Introduction and basics:

Motor Unit:

Motor unit is an alpha motor neuron and the muscle fibers it supplies. Motor units vary in size, smaller motor units supply few muscle fibers and larger motor units supply many muscle fibers. The motor units follow ‘All-or-None’ law. When a motor unit fires, it stimulates all the muscle fibers simultaneously.

For object manipulations we apply forces according to the object’s size. For example, picking up a coin and a heavy book involve different force levels. How do we grade this force level?

Supposing if we flex our elbow to pick a heavy book, are we applying the maximal force at once? Does the force level peak as we start picking the book?

Recruitment:

Here is where Henneman’s size principle come into play. The motor units are recruited in a graded manner – from small to large. Recruitment occurs across the motor units.

Rate coding:

Within each motor unit, initial force production is lower when compared to the later force production. As the rate of firing increases, ’summation’ effect takes over and builds over the initial force. i.,e initial small twitch like contraction will build over to produce a constant higher force contraction.

Ref: Henneman, E (1957) Science 126, 1345-1346.

When we use a measuring device in the lab to measure something, we need to make sure that our test is valid and reliable.

So what do they mean?

Validity:

Validity means our device measures what we want to measure in a fairly accurate way. How do we know that our device measures precisely? We might have some universal measurement and if our device shows a good correlation with that universal measurement, then we could say proudly that our measuring device is valid  So, what you do is basically compare your measurement/test with another valid test.

Reliability:

Reliability is the repeatability of our test. That is, how consistent is our measurement every time.

Example 1: Supposing our device is a weight measurement device and each time it shows a different weight, say 100 lbs one time and after 10 minutes 150 lbs, can we rely on that measurement? The test-retest is not reliable.

Example 2: Supposing we are using a new-goniometer-kind of device to measure the joint angle for an individual. Person A is recording 50 deg, while person B is recording 70 degrees for the elbow flexion of the same individual. Can we rely on this device? Each person is getting a different output.  The inter-rater reliability is bad.

The picture depicts the targets of an archer. The blue clustered targets show that the archer is way-off from the actual target (in our case, measurement) but is consistent. However, our measurements need to be close to the target in order to be valid. Therefore, reliability does not guarantee that our device measures fine. We need validity so that we can say that our device measures what we actually want to measure.

What is sampling frequency?

When we convert an analog (continuous) signal to a digital (discrete) one, the frequency at which we sample the signal is termed as sampling frequency or sampling rate. How frequent are we sampling is the sampling frequency. Supposing we sample at 1000 cycles  or units per second, then the sampling frequency is 1000 Hz.Either we can mention the digital signal by its sampling frequency or by the sampling interval. Sampling interval is the interval between any two samples. Here in our case (1000 Hz-sampling frequency), the sampling interval will be 1/1000 = .001 (1 millisec).

To find  a threshold in a one-dimensional array and plot the same in Matlab: Here is the plot you will get after running the program.

a=[1 2 4 6 8 12 15 -18 25 -35 3 4 8 -3 10 33];    % one-dimensional array

b=abs(a);  % rectifying the data

c=max(b);  % finding out the maximum value

m=min(a);

d=.7*c;    % finding the threshold value, say 70 percent of the maximum value

k=1;

for i=1:size(a,2) % size of the array

if b(i)>=d

k=i;

break

end

end

plot(a);

line([k,k],[c,m],’Color’,'r’,'LineStyle’,'-’,'LineWidth’,1);

Diffusion?

Arithmetic sequence:

If you take a sequence of numbers, the difference between any two numbers will be constant.

Eg: 2, 4, 6, 8, 10, 12, 14…..

Arithmetic series:

Sum of the above mentioned arithmetic sequence of numbers.

Eg: 2+4+6+8+10

Here is a question for u. How will you calculate the sum of the arithmetic series 2+4+6+8+10?

The formula is s = ((a₁+a_n)/2)*n, where a₁ is the first number, a_n is the last number and n is the number of sequence.

S = ((2+10)/2)*5 = 30

What if you want to read the second column from the two dimensional array given below. Two for loops – one nested inside will read it. 

Click on the following figure to get a clear view!

What about writing it in c??

 Here is the program.

