Tail flip

Evidence in favor of dynamic disorder in a-CO was also obtained from nuclear quadrupole resonance studies [199, 369] and from dielectric measurements [251], which also indicate short-range antiferroelectric order [251]. The rate of molecular reorientation leading to head-tail flips was found to become vanishingly small at low temperatures A head-tail reorientation time of about 5 X lO hours was estimated [369] at a temperature of 10 K. Thus, the extremely slow kinetics at the low temperatures which are energetically necessary to allow for head-tail ordering seems to prevent head-tail ordering in the bulk CO phase. 

Based on this modeling, molecular dynamics simulations [140] for a complete Vs monolayer are carried out from 10 K to 80 K—that is, ranging from the harmonic herringbone solid through the orientationally disordered solid to the fluid. The herringbone transition occurs at around 22 K, below which enhanced 180° head-to-tail flips of the homonuclear molecules occur. The sixfold symmetry in the orientations persists up to about 50 K,... 

The term Monte Carlo is often used to describe a wide variety of numerical techniques that are applied to solve mathematical problems by means of the simulation of random variables. The intuitive concept of a random variable is a simple one It is a variable that may take a given value of a set, but we do not know in advance which value it will take in a concrete case. The simplest example at hand is that of flipping a coin. We know that we will get head or tail, but we do not know which of these two cases will result in the next toss. Experience shows that if the coin is a fair one and we flip it many times, we obtain an average of approximately half heads and half tails. So we say that the probability p to obtain a given side of the coin is k A random variable is defined in terms of the values it may take and the related probabilities. In the example we consider, we may write... 

For rats and mice, the animal is either grasped by its tail and flipped in the air or held upside down and allowed to drop (2 ft above the cart surface) so that it turns head over heels. The normal animal should land squarely on its feet. If it lands on its side, score 1 point if on its back score 2 points. Repeat 4 times and record its total score. For a rabbit, when placed on its side on the cart, does the animal regain its feet without noticeable difficulty ... 

We will start with a very simple situation to see how we actually calculate p-values. Suppose we want to know whether a coin is a fair coin by that we mean that when we flip the coin, it has an equal chance of coming down heads (H) or tails (T). 

We now need some data on which to evaluate the hypotheses. Suppose we flip the coin 20 times and end up with 15 heads and 5 tails. Without thinking too much about probabilities and p-values what would your intuition lead you to conclude Would you say that the data provide evidence that the coin is not fair or are the data consistent with the coin being fair ... 

For 20 flips we get the probabilities by multiplying (1/2) ° by the number of combinations that give rise to that particular outcome, so for example with 12 heads and 8 tails this is 20 (12 x 8 ) where n denotes nx(n—l)x...x2xl. 

The statistical test procedures that we use unfortunately are not perfect and from time to time we will be fooled by the data and draw incorrect conclusions. For example, we know that 17 heads and 3 tails can (and will) occur with 20 flips of a fair coin (the probability from Chapter 3 is 0.0011) however, that outcome would give a significant p-value and we would conclude incorrectly that the coin was not fair. Conversely we could construct a coin that was biased 60 per cent/40 per cent in favour of heads and in 20 flips see say 13 heads and 7 tails. That outcome would lead to a non-significant p-value (p = 0.224) and we would fail to pick up the bias. These two potential mistakes are termed type I and type II errors. 

The Problem When you roll a die and flip a coin at the same time, what is the probability that you get an even number on the die with tails ... 

When flipping a fair coin, the probability is 50 percent that it ll be heads and 50 percent that it ll be tails. 

When you flip a coin, the probability of its landing on each side is p = q = I in Equations 28-2 and 28-3. If you flip it n times, the expected number of heads equals the expected number of tails = np = nq = n. The expected standard deviation for n flips is crn = /npq. From Table 4-1, we expect that 68.3% of the results will lie within lrr and 95.5% of the results will lie within 2cr . 

Figure 7.5 Example of a chimeric oligonucleic acid and its modification. Chimeric RNA-DNA hybrids are used for correction of point mutations in target genes. One strand of this oligonucleic acid is composed of O-methyl-RNA (outline) with an interruption of 5 bases of deoxyribonucleic acid. X and Y are target residues for correction. In the complementary strand, there is a DNA nick, and T residues loop both ends. 3 -exonuclease and FEN-1 may act on the nick, PARP-1 possibly binds to and is activated by the nick, resulting in activation of damage response pathways. In the modified version, the 3 end is replaced by ribonucleic acids. The 5 end is extended, and the flipped back RNA tail is added. Thus, the nick is expected to be resistant to 3 -exonuclease and FEN-1. In addition, PARP-1 may not be activated by such a nick.

One of the most basic problems in statistics is called the random walk problem. Suppose you take a total of N steps along a north-south street, but before each step you flip a coin. If the coin comes up heads, you step north if the coin comes up tails, you step south. What is the probability that you will end up M steps north of your starting point (in other words, the probability that you will get M more heads than tails) ... 

FIGURE 4.1 Dots Probabilities of getting M more heads than tails out of 10 coin flips. Solid line Gaussian function, as introduced in Section 2.2... 

Sometimes we know a great deal about the expected statistics of a measurement. Suppose we actually flip the same coin 10,000 times, and get 5500 heads we showed that the chance of getting this many heads or more is less than 10-23. We could conclude that we were just extremely lucky. However, it is more reasonable to conclude that something is biased about the coin itself or the way we tossed it, so that heads and tails do not really have equal probability. Would we draw the same conclusion if we got 5200 heads (the chance of getting this many heads or more is 3.91 x 10-5) Would we draw the same conclusion if we got 5050 heads ... 

The lipids themselves are highly mobile. Steady state and time resolved spectroscopy (absorption, emission, ir, raman, nmr, epr) and anisotropy measurements have revealed rotational, vibration and segmental motions of the headgroups and the hydrocarbon tails of the lipids. Translocation of a lipid from one half of the bilayer to the other, ("flip-flop ) as well as intermembrane... 

Lobsters are most active at night. During the day they typically hide in burrows or cavities in rock piles, which they enter by backing in. Lobsters can crawl in all directions, but when they are foraging they mostly proceed in a forward direction. Smaller lobsters can swim jerkily, by rapidly back-flipping their tail fan. 

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