What is Differentiation?

I am going to explain what is differentiation. I will explain it with a real life example. Suppose you are driving a car and you are climbing a small hillock, but you have put second gear all along and constant push in the pedal. I want to know what is the acceleration of the car at any given point. Speed changes as you move along, because when you climb the hill, speed is going to decrease, because gravity pulls the vehicle. When you reach the top and climb down with the same gear, the speed is going to increase, again because gravity pulls you. We will see it in a diagram
 
Suppose the car starts at the speed of 9 Kilometres/Hour ( For convinience ) from the foot of hillock and in 3 hours it reaches the top of the hillock. Now what differentiation is doing here. Differentiation helps you to find the acceleration of the vehicle at any point in the journey. Acceleration is nothing but how rapidly the speed of vehicle changes.

Now we will get into mathematics,
At point A, suppose the car starts at a speed of 9 kmph, which is at the bottom of the hillock. Supposing we are giving a certain push in the accelerator, speed keeps on decreasing and at point B, the car has stopped, we assume that it stops at the top of the hillock. After that, the speed starts increasing, because gravity increases its speed. If we put this graph in a mathematical equation, it would be y=(x-3)^2, where y is speed and x is time. The acceleration of the vehicle at any point is the slope of a tangent on that particular point.
Suppose, we want to calculate the acceleration of the vehicle after 2 hours, we have to draw a tangent at the intersection of x = 2 and the parabola. (Tangent is a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point. Parabola is name of the curved graph.) The slope of that tangent is the acceleration of the car at that point. It is tedious to find the acceleration of the vehicle by drawing tangents and graphs. So guess, who solves it. Differentiation. If we differentiate an equation like this parabola, it will give a general formula, which will tells us the acceleration of the car( change in the speed of the car) at any point in time.
More mathematics,
We will study the graph, at Point E, the slope of the tangent to the graph is high and when it reaches the point C, the slope becomes lesser and lesser and it becomes 0 at point B. Again it starts increasing. 
Now we will try to differentiate this graph y = (x-3)^2 using graphic method, to actually understand why we get the differentiation formulas. If we differentiate this parabola, what we get is the general formula which tells about slope( acceleration) of the parabola at every point, as x ( Time) changes. We will plot three points in the parabola and find the slope at that three points.

We know that the slope of the tangent decreases slowly from point E to point B, where it becomes 0. So, there must be some point in the parabola, between point E and B, where the slope of the curve becomes 1. Plot a triangle, such that the adjacent side ( Time axis ) and opposite sides ( Speed axis ) are equal, and the hypotenuse side ( Tangent ) touches exactly at one point in the parabola. By trial and error method, we can find the point at which x and y are equal and solves the parabola curve. i.e if we substitute x and y in the equation y = ( x - 3 )^2, the equation solves. Since the opposite and adjacent sides are equal, the slope of the hypotenuse side is exactly 1. Since hypotenuse side touches at only one point in the parabola, it becomes the tangent to the curve at that point.

If we plot a line with x axis as time and y axis as slope of the tangent of the parabola at that point, we will get the following equation y = 2x - 6. [ Note : We can find that from equation y = mx + b, where m is slope. Since we know 3 points in the line, we can form the equation. ]

If we differentiate y = ( x - 3 )^2 , we get the same equation dy/dx = 2x - 6. So differentiation is nothing but rate of change. Why do i need a rate of change of speed ( acceleration ), because it will come handy in lot of places like launching a rocket. we need to know and adjust acceleration to put our satellites exactly in the orbit.

We will get into sine curve
If we plot rate of change of sine curve ( i.e slope of tangent to the curve ), naturally we get a curve and it happens to be cosine curve.
 

Silly idea for little cents

I just thought of a silly idea solving a simple problem. How to deal with paisas or cents, when you don't have many coins. It may be applied while buying bus tickets, in giving change to petty shops or wherever you need to give change. The idea is to start a wallet or add this feature to already existing wallet. Just reduce the security checks, when we are using the wallets of change. Just load the change wallet with multiples of 100 rs, if in India. As long as there is money in change wallet, you can use it, without actually transferring any money. Suppose i load my change wallet, with 100 rupees. It goes to the common change wallet. I board a bus, conductor says 13 rupees, you give him 10 rupees in cash and 3 rupees through change wallet or 13 rupees through change wallet. To transfer money just connect the device of conductor and passenger, with whatever technique you use. Bluetooth or simple taps, whatever. Then conductor types 3 rs in his device and receives a 3 digit code. Passenger types the code in his device. 3 rs transfer. Yes or No. Press Yes. That's it. Money transferred. Conductor can also give change the same way. Actually only digital money. There is a common change wallet, which monitors all transactions, but transfers actual money, only when you need it. To ur Bank account or main wallet. So i have 100 rs while i start a day, i go to market, buy some vegetables, do 5 transactions, board a bus 2 transactions. Spend 23 rupees. Collect 13 rupees. Net value 90 rupees. No need to encash it. Use it tomorrow. No actual money transfers, only virtual money.

