Function

[math]2x \; cM[/math] is [math]2x[/math] centimorgans, or a recombination frequency of [math](2x)\%[/math]. This means that there is a chance of [math]x\%[/math] per recombinant allele to 'exist' as a consequence of crossing-over. I'd just like to know which allele is recombinant and which is not.

Hello everyone

This would be my very last question concerning genetics.

Imagine a crossing of an organism with genotype AaBb, and an organism with organism aaBb.

Between the alleles A(a) and B(b) is a distance of [math]2x\; cM[/math].

What is the chance of getting an organism with genotype Aabb?

[math]\begin{tabular}{|c||c|c|c|c|}\hline & AB & Ab & aB & ab \\ \hline\hline aB & AaBB & AaBb & aaBB & aaBb \\ \hline ab & AaBb & Aabb & aaBb & aabb \\ \hline aB & AaBB & AaBb & aaBB & aaBb \\ \hline ab & AaBb & Aabb & aaBb & aabb \\ \hline \end{tabular}[/math]

Now, in order to solve the question, I have to know which of the alleles of both organisms are recombinant. How can I do this?

Thanks!

Function

Ah yes. Very well. Thank you. I will try to remmeber this for the exam.

Hello

Another question of my med school approval exam:

(Really don't know how to begin this one)

A fish swims 80 cm below surface. The breaking index of water is 1.33. The depth at which a person who looks perpendicular on to the water, right above the fish, sees this fish is

A. 33 cm

B. 60 cm

C. 75 cm

D. 107 cm

---

So I began with Snell's law: [math]n_1\cdot\sin{\theta_1}=n_2\cdot\sin{\theta_2}[/math]

[math]\Leftrightarrow -1=1.33\cdot\sin{\theta_2}[/math]

[math]\Leftrightarrow\sin{\theta_2}\approx -\frac{3}{4}[/math]

So [math]\theta_2 \approx 50^{\circ}[/math]

But I don't know if I am something with this?

Could someone help me on this one?

I might think that I could pick the point (0;-0.8) and rotate this over an angle 90°-arcsin(-3/4) until it hits the refracted 'light ray'?

Thanks.

F.

The force and distance act along the same line in this case so the cosine is not invoked.

 

That is the angle between the line of movement and the line of action of the force is zero and the cosine is therefore unity.

 

The positive or negative sign is relative to our statement of which way the energy flows or what force does work on what body.

 

This depends upon our statement.

 

In this case the question was what work does the oil do on the ball?

 

Well it doesn't. Where would it obtain the energy?

 

What actually happens is that the ball looses some potential energy in falling.

This energy is transferred to the oil as work done by the ball on the oil.

 

Since the oil does no work, we can call the energy it receives, by way of work done on it, negative work.

 

This idea is important because it is the cause of many errors in the application of the first law of Thermodynamics.

Ah, very well then, the energy that the ball loses and thus the energy the oil receives is 0.025 kg * 10 ms^-2 * (-0.4) m = -0.100 J?

But then the problem is that you say that "Since the oil does no work, we can call the energy it receives, by way of work done on it, negative work."

So the "work" done by the oil should be the opposite, thus 0.100 J?

If this is not the case, and 0.100 J is the amount of energy received by the oil, I'd say that W = E₁-E₂ = 0 J - 0.100 J = -0.100 J

It's getting rather complicated now, and I think I'll just stick with forces: it is still the frictional work, done by the oil which is asked... It seems best to me just to work with frictional force then, and distance

Oh dear, those are a lot of English scientifical words

I see how they are additive etc. and two inverse senses will cancel each other out, but do you have any idea what the meaning is of the crosses and the points under and above A, B, C and D?

Because I don't really believe those are conductors?

I'd say it has something to do with the distance from C and D to both the conductor with 20 A and the one with 5 A, but it doesn't make sense to me why the 'things', whether they are conductors or magnetic field lines, above and under C (and D) are opposite to each other?

Notice that, and I might've wanted to say this earlier, originally, only the 2 straight conductors, current and the dot line were given, not the crosses and dots! So this professor solved this exercise by putting these herself in this drawing. Why and how, however, is still not clear to me.

(& aren't your mistaken in the direction of the arrows in the magnetic field around your 5 A-conductor?)

Yes in the work equation delta x is a vector.

 

The work = force x distance ........... where x is the cross product

 

Thus the cosine is unecessary, since it is inherent in the cross product of two vectors.

