Details
Published: Saturday, 05 October 2024 00:24
Hits: 329

Human cells:

Before we dive into human cells, let's look at basic cell in general.

Cells:

Cell is the structural and functional unit of life. Cells have genes in them that decides how the cell is going to grow over time, and pass it's characteristics to new cells that develop from it. Cells reproduce through a process of cell division, in which the parent cell divides into two or more daughter cells and passes its genes onto a new generation. Though almost all life consists of cells, some life such as Viruses are non cellular. However, whether virus should be considered living being or not is controversial. They have been described as "organisms at the edge of life"  because they possess genes, evolve by natural selection, and replicate by making multiple copies of themselves through self-assembly. However, viruses do not metabolise and they require a host cell to make new products.

We'll mostly be talking about uni cellular and multi cellular life. Before that we will learn a bit about cell.

Video on cell structure => https://www.youtube.com/watch?v=URUJD5NEXC8

There are two kinds of cells, both of which consist of Cytoplasm enclosed within a membrane and contain many biomolecules. All cells have 3 things in common => cell membrane (to protect cell), cytoplasm (a jelly like liquid) and a genetic material (usually within a nucleus which determines what the cell is going to be like). The 2kind of cells are:

  • Prokaryotes: Prokaryotes are single celled organisms that lack a nucleus and other membrane bound organelles (organelles are little organs within cells). The word prokaryote comes from the the word pro meaning before and karyon meaning nut o kernel. Besides the absence of a nucleus, prokaryotes also lack mitochondria, or most of the other membrane-bound organelles that characterize the eukaryotic cell. Prokaryotes are asexual, reproducing without fusion of gametes. Link: https://en.wikipedia.org/wiki/Prokaryote
  • Eukaryotes: Eukaryotes are single or multi celled organisms that have a nucleus. All animals, plants, fungi, and many unicellular organisms, are eukaryotes. The word eukaryote comes from the the word eu meaning good and karyon meaning nut or kernel. Besides the presence of a nucleus, eukaryotes also contain other membrane-bound organelles such as mitochondria and Golgi apparatus. Mitochondria is the main powerhouse of the cell. Eukaryotes developed around 2 Gya. Link: https://en.wikipedia.org/wiki/Eukaryote. Eukaryotes can reproduce both asexually through mitosis and sexually through meiosis and gamete fusion.
    • mitosis reproduction (asexual): In mitosis, one cell divides to produce two genetically identical cells.
    • meiosis reproduction (sexual): In meiosis, DNA replication is followed by two rounds of cell division to produce four haploid daughter cells that act as sex cells or gametes. Each gamete has just one set of chromosomes, each a unique mix of the corresponding pair of parental chromosomes resulting from  genetic recombination during meiosis.

Sizes: Size of atom is about 0.2 Angstrom. Small molecules are about a nm. Proteins are about 10nm, while Viruses are about 100nm. Single cells start from about 1um, while multi cellular organisms are upto few mm. This link shows relative size of cells: https://en.wikipedia.org/wiki/Bacteria#/media/File:Relative_scale.svg

Plant and animal cell:

Video in detail (Intro to cell structure) => https://www.youtube.com/watch?v=vwAJ8ByQH2U

Cells will need to talk to each other if they need to transport information. In between the cells, we have a fluid called interstitial fluid. Interstitial fluid is mostly water with other dissolved substances in it like salt, sugar, protein, waste etc.The fluid inside the cell is called cytoplasm, but inside is referred to as cytosol. The cell membrane surrounding the cell separates these 2 fluids, but allows mechanism for solutes (or particles in interstitial/cytosol fluid) to flow in or out of the cells.

Intracellular and Extracellular fluids => https://courses.lumenlearning.com/suny-ap2/chapter/body-fluids-and-fluid-compartments-no-content/

Cell Membrane structure => https://www.youtube.com/watch?v=fJfTDc3WzQ8

Cell Membrane is made of molecules called phospholipids. Read more about it in Biology section. The bilayer phosphid forms a very close knit structure so that no external molecules can pass thru, unless they are very small in size and non polar (by being non polar, they can get inside to the tail of phospholipd molecule which is nonpolar). Besides the phospholipd bilayer structure, a cell membrane contains few more structures:

  • Chloesterol => controls what can pass thru the cell
  • Proteins => They behave like openings in the cell membrane and control what bigger particles can pass thru them.
  • Carbohydrates => Involved in cell identification

Transport across a membrane => https://www.youtube.com/watch?v=J5pWH1r3pgU

Receptors:

These protein structure in the membrane that we saw above allow movement of solutes in or out of the cells. They are called as receptors. They are selective as to what they will allow to pass depending on the protein structure. A cell has multipe of these protein receptor and each is selective. Different kind of cells have different receptors, i.e heart cells have different receptors than lung cells.

