I was pondering this idea for a while and came up with another variation of itthat I find interesting. The core idea is same, we maintain two estimators overthe data set, the previous and the current one. But after the switching to thecurrent one (at the observation xk on the diagram) instead ofkeeping the previous one as static we still append new observations to it. Inthis way instead of the target window quantile estimation we get twoestimations, one for the bigger window and one for the smaller window, as onthe following diagram.

Having this in mind I was curious about another bit of code. For everyobservation the algorithm needs to find out to which interval the observationbelongs to. In the current implementation it boils down to many comparisonslike:


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This brings us to a question: if everything boils down to repeating the study a large number of times and getting different answers each time, can we reduce the range of uncertainty to something that could actually be helpful? Here is where 95% confidence intervals (CI) come into the picture. Means, differences between means, proportions, differences between proportions, relative risks (RRs), odds ratios, numbers needed to treat, numbers needed to harm, and other statistics that are obtained from a study are accurate only for that study. However, what we really want to know is what the values of these statistics are in the population, because we wish to generalize the results of our study to the population from which our sample was drawn. We cannot know for certain what the population values are because it is (usually) impossible to study the entire population. However, the 95% CI can help give us an idea. Whereas the 95% CI, like the P value, is also frequently misunderstood; here is an explanation. If we repeat a study in an identical fashion a hundred times, then 95 of the 95% CIs that we estimate in these studies would be expected to contain the population mean. So, by inference, if we examine the 95% CI that we have obtained from a single study, the probability that this particular CI contains the population mean is 95%.[6]

Explained with the help of an example, consider the RCT in which we found that the RR for a response to the study drug (vs. placebo) was 1.00 (95% CI, 0.55-1.83). We should not interpret this finding as nonsignificant; rather, we should consider that the most likely interpretation is that the drug is no better or worse than placebo, and that lower efficacy (to the most extreme and least likely value of 45% worse) and higher efficacy (to the most extreme and least likely value of 83% better) possibilities are also compatible with the data recorded in the study. The reader is once again reminded that statistical significance does not enter the picture anywhere.

Whereas a threshold for statistical significance could be useful to base decisions upon, its limitations should be recognized. It may be wise to set a threshold that is lower than 0.05 and to examine the false-positive rate associated with the study findings. It is also important to examine whether what has been accepted as statistically significant is clinically significant.

Although these assumptions are rarely true in the natural world,they allow us to calculate an expected allele frequency. Significantdifferences between the observed and expected frequencies indicatethat "something" (i.e. one or more of the above) is going on, andtherefore tell us that "microevolution"is occurring.

Joe Silverman's comment gives the method. (if the square root of A mod p is 0 you have any easy first step.... let $\gcd(A\ ,p^n)=p^j.$ If $j$ is odd, give up, otherwise let $A=p^{2k}B$ and find the $\mod p \ $ square root of $B$ (if it is a quadratic residue.)

Dickson's History Of Numbers Vol 1 has formulas that find modular square roots for powers of prime modula. See p215 for Tonelli's algorithm and p218 for Cipolla's algorithm. Dickson's work can be found online at

When something is known about $\Z_n$, it is frequently fruitful to askwhether something comparable applies to $\U_n$. Here we look at $\U_n$in the context of the previous section. To aid the investigation, weintroduce a new quantity, the Euler phi function, written$\phi (n)$, for positive integers $n$.

One can think of "injective" linear transformations as those that are good enough so that $T(v_1),\dots,T(v_n)$ forms a basis for the image of $T$. This means exactly that the image of each basis vector is again linearly independent. Another way of saying this is that $a_1T(v_1)+ \dots a_nT(v_n)=0 \implies a_1=\dots=a_n=0$. But, using linearity, we see that this is finding exactly the kernel of $T$:$a_1T(v_1)+ \dots a_nT(v_n)=0=T(a_1v_1+ \dots a_nv_n)=0$.