 

If you keep the cosine the delta x has to be considered as a scalar, but then the cosine can be positive or negative depending upon its quadrant.

Ah yes.. So, cosine is actually more to calculate the magnitude of W, whereas vectorial product is used to define the sense of W?

What are the continuous lines with 20A and 5A by them?

Those are straight conductors

What sort of conductors do the cross and point represent?

Are they straight wires only or are they part of a loop?

And are they connected to each other?

I don't think the cross and point represent conductors, but the sense of the magnetical induction field (don't know if that's the same as magnetic field)

Believe me, the diagram isn't clear to me, either! The professor just mentioned something about: here 'it' (whereof I assume she meant the sense of the magnetical field) points in the plane, here out of the plane, ...

What the page literally says:

"MAGNETIC FIELD AS A CONSEQUENCE OF A CURRENT-CARRYING WIRE

Magnetic field: [math]\left|\overrightarrow{B}\right|=\frac{\mu_0\cdot I}{2\pi r}[/math]

Unit magnetic field: [math]1\;T=1\frac{N}{Am}[/math]

[DRAWING OF THE RULE OF THE RIGHT HANDGRIP (relation sense B and I)]

[DIAGRAM]

The magnetic induction field is zero in

A

B

C

D"

There are two ways to look at this.

 

"Calculate the frictional work done by the oil"

 

Firstly does the oil receive energy or give energy?

 

If the oil gives energy the work done by the oil is positive.

 

If the oil receives energy the work done by the oil is negative.

 

Alternatively.

 

Work equals force times distance moved against that force.

 

The direction of the force applied by the oil is positive ie upwards, but the distance moved is downwards ie negative.

 

positive times negative make negative.

Ah, but of course! [math]W=F\cdot\Delta x\cdot \cos{\theta}[/math]

In casu: [math]W=F\cdot\Delta x\cdot\cos{180°}=-F\cdot\Delta x[/math]

How could I forget that

Is that cosine the key issue here? That I forgot that?

Or should [math]\Delta x[/math] also be a vector, instead of just a scalar?

Hmm... But the force, and thus also the work, of the oil would be pointed upwards, whereas the one of the ball would be downwards; considering 'up' as positive, the force, and thus also the work of the oil should be positive, as is my answer?

Hello

In my papers in preparation for the med school approval exam, there's an exercise I don't really understand: the professor who solved the exercise, failed to explain why the magnetic induction at the top of A is, as it is in the bottom, pointed in the plane of the paper (cross), same for B, and why it is pointed out of the paper under points C and D. (see drawing)

Asked is the point in which the magnetic induction is zero. I do understand that both conductors give the same magnitude of induction in C (which is the answer) but I don't get why the directions are opposed.

Could someone please clarify this to me?

Thanks.

Hello

A question in preparation of my med school approval exam:

"A small ball with a mass of 25 g falls with a constant velocity of 0.1 ms^-1 in oil. The frictional work, done by the oil if the ball has dropped 40 cm into the oil, is:

A. 0.100 J

B. 0.000125 J

C. -0.100 J

D. -0.000125 J

---

Here's how I'd like to solve this:

According to Newton's second law:

[math]\sum{\overrightarrow{F}}=m\cdot \overrightarrow{a}[/math]

Since the ball travels with a constant velocity, [math]a[/math] and thus [math]\sum{\overrightarrow{F}}[/math] must be 0.

As far as I'm aware of, there're only 2 forces influencing the ball: gravitational force [math]\overrightarrow{F_z}[/math] ("z" for "zwaartekracht", Dutch for "gravitational force") and frictional force [math]\overrightarrow{F_w}[/math] ("w" for "wrijving", Dutch for "friction"):

[math]\begin{array}{rccl}& \overrightarrow{F_w} & = & -\overrightarrow{F_z}\\ \Leftrightarrow & \overrightarrow{F_w}&=&-m\cdot\overrightarrow{g}\\ & \overrightarrow{W_w}&=&\overrightarrow{F_w}\cdot\Delta x \\ \Leftrightarrow&\overrightarrow{W_w}&=&-m\cdot\overrightarrow{g}\cdot\Delta x\\ \Leftrightarrow & \left|\overrightarrow{W_w}\right|&=&-m\cdot\left|\overrightarrow{g}\right|\cdot\Delta x\\ \Leftrightarrow & W_w & = & m\cdot g\cdot\Delta x\\ \Leftrightarrow & W_w&\approx & 0.025\; kg\cdot 10\; ms^{-2}\cdot 0.4\; m\\ \Leftrightarrow & W_w & \approx & 0.100\; J\end{array}[/math]

(Mind the approximation of [math]\left| g\right|[/math]: no calculators are allowed on the exam)

This is what I'd pick: answer A.