 

 

 

Details
Published: Wednesday, 02 October 2024 22:36
Hits: 561

House Buying/Selling in USA

House Buying in USA is pretty relaxed process compared to buying a house in India. From start to finish on a house ready to move in,  you can move into the house in < 21 days. On a house that is going to be started on a new lot, it may take anywhere from 3 months to a year. House selling is equally easy. Let's explore the process.

Real Estate sites:

There are lots of real estate websites to start looking at houses. Few of the biggest ones that you start your search from are www.realtor.com, www.redfin.com, www.zillow.com, etc. They all have the same info, only difference is in the way they allow you to filter houses.

New houses vs used houses:

You should start the house search on your own. Look at the areas where you want to live, and the prices in that neighborhood. If the area is till developing, you may see new houses on sale too. My preference is to always buy a new house. 3 things in life that you never want to get used => Cars, Houses and Spouses !!

Reasons on why you should always buy a new house if possible:

  • New homes come stress free. Everything in the house is covered for a year (some cover for 2-3 years too). No matter what breaks, Builder will have it fixed for free.
  • You get a better price with new houses. Old houses are sold by people who are looking to make a profit. No one lists their houses to be sold for a loss. However, builders are willing to take a loss on a new house, especially if it' sitting on the market for quite some time. Their goal is to make cummulative profit. Even if they sell few houses at a loss or breakeven, it doesn't matter to them. Many times you will find "spec" houses, which are houses that the builder already built and is ready to move in. He doesn't have a buyer for it yet. In a down market, such houses sell for lower than market price. Everyday such a "spec" home sits on the market, builder has to pay for all the property taxes, utilities, maintenance, insurance, etc. So, it's in his best interest to sell the house asap.
  • First few houses in any new community being built are sold at lower prices than the houses which sell later. So, buy a house in a comunity which is just getting started. Builders will rarely reduce prices of houses selling later, as they don't want to ire previous homeowners who already bought houses in that community for a higher price.
  • Insurance rates on a new house are about couple of hundred dollars cheaper than on a used house.
  • Most realtor agents will give you a better cashback on a newer home than on a new home. See next section.

Agents:

The agent landscape is very competitive where there are more real estate agents than the number of houses that sell in a year. That means each agent is able to sell just 1 house on avg in one year. So, you can negotiate for cashback from these agents. Listing agent usually gets 6% commission on selling the house. The seller pays the commission, so buyer never sees the expense. However if the buyer also has an agent, then the selling agent splits the commission equally, resulting in 3% for each. Most of the times, buyer's agent will give 2%-2.5% cashback to the buyer, and keep 1%-0.5% to himself. This money can be put into the closing costs or can just be cashed out. There is no tax implication for this, as it's a rebate on the purchase.

Below realtor offers 2.5% on a new house and 2% on a used house. She's pretty reliable with rebate. Definitely inquire her and also shop around to see if you can get more cashback.

Link => https://texashomes2percentrebate.com/

 

 

 

 

Details
Published: Sunday, 15 September 2024 15:25
Hits: 561

Trignometry: Trignometry is a branch of Geometry that deals exclusively with triangles. You may wonder how come triangles have a whole branch of Mathematics dedicated to itself !! There are lots of things that's possible with triangles, and knowing triangles well forms the basis of Geometry.

We learned about drawing various triangles, finding angles of a triangles, and sides of a right angle triangle.

We can find all sides of a triangle given it's angles or vice versa. We need to know sine, cosine and tangent for that. We'll learn about right angle triangles and then move to other generic triangles.

Radians: So, far we learned that unit of angle is degrees. That is what our protractor also shows. One other unit of angle is radian. It's very widely used in scientific community, because many ratios cancel out nicely when using radian. 180 degrees is defined as π (pi=3.14) radians.

