text:
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01mp48sg38t
DC FieldValueLanguage
dc.contributor.authorMarconi, Dario-
dc.contributor.otherGeosciences Department-
dc.date.accessioned2017-07-17T20:31:15Z-
dc.date.available2017-07-17T20:31:15Z-
dc.date.issued2017-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01mp48sg38t-
dc.description.abstractThis thesis uses measurements and models of the 15N/14N and 18O/16O (δ15N and δ18O) of nitrate (NO3-) to gain new constraints on the δ15N of sinking nitrogen that derives from the photosynthetically active surface layer and is remineralized in the ocean interior. The δ15N of sinking nitrogen, in turn, reflects important biogeochemical processes in the ocean. For example, it can reveal (1) the spatial distribution of N2 fixation, the dominant source of biologically available nitrogen (“fixed N”) to the ocean and (2) the transport of nitrate from high to low latitude regions and its subsequent processing. Moreover, better information regarding the δ15N of sinking N would significantly improve our ability to simulate denitrification, the dominant loss mechanism for oceanic fixed N. The fixed N budget is central in the debate regarding the degree to which interactions among ocean organisms stabilize the ocean’s biogeochemical cycles, with implications for the variability of global biological fertility and of CO2 and O2 concentrations in the atmosphere. The system of nitrogen isotopes can constrain the fixed N budget, but this requires a robust estimate for the isotope effect of water column denitrification (εwcd). N isotope budgeting using an εwcd of ~25‰ (inferred from treating observations from ocean suboxic zones with the Rayleigh model) result in a global denitrification rate that is much higher than the global rate of N2 fixation and thus an ocean N budget far in deficit. Recent culture experiments indicate that εwcd may be much lower (13‰). In the context of the isotope budgeting, this value would imply a lower global rate of denitrification and a roughly balanced fixed N budget. Chapter 2 explores the case for a lower εwcd using a multi-box model framework under various assumptions regarding the routes of nitrate-bearing water transport from the high latitude regions to the denitrification zones and the δ15N of the sinking N that adds nitrate to this water during its transport to these zones. The analysis shows that, assuming a plausible δ15N range for sinking N in the low latitudes, denitrification zone observations can be reproduced with a low isotope effect of ~13‰. Further, the estimates supporting the canonical εwcd of ~25‰ may be an artifact of the inaccurate assumption that the regeneration of sinking N is a minor influence on the nitrate isotope distributions near denitrification zones. In the Atlantic, the lack of substantial water column denitrification implies that the δ15N of sinking N is exclusively sensitive to (1) the δ15N of the nitrate supply to the euphotic zone, (2) the degree of nitrate consumption in surface waters, and (3) the input of N to the surface by N2 fixation. In a large fraction of the low- to mid-latitudes of the Atlantic, surface nitrate consumption is complete, further reducing the number of potential drivers of sinking N δ15N change. The implication is that meridional gradients in the δ15N of sinking N in the Atlantic, mostly reflect the input of fixed N by N2 fixation. Given enough information on the δ15N of the nitrate supply to the euphotic zone, this link can be used to investigate the distribution of N2 fixation in the North Atlantic. Chapter 3 investigates the impact of the subduction of high latitude surface waters (SAMW) with high-δ15N (~6.2‰) and high-δ18O (~3.5‰) nitrate on the δ15N of nitrate supply to North Atlantic euphotic zone (from ~20°N to ~40°N). Nitrate isotope measurements along the zonal US GTUS transect indicate that the nitrate δ15N of SAMW- derived waters is up to ~0.6‰ higher than the δ15N of deep nitrate (~4.8‰) while the δ18O is not similarly elevated. Its low δ18O reflects that nitrate at shallow and mid-depths is mostly regenerated, masking the high δ18O of preformed nitrate from the Southern Ocean. The input of fixed N by N2 fixation to the Atlantic is reflected by (a) the isotopic difference between the nitrate δ15N of SAMW- derived waters from the US GTUS transect (~5.4‰) and the nitrate δ15N of SAMW in the Southern Ocean (~6.2‰) and (b) the low nitrate δ15N measured for southward flowing NADW in the face of the substantial contribution of SAMW-derived water (with its high nitrate δ15N) to the formation of this water mass. From an isotopic mass balance between southward- and northward- flowing waters, it is shown that most of the input of newly fixed N is accomplished south of ~40°N. Chapter 4 reports and interprets nitrate isotope data along the CLIVAR A16N, a hydrographic section from south of Iceland to 6°S in the tropical Atlantic that provides a meridional view that is closely related to the largely north/south subsurface circulation of the Atlantic. Three approaches are used to calculate the δ15N of regenerated nitrate and of sinking N. At 6°S, the nitrate δ15N of SAMW- derived waters is as high as the nitrate δ15N of SAMW in the Southern Ocean (~6.2‰), and the δ15N of sinking N is similarly elevated or higher. This result indicates that (a) nitrate assimilation is complete at the low latitudes of the Atlantic such that δ15N of sinking N is as high as the δ15N of SAMW and (b) only a small amount of newly fixed N is added to the nitrate pool in the South Atlantic. The regeneration of this high δ15N sinking N smears down high δ15N nitrate to levels deeper than northward flowing SAMW, raising the nitrate δ15N of southward flowing NADW. North of the equator, the δ15N of sinking N declines northward, with most of this decline being accomplished well south of the subtropical gyre. This suggests that the highest rates of N2 fixation for the North Atlantic occur south of 10°N, a result with implications for what controls the N2 fixation process in the basin. Chapter 5 uses nitrate δ15N measurements along different transects of the Atlantic (including A16N and US GTUS) to pursue the question of the controls on the rate of N2 fixation in the Atlantic basin. A novel strategy is developed for calculating the rate and spatial distribution of Atlantic N2 fixation, based on isotopic differences between northward- and southward-transported nitrate. It is found that 90% of the total rate of Atlantic N2 fixation (30.5 Tg N/yr north of 30°S) is controlled by the supply of excess P. This link has important consequences for the stability of the fixed N budget, implying that Atlantic N2 fixation can stabilize the ocean N-to-P ratio over the relatively short time scale of ocean overturning (~2000 yrs). However, the Atlantic currently accounts for only ~25% of global ocean N2 fixation (130 Tg N/yr), requiring that N loss in the Pacific and Indian basins is largely compensated by N2 fixation within those basins.-
dc.language.isoen-
dc.publisherPrinceton, NJ : Princeton University-
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu> catalog.princeton.edu </a>-
dc.subject.classificationBiological oceanography-
dc.titleUSE OF THE NITRATE ISOTOPES IN THE OCEAN INTERIOR TO EXPLORE THE ISOTOPIC COMPOSITION OF SINKING NITROGEN AND ITS IMPLICATIONS FOR MARINE BIOGEOCHEMICAL CYCLES-

