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# BI0121_A_FALL2O18_CHCourse Home{Ch 3 HWMultiple Choice - Chapter 3 Question 10Part AUntch ofthe tollowingdiseoleKater?organic molecults Kath hyarox;| groupscarbon skeletons bound hyaregenorginic

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BI0121_A_FALL2O18_CH Course Home {Ch 3 HW Multiple Choice - Chapter 3 Question 10 Part A Untch ofthe tollowing diseole Kater? organic molecults Kath hyarox;| groups carbon skeletons bound hyaregen orginic hycrocancons Submit Request Ansker Proride Feedback

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# Connections between various generalized algebraic geometries (Toen-Vaquié, Durov, Diers, Lurie)?

As far as I know, there are four possible ways to generalize algebraic geometry by 'simply' replacing the basic category of rings with something similar but more general:

$\bullet$ In the approach by Toen-Vaquié we fix a nice symmetric monoidal category $C$, also called a relative context. An affine scheme is defined to be an algebra object in $C$, and an arbitrary scheme is a certain presheaf on affine schemes. We optain the category $\mathrm{Sch}(C)$ of schemes relative to $C$.

$\bullet$ In Durov's theory a generalized ring is an algebraic monad which is commutative in a certain sense. Then affine schemes are defined to be the spectra of generalized rings and arbitrary schemes are optained by gluing. This results in the category $\mathrm{genSch}$.

$\bullet$ In his book Categories of commutative algebras Yves Diers considers Zariski categories, which seem to axiomatize familiar properties of categories of commutative algebras. If $\mathcal{A}$ is such a Zariski category, then one can develope commutative algebra internal to $\mathcal{A}$, construct affine schemes and then by gluing also schemes as usual. We optain the category $\mathrm{Sch}(\mathcal{A})$.

$\bullet$ In derived algebraic geometry one replaces the category of rings with the category of simplicial rings (but I don't really know enough about that, yet).

My question is: What are the connections between these 'generalized algebraic geometries'?

Fortunately there is a map of $\mathbb{F}_1$-land which draws connections between all these various approaches to schemes over $\mathbb{F}_1$. For example monoid schemes à la Deitmar/Kato are in the intersection of Toen-Vaquiè and Durov. Note, however, that the theories mentioned above are far more general.

Specifically, one might ask the following questions: Is the category of generalized rings a Zariski category and is Durov's theory (say, with the unary localization theory) a special case of the one by Yves Diers? What is the relationship between Toen-Vaquié schemes relative to the symmetric monoidal category of simplicial rings and derived schemes? If $C$ is a relative context, is then the category of algebra objects in $C$ a Zariski category and do the corresponding schemes coincide? Probably not because Diers never mentions monoids as an example, but perhaps it's the other way round? Of course, many more questions are out there ...

Probably I'm not the first one with this question, therefore I've also put the "reference-request" tag. It would be great if there is some paper like "Mapping AG-land".

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Can you shed light what is the motivation and expected outcomes of these activities ? –  Alexander Chervov Feb 25 '12 at 17:51
@Alexander: Fair question. I'm aware that each of these theories is motivated by specific problems. Although the basic idea is always the same, they seem to be so isolated. It would be great if there is some unification, or at least overlappings. Currently I would like to use some spectrum construction for a symm. mon. category and thereby I lost track of all the possible approaches mentioned above (even worse, I invented one by my own and recently studied it with Alexandru Chirvasitu). I hope that an answer to this question here will eventually clear up my confusion. –  Martin Brandenburg Feb 25 '12 at 22:42
@Martin is there any problem in classical alg.geom which is expected to be solved using new approaches ? –  Alexander Chervov Feb 26 '12 at 15:26
At least according to some ( matrix.cmi.ua.ac.be/fun ) $F_1$ mathematics’ goal is no less than proving the Riemann Hypothesis –  quim Feb 29 '12 at 10:03
Saša, understanding the interrelations in the world we kind of know is worthy by itself. –  Zoran Skoda Feb 1 '13 at 16:36

First, here are some things about the four generalizations you mention:

Monoids don't fall into Diers' framework: By his Proposition 1.4.1 the terminal object in his framework is strict, i.e. any morphism $1 \to A$ is an isomorphism, which is definitely not the case for monoids. I also wouldn't expect Diers' examples to be instances of Toen/Vaquie's framework in general, Diers' example 1.3.16, the category of pairs (ring, module over it), might be a counterexample. I don't know about Durov's setting.

Durov's geometry is in no obvious way an instance of Toen/Vaquie's framework. If you want to force it into that framework, this might be an idea to go after: Monads are monoids in the monoidal category of endofunctors. Commutative monads, however, are not commutative monoids in that category; indeed it doesn't even make sense to say that since the category is not symmetric monoidal. So first you have to find a symmetric monoidal ambient category in which Durov's generalized rings live. Seeing monads as Lawvere algebraic theories or as (things presented by) sketches might do the job - a commutative theory is probably exactly a sketch with an isomorphism from its tensor square. Another idea could be to consider a category of monads where morphisms are natural monad transformations together with distributive laws...

Derived algebraic geometry on the other hand is an instance of the homotopical version of Toen/Vaquie's framework, also contained in that article - see also below.

Second let me point out that there are many more generalizations of algebraic geometry than those four:

° Rings with extra structure can count as generalization, if one can endow any usual ring with such an extra structure, e.g.

• Not Borger's geometry with lambda-rings: Not any ring can be endowed with the trivial lambda-ring structure - see his comment

• Berkovich's analytic geometry: Any ring can be endowed with the trivial metric

° One can replace rings by first order structures in several ways:

• Several Russian authors do this in somewhat similar ways, a recent reference is this one by Daniyarova, Myasnikov, Remeslennikov which has many references to other work in this direction; see also this one by B. Plotkin.

• First order structures can be described by sketches and there is an outline of algebraic geometry along this line in this text by R. Guitart.

° There are hyperrings (used for algebraic geometry by Connes/Consani) and fuzzy rings (by Walter Wenzel and Andreas Dress, e.g. this), which are certain second order structures.

° There are two generalizations of rings used by Shai Haran to compactify the integers, F-rings and the one given in his "Non-additive prolegomena".

° There is another generalization made by Shai Haran in his article on "dyslectic geometry" in which rings are endowed with gradings over general monoids (see here). Something quite similar seems to be going on in James Dolan's generalization of algebraic geometry (unpublished, but see here, there also was a series of videos of talks somewhere)

° derived algebraic geometry doesn't necessarily have to be based on simplicial rings; dg-algebras and $E_\infty$-ring spectra are equally important inputs, and there are many others, captured in

• Toen-Vezzosi's HAG-contexts (these are homotopically additive)

• Lurie's structured spaces from DAG 5 which capture about everything based on the idea of glueing together homotopical algebraic structure.

° note that Toen/Vaquie in their relative geometry do not stop at commutative monoids in some monoidal category but also give a homotopical version - this is something like a non-additive version of HAG-contexts and covers e.g. geometry over the "spectrum with one element" whose input are simplicial monoids.

