy archaic and was no improvement over the existing optical telegraph of the day.

Take two pieces of metal: copper and zinc which you connect to conducting wires and you then submerge the metals in an electrolyte in this case vinegar.

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Towards the end of the 18th century Alessandro Volta found that chaining these cells together would amplify this flow of charge. By he simplified things even further removing the jar which provided more electrolyte than was actually needed - replacing it with a thin sponge material soaked in electrolyte.

Btc 1 semestro egzamino data simple cells could be stacked together on top of each other. Bitcoin skrydžio bilietas pile, the first battery in history to provide a continuous flow of electrical charge, or current.

This system was never adopted. In it was found that if we simply pass a wire near a compass and connected to a battery as soon as the wire made contact with the battery the needle jumped without any physical contact.

By William Sturgeon demonstrated a way to increase the strength of this field even more, simply by wrapping a coil of wire around a piece of iron such as a nail.

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Suddenly it was possible to create magnetic fields which could move needles with precision and force using electric current applied at a distance using a long loop of wire and a strong battery. Paskaitos: 1 Symbol rate 2 Channel capacity Primary symbols - letters Secondary symbols - Morse Code btc 1 semestro egzamino data the lower-level signaling events, such as pulses of electricity Baudot Multiplex System consisted of 5 keys which could be played in any combination.

The code assigned the 32 different chords to each letter of the alphabet with the leftovers used for carriage returns, new line and spaces. The iambic counter, the mechanical nerves of the system, change words to holes on tape, and the holes on tape to electrical impulses speeding over the wires.

The speed of transmission was physically limited by the minimum spaces between these impulses or the pulse rate. Sending pulses too fast, results in inter-symbol interference. The symbol rate is the number of signaling events which can be squeezed together in one second There was one other way to increase the capacity of a communication system - We can increase the number of different signaling events. This was an idea implemented by Thomas Edison, which he applied to the Morse code system, and it was based on the idea that you could use weak and strong batteries to produce signals btc 1 semestro egzamino data different strengths.

He also used two directions, as Gauss and Weber did, forward versus reverse current and two intensities. So he had plus three volts, plus one volt, minus one volt, and minus three volt.

Four different current values which could be exchanged.

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Quadruplex telegraph used such a system and continued to be used into the 20th century. Fine grained differences lead to difficulties on the receiving end. The capacity of a communication system can be defined using these two very simple ideas: First, how btc 1 semestro egzamino data symbol transfers per second? Which we called symbol rate.

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Second, how many differences per symbol? Which we can think of as the symbol space. And we can call this s.

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The message space is simply the width of the base of one of these trees. It defines the total number of possible btc 1 semestro egzamino data one could send given a sequence of n symbols. Channel capacity of a given channel is the highest information rate in units of information per unit time that can be achieved with arbitrarily small error probability.

Informacijos kiekio pamatavimas. Markovo grandinės. Paskaitos: 1 Measuring information 2 Markov chains Information measuring is based on the minimum number of questions btc 1 semestro egzamino data define the message or the height of the decision tree, and since it is usually transmitted as binary digits, we can shorten this and call our unit the bit, instead of binary digit. It is calculated as the logarithm of the number of possible symbol sequences.

Markov proved that as long as every state in the machine is reachable, when you run these machines in a sequence, they reach equilibrium. The concept of modeling sequences of random events using states and transitions between states became known as a Markov chain. Informacijos entropija Paskaitos: 1 A mathematical theory of communication 2 Information entropy InShannon used Markov models as the basis for how we can think about communication: Imagine text written in letters A, B, and C.

You notice As seem to clump together, while Bs and Cs do not. We start anywhere and pick a tile, and we write down our output the first letter Then we move to the cup defined by the second letter. We pick a new tile, and repeat this process indefinitely Notice that this sequence is starting to look very similar to the original message, because this model is capturing the conditional dependencies between letters.