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# Solve the following

Question:

Let $\alpha$ and $\beta$ be the roots of the equation, $5 x^{2}+6 x-2=0$. If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3, \ldots$, then :

1. (1) $6 S_{6}+5 S_{5}=2 S_{4}$

2. (2) $6 S_{6}+5 S_{5}+2 S_{4}=0$

3. (3) $5 S_{6}+6 S_{5}=2 S_{4}$

4. (4) $5 S_{6}+6 S_{5}+2 S_{4}=0$

Correct Option: , 3

Solution:

Since, $\alpha$ and $\beta$ are the roots of the equaton

$5 x^{2}+6 x-2=0$

Then, $5 \alpha^{2}+6 \alpha-2=0,5 \beta^{2}+6 \beta-2=0$

$5 \alpha^{2}+6 \alpha=2$

$5 S_{6}+6 S_{5}=5\left(\alpha^{6}+\beta^{6}\right)+6\left(\alpha^{5}+\beta^{5}\right)$

$=\left(5 \alpha^{4}+6 \alpha^{5}\right)+\left(5 \beta^{6}+6 \beta^{5}\right)$

$=\alpha^{4}\left(5 \alpha^{2}+6 \alpha\right)+\beta^{4}\left(5 \beta^{2}+6 \beta\right)$

$=2\left(\alpha^{4}+\beta^{4}\right)=2 S_{4}$


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# Does doubling density (keeping average gas molecule speed the same), increase temperature recorded on a thermometer?

Assuming an ideal gas, if you are keeping the average speed of the molecules the same then you are holding the temperature of the gas constant. Assuming the container keeps the same volume, by the ideal gas law it must be that the pressure of the gas increases as you add more molecules.

Yes there are more molecules hitting the thermometer, but that also means there are more molecules hitting the thermometer. What I mean by this is that energy can be transferred to the thermometer at a higher rate due to collisions, but collisions at the same increased rate will then transfer that energy from the thermometer back to the gas (and the same vice versa). This is how thermal equilibrium works.

So no, just because you have more gas at the same temperature doesn't mean you will record a higher temperature. More gas will just mean fewer fluctuations about the same temperature.

In addressing points made in the