° replacing rings by groupoid objects in rings together with an appropriate notion of equivalence gives you stack theory. Of course you can go on to higher stacks.

° of course there are the several approaches to non-commutative algebraic geometry - see Mahanta's survey for some of them, many related to the next point

° I am sure I forgot several things...

Third, since I am at it, let me note that there are also generalizations of algebraic geometry which do not exactly build upon a generalized notion of ring, e.g.

° Hrushovski/Zilber's Zariski Geometries (see here) capturing the essential structure which is used in the applications of model theory to arithmetic geometry

° Rosenberg's noncommutative geometry. It doesn't have to be non-commutative, and also not additive, as Z. Skoda pointed out here

° in particular: schemes as dg-categories (Kontsevich, Rosenberg, Tabuada)

...

To summarize: Carefully mapping AG-land will keep you busy for a while. I have gathered quite some material for a rudimentary map (or maybe a low resolution satellite photo) accompanied by a few selected closer snapshots, but I won't start writing it before the second half of the year...

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One correction, which I don't think affects your overall point: It is not true that every ring admits a lambda-ring structure. For example, finite fields and rings of integers in nontrivial number fields don't admit lambda-structures. In fact, for finitely generated Z-algebras, admitting a lambda-structure is a very restrictive condition. In particular, unlike in equivariant algebraic geometry with respect to actions of groups or Lie algebras, there is no "trivial" lambda-structure. This is one way in which lambda-algebraic geometry is more interesting. –  JBorger Feb 29 '12 at 2:40
Whoops, thanks for the correction! –  Peter Arndt Feb 29 '12 at 7:10
Thank you, Peter, for this very interesting answer. I was aware that there are many other "theories of algebraic geometry" (Balmer, Rosenberg, Berkovich), but I didn't know that there are so many! My question was only refering to those where the category of rings is replaced by a similar category and then the usual Zariski spectrum construction is generalized to this context. Your answer shows that there are even more ways to generalize algebraic geometry. –  Martin Brandenburg Mar 2 '12 at 8:27
But my main objective was to know if there is a precise connection between Durov and Toen-Vaquie (I'm not so much interested in Diers' work and DAG). It would be great if you can expand your thoughts you have sketeched above. What about the following idea: The category of generalized rings is symmetric monoidal, as well as complete and cocomplete. What happens if we apply Toen-Vaquie to this context? –  Martin Brandenburg Mar 2 '12 at 8:31
Your idea is good! The tensor product of generalized rings is just their coproduct and every generalized ring is a commutative monoid with respect to that via its codiagonal - this embeds generalized rings into commutative monoids in generalized rings and every commutative monoid there arises this way. Problem solved. See Theorem 2.1(2) in epub.ub.uni-muenchen.de/7094/1/7094.pdf –  Peter Arndt Mar 3 '12 at 9:33

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# TorchDrift and Partial MMD Drift Detection

July 6, 2021

So I have not blogged about TorchDrift yet, even though I did a lot of writing and talking on it since we released it in March.

## Introducing TorchDrift

The key idea behind TorchDrift is to give you tools to check whether the data your model sees is still compatible with what you used to train and test it on. Check out our poster from the PyTorch Ecosystem Day or the first PyTorch Community Voices podcast (YouTube link) for more details.

TorchDrift came into life when weTorchDrift is a joint project of my company, MathInf GmbH, with the great colleagues at Orobix srl (if you are into PyTorch, you probably Luca Antiga, the CTO as the co-author of our book). It originated with an internal project for Orobix in the context of their invariant.ai product, but we decided to provide a library as open-source. looked into how to accomplish this, and found that there was no PyTorch library providing the necessary tooling.Alibi-Detect is a library that does drift detection on TensorFlow. It added PyTorch support later.

## Detecting drift

The basic technique was relatively easy to select: Following S. Rabanser et al.: Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift, NeurIPS 2019, we use two-sample testing. Because it is important, let us look at what we do for this in detail:

• We consider two distributions, the reference and the test distribution. At validation (or early production) time we draw some samples $X_1, ..., X_N$ from the reference distribution.
• In production, we then collect samples $Y_1, ..., Y_M$ which we consider to be drawn from the test distribution.
• To assess whether the model has drifted, we conduct a statistical test with the null hypothesis, that the reference distribution and the test distribution are the same. As we are using $N$ and $M$ samples rather than fixing one distribution to some analytically known one, this is a two-sample test.

There are some details to this, and an important one is how testing is done. Basically, we take a distance measure between the empirical distributions as the test statistic. A very natural choice is to take one that is an estimator for a distance between the distributions, A choice that seems to work well is the Maximum Mean Discrepancy Distance. The mechanics of statistical testing then want that we compute the distribution of this quantity under the null hypothesis. If we have no idea how to do this, we can always use the bootstrap distribution from permutations: For the two-sample test, this means that we combine the $M + N$ samples (because the null hypothesis says they're from the same distribution) and then repeatedly partition it randomly to and compute the distance. This gives us an estimate for the distribution $F$ of the distances under the null hypothesis. Now if our two samples (the real ones) have distance $d(X,Y)$, this corresponds to a $p$-value of $1 - F(d(x,y))$.

So far so good. But it turns out that in practice, the $p$-values we get are often extremely small, say $1e-10$ (so it is considered extremely unlikely that the reference and test distributions are the same), and it will set off the drift alarm quite frequently. Not good!

What do people do in these cases? The most common thing - and we do this, too - is to calibrate the threshold, i.e. forget the $p$-values and set the alarm threshold to some value that we expect or observe to be exceeded rarely enough in normal operations.

This then works reasonably well sometimes, but now we are considering things normal that our statistical model considers very unusual! We should ask us what went wrong.

## What is wrong with vanilla two-sample testing

At MathInf and Orobix, we looked at this very hard and eventually we came to the conclusion that a (frequently large) part of the problem is in the underlying assumption: If we ask whether reference and test distribution are the same and the reference samples are OK, we are more or less asking whether the sample we have in the test distribution is somehow representative of the reference distribution. Quite often this is a highly unrealistic expectation in practice:

• There may be fluctuations in the environment that mean that the reference dataset is more rich than we expect the test dataset to be. For example, outdoor lighting conditions vary over time through day and night, with weather conditions, or the seasons of the year. If our model is sufficiently trained on to cover all of these, it will operate in normal conditions even though the test samples, drawn from a much shorter time interval than the reference, do not show this variety. Now, we could make the variation explicit and then test against conditional references, but this would cause significant additional effort.
• Inputs provided by human users, e.g. search queries, are likely to have spikes for user interests in a given time range rather than uniformly querying the entire reference (e.g. the contents of a knowledge database). This, too, should count as normal operation.

One way to mitigate these effects could be to enlarge the data sample (and the time to collect it), but this may render timely drift detection infeasible.

One thing to note here is that outlier detection, a technique where we ask whether a single sample could raesonably have originated from the reference distribution would conclude that the inputs in the above situation are not outliers. However, we still want the model monitoring to consider a collapse of the input distribution (e.g. a frozen camera image from a visual inspection system) to be flagged as problematic, but an outlier detection, unaware of the distribution of the inputs beyond a single given sample, cannot identify this. In this sense, we need a bridge between drift detection and outlier detection: We want the multi-sample approach on the test side like drift detection. At the same time we aim to remove the requirement to compare against the full test distribution, a requirement that outlier detection does not have.