So 1 radian = 180/π degrees (approx 57.3 degrees). So, 1 radian of angle is an angle which is slightly less than 60 degrees.

Right angle Triangle:

For a right angle triangle with any one of the angles as Θ, we will have ratios of all 3 sides of triangle fixed, i.e if we make any other right angle triangle with this angle, that triangle will be similar to this triangle. Infact all such triangles will have same shape, they will just differ in the scaling. it makes sense to define the ratio of the sides for all right angled triangles for a given angle Θ on it's base.

Consider right angle triangle with sides a,b,c, where a=vertical side, b=base, c=hypotenuse, and angle Θ = angle b/w hypotenuse and base. Then we have six ratios that we can define between the 3 sides. Below we define those six ratios.

sin(Θ) = a/c  cosec(Θ) = 1/sin(Θ)  = c/a (aka cosecant)
cos(Θ) = b/c sec(Θ)    = 1/cos(Θ)  = c/b (aka secant) => cos was already used up, so putting co again sounds weird cocosecant, so we stick with secant
tan(Θ) = a/b cot(Θ)    = 1/tan(Θ)  = b/a (aka cotangent)

This is the definition for all 6 ratios. Sine, cosine and tangent are the ones most commonly used. There are tables that give values of sine, cosine and tangent for all values of angle Θ, from 0 degrees to 90 degrees. By looking at the table, we can figure out lengths or angles for any given triangle.

Few basics of terms above:

  • All 6 of the ratios are periodic. Sin/cos are periodic with period of 2π (360 degrees), while tan has a period of π (180 degrees).
  • Sin, cos are continuous while tan becomes discontinuous at any odd multiple of π/2 (90 degrees, 270 degrees, etc).
  • Cosine is just a shifted version of Sine, where the Sine function is shifted to the left by 90 degrees to form cosine

I've put the most common theorems for these 6 defn, and their relationship at 90, 180 and 360 degrees. It's easy to see these relations from the graph itself, or by using the formula defn of the  triangle

Link => SIN/COS/TAN waveforms and equations

There are lot of theorems that can be derived for these 3 equations defined above. Lot more theorems are on link below.

  1. sin2(Θ) + cos2(Θ) = 1 (This can be proved by Pythagaros therem: (a/c)^2 + (b/c)^2 = (a^2+b^2)/c^2 = c^2/c^2 = 1). Most IMP formula, one you can't afford to forget.
  2. sin(Θ)/cos(Θ) = tan(Θ) (this can be proved by dividing sin and cos eqn above)
  3. sin(Θ) = cos(90-Θ). Similarly cosΘ) = sin(90-Θ). This can be proved by looking at the right triangle, and finding sine and cosine for the other angle which is (90-Θ). OR by noting that cosine is a 90 degree left shifted version of sine. See link above.
  4. 360+Θ is same angle as Θ, as 360 is one full rotation and comes back to starting line. So, is 360*n+Θ where n is an integer number. So, all 6 definitions above give same result for 360+Θ, i.e Sin(360*n+Θ)=Sin(Θ), where n is an integer (+ve or -ve)
  5. For all other angles between 0 to 360 clockwise (treated as +ve), above equations are defined depending on whether base and height are +ve or -ve. Hypotenuse is always taken as +ve. Height and base are taken as +ve or -ve depending on X and Y coordinate. Similarly for angles going anticlockwise, we treat those angles as -ve, and again define all equations above the same way. These equations are defined in this way, so that the same sin, cos, tan eqn will work in all quadrants.
  6. Many more formulas, and definition for angles > 90 degrees and < 0 degrees are in "unit circle" link below: 
    1. One other imp formula is sum of angles: Sin(a+b) = Sin(a).Cos(b) + Cos(a).Sin(b). This can be used to derive Sin(a-b), Cos and tan sum/diff formula ver easily. This is harder to prove. One such proof is on Khan
    2. Academy => https://www.youtube.com/watch?v=R0EQg9vgbQw
  7. Cheat sheet for imp formulas => trig_cheat_sheet.pdf

So, we see that all 3 definitions above for sine, cosine and tangent are related to each other. If we know any one of the sine, cosine or tangent we can know the other 2 easily.