I'm afraid, though, it's a bit too.. logic.

Could someone review this please?

Thanks.

Function

So do you "feel" it when the phenomenon occurs, and then feel something else when during the phenomenon a metalish object is brought close to your forehead ?

 

Are there types of material that do not trigger it at all ?

The feeling is the phenomenon and occurs, so I found out, with most small objects

The most likely explanation is that it's psychosomatic.

I was afraid you'd say something like that... Sounds a bit like I'm getting mental

I think it'd be very interesting getting a ct-scan or mri while trying to trigger this phenomenon, whether it's psychosomatic or not.

Now, I must confess that I have experienced this also, occasionally (rather rare, actually), in bed, just trying to sleep, when nothing is near my forehead.

Hmm..

I start doubting:

If the recombination frequence is, let's say 20 cM, and in the mendelian, ideal square, 4/16 is not recombinant (e.g. crossing of GgVv x GgVv), so 12/16 is recombinant, then is the total chance to get Ggvv 20%*1/12 or 20%*1/16?

So, actually, this is my reasoning:

Of all F1-products, 18% is recombinant (something else than RRgg and rrGg)

Of all recombinants (since Mendel is in casu only having recombinants), 50% is what's being asked.

The total amount of what's being asked is thus 18%*50% = 9%.

But, let's imagine the crossing of AaBb x AaBb, with a distance between A/a and B/b of 20 cM.

Mendelian genetics:

AABB: 1/16

AABb: 2/16

AaBB: 2/16

AaBb: 4/16

AAbb: 1/16

Aabb: 2/16

aaBB: 1/16

aaBb: 2/16

aabb: 1/16

---

Now, you'd like to know how big the chance is to get, for example, Aabb, which is a recombinant.

On first sight, I'd say 2/16 * 20% = 12,8%*20% = 2,56%

But, in this Mendelian genetics, 4/16 is not recombinant! Do we have to take this into account?

So there are 16 F1-products, of which 12 recombinant. Of this 12, 2 have the asked genotype (Aabb)

So on second sight, I'd say 2/12 * 20% = 3,33%

1) Which is the correct one?

---

2) Is it, by the way, correct, that the total chance of getting a recombinant genotype, is 12/16 * 20% = 15%?

---

3) But then, what's the chance to get a non-recombinant genotype (i.e. AaBb)?

Is it just 80%? For there are 12 recombinants, of which 12 recombinant (you wouldn't say this, huh? ), so, as we stated, 12/12 * 20% = 20% recombinant, so 80% must be non-recombinant?

---

Thank you in advance for helping me understand genetics as I have to get it

Hello everyone

This is probably my last question concerning genetics.

It's a question about recombination frequence, and thus also the centimorgan (cM).

Given out of my book for preparation on the acceptance exam most of you probably already know the existance of:

"With tomatos, a red colour is dominant over a yellow colour. The allele for a big plant is dominant over that for a small plant. A farmer wants to optimalize his harvest. In the future, he'd like to get only plants that are both big and produce red tomatos. He asks you to do a test-experiment on his land. He gives you a seed that is the result of the crossing of a small plant of pure race for red tomatos with a big plant with yellow tomatos. Of this last plant, he's sure that it's the result of a big plant and a small plant, both of pure race. You decide to perform a testcross as first experiment. If you know that the genes for the colour and size are on the same, autosome on a distance of 18 cM, then what is, after your testcross, the percentage of big plants with red tomatos?"

(Sorry if there're lots of mistakes in this text, I translated it quickly)

Now, I know the answer is 9%.

On first sight, I'd just say 18%, which is wrong, so I started wondering how I could get to 9%.

So I drew a square for dihybride crossing: RRgg x rrGg.

In this square, I could see that 1/2 of all possibilities, working with mendelian genetics, are big plants with red tomatos (RrGg) (pretty logic: RR x rr always gives Rr and Gg x gg gives in 1/2 of all cases Gg).

And then I started reasoning: Mendel assumed that 100%*1/2 of all F1 are RrGg, but he didn't bring the distance between genes into account.

1/2*18cM = 9cM = 9% = the correct answer.