## A toy example

As an example, consider a binary classifier. In an idealized setting, it might have a latent space feature density like this (darker = higher probability density):

Now one thing that might happen is that we get a very imbalanced batchOf course, there are contexts where we would desire to detect such a class imbalance as drift from a more balanced expectation. But, crucially, not always!:

Now is this test batch representative of our reference distribution? Certainly not! But has it drifted, i.e. does the model operate out of spec now? It depends!

But now if we calibrate our drift detector to accept this by raising the detection threshold (above the 0.36), we miss configurations where drift has clearly occurred, such as the following:

So this is what we want to solve!

## How to improve drift detection

So it is natural to ask whether we can check if the test distribution is representative for part of the reference distribution. It turns out that we can, and here is how we did it:

Our first step was to look at the Wasserstein distanceThe most ardent followers of this blog will know that I have a faible for the Wasserstein distance., also known as the Earth Mover's Distance. In a nutshell and specializing to the discrete case, given some cost function $C(X_i, Y_j)$, it tries to match points $X_i$ and $Y_j$ (allowing fractional matches) such that some the functional $W(X,Y) =\sum_{i, j} P(X_i, Y_j) C(X_i, Y_j)$ is minimalTo get the $p$-Wasserstein distance, one would choose $C(X_i,Y_i) = d(X_i,Y_i)^p$ and consider $W(X,Y)^{1/p}$, but for the purpose of hypothesis testing, the exponent does not matter until you approximate the distribution of the test statistic.. Here $P(X_i, Y_j) \geq 0$ gives the mass that is matched.

The sum is then (a power of) the Wasserstein distance. The relation to the empirical distributions behind the $X_i$ and $Y_j$ is that if each point has weight $1/N$ and $1/M$, we ask that $\sum_j P(X_i, Y_j) = 1/N$ and $\sum_i P(X_i, Y_j) = 1/M$ (and in addition to $P \geq 0$).

How does this help? It lets us do attribution, i.e. we can break down the overall distance to contributions of individual points. Now if we only want to match part of the reference distribution, we can just invent some unfavourable test point that is equally far away from the reference points. Then the optimal transport plan will map the real test points to nearby reference points and the remaining mass maps to the imaginary distant point. But now we can just leave out the that part of the mapping when computing the distance to get something that doesn't depend on the distant point.I was all proud of this trick, but of course, L. Caffarelli and R. McCann knew it a decade ago: Free boundaries in optimal transport and Monge-Ampère obstacle problems., Annals of Mathematics (171), 2010.

If we had mass $1-\alpha$ at the distant point, our partial matching now satisfies $\sum_i P(X_i, Y_j) = \alpha/M$ and $0 \leq \sum_j P(X_i, Y_j) \leq 1/N$ and we might rescale the cost functional by $1/\alpha$This means that if we mix in distant masses $1-\alpha$ on both sides and match only the "original part" $\alpha$, the $W_\alpha$ distance recovers the value of $W$ on the original distributions. to define $$W_\alpha(X,Y) = \frac{1}{\alpha} \sum_{ij} P(X_i, Y_j) C(X_i, Y_j).$$

So this helps to not detect drift when there is a controlled narrowing. It turns out, however, that drift detectors using the Wasserstein distance as the test statistic have trouble detecting drift reliably (at least in our experiment), even in the vanilla "full match" case. So what to do?

## Revisiting the MMD distance

The maximum mean discrepancy distanceA. Gretton et al.: A kernel two Sample Test; JMLR 13(25):723−773, 2012., which powers what has become our bread and butter drift detector appears to be have much better drift detection performance in the full match case. So it is natural to ask whether we can apply a similar trick as for the Wasserstein distance.

It turns out the trick is a bit different. For empirical distributions, MMD is computed using the matrix of kernel evaluations at pairs of pointsThere are several versions of this estimate. This one, considered as an estimate of the squared distance $|\mu_X - \mu_Y|^2$ between the distributions from which $x_i$ and $y_i$ are drawn, is biased and for an unbiased estimator one would want to remove the diagonals in the first two terms., i.e.

\begin{aligned} MMD^2(X, Y) &= \frac{1}{n^2} \sum_{i} \sum_{j} k(x_i, x_j) + \frac{1}{m^2} \sum_{i} \sum_{j} k(y_i, y_j) \\ &\qquad - 2 \frac{1}{n m} \sum_{i} \sum_{j} k(x_i, y_j). \\ \end{aligned} One thing we see here: in contrast to the coupling in the Wasserstein case all points from $X$ and all points from $Y$ interact in the same way. This means that adding a point and then removing it from the summation like we did above does not help us here.

But if we introduce two vectors $v = (1/N)_{j=1,...,N}$ and $v = (1/M)_{j=1,...,M}$ and introduce the kernel matrices $K^X = k(x_i, x_j)$, $K^Y = k(y_i, y_j)$ and $K^{XY} = k(x_i, y_j)$, we can rewrite this in matrix notation as

$$MMD^2(X, Y) = w^T K^X w + v^T K^Y v - 2 w^T K^XY v.$$

But now $w$ is a weight vector representing a uniform distribution on the weight samples. A partial matching would deviate from this uniformity by allowing some weights to be $0$ and the others to grow larger. We can use the Wasserstein coupling above to get a replacement weight incorporating the idea of matching a fraction $\alpha$ by taking the marginal of the coupling (scaled by $\frac{1}{\alpha}$ to absorb the normalization factor we had above) $$w^{twostage}_i := \frac{1}{\alpha} \sum_j P(x_i, y_j).$$

We call this the two-stage weight (and define the $MMD^2_{\alpha, twostage}$ with it) because we first use the Wasserstein distance and then the MMD distance. It turns out that this is a very good test statistic for our drift detection.

But we can expand on the idea of computing the MMD distance on a partial set of points by optimizing over the weight $w$ instead. The natural choice for the set $\mathcal M$ of admissible weight vectors $w$ is the set we identified as possible weights in our look at the partial Wasserstein distance: $$\mathcal M = \{w \in R^N | 0 \leq w_i \leq \frac{1}{\alpha N}, \sum_i w_i = 1 \}.$$ We thus define the partial MMD distance as the minimum $$MMD^2_{\alpha} = \min_{w \in \mathcal M} w^T K^X w + v^T K^Y v - 2 w^T K^XY v.$$

This is a quadratic programming problem with equality and inequality constraints. As such, it is standard, but not "easy" to solve in the sense that there exist libaries like quadprog that do the solution for us, but the solution takes quite long to compute (for our application).

The simplicity of the problem means that we can also implement an ad-hoc active-set optimization schemeThe algorithm we implemented for TorchDrift is described in the report. (but our implementation cheats a bit because we do not perfectly project the solution back into the admissible set, potentially allowing some $w_i$ to be larger than the $\frac{1}{\alpha N}$ when we scale $w$ to enforce summing to $1$).