Balancing the loss caused by Non- Performing Assets in banks.

This is a hot topic and i have a solution to this problem without getting into the numbers, which needs research. So first, if a bank lends a loan to a firm, it should be categorized according to low risk, high risk and the prospects of its growth of different sectors. The idea is to put a percentage point, which i would call Risk- Profit Share Percentage Point(RPSP) or whatever is apt, based on that research. RPSP can be calculated every year, by a separate entity or a consortium of banks. So, if we put this RPSP as 2%(needs research) to say mining industry. If a mining company gets a loan from bank, it has to pay RPSP percentage along with the interest to the bank, only if it makes profit. If it makes loss, this RPSP percentage is exempted. If it goes for Insolvency code, also RPSP waived, bank even makes haircut. This RPSP will be high for a risky business. This RPSP will be purely based on Net Profit and how much the loan contributes to its whole asset. So, if a company makes profit, we get a little percentage to compensate for the loss if a company goes bankrupt.

How to deal with fake news in social media

My idea may not be profound or a complete solution. Just a direction I thought of. So basically no news shared in social media like Facebook, Twitter or even YouTube can be strictly classified as fake or not. We can only facilitate a authenticity debate. Coming to the idea. First, if somebody posts a video or something, he has to classify on what topic he is posting, like US presidential election or simply about a jelly. Like politics -> US -> Trump. Or food-> jelly -> companyA. The topic posted on will have Trump or companyA as title. Other details will go to a consortium of companies or organisations who has a foothold on social media. Once a news, considered fake or not is posted in social media about companyA, it will be notified to companyA. You may ask there may be huge amount of news posted about companyA at a particular time. So, the posts which is highly liked or shared is all that the company is bothered, not about posts which has a few sharing. There will be descending order of most shared posts about companyA. Start from the most shared to the least shared. So the idea is once a post is identified belonging to a company, the company will be notified about it, it will be screening it, if it finds the news fake, it has to start a "authenticity debate". So every post will have two more icons, "originator" or whatever you call the guy who originally posted it, not somebody who simply shared it, and " authenticity debate". Authenticity debate will be only between originator and companyA, otherwise if u include everybody, it will be a trash. CompanyA can put videos, links or whatever to tell their viewpoint or put enough evidence to say the post is a fake news. This debate once done as approved to be over by both parties or once a time limit is over, will be shared again with the recipients with the debate. Because you may ask once the news is spread, it's already viewed. Only when you press authenticity debate icon, you can view the debate. Once the viewers view the debate, they can choose two options, fake or not. This option is Not to delete the post, but to show the viewers who are viewing posts from a particular guy, whether he is doing the job of putting fake news all the time. There will two coloured lines in every post from this guy, indicating accumulated viewers scoring his authenticity and another all organisation scoring his authenticity. You can ask what if someone creates a fake page for every fake news. There is no credibility to his news as indicated by his coloured line and also you have to again add whole lot of people, to again spread fake news.

World without remembering passwords

This technology I am going to tell is based on bio-metric with more research to make it more robust. So first you need to have a wrist band or watch or health band in your hand. This band will identify with the owner based on biometrics like colour of your skin, complexion, grip on your hand, hair on your hand, length of hair as it grows, thickness of hair, distance between two hair strand, position of hair strand, pulse in your hand and new biometrics which can be tested in ur hand. In the future, I hope they scan your DNA. First we will consider offline scenario. So, when you are configuring Microsoft Windows, first you need to sync it with Microsoft watch ( hopefully soon), once you are done, there will be a password generator app in the watch as well as in Windows. It will generate password which will change every 2 minutes. Different algorithm for different users. You can update and change password generators any time. You can update only both at a time and keep it in sync. So every time you want login. Open Microsoft app in the watch. Ask for password , it will check your biometrics if found matching, it will generate a password and give it to you. Login. Online is much better, because you don't need to worry about whether password generator hardware is broken or not. In the future, may be there be a common password generator for mail, Internet banking and on and on so you install the app in your watch you click your intended option like hotmail, it checks your biometric and generates a password. Same as before. You can also make this password entering automatic. No need to manually enter. Even if loose ur watch, nobody can use it. You will be well aware if u have lost the watch, than cellphones. You can check the liveliness of your hand, whether it is live tissue or fake substance, video or whatever by asking the user to press the top of the watch at a point displayed by a compass on the screen. Campus will point to different points on the circumference during each check. Capture the picture and the video to check the liveliness of the hand.