Unit Circle: We can also use a unit circle to learn these ratios. There is a unit circle that can be drawn. Then sin, cos, tan etc are just sides of that triangle inside and outside the circle.

Explained on this link: https://www.math10.com/en/algebra/sin-cos-tan-cot.html

 

Graphs of transformation of sin/cos functions:

So far we saw drawing Sin/Cos functions. However if we transform the eqn to be more generic like y = A*sin(B*x-C) + D, then sin/cos func is compressed/expanded + shifted up/down or left/right. It's similar to transformation of any function that we saw in earlier section. When f(x) gets transformed to A*f(B*x-C) + D, func shifts as well as get compressed/expanded. Exactly the same thing here with sin/cos. Below link explains well.

Link => https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/02%3A_Graphing_Trigonometric_Functions/2.04%3A_Transformations_Sine_and_Cosine_Functions

 

Inverse functions:

So far we saw drawing Sin/Cos functions. We have inverse functions for any given function.For ex, the inverse of square function is square root function, etc. For sin/cos/tan etc, the direct function converts from angle to a number. The inverse function gives us the angle back from that number. So, the domain of inverse function is from -1 to +1 and range is from -∞ to +∞. However since the forward function is periodic, the reverse func will give us multiple values of Θ for a given number. That violates the defn of func, which states that there can be a max of 1 Y value for a given x. To make it fit, we choose a range for inverse function so that none of the Y values are repeated. We define our inverse function only in this range. That's how officially inverse func for sin/cos/tan etc are defined.

Link => https://math.libretexts.org/Courses/Monroe_Community_College/MTH_165_College_Algebra_MTH_175_Precalculus/06%3A_Analytic_Trigonometry/6.01%3A_Inverse_Trigonometric_Functions

 

 

 

Drawing Right angled triangles:

It's important that kids draw right angled triangles. Then they should be able to figure out by themselves if they can draw a unique right angled triangle for a given angle. Following are cases where info is enough to draw a unique right angles triangle.

  • Given Any 2 sides of right angles triangle => Pythogaros Thm gives us 3rd side, and all 3 sides (SSS) gives us unique triangle
  • Given any one angle and one side of right angled triangle => Since 1 angle (X) is given, we can find out other angle (90-X). So, all 3 angles are known, and 1 side is known, so unique triangle can be drawn using ASA.

Ex: Draw a right angled triangle, with one angle=30 degrees. You can draw bunch of such triangles since length of any of the sides is not given. However, all these triangles are going to be congruent or similar to each other. Also, make sure the kids realize that the sides seem to have a fixed ratio to each other for a given angle. Make them find sine, cosine and tangent by measuring the lengths a, b, c and finding the ratios.

Ex: Repeat the exercise above with the other angle of the right angled triangle = 45 degrees. Again make the kid find out sine, cosine and tangent by measuring

Now, instead of drawing, let's try to find sine, cosine and tangent for special angles = 30, 45, 60. For angle=45, it's easy as the 2 sides are going to be the same (3rd side can be computed via pythagoras  theorem), so ratios can be computed easily. For angle=30, we can make a reflection of the triangle, so that the 2 triangles combined become an equilateral triangle. Or we can draw an equilateral triangle and cut it in half. So, each half becomes a right angled triangle and the 2 halves are equivalent triangles, so, base is divided in half. Height can be found out by employing pythagoras  theorem (h^2=a^2 - (a/2)^2 => h = √3/2*a.

For 0 degrees, the height of triangle is reduced to 0, so hypotenuse is equal to base. That gives us the values for 0. For 90 degrees, the base of triangle is reduced to 0, so hypotenuse is equal to height. That gives us the values for 90 degrees.

So, now we know to compute these for these important angles:

The easiest way to remember the basic values of sin and cos at the angles of 0°, 30°, 60°, 90°: sin([0, 30, 45, 60, 90]) = cos([90, 60, 45, 30, 0]) = sqrt([0, 1, 2, 3, 4]/4) 

We can use the trignometric identities discussed earlier to get sin, cos, tan for 15 degrees and 75 degrees too.