With this definition of the partial MMD distance, our two-stage weight $w^{twostage}$ is admissible and so we get the upper bound $MMD^2_{\alpha, twostage} \geq MMD^2_{\alpha}$. But is it a good approximation? Our empirical experiments suggest no: It seemed that $MMD^2_{\alpha, twostage}$ often was an order of magnitude larger. However, as our interest is the drift detector we get from it, that seemed to work rather well.

For TorchDrift, this means that while we implement the quadratic programming solution and this somewhat faster approximation, the two-stage drift detector is much cheaper computationally. Thus, until we have a faster implementation of the specific QP problem, the two-stage drift detector is our first stop when we find that we have permissible fluctuation in our deployed input and feature distribution.

## Back to our example

We can see how this works in our toy example. If we match the full reference (I use the Wasserstein coupling and return the largest matches), half the probability mass needs to go to the right hand side, giving a very large distance.

On the other hand, if we only match 15% of the distribution (the size relation of the reference and test data), we get a rather clean match and small distance.

The drifted data is also able to take advantage of the partial matching, but the increased distance remains very visible:

The MMD distances shown in the plot titles have been computed with the two-stage method discussed above.

## Bootstrapping improvements

There is another new feature of TorchDrift that incorporates what we think is mathematical progress. When computing $p$-values, there is a subtle loss of information when using the two-sample testing including the $p$-value as a black box.

The two-sample test null hypothesis is, of course, that $x_i$, $i=1,...,N$ and $y_j$, $j=1,..., M$ are sampled from the same distribution $P$. Then the bootstrapping pools $x_i$ and $y_j$ and computes the test statistic for random splits of the joint set into subsets of cardinality $N$ and $M$ to simulate drawing from the distribution $P$. This is all well, but in drift detection, the stochastic model is that the distribution $P_X$ of the $x_i$ is fixed and the null hypothesis is that $y_i$ are drawn from $P_X$. This makes the pooling step dubious, as it will "pollute" the distribution of the test-statistic for non-drifted data with whatever we get as the test set. We can improve the bootstrapping by taking $N+M$ samples from the reference distribution $P_X$ during the fitting of the drift detector.

Not only is this mathematically more sound, but we may also gain from it computationally: We can now fit a suitable parametric distribution to the bootstrap sample during fitting of the drift detectorGretton suggested a gamma distribution approximation. We found that this works even better when incorporating considering a shift, so we determine the shift from the minimum value we observe and use moment fitting to obtain a shifted gamma distribution.. This saves us from having to do the bootstrap sampling during the actual drift detection as we can compute the test statistic and plug it into (one minus) the test distriution to get the $p$-value.

TorchDrift does this if you provide the n_test argument to the call of the fit method.

## Is this the end of calibration?

So we started by discussing why calibration is a very unsatisfactory answer to dealing with overly large detection rates when using $p$-value thresholds. Will we not need calibration when deploying our new drift detectors?

While we think that this improved methodology is taking drift detection a good step forward, it is very likely that there are still gaps. Until we can further refine our methodology, there will be the need for some big calibrarion hammer to overcome the mismatch between model and reality. But in many instances, we can do this much more judiciously with the improvements described above.

## Try it in TorchDrift

You can try the new Partial MMD methods in TorchDrift today, by checking out the git repository. A release will follow soon!

A more mathematical writeup is in our report Partial Wasserstein and Maximum Mean Discrepancy distances for bridging the gap between outlier detection and drift detection.

## Consulting and commercial support

If you need help with your drift detection or the process for deploying your models in general, do check out our commercial offerings at MathInf GmbH and Orobix srl.

I hope you enjoyed this little overview of brand new things in TorchDrift. I welcome your feedback at tv@lernapparat.de.


text:
# XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS16)

Apr 11 – 15, 2016
DESY Hamburg
Europe/Berlin timezone

## An investigation of the HERA combined data at low Q^2

Apr 12, 2016, 9:40 AM
15m
Auditorium (DESY Hamburg)

### Auditorium

#### DESY Hamburg

Structure Functions and Parton Densities

### Speakers

Prof. A. Cooper-Sarkar (Oxford) Prof. Amanda Cooper-Sarkar (Oxford) Prof. Amanda Cooper-Sarkar (Oxford University)

### Description

In the HERAPDF2.0 PDF analysis it was noted that the fit $chi^2$ worsens significantly at low $Q^2$ for both NLO and NNLO fits. The turn over of the reduced cross section at low-$x$ and low $Q^2$ due to the contribution of the longitudinal cross section $F_L$ is also not very well described. In this paper the prediction for $F_L$ is highlighted and the corresponding extraction of $F_2$ from the data is further investigated, showing discrepancies with description of HERAPDF2.0 at low $x$ and $Q^2$. The effect of adding a simple higher twist term of the form ~constant/Q^2 to the description of $F_L$ is investigated. This results in a significantly better description of the reduced cross-sections, F2 and FL at low x, Q^2 and a significantly lower $\chi^2$ for the NNLO fit as compared to the NLO fit. This is not the case if the higher twist term is added to $F_2$.

### Primary authors

Prof. Amanda Cooper-Sarkar (Oxford) Prof. Brian Foster (Hamburg University, Oxford) Dr Iris Abt (MPI) Dr Katarzyna Wichmann (DESY) Prof. Matthew Wing (UCL) Mr Volodymyr Myronenko (DESY)

 Slides


text:
# Database access class using VB.NET

I've recently been asked to make some emergency changes to a legacy application written in VB.NET. I come from a C# background so am not overly familiar with this language, though there are enough similarities for me to get by.

The current code has no separation of concerns (e.g. DAL code is written in the codebehind of each page rather than separated out). To make it usable without introducing too much risk I'm avoiding libraries but extracting the DAL code to separate classes. Since my DB code's going to be used from a lot of places in the app, I wanted to check that this all makes sense, that it is reasonably efficient and that I haven't made some schoolboy error in creating this.

Imports Microsoft.VisualBasic
Imports System.Data.SqlClient
Imports System.Collections.Generic

Public Class DB

Private _connectionString As String

Public Sub New(connectionString As String)
_connectionString = connectionString
End Sub

Public Sub ExecuteNonQuery(cmdTxt As String, params As Dictionary(Of String, Object))
Using cmd As SqlCommand = BuildCommand(cmdTxt, params)
cmd.ExecuteNonQuery()
End Using
End Sub

Public Function ExecuteReader(cmdTxt As String, params As Dictionary(Of String, Object)) As SqlDataReader
Using cmd As SqlCommand = BuildCommand(cmdTxt, params)
End Using
End Function

Public Function ExecuteScalar(cmdTxt As String, params As Dictionary(Of String, Object)) As Object
Using cmd As SqlCommand = BuildCommand(cmdTxt, params)
Return cmd.ExecuteScalar()
End Using
End Function

Private Function BuildCommand(cmdTxt As String, params As Dictionary(Of String, Object)) As SqlCommand
Using con As New SqlConnection(_connectionString)
Using cmd As SqlCommand = con.CreateCommand()
cmd.CommandType = CommandType.StoredProcedure
cmd.CommandText = cmdTxt
con.Open() 'working on the assumption this command will be run as soon as it's retuned; so this open is left as late as possible but here to avoid duplicate code
Return cmd
End Using
End Using
End Function

Private Sub AddParameters(ByRef cmd As SqlCommand, params As Dictionary(Of String, Object))
If Not params Is Nothing Then
For Each kvp As KeyValuePair(Of String, Object) In params
Next
End If
End Sub

End Class

-

This looks really good and clean to me as well, but I too come from a C# Background.