If you say that it is possible to hack a watch. Let's make the watch simply a device to get your biometrics, it can work only online. Whenever you need a password, your device will take a picture of your hand and collect liveliness data. It simply sends the data to the server. Server holds all the biometric data. You can't hack a server, that much easily. It gets hardware-software combo information of the watch which will itself change every 10 minutes, not revealing anything about it to the user and biometrics. This information is a combination of software and hardware. This software uses thousands of algorithms, which changes from watch to watch and time to time. So the server compares biometric and encrypted hardware-software combo info with server data and sends you a password, which will last only 10 minutes. Even if you bypass this, which is impossible, I guess, the server will first send a beep signal to the watch, whenever some login happens, and only if you press a button in the watch, will a login happen. We can even set the time how much time a login last, before session expires. If you set half-an-hour, a small drop-down box comes every half-an-hour and asks for the current password. If you fail to provide latest password, it will logout. Also, if you want to change a setting, like time limit for logout. You have to enter new password and this will be generated immediately without waiting for 10 minutes. I think this is already existing procedure to ask password again. Only difference is a new password is created.

So basically, there is always a race between hackers and software producers. Who runs ahead will be the winner. If u are complacent and stand in a place, certainly one day hackers will run ahead of you. Software should always evolve with the time. No technology is unbreakable beyond a certain time.

Suppose military wants to use this technology. And u r caught in enemy territory with this watch, you have to utter a code( whatever u set), like AFD25, it will permanently lock the watch. Microsoft can even develop custom watches, which looks like ordinary or luxury watches, with this technology, for a premium fees for different needs, as required.

Instant Banking

In this idea, we can explore a new concept, never before tried in banks with currency notes. Here, Customer who wants to deposit from small amount of money like 100 rupees to 10,000/day can use this facility. The amount to deposit should be a single note( Notes of Rs.100,Rs.200,Rs.500,Rs.2000). A single customer can deposit up to 5 notes in a day.
First, the customer has to install Mobile Banking App in cell phone. The Mobile Banking App will have all the details of the customer’s account. In that App, a new option for scanning currency notes has to be provided. The App scans the currency note, the customer wants to deposit. App will take a picture of the currency note and reads the currency note number. It verifies the note number by asking confirmation from the customer. Currency Notes picture and number will be sent to Bank’s Central database. After this, the customer should go to the bank and simply deposit the currency note in a specially designed Currency Collector Machine. This Machine will receive currency note numbers from central database, updated every 5 minutes. When a customer feeds the Currency Note he has scanned in Mobile Banking, Currency Collector Machine simply scans the note and checks whether the note is not fake, not damaged. Then, checks if a match is found in the database, displays the name of the Account Holder in the display attached with the device. If Name is correct, the customer presses ok button. Then, the Transaction is approved and a confirmation slip with account number and a transaction number is ejected. The customer takes the slip and leaves. Once the transaction is approved, the Currency Note Number will be deleted from the bank’s central database and the note can be recycled for future transactions. If for some reason, the Currency note did not match ( the only criteria for approval), the note is ejected and returned back to the customer. Fake notes can be confiscated. Once approved, account will be updated with the money deposited within 5 minutes. Approval through sms will be sent to the account holder’s Cell Phone. This whole process will take maximum 10 seconds per transaction. There is no necessary for different banks to hold a common centralized database. Each can have it’s own separate Central Database. Because, even if same note is scanned in different banks, it has to be deposited in a bank to make the transaction complete. Once a Customer, scans a Currency Note in their mobile App, they will be allowed to hold on to the note for a maximum of 5 days. After that, the App will delete the hold and he has to scan again, with the Currency note (Same note, earlier used or a New note. It makes no difference). If a note is
scanned in a particular bank’s mobile App in an particular account, the same note will not be allowed to be scanned in a different account in the same bank. For recycle, either the time period of 5 days is exhausted for the first scan or the Currency Note is deposited and approved by the Currency Collector Machine.

Train Track Anti-Tamper System

This system can be implemented without centralized monitoring. Basically a part of track between two nodes is tested by sending a signal from one node to other and receiving it back and testing whether signal is tampered or not. It avoids accidents, in case miscreants damaged the tracks or it got damaged for some other reason. 

So we will start with a train track that has S – Station and A,B,C,D and so on are consecutive nodes. 

There are four types of signal in this system.

1.Test Signal(TS) – which tests the portion of the track in which the signal is sent, whether track is tampered or not. It does it by sending a signal from A to B, then from B to A. If A got original signal, test is successful.