  • 15 degrees: Use Sin(A-B)=Sin(A).Cos(B)+Cos(A).Sin(B) => Sin(15)=Sin(45-30)=Sin(45).Cos(30)+Sin(30).Cos(45)=√2/2*√3/2+1/2*√2/2 = √2/4*(√3-1)
  • 75 degrees: Use Sin(A+B)=Sin(A).Cos(B)+Cos(A).Sin(B) => Sin(75)=Sin(45+30)=Sin(45).Cos(30)+Sin(30).Cos(45)=√2/2*√3/2+1/2*√2/2 = √2/4*(√3+1)

There are trignometric tables provided which lists sin, cos, tan for all angles between 0 deg to 90 deg. These tables are very useful to find out sides or angles of a right triangle.

 

Details
Published: Thursday, 22 August 2024 07:22
Hits: 254

Car Tire Change

You should always know how to change the tire of your car, when it goes flat. Most of the people have never changed tire in their life. So, when they get stranded, they have no idea of how to change one. Internet is of course not reaching there, so you are out of luck. Don't be that guy.

Find out where the tire changing equipment and the spare tire is for your car. Usually tire changing equipment is in the trunk of your car, under some hidden box, while tire is also in the trunk. Sometimes spare tire is put in the bottom of the car, when there's not enough space to put it inside the car. Watch a video on youtube on exactly how to change the tire for your car. Then practice it once on your car on one of the tires.You will thank yourself later.

Below is a video on changing tire on Toyota Sienna Minivan: https://www.youtube.com/watch?v=mvC0SrMZ4l0

Do the same for your car. This is a generic tire changing video: https://www.youtube.com/watch?v=0KDMdYww4VE

Happy Driving !!

 

Details
Published: Thursday, 08 August 2024 00:50
Hits: 404

World Assets

This article goes over all the assets in the world and the ownership of those assets.

ASSETS

sifma.org is a very good resource for global capital market. Link for assets per year: https://www.sifma.org/resources/research/fact-book/

You can also find a pdf on the right side that has lots of detail for each year. For 2023: https://www.sifma.org/wp-content/uploads/2023/07/2024-SIFMA-Capital-Markets-Factbook.pdf

Total assets ib the world may be found out by adding up the price of all assets in the world. It's hard to find data for the world, but USA data is readily available. US wealth (excluding housing) was ~$70T in 2023.

  • World stock market => ~$100T ($50T in USA). Assume most of it is owned by individuals, or finally goes to the individuals (i.e Pension funds, etc). About $0.5T of new equity is issued in the market
  • World housing market => No matter which country house prices everywhere are soaring due to cheap money supply. In US, total residential Housing asset is ~$45T (as of 2023), so we may guess that housing market may be close to stock market valuation. So, about $100T in housing asset (minus the amount of mortgage loan, but that will be paid off eventually)
  • Bonds => Bond market is $150T of
  • Cryptocurrency => These have added $2T or so to world assets as combined market cap is ~$2T as of 2024. Top 5 cryptocurrency comprise 80% of the market. They are all traded on stock exchanges just like stocks.
    • Bitcoin (BTC) = $1.2T or about 55% of market,
    • Ethereum (ETH) => $0.3T or about 15% of market,
    • Tether USDt (USDT) @$115B, BNB (BNB) @80B and Solana (SOL) @60B comprise next 12%

 

 

 

 

Wealth:

When it comes to wealth, developed economies have a lot of wealthy people. Though number of Billionaires reported as of 2022 is ~4K or so, I believe there are probably close to 10K billionaires in the world.

Billionaires by Country (US, China and India take top 3 positions)  => https://en.wikipedia.org/wiki/List_of_countries_by_number_of_billionaires

To be in the top 1% of the population in any developed country, you need to have ~$1M in net assets. In USA, you need about $12M to be in the top 1% of households (see in USA section).

Top 1% wealth threshold per country => https://www.msn.com/en-us/money/personalfinance/america-s-richest-1-s-staggering-wealth-and-how-it-compares/ss-AA1fbf0q

Total wealth owned by individuals reached $600T as of 2023. It keeps rising at 5%-10% per year. Total number of millionaires in world is about 100M.

Link => https://www.msn.com/en-us/money/markets/global-household-wealth-declined-in-2022-the-first-dip-since-the-2008-financial-crisis/ar-AA1fjuRf

 

More Articles ...

  1. Clock Gating
  2. Car brake change - DIY
  3. Past Imperfect Tense
  4. Participle form of verb