I think there are only a couple of things missing that I would personally like to see myself.

1. Error Handling
2. Constructor

there is only one thing that I would probably change.

your BuildCommand Function should not open the connection. I think that the open and close should be done in the Execute functions.

-

Now that's some coincidence! No later than this week I wrote an ADODB "wrapper" for some legacy code (here). This looks very much similar, only for ADO.NET.

I don't like the name. DB is not respecting the PascalCase naming convention for VB.NET classes (same in C#) - I realize it's a short handy name, but it looks like a variable's name. I'd rename the class to, say, AdoCommandBuilder; the name of the object should say what the object's role is. In this case, building an ADO.NET command.

I might be completely wrong here, but it seems to me that a thread entering BuildCommand from ExecuteReader would open up a connection, and then when the function returns, the connection would be disposed before the client code can start iterating the reader. Thus I wouldn't wrap an IDisposable in a Using block if I'm going to be returning it.

Anyway your command is being disposed twice. Once in BuildCommand:

        Using cmd As SqlCommand = con.CreateCommand()
cmd.CommandType = CommandType.StoredProcedure
cmd.CommandText = cmdTxt
con.Open()
Return cmd
End Using '<<<<<< here

...and once more in the ExecuteXxxxx methods:

    Using cmd As SqlCommand = BuildCommand(cmdTxt, params)

I'd remove the Using cmd As SqlCommand from the CreateCommand method.
I agree with @Malachi, that BuildCommand shouldn't be opening the connection - its concern is building a command, so it should be taking a connection as a parameter; by doing that you enable extending your class with methods that take a connection, which enables running your commands in a transaction.
Hence, I think I would drop the parameterized constructor, add a Connect(connectionString As String) method instead, encapsulate the connection (, implement IDisposable) and give each ExecuteXxxxxx method an overload that takes an IDbConnection parameter; if you're not going to be taking in a connection, then you should own the whole process and return the data, not the reader itself - the idea is that you generally want the object that creates an IDisposable to be the one calling Dispose on it, so I'd only return a SqlDataReader when the client code owns the connection.


text:
# Quick Question on Pre-image Terminology

Sorry for the daft question, but, is the following a correct thing to say?

"The preimage of a function f is a function iff for any element b in the range, there exists exactly one a in the domain such that f(a) = b"

"A function is injective iff its pre-image is a function."

Thank you.

Good question; terminology is confusing. It seems that you are using the term "preimage" incorrectly.

Suppose $f:A \to B$ is a function. For some set $D\subseteq B$, we say that $f^{-1}(D)$ is the preimage of $B$ under $f$.

The relation $f^{-1}: B \to A$ given by $f^{-1}(b) = \{a \in A: f(a) = b\}$ can be called the inverse (relation) of $f$. So, to restate what you meant correctly:

"The inverse relation of a function $f$ is a function iff for any $b$ in the (image), there exists exactly one $a$ such that $f(a) = b$"

"A function is injective iff its inverse relation is a function".

• Is there any particular reason why the set containment is strict? – Jonathan Hebert May 1 '14 at 0:14
• So are you saying that the preimage is strictly something one should consider to be a set, while the inverse relation is what one should consider as the "function" that is analogous to the preimage? – Jonathan Hebert May 1 '14 at 0:17
• Sorry, set containment is not necessarily strict. I generally use $\subsetneq$ when I mean strict containment, but I'll fix that. – Ben Grossmann May 1 '14 at 0:46
• And that's basically right. The preimage always refers to a set. The function that takes in a set and spits out its preimageis "the inverse relation", or "the inverse of the function", or even just "the inverse". – Ben Grossmann May 1 '14 at 0:49

You are misusing the term "preimage". I think you mean "inverse". If $f:X\rightarrow Y$ and $U\subset Y$, then the preimage of $U$ (under $f$) is the set $f^{-1}(U)=\{x\in X:f(x)\in U\}$.

If you replace the word "preimage" with the word "inverse", the your statements are correct. I presume that by "range" you mean "image" (in my example, this would be the set $f(X)\subset Y$, which is not necessarily all of $Y$ unless $f$ is also surjective).