2.Arrival Signal(AS) – which informs to node left to it( in case of signal arising from Station) or node which is at second position left to the originating node, that the train has already arrived at the originating node and has started its journey past the node. This signal triggers further action by receiving nodes. If a train crosses a node, which exhibits Pass Signal(PS), it is compulsory to send  a arrival signal to the node which is at second position left to it.

3.Distress Signal(DS) – which finds that Test Signal(TS) sent by a node has not been received properly back by it. This says that, that particular part of track is tampered. This  Distress Signal(DS) is always sent by a node to the node right of it, so that, train is stopped before hand and enough time is provided to the train to put a brake.

4. Clearance Signal(CS) – which informs the node that sent the Test Signal(TS) has been received properly back. This says track is not tampered. This Clearance Signal(CS) is always sent by a node to the node right of it.

5. Stop Signal(SS) – which tells the train cannot move forward, in case train is in station. If the train is moving, it has to stop before the next node arrives. Stop Signal(SS) can be generated only if a node receives Distress Signal(DS) from the node left to it.( Exception Station node)

6. Pass Signal(PS) – which tells the train can move ahead to next station. Pass signal can be generated  by a node only if it receives Clearance Signal(CS) from node left to it.

Figure -1

In the beginning, The Train Track Ant-Tamper System at node S, which is at the station sends a Test Signal(TS) from S to Node A and receives it back. The signal is randomly generated and changes every time. If the signal received back is same as the one sent, S gives a Pass Signal(PS) to the train. If the signal received back by S is not same, S will give a Stop Signal(SS). In a Stop Signal(SS), train can’t move ahead, if it is in station or should stop before reaching the next node( left to it), if it is a moving train. In case, S gives a Stop Signal(SS), explanation is in Fig 2. In case S gives a Pass Signal(PS), explanation is in Fig 3

Figure – 2

Here, S gives a Stop Signal(SS). So Train does not move.

Figure – 3

Here, S gives a Pass Signal(PS). So S first sends an Arrival Signal(AS) to A. Arrival Signal(AS) is a signal, which says train has arrived on that node, which sends the signal( in this case S) and has started moving. Usually Arrival Signal(AS) is transmitted to the second node left to it. But since the train is in station S, exception is given( node A receives Arrival Signal(AS)). Next to Fig 4.

Figure – 4

Here Since A receives Arrival Signal(AS), it sends a Test Signal(TS) from A to B, to check whether track is tampered or not. Whenever a node receives a Arrival Signal(AS), it sends a Test Signal(TS) to the node one step left to it. If A does not receive the same Test Signal(TS), next flow is explained in Fig 5. If A receives the same Test Signal(TS), next flow is explained in Fig 6.

Figure – 5

Here , A sends a Distress Signal(DS) to S, since same Test Signal(TS) is not received back by A from B, which means Track A to B is tampered. Whenever a mismatch occurs, the node should send a Distress Signal(DS) to the  node right of it( in this case S), to warn the train before hand about an impending danger. Since S receives a Distress Signal(DS) it puts on Stop Signal(SS) in that node.

Figure – 6

Here , A sends a Clearance Signal(CS) to S, since the same Test Signal(TS) is received back by A from B, which means track A to B is not tampered. Since S receives a Clearance Signal(CS), it puts Pass Signal(PS) in that node. Next to Fig 7.

Figure -7

Arrival Signal(AS) is always sent to the node which is at second position left from it. Only in case of train standing in station, Arrival Signal(AS) is first sent to the next left node, than again to the node at second position left from it. All signals are encoded by some method. When a Node sends an Arrival Signal(AS)( in this case S), it will send some form or other a number 2( for simplification), which will be received by the next left node( in this case A). On seeing an Arrival Signal(AS), the node ( in this case A) reduces the number by 1 and sends it to the next left node( in this case B). The receiving node(in this case B) checks the number, if it is 1, starts the further process. After sending Arrival Signal(AS), the train starts to move. Next to fig 8.

Figure 8

Here , B receives Arrival Signal(AS). So it sends a Test Signal(TS) to the next node C. If B does not receive the same signal from C, B sends a Distress Signal(DS) to the previous node A( Fig 9). If B receives the same signal from C, B sends a Clearance Signal(CS) to A.(Fig 10)

Figure 9

Here, A receives Distress Signal(DS), So A puts up a Stop Signal(SS) and the train reaching node A finds that A has a Stop Signal(SS), so it has to stop before next node B.

Figure 10

Here, A receives Clearance Signal(CS). So A puts up a Pass Signal(PS). The train on reaching A sees a Pass Signal(PS) and so crosses it. Whenever a train passes a Pass Signal(PS) node, it sends a Arrival Signal(AS), which is received by the second position node left from it. Next to Fig 11

Fig 11

Here , Train sends Arrival Signal to C

The process is repeated forever.

Happy Journey.