Is this way to solve it the correct way? In other words; is this correct:

[math]P(X)=P(X_{\text{mendelian genetics}})\cdot (\text{distance between the two alleles resulting in X})[/math]

Thanks.

Ta-ta

Function

P.S. Could anyone of the moderator team please change the title to "Morgan's genetics: the cM"? Thanks.

One more thing, just to be sure:

Imagine a recessive, X-linked disease.

Father is carrier of the allele, and must thus be sick. Mother is not carrier of the allele. Conclusion: all the daughters are carriers of the allele, and none of the sons are, and none of the children is affected by the recessive disease.

Reasoning: X_DX_D + X_dY_D = X_DX_d, X_DX_d, X_DY_D, X_DY_D

With (X/Y)_D a sex-chromosome without the disease causing allele, and X_d an X-chromosome with the disease causing allele.

Healthy dominates sick, so none has the disease, but 2/4 are carriers.

Correct?

 

I meant the affected grandmother and the unaffected Uncle. I counted that wrong yesterday.

 

Yes. In an X-linked recessive disease, any sons of an affected Mother will have the disease. The Y-chromosome does not compensate for this. If this disease were X-linked then the Uncle should be affected. That he is not means it is autosomal.

Ah, wonderful. I think I get it +2

Thanks!

 

You are right, this is a recessive trait, which means that the great-grandmother has two copies of the disease causing allele. If it were X-linked, the grandmother's brother would be affected as it is almost certain he would get a disease causing allele.

I'm afraid I still don't really get it. Why do you suddenly bring in a great-grandmother? I thought it was just the grandmother who has two copies of this recessive disease-allele? And nothing is given of grandmother's brother. He's not in this family tree. Perhaps you mean mother's brother?

If this is the case, I think I get it: uncle gets one of the two affected X-chromosomes of grandmother, so should have the disease (I just accepted this; is the Y-chromosome not affecting the result, even when it doesn't carry the recessive-disease-causing allele? I mean, will a X-linked disease always affect a male when his mother has two copies of the causing allele, even when he has a completely healthy father, resulting in chromosomes XdYD? (Xd is X-chromosome with causing allele, YD is Y-chromosome with no causing allele)), but he hasn't, so the disease is not X-linked but autosomal?

Hello

In preparation for the acceptance exam for Med school, inheritance is very important. I just discovered how I can see whether a disease is dominant or recessive.

There's only one problem: I don't know how to tell if the disease is so-called 'gender-related' (or X-chromosome linked).

Take the following example:

Healthy brother has an affected sister. They have an affected father and a healthy mother. The affected father has a healthy sister. They are the result of healthy parents. The mother has a healthy brother. They are the result of a healthy father and an affected mother.

I can tell this disease is recessive. I do this by reasoning as following: (please tell me if there's a shorter way)

Let's assume the disease is recessive and displayed by genotype aa. Healthy would thus mean a genotype Aa or AA.

Daughter has sickness: aa

Her brother (son): Aa or AA

Father: aa

Mother: Aa or AA

Should mother be AA, then daughter should also be Aa, which is not the case --> mother: Aa

Result: brother: Aa

Mother's father: aa; since mother: Aa, mother's mother must be Aa.

Result: mother's brother: Aa

Since father: aa, both his healthy parents should be Aa. Result: father's brother: Aa.

No problems are found, so the disease is recessive.

Affirmation: suppose the disease is dominant.

Daughter: Aa/AA

Brother: aa

Mother: aa

Father: Aa (since daughter must have an A)

Father's healthy parents: aa; since both his parents should be aa, he could not be Aa.

Result: the system is in error, so the disease cannot be dominant.

So, it's confirmed the sickness is recessive.

2 questions:

* Can this be done in a shorter way?

* How can I see this disease is not X-chromosome linked? I don't really get this part, because I'd say that it is X-chromosome linked, for both the daughter and her father have the disease. In some way, thus, I guess mother's mother must have something to do with it?

Thanks.

Ta-ta

Function

Hello everyone

Let me get straight to the point:

About every morning, we have dozens of grey/dark brownish worms or maggots crawling around on our terrace (blue/grey stone). In the afternoon, they all crawl in the corner of 2 walls, away from sunlight (I guess)... The morning after, they're all dead (they look black and dehydrated and much smaller), but another wave of worms/maggots has arrived

And so on...