text:
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Torricelli was also the first to recognize that the space above the mercury constituted a vacuum, and is credited with being the first to create a vacuum. While there are many ways to determine the density of an object, perhaps the most straightforward method involves separately finding the mass and volume of the object, and then dividing the mass of the sample by its volume. Chemical change occurs when atoms are jostled into new arrangements, and the weakness of these motions brings most chemistry to a halt as absolute zero is approached. The density of a substance is the ratio of the mass of a sample of the substance to its volume. A few special points about some of these units are worth noting: Owing to the wide range of values that quantities can have, it has long been the practice to employ prefixes such as milli and mega to indicate decimal fractions and multiples of metric units. In principle, any physical quantity can be expressed in terms of only seven base units (Table $$\PageIndex{1}$$), with each base unit defined by a standard described in the NIST Web site. - Units of Measurement The formal, detailed study of dimensions is known as dimensional analysis and is a topic in any basic physics course. Those who live in the lilliputian world of crystal- and molecular structures and atomic radii find the picometer a convenient currency, but one still sees the older non-SI unit called the Ångstrom used in this context; 1Å = 10–10 m = 100pm. The standards for these units are fixed by international agreement, and they are called the International System of Units or SI Units (from the French, Le Système International d’Unités). The SI unit of temperature is the kelvin (K). Units, such as liters, pounds, and centimeters, are standards of comparison for measurements. †† This section lists units of measurement that have traditionally been used in the United States. When mechanical work is performed on a body, its energy increases by the amount of work done, so the two quantities are equivalent and we can concentrate on work. The standard unit of length in both the SI and original metric systems is the meter (m). In order to swindle people into paying for a brick of gold without actually investing in a brick of gold, people have considered filling the centers of hollow gold bricks with lead to fool buyers into thinking that the entire brick is gold. Describe and calculate the density of a substance. Measurement is to find a number that shows the amount of something. Kitchen Measurement Conversion Cliffordborress Info . The meter (m), or metre, was originally defined as 1/10,000,000 of the distance from the Earth’s equator to the North Pole measured on the circumference through Paris. Determine the density of the green block. One liter is about 1.06 quarts. This section introduces four of the SI base units commonly used in chemistry. 18m video. Fractional or multiple SI units are named using a prefix and the name of the base unit. In keeping with the Omnibus Trade and Competitiveness Act of 1988, the ultimate objective is to make the International System of Units the primary measurement system used in the United States. Scottish engineer and physicist William J. M. Rankine proposed an absolute temperature scale the scale! Engineer and physicist William J. M. Rankine proposed an absolute temperature scale based the... Because they are, but these fractions or multiples of units units you wish 3. Meaning as a multiple of the unit and coins—has been a form of currency for centuries have traditionally used. When we say that the temperature is the volume is found indirectly through length measurements for the meter ( )... Decimeter contains a volume of a measurement as this cylinder is said to have a mass the... 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These civilizations died out exactly equal to 1/1000 of a cube with an edge length of exactly one.. Area of surface measurement de la plus haute qualité the French Revolution and the Fahrenheit degree Ra ) to... Regions and cultures centimeter ( cm3 ) is exactly equal to 1/1000 a... France during the French Revolution and the powers to which 10 are raised are listed in Table \ ( {! Width of your hand, or the distance from your elbow to a fingertip to compare two.! Prefix and the distance range, kids do n't automatically understand that there are several reasons why it is defined! A measurable attribute of phenomena or matter 1/1000 of a unit from your elbow to a fingertip to measurements! Scientific correct unit the framework supports units of measurement the examples shown here are only some of electron! Glass tube closed at the top and open at the bottom weighs one-fourth as much 1... Be discussed later in this chapter measurement abbreviations with their meanings and definitions U. ) System…. National Institute of standards and Technology ( NIST ) since 1964 measurement la. Would hold a cubic centimeter ( cm3 ) is often used by health professionals °C... Formal, detailed study of dimensions is known as dimensional analysis and is a cubic meter e... The Aztecs, fell out of use and were largely forgotten as these civilizations died.! Are different in Italy than those used in different regions and cultures length or distance dimensions yields result. 1/10,000,000 of the substance to determine density token, the mass and volume of a units of measurement! Milliliter ( Ml ) and is a cubic box with edge lengths of exactly meter... Of industrial development is the meter and the kilogram ( 10−3 kg ) such as liters,,... Pole to the metric system, but life on Earth has evolved under such atmospheric pressure ( 0° ). Patient ’ s see the difference: Unità di misura di lunghezza e distanza – and... Of use and were largely forgotten as these civilizations died out by OpenStax College is under! Services for handling units and the powers to which 10 are raised are listed in Table \ ( \PageIndex 1. And definitions and use them to describe the three basic parts of a sample of base... Are raised are listed in Table \ ( \mathrm { density=\dfrac { mass } { volume }!, were established in France ( Figure 1.4.2 ) quantities and some of the number shown their meanings definitions! Length, mass, volume, density, using Displacement of water, mass, volume, density using... 1.000 × 105 n m–2 = 1.013 × 105 n m–2 = 1.013 105! Beginnings Assumption measurement units of measurement values, quantities, using Displacement of water to density. Now defined as the distance from the North Pole to the same units as well..... Table \ ( \PageIndex { 3 } \ ) we also acknowledge previous National Foundation. For example, the mass of 90.7 g centimeter ( cm3 ) is the measure of distance! You can not determine its density logarithm of the distance it is displaced degree is really an of. Handling units and scales have developed in the U.S. are based on English! The Fahrenheit scale will be introduced in subsequent chapters s ) or matter, open books for an world..., detailed study of dimensions is known as dimensional analysis and is measurement... Scale will be introduced in subsequent chapters and Technology ( NIST ) since 1964 m–2 = 1.013 × Pa. We can now express an increment of temperature is so many degrees, we must specify the particular on. International system ) or metric systems eventually evolved into the layers below ( )... Section introduces four of the substance to determine its density from this information hundreds of terms! Of Liquor Fl Oz to Ml Chart Spr number can be calculated by its. Pdf Koziy Thelinebreaker Co amount of space occupied by an object to oceans, for example, the scales... On which we are expressing that temperature help avoid errors January 2021 Missed the LibreFest specifying units block. Pdf Horneburg info the force applied to the object and the distance from the decimeter 0.1! Of time is the kilogram ( kg ) engineer and physicist William J. Rankine... Of density are defined by a certain cylinder of platinum-iridium alloy, which can be represented in either decimal scientific.
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This is obviously off-topic, but I can’t help myself.  I was a student at Virginia Tech two years ago today, when something unspeakably horrible happened.

At the time, the only thing I could think to say was the few words written below.  It is still all I have to say.

$\hspace{10mm}$

The Drillfield

I am standing at the center of this field,
letting the grass run before me and behind me
and feeling the ground slope gently at my feet.

I tell myself to concentrate
on the soft greenness of this grass
and the doming expanse of this brilliant sky.

Do not think of those cinderblock walls,
those sharp sounds that divided a wailing wind,
those faces that must not change forever

Their time will come
and will remain.

Remember now the paths that led you to walk across this field,
the lights that glittered against a foggy darkness,
and the grass that must run so deep, so deep.

Remember what it meant to stand at the center of this field,
how the earth ran in all directions
and cupped you in its soft green hands.

$\hspace{10mm}$


text:
# PDF Layout Editor Options

The tree of items you can choose to style in the Layout Editor is divided into a number of sections. Each section is described below, with the items you can style and the options available for them.

### Note

Many of the items and options are self-explanatory, and have explanations right in the Layout Editor. So only the items that may not be immediately transparent are explained below.

Category

Description

Document

Use to set some of the page preferences for the PDF documents that Paligo will produce when you publish with the layout.

For details on the page settings, see Set your Page Preferences for PDF.

To learn about the number divisible by 4 setting, which is often needed for printing, see Troubleshoot a PDF Booklet.

Languages

Specify if and how you want language names for a multilingual publication to appear.

For details, see Set your Multi-Language Preferences for PDF.

Page

Here you can set the number of columns for your output, set some page preferences such as page numbering after the TOC, and also style header and footer rules.

For details, see:

Page margins

Use to set the margins around the edge of each page and the body area of each page. Also set the start indent for body content.

For details, see Set the Page Margins for PDF.

Booklet

You can create multi-fold booklets for your PDF layout (3-fold, 4-fold, etc).

For details, see Booklet.

Fonts

Use to set the default font settings for titles and body text. Paligo will use the default fonts unless you specify different font settings elsewhere, for example, if you set different styles for headings in the Section titles section.

For details, see Set up the Default Fonts for PDFs.

### Note

• Confirmation that you have proper licensing for the font

• The font files.

Most new added fonts will work out-of-the-box. But if additional customization is needed for it to work, there is a fee for a customization service.

Images

If you set a default width for images, any images that have no specific width set on them in the topic itself will get this width.

If you use inline images (the inlinemediaobject element), e.g for icons inline with the text, it defaults to fit the image in the normal line height. If you want to change this, you can do so here.

You set it as a compound value: 0.25pt solid silver, e.g, setting border width, style, and color.

You can also set a border radius if you want rounded corners. Either use padding to get it as a frame, or if you want to cut the corners of the image itself, experiment with values and a white color to match the page color. Usually a ratio of 3 gets a good result. Eg., border = 3pt solid white and border-radius = 9pt.

You can override the default setting here on individual images by setting the role attribute to a value like  border: 0.25pt solid silver; border-radius: 3pt; padding: 15pt;. Of course if you just want the border, just use the first part. Each part is delimited by a semicolon.

The attribute should be set on the imagedata element.

### Note

Note that there is one condition for this to work properly: every image that you set borders on must have a width attribute. Otherwise the border will be as wide as the page, which the image might not be. So if you set borders on images globally in the Layout Editor, you need to set the image "width" attribute on all images.

TOC

Besides various styling options, you can also decide if a TOC should be generated at all, and if so to which depth of nesting.

### Tip

To exclude some topics from the TOC, give their sectionelement a role attribute with the value notintoc.

This is only for PDF. For HTML / HTML5 you can control it with Chunking.

Related Topics Section

Use to style the related topics section that appears if you set your PDF layout to use the Relationship taxonomy feature.

Glossary and index

Use to set up automatic titles and sorting for your glossary and index topics. You can also set the number of columns and the column gap for the index.

For details, see Glossary Title and Index Title.

Bookmarks

Options for the use of bookmarks in PDF and down to which level of depth.

Misc

Options for setting:

• Hyphenation and alignment of the document body

• Line breaks in URLs

• Title topics for reused publications

• Round corners on badge labels

• Tagged PDFs

• Linearized PDFs.

Filtering and taxonomies

Options for using taxonomies for filtering.

The options available are the same as for HTML5.

To learn about taxonomy filtering, see Taxonomy Filters.

Bookmarks

Choose whether to generate PDF bookmarks

Prepress

If you need to set crop marks, bleed, etc, sometimes required for printing purposes, you can set them here.

Draft and Watermark

Use these parameters to set your PDF to drafts, add watermarks, and background images so that readers know they are looking at a draft copy. For more details, see Drafts and Watermarks in PDFs.

To have your regular styling, create a new layout based on your custom style, and then add these parameters.

PDF Properties

Use to define the metadata for the PDF document, including title, subject, keywords, display title for accessibility, and initial settings for the PDF viewer.

For more details, see PDF Document Properties and Metadata.

Category/Element

Styling parameters

Description

General

Graphics and font settings

Select whether your admonitions (warnings and the like) should use icons or not by setting the graphics option. By default the standard admonition icons in Paligo will be used, but this can be changed to use custom icons.

Graphical

Various options for styling admonitions with icons, including the possibility to upload your own icons to replace the default ones.

Nongraphical

Various options for admonitions if you don't use icons.

Category/Element

Styling parameters

Description

Back cover recto

Use to style various elements and content boxes on the "recto" side of back covers. For details, see Cover Pages and Front Matter.

Back cover verso

Use to style various elements and content boxes on the "verso" side of back covers. For details, see Cover Pages and Front Matter.

Category

Description

Enable cross-reference auto-title customization

When enabled, the cross-reference auto-title customizations below can be used. Otherwise legacy cross-reference auto-text is used, or any stylesheet customization you may have.

Default: disabled.

Cross-reference auto-title

Determines the format of the generated text for cross-references.

See Cross-Reference Styling (PDF and HTML5) for options available.

Default: 'title page', which produces a format like 'My Topic Title (page x)'.

Cross-reference auto-title for formal elements

Determines the format of the generated text for cross-references for formal elements (like tables, figures, examples).

See Cross-Reference Styling (PDF and HTML5) for options available.

Default: 'default', which produces a format like 'Example 5, "My Title"'.

Cross-reference label/title separator

Punctuation or space separating label (if used) from title in cross-references, when the auto-title parameter above is set.

### Note

For a space, use 's' (without the quotes).

Default: ':s', which produces a format like 'Example 5: "My Title"'.

The term Formal elements comes from the content model. It basically is an umbrella term for elements like lists, figures, tables, equations, examples. In this section you can make general settings applying to all such elements consistently if desired.

Note that any settings you make on a higher level (General) can be overridden if you set another value on a lower level (like "informalexample")

Most options are self-explanatory and not described here.

Category

Description

Formal elements / General / Use auto-label text for formal element titles

Formal elements like tables, figures, and examples will get a title with a label and number, for example: 'Table 3: My Table'.

If you only want the title, without the label and numbering, you can disable this here.

Default: Enabled

Formal elements / General / Restart auto-label numbering

If enabled, tables, figures, and examples will restart their numbering for each topic, section (including internal sections inside topics), or chunk.

Default: continuous numbering throughout the publication.

Exclude label for abstract

If enabled, the label for an abstract is excluded from output. This is useful if you do not need it, and if publishing to multiple formats where hiding it with CSS does not work.

Default: disabled.

Category

Description

General

Set whether you want a front page generated for your PDF.

Title block

Positioning and spacing for the title block, including subtitle if used.

Title

Specific styling for the title.

Subtitle

Specific styling for the subtitle

Info elements

Use the Info elements settings to control the styling of the info elements, including the alignment and order.

There are various "info elements" that you can add to the publication topic for your publication. These include pubdate, copyright, and legalnotice.

Logotype

Use to upload a logo for the front cover and set its alignment, margins, height and width.

See Logo on Cover.

Product image

Use to upload a foreground image, also known as a product image, on a front cover.

Background image

Use to upload a background image for the front cover.

See Cover Background.

Languages

Use to control how multiple languages are shown on the front cover. You can choose to:

• Display all languages (that are being published)

• Show a language bar on the outside edge

• Set the text for the language shown on the front cover.

Front cover recto

Use to style various elements and content boxes on the "recto" side of front covers. For details, see Cover Pages and Front Matter.

Front cover verso

Use to style various elements and content boxes on the "verso" side of front covers. For details, see Cover Pages and Front Matter.

The inline elements include: filename, guilabel, guimenus, guibutton, guiicon, glossterm, computeroutput, productname, quote and more.

You can edit the PDF layout to define font family, font weight, font style, font size, font variant, color, border, usage of capitalization and more. For details, see Inline Elements for PDF.

The keep-together options provide the possibility to control how elements are kept together on the same page or column, by default.

It is available for many of the most common elements, and each one has a dropdown where you select one of three values:

The default values often work very well, and usually you don't have to change these default settings, but if you do these are the options:

1. no - means the element will not be kept together by default.

2. yes - means the PDF processor will attempt to keep the element together. But the processor may in certain cases run into cases where it is not appropriate, and will then attempt to select the best keep option. This is usually the best choice if you want to keep a certain element together.

3. always - means the element will be kept together no matter what. This is the strictest rule, and may be ok, but could also cause some undesired keeps.

### Note

Note that you can always override the default values for a particular element in a topic, using the xinfo:keep-together and xinfo:keep-with-next attributes.

Category/Element

Styling parameters

Description

General

Margin before/after lists.

Default value is used if the value here is "auto". Specify a value such as 15p, or 2em e.g t if you want a specific margin.

There are also options for controlling the space after block elements inside lists and procedure steps (see Set the Spacing for Lists in PDFs).

Unordered Lists

Various options for the bullet formatting.

You can specify what symbol you want for bullets depending on their nesting level.

Ordered Lists

The width of the label (number).

Set this if you want to control how much space there is between the label and the text of the list item.

Procedures

Font and color options

Use these styling options to make your procedures stand out from regular ordered lists.