Follow the path forward while Gemini tells you some facts about the Grand Exhibition's history. When you reach the open area with the fountain you will be able to see the Exhibition up the hill. Check the staircase on the left side of the fountain to find a Dark moon Moonstone of the Covenant. At the top of the stairs are some enemies and the locked front door of the exhibition, but no items so we can ignore it and go back down the stairs.

Find a Dim Ergo Fragment by the lamp in the back corner of the plaza. Go through the gate near the lamp and you will find yourself in a small park with a tree in the middle. There are two swordsman puppets and a dog here, try and draw them out one by one rather than battling them all at once.

As usual, we are going to stand back, well out of his melee range. We are waiting to see two attacks: his weapon swing into overhead fist slam, and his full body spin attack. Both of these have huge lag time afterwards, and both advance forward when he uses them. Step back as he comes toward you, then lay into him with a few attacks while he stands back up. When you see him charging up his Fury attack, its best to just run away and wait for something else.

Go back to the staircase we ignored earlier and ascend it to make your way to the top of the building. Go right from the top of the stairs and you will find a Legion Magazine on the balcony. Then make your way to the other side of the balcony where you will find a tram. Go inside and pull the lever to ride it forward.

The tram will take you to a balcony attached to the Grand Exhibition building. Make your way inside where you will find yourself on a balcony overlooking the main room of the exhibition. Lower the nearby ladder, then climb down and activate the Stargazer.

Deal with the soldiers and sawblade puppet as you make your way forward. Also be sure to check behind the curtains across from the info desk where you can find a Half Moonstone on a wooden box.

At the end of the path step up onto the platform with the large rug on it where you will find an Attribute Resistance Ampoule behind some boxes. Then go up the stairs on the right to reach the second level.

Cross over to the right side where you will find a ladder leading down to the floor below. Here you can activate a shortcut that creates a bridge back to where we battled the three jugglers before. Turn left here to find an Acid Abrasive and a door leading to a new area.

Go through the smashed doors and follow the path forward, past some more displays. Go up the stairs at the end which lead you to some kind of operation room. Walk onto the catwalk on the opposite side of the room then go left where you will find a ringing telephone.

If you read the Hint we just got from the King of Riddles, you may already have a feeling we need to do something here. Approach the statue on the right and interact with it twice to open a hidden compartment, with the Trinity Key inside.

Exit through the door opposite the statues to find yourself in a large exhibition hall with a tram in the middle. There are a few gunner enemies wandering around here. Pick them off one by one and don't let them gang up on you. You can run into the tram if you need to break their sight lines.

A number N is given finding the above number is P^Q(P power Q) form or not. I did the question using Brute force method (satisfying for individual number) but that result in time out. SO I need Efficient algorithm.

In Statistics, the researcher checks the significance of the observed result, which is known as test static. For this test, a hypothesis test is also utilized. The P-value or probability value concept is used everywhere in statistical analysis. It determines the statistical significance and the measure of significance testing. In this article, let us discuss its definition, formula, table, interpretation and how to use P-value to find the significance level etc. in detail.

Kepler's third law - shows the relationship between the period of an objects orbit and the average distance that it is from the thing it orbits. This can be used (in its general form) for anything naturally orbiting around any other thing.

Formula: P2=ka3 where:P = period of the orbit, measured in units of timea = average distance of the object, measured in units of distancek = constant, which has various values depending upon what the situation is, who P and a are measured.This is the general form of the formula, so obviously you need at least two of the quantities to find the third. "k" is the trickiest thing since it depends upon the objects that are involved and how you measure "P" and "a". Since "P" can be measured in any unit of time (seconds, days, years, etc), and "a" can be measured in any unit of distance (meters, km, AU), the value of "k" can be quite diverse from one system to another.There is a simplified version of this law: P2 = a3 where: The object must be orbiting the SunP = period of the orbit in yearsa = average distance of the object from the Sun in AUThis version is much more simple, since it has "k" = 1, so it is ignored when those units of measure are used. ff782bc1db

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