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Published: Monday, 07 October 2024 00:05

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Integumentary System:

Integumentary system consists of skin and appendages as hair, nail. It also includes glands that generate sweat. The cells on top layer of skin as well as nail, hair, etc are dead cells.

Khan academy => https://www.youtube.com/watch?v=4zKjzl0futI&list=PLBWKfzsMAETxjVs5C_-vdYhZGIvQzIzfO

Skin:

Skin is impermeable, meaning it can't allow water to get in the body via the skin. Skin has multiple layers.

1. Epidermis => The first 5 layers of skin. and are called strata or stratum. They are all keratinocytes or cells with keratin. The top 2 layers re dead, while next 3 are alive. These layers don't have any blood vessels as our nutrients and oxygen come from below, and hence it's harder and harder to get to the top cells. Hence top cells starting going dead.
   1. corneum: These are 15-20 layers of these cells which are flat cells. Word comes from "coroner's office" or where dead bodies go. This is the layer that gets shed from our body. Reptiles shed this layer in one piece, but for humans, this layer is in very small pieces that fall off our body w/o us seeing them.
   2. lucidum: These are dead cells. They lose their nuclei and other organelles.
   3. granulosum: They are keratin handling cells. These releases lamellar bodies, which provides the lipid layer that makes our skin impermeable. These cells work very hard, and so they are dead by the time they move to the upper layer or lucidum.
   4. spinosum: This is a spiny layer. The cells here are keratinocytes. The cells here overlap with each other, and the overlapping area is called desmosome. When we have less moisture or water in our body, these cells lose water and become shriveled. This causes them to become spiny (in star shape). There are also langerhans cells here, which provides immunity as it eats external invaders.
   5. basale: It's called basale, as it's the basal layer or the bottom layer. The cells here are keratinocytes (cytes mean cells). Rapid cell division happens here. Skin color comes from here. These cells are called melanocytes. This cells make special pigment called melanin. People with any skin color have same number of melanocytes, but the amount of melanin produced differs. Darker skin ppl have more melanin pigment in this layer.
2. Dermis => The next 2 layers of skin are called dermis. Both the layers have connective tissues (CT), i.e kind of tissues that hold bones to muscles etc.
   
   1. Papillary dermis => It has loose CT, It's the 1st layer that has blood vessels. It has arterioles coming in, branching to become capillaries to transfer oxygen, nutrients to cells via diffusion to cells surrounding it. They finally join back tobecome veins, which carry deoxygenated blood back to heart, This layer also has nerve endings to feel touch/pain etc. The cell body for this nerve starts somewhere depper in Hypodermis layer. The nerve ending passes thru the Reticular dermis and ends in this layer.
   2. Reticular dermis => This has thicker, dense CT. It has tons of glands to secrete our sweat. It also has hair follicles from where the hair grows, and protrudes out from our top layer of skin. A muscle, arrector pilli muscle is attached to the follicle, which alows our hair to stand up )giving us goosebumps). This is involuntary muscle, so we have no control. It's more important for animals, where these muscles make hair stand up in cold weather. That allows warm insulating air layer embedded in the hair that gives warmth. This muscle is a vestigial organ, as it's there but is just a left over from our evolution. There are 3 types of sweat glands in this region:
      1. Holocrine glands => These are in the face, chest an back. They release sebum, an oily substance. They lubricate skin,which slows bacterial growth.
      2. Apocrine glands => These are in nipples, armpits, groins, etc. They are also called emotional glands, as they are released when are in stress, etc. They develop around puberty. These are used in animals to attract mates. Not so much in humans.
      3. Merocrine glands => They are found in rest of the body and are most common sweat glands. It's mainly water and salt that comes out from these glands.
3. Hypodermis => Hypo means below, so this surface is just below the skin. It's also called subcutaneous layer. This layer has mostly fat. It's not part of skin. Muscles and bones sits below this layer.

In a hot environment, blood arteries relax. Relaxing blood vessels allow more blood to flow. They have RBC, WBC etc which bounce against the walls and transfer the energy to the walls of skin so that internals of the body gets cooler. Reverse happens when the it's colder outside, where arteries contract.

Burns: 1st, 2nd or 3rd degree burns are characterized by what layer of skin cells have burned. Buring of epidermis layer is 1st degree. Causes reddening of skin and lot of pain. 2nd degree burn is n=burning of Dermis layer and doesn't cause any pain as nerve cells themselves get burned. 3rd degree burn is burning of hypodermis and muscles/bones below it.

Hair and nails:

Hair and nail are comprised of cells. But they are not living cells, but dead cells. The only living cells in nails/hair are the cells at the root of these. As the cells die, they are pushed up by new living cells being formed.

Hair and Nail structure => https://www.youtube.com/watch?v=9zh-7hIiP3Q

Nails => nails are found in epidermis layer, with Nail root originating from there. Nail is actually part of epidermis. Nails are made of thick keratin, which are dead cells packed with keratin. Basale layer starts the growth process, with keratonocytes moving up and getting dead. Some of these move to the top of skin, while move sideways giving rise to nails.

Hairs => Hair is over all of our body, though the hears in some part as head grow lot more.Hair grows from the dermis (2nd layer of skin) and not from Epidermis. Hair follicle or hair root is in Reticular dermis as mentioned above. Hair grow about 1.25 cm/month (about 1/2 inch). That's why you need haircut every 3 months !! Hair shaft is the long pointy part of hair that goes thru the dermis, the epidermis and then protrudes out. HAir shaft is also all deead cells filled of keratine.

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Published: Saturday, 05 October 2024 00:24

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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.

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Published: Wednesday, 02 October 2024 22:36

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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/

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Published: Sunday, 15 September 2024 15:25

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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.

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.