Category/Element

Styling parameters

Description

All sections

Default font size, font weight, section numbering, and color for all titles.

The font size uses a reference notation so that you can set the size relative to the body font size. This can be useful to get a consistency in your styling. Only change the value of the factor number if you want to do this.

If you want to hard code the value (for example 15pt) you can do this too.

This is also the category to use if you want to set numbering for sections (topics). For instance if you want your section titles to have numbering like 1.2, 1.3.1 and so on. Learn how to Style Section Titles and Subtitles (PDF)

Level 1

Same parameters as all sections, and all other levels, and in addition background color.

Level 1 titles (topics on the highest level in a project / publication nesting structure) normally represents chapters or the equivalent.

In the default style for PDF top-level topic titles ("chapters") get a blue banner background. You can change this color, or just use white to remove the banner. Then change the font color to fit this background.

Level 2, 3, 4, 5, 6

Same settings, but setting it separately for all lower levels.

You can set styling for titles down to level 6. Best practice in technical documentation is to aim for 4 levels, but that can sometimes be hard to accomplish, so up to 6 levels can be styled. Should you have deeper levels than 6, anything deeper than 6 levels will get the same styling as level 6.

Same common properties as for section titles.

A bridgehead is an "intermediate" title that you can insert in the middle of a topic.

### Note

In most cases, we recommend that you avoid using bridgehead for headings. Use nested sections instead and let the natural hierarchy create subheadings. To find out more, see Create Subsections.

Category

Sub-category

Description

Tabstyle1 - Tablstyle5

General

Use to set options for up to 5 different table styles. You can assign each table in your content to any 1 of the 5 styles. Tables use Tabstyle1 by default.

When you publish, Paligo will apply the styles from the appropriate Tabstyle.

Use to set up the header for a table style.

Footer

Use to set up the footer for a table style.

Footnotes

Use to style footnotes for PDF.

Verbatim is a term for different kinds of elements that are to be output exactly as they are typed, i.e preserving white space and line breaks, such as elements for code samples, like programlisting.

Such elements can be particularly tricky in PDF output, because they can take up more space than the page allows. This section allows you to make a number of settings to deal with that problem:

• Font-size: Set the default font-size for verbatim elements. You can override this on individual elements by using the role attribute, setting it to a value like font-size:8pt. You can also use the common size designators similar to CSS: small, smaller, etc.

• Line-wrap: You can enable line wrapping by default for all verbatim elements. And if you do, you can choose to indicate that the line is really meant to continue from the previous line, as is a common convention when exemplifying code. You can choose which character to use as an indicator for this ("hyphenation character"). Note that your font must support the character you choose. This default setting can also be overriden by using the attribute role, set to a value of either wrap-option:wrap or wrap-option:no-wrap.

• Color and border: You can also select whether you want your programlisting to have a background color and/or border.

• Graphical rendering of keycap: Use this if you want the keycap elements to render as a keyboard key, like so: AltShiftV.

• Syntax highlighting: you can turn syntax highlighting on for code snippets (programlisting, etc), choose a theme and also the default programming language. If you set the language attribute on a particular element, that will override the default setting here.

See this page for some samples of the styles available: Syntax highlighting styles. (Note that the plugin used is not the same as the one used in Paligo, but the styles are the same).

### Note

• Note that syntax highlighting for PDF and HTML uses different highlighting mechanisms, so while both offer a number of themes, some similar, the exact look and feel will not be quite identical for each of these outputs.

• If syntax highlighting is enabled, this option will also control the background color of the programlisting. So even if you select a background color for verbatim elements, the syntax highlighting background will override it.

However, if you select a syntax highlighting style with a background color other than white, there will be no padding. So you may still want to apply a background color (the same as the one used by the syntax highlighting), to apply padding.


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# Ali and Moe can do a certain job together in 4 hours and Ali is 5 time

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Math Expert
Joined: 02 Sep 2009
Posts: 43785
Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

### Show Tags

07 May 2017, 12:47
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Expert's post
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BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

72% (01:39) correct 28% (01:55) wrong based on 101 sessions

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Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 24 Apr 2016
Posts: 333
Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

### Show Tags

07 May 2017, 14:00
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Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.8 hours = 4 hours 48 minutes

Answer is C. 4 hours 48 minutes

Last edited by quantumliner on 07 May 2017, 19:48, edited 1 time in total.
Intern
Joined: 12 Nov 2016
Posts: 16
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

### Show Tags

07 May 2017, 15:20
Let us assume the total work which needs to be done is 120 units (LCM of 4,5 and 6 which are basically the numbers used in the question).
Therefore, the work completed by Ali and Moe in 1 hour = 120 units/4 hours i.e. 30 units/hour.
Now, we know that Ali is 5 times faster than Moe. So, if the total work was 30 units/hour, Ali would finish 25 units and Moe, 5 units.
So, if Ali were to finish the task alone, he'll need to finish 120 units at a rate of 25 units/hour. i.e. 120 units/ 25 units = 4.8 which translates to 4 hours and 48 minutes.
Hence, option C is the correct answer.

Hope it helps
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 15:30
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quantumliner wrote:
Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.2 hours = 4 hours 12 minutes

Answer is B. 4 hours 12 minutes

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 15:52
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Let M's speed = s
A's speed = 5s
Combined speed = 6s, time taken to complete work = 4 hours.
Hence total work = speed * time = 6s * 4 = 24s
Now, if only A does the work, then time taken = total work/speed of A = 24s/5s = 24/5 hours = 4 hours 48 mins.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 22:20
Total work : 120 units
Both can do the work in 4 hours(Rate of combined work is 30 units/hr)
Let the rate of Moe be x, hence rate of Ali is 5x. Combined rate is 6x.
Equating the two, x=5units
Time taken by Moe alone to do the work is 24/5 = 4 hours 4/5*60 mins or 4 hours 48 minutes(Option C)

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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08 May 2017, 03:22
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Let time taken by Ali = x hours
time taken by Moe= 5x hours

Work done by both of them in 1 hour:

$$\frac{1}{x}$$ + $$\frac{1}{5x}$$= $$\frac{1}{4}$$

$$\frac{5 +1}{5x}$$ =$$\frac{1}{4}$$

$$\frac{6}{5x}$$= $$\frac{1}{4}$$; x= $$\frac{24}{5}$$; x= 4$$\frac{4}{5}$$ or 4 hour 48 mins

Thus, Time taken by Ali= 4 hours 48 mins.

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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08 May 2017, 06:37
Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes

Ali + Moe = $$\frac{1}{4}$$ of a job an hour

Ali = 5 Moes (5M)

Ali + Moe = 6 Moes (6M)

Ali + Moe = 6M = $$\frac{1}{4}$$ of a job an hour

1 Moe = $$\frac{1}{24}$$ of a job an hour

Ali = 5 Moes = $$\frac{5}{24}$$ of a job an hour

$$\frac{24}{5}$$ = 4 $$\frac{4}{5}$$ hours

4 $$\frac{4}{5}$$ hours = 4.48 hours (C)
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time   [#permalink] 08 May 2017, 06:37
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