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Next, Shannon applies this exact same logic to actual English text, using statistics that were known for letters, pairs, and trigrams, etc. He shows the same progression from zeroth-order random letters to first-order, second-order and third-order kaip sekti bitcoin adresą. Entropy or H, is the summation for each symbol of the probability of that symbol times the logarithm base two of one over btc 1 semestro egzamino data probability of that symbol.

Entropy is maximum when all outcomes are equally likely. The fundamental idea is that, if the entropy of an information source drops, that means we can ask fewer questions to guess the outcome. Kompresijos kodai ir klaidų korekcija. Paskaitos: 1 Compression codes 2 Error correction When we represent information, such as an image, digitally, it means we must slice it up into tiny chunks.

This allows us to send an image as a sequence of color symbols, and these colors can be represented as unique numbers, using some code.

David Huffman famously provided the optimal strategy, which he published inand based on building a binary tree from the bottom up. Huffman Coding: First, list all symbols at the bottom nodes. Then we find the two least probable nodes, in this case B and C, and merge them into one, and add the probabilities together. Repeat with the next two least likely nodes, and continue merging until you have a single node at the top.

Finally, we label the edges in this tree with 0 or 1 in any order. The code for each letter is just the path from the top of the tree to the given letter. Claude Shannon was the first to claim that the limit of compression will always be the entropy of the message source.

As the entropy decreases, the ability to compress increases In the s, Richard Hamming designed a method which could automatically detect and correct single bit errors, without interrupting calculations. A parity bit is a single bit which is added to the end of a message, and indicates whether the number of ones in the message is even or odd. If a single error occurs, the receiver could then detect it, because the parity bit will no longer match.

However to detect crypto prekybos programa correct single errors, Hamming needed to add more parity bits to identify the error location. This leads to his seven-four code, which adds three parity bits to each block of four data bits as follows: First we start with the three parity bits, which can be represented by a circle. The btc 1 semestro egzamino data data bits are placed inside these regions in a specific order. To calculate the parity bits, we look at each circle one at a time, each containing three data bits.

This system can automatically correct single errors with a simple rule: If a single error occurs, two or more of the parity bits will be incorrect, and wherever they intersect is the location of the error.

All error-correction codes increase the size of the source messages slightly, at the expense of automatically correcting errors. Claude Shannon used this idea of redundancy to redefine the capacity of a communication channel, because as the noise on your channel increases, we must increase the amount of redundancy to communicate error-free.

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This must then decrease the effective amount of information you can send per unit time. SETI projektas Paskaitos: 1 The search for extraterrestrial intelligence The modern search for extraterrestrial intelligence, or SETI, began in with two Cornell physicists, Giuseppi Cocconi and Philip Morrison Researchers assume that any intelligent civilization will have discovered the ability to transmit radio waves.

At the first SETI meeting inJohn Lilly proposed that researchers study dolphin languages to help them learn more about what extraterrestrial signals might be like. Flat slope on graph However, as children learn the language of their parents, structure is imposed on our speech patterns. If we plot all sounds by how often they appear, the slope of this btc 1 semestro egzamino data converges towards a 45 degree angle, or a -1 slope on a log-log chart. Even more surprising is that this pattern also emerged when studying dolphin communication.

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Doyle and McCowan calculated the entropy for different depths, or orders, so single words is first order, groups of two words is second order, groups of three words is third order, and so on. Then they plotted the value of information entropy against this depth.

For adult humans, as we may expect, they found that the information entropy decreases as the depth increases. Amazingly, Doyle and McCowan did the same thing with dolphin languages, and found the same pattern.

Binomial Coefficient: Mean Expected value of X : Variance deviation : A binary symmetric channel or BSC is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit a zero or a oneand the receiver receives a bit. This channel is used frequently in information theory because it is one of the simplest channels to analyze.

This result was presented by Claude Shannon in and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley. Šaltinio kodavimo teorema. The source coding theorem shows that in the limit, as the length of a stream of independent and identically-distributed random variable i.