They are 1-2cm long, look like them on the photo in the link in the post scriptum, but they're not as thick. Deriving from their behavior, I suspect they don't like warmth, for they prefer the cold bluegrey terrace stone and shade.

Temperatures here (Belgium) have been about 15-20°C the last few weeks, we have 2 cats catching almost every day a mouse (which we don't discover instantly; could this be the source?), and there are some birds coming each day eating seeds.

They are, what I'd call, a serious plague and we'd love to know what they are, where they come from, and what we can do against them.

Thanks.

Ta-ta

Function

P.S. here's the image

http://www.whatsthatbug.com/wp-content/uploads//2009/07/soldier_fly_larvae_compost.jpg

The notation for probabilities sort of depends on what exactly you're trying to say, how precise you're trying to be, etc.

 

As an example, take the case of rolling one six-sided die. Then our sample space is [math]\Omega = \{1, 2, 3, 4, 5, 6\}[/math]. Now say we're interested in the probability that the result of a single die roll (denoted [math]X[/math]) will be both less than five and even. As a shorthand, we might write [math]P(X \textnormal{ is less than 5 and } X \textnormal{ is even})[/math] or [math]P(X < 5 \wedge 2 | X)[/math]. If we were writing a paper or something, then we'd probably want to take [math]P[/math] as the function I described in your recent thread, and letting [math]A = \{1, 2, 3, 4\}[/math] and [math]B = \{2, 4, 6\}[/math], we'd write [math]P(A \cap B)[/math]. Of course, it's easy enough to see that [math]A = \{x \in \Omega \mid x < 5\}[/math] and [math]B = \{x \in \Omega \mid 2 | x\}[/math], so writing [math]P(A \wedge B)[/math] probably wouldn't get you lynched by the mathematical community, but it'd look a bit strange.

Ah, well... Very well explained. +1

Thanks.

So it's mostly appreciated defining the sample space and sets with conditions for the probability?

If you take a look at the laws of Boolean algebra and set algebra, you'll notice the logical and set operators share quite a few properties. This perhaps becomes clearer if you consider set builder notation, where we say things like [math]A \cup B = \{ x \mid x \in A \vee x \in B \}[/math] or [math]A^{C} = \{ x \mid \neg ( x \in A) \}[/math] (though for the latter, we'd usually say [math]x \not\in A[/math] instead). That is to say, we define our set operations in terms of combinations of sentences connected or modified by logical operators.

 

The difference, then, lies in what objects are used with each set of operators. The logical operators are used for combining or modifying logical statements, while the set operators are used for denoting various collections of elements from sets or their complements.

Now, for probabilities; let's define events A and B, then the probability of 'not A' happening, would be [math]P(A^c)[/math] or [math]P(\neg A)[/math], the probability of B and A happening = [math]P(B\cap A)[/math] or [math]P(B\wedge A)[/math]?

Your third and fourth equations should be [math]2527 = A \vee (A \wedge B)[/math] and [math]2234 = B \vee (A \wedge B)[/math], respectively, though I don't think Boolean algebra really works here, since it deals with truth values not general numbers. I think you should instead look at this in terms of sets and make use of the principle of inclusion-exclusion.

 

We know [math]|A| = 2527[/math], [math]|B| = 2234[/math], and [math] |A \cup B| = 6000 - 1846 = 4154[/math], so we just need to solve for [math]|A \cap B|[/math].

Ah yes, thanks

The result is thus 607.

Is there btw any difference between e.g. [math]\wedge[/math] and [math]\cup[/math]?

Hello everyone

Here's a question from the acceptance exam for Med school:

6,000 people undergo an ABO-bloodtest. 1,846 are not positive for antigen A, nor B. 2,527 are positive for antigen A, while 2,234 are positive for antigen B. How many are positive for both antigens?

First thing that came up in my head, was to substract

First thing that came up was Boolean algebra, where:

[math]6 000 = \neg(A\vee B) + A + B + (A\wedge B)[/math] (O, A, B and AB)

[math]1 846 = \neg(A\vee B)[/math] (O)

[math]2 527 = A\wedge (A\wedge B)[/math] (A and AB)

[math]2 234 = B\wedge (A\wedge B)[/math] (B and AB)

But there's a problem: [math]A\wedge (A\wedge B) = (A\wedge A)\wedge B = A\wedge B = 2 527[/math]

and

[math]B\wedge (A\wedge B) = \cdots = A\wedge B = 2 234[/math]

Which obviously isn't right. Can anyone help me on this one?

Thanks.

F.