#include <stdio.h>

int main()

{

int a[3][4];  //allocate space for 2-dimensional array

int i, j, p;

for(j=0;j<3;j++)  // to generate the 2-dimensional table – nested loops

{

for(i=1;i<5;i++)

{

a[j][i]=i;

printf(“%d “, a[j][i]);

}

printf(“\n”);

}

printf(“enter column number: “);  

scanf(“%d”,&p);

for(j=0;j<3;j++)

{

for(i=1;i<5;i++)

{

if (i==p)   // to print the rows in that particular column

{a[j][i]=i;

printf(“%d”, a[j][i]);

}

}

printf(“\n”);

}

}

The quickest way to remember the doubling time if you know the rate of growth (provided it is constant) is to remember this formula:

T₂ = 70/rate

You can ask me how did I get this. Its simple, just take the use of exponential function.  .7 is nothing but the natural log of 2 to base e.

Example: if you have $10,000 in the bank with a constant rate of growth, say 3%. So, when do you think you could get the double amount?

70/3 = 23.3 years. So, in 23 years whatever you’ve invested will double.

Supposing you are holding a pen statically. The weight of the pen is acting downward which is opposed equally with an opposite upward force by the friction force (F). The perpendicular force that acts across the surface area of the pen will be the normal force (N). At any given time, the friction force will be the product of the normal force and the coefficient of static friction (µ). i.e., F = N * µ.

If the coefficient of friction is high, like in a rough surface, then the normal force required will be less. If the coefficient of friction is very low, like in silky smooth surface, then the normal force will be high to compensate for the slippage.

To put it in other words, the coefficient of friction will be the ratio of the friction force to the normal force. µ = F/N (parallel force/perpendicular force)

It is the winter – The ground is covered with a white carpet of snow. You cannot wander outdoors because of the bone-chilling cold and the freezing water. You sit inside your thermal regulated house, sipping piping hot coffee and lazing around in front of your fireplace. Now tell me, how many of you have wondered about the poor tiny little birds that used to flock your backyards in the spring? Are they still out in the cold or have they gone elsewhere?

Looks like except for a few residential species, most of the birds are vacationing in the warmer south. Can you believe, in North America alone, 5 billion birds annually leave their breeding grounds to go south for winter? So, why do they migrate? It’s for survival – to survive from food scarcity and the harsh winter. Migration is probably the most amazing, inspiring natural phenomenon – Imagine a tiny little bird against the most ferocious elements of nature – it has to overcome the inclement weather, heat exhaustion, fiery wind, and other natural disasters to reach its destination.

Let me show you some of the perilous journeys these birds take. The Arctic terns breed in the arctic summer. They follow the coastline of Africa to reach the Antarctic in November and enjoy the summer there – a total distance of 10,000 miles – they do it twice a year, every year till they perish.

Take the case of barn swallows. Have anyone seen a swallow? It such a teeny-weeny little bird that weighs only a mere 20 g. It nests in the British midlands and go all the way to South Africa, an epic journey of 6000 miles, crossing the formidable Sahara desert that itself stretches around 1000 miles. Of the 5-6 offspring that start the journey, only one will return, a mortality rate of 80%.

Or take the example of bar headed goose. They travel from central Asia to the winter grounds in India – they cross the Himalayas at a height of up to 29,000 feet.

Coming to North America, the tiniest bird that you see in your backyard, the ruby throated humming bird has come from the Yucatan Peninsula crossing the Gulf of Mexico to breed and spend its summer here in the east coast. For that matter, most of the colorful song birds that you see and hear their songs like warblers, thrushes, tanagers, and the birds of prey like hawks, eagles, falcons and ospreys have traveled between 1000 to 8000 miles to breed in the Northern hemisphere. Most of them have wintered in central or south America.

Now that we are in Delaware, can we witness this bird migration first hand? Yes you can. The best place to watch the spring migration of the shore birds is to go to the Delaware Bay in May. Thousands of exhausted shore birds like red knots, sander lings, sandpipers arrive here to feed on the horseshoe crab eggs before continuing their journey to their breeding grounds in the Tundra and Boreal forests of the north.

The best place to watch the fall migration is Cape May. Here you can observe the migratory hawks and millions of songbirds. Here they concentrate in huge flocks to wait for the right weather conditions to cross the Delaware Bay to go south.

Now, next time in spring when you see a colorful bird or hear a heart-rending melodious song, please remember, these tiny little heroes travel thousands of miles every year against all odds just to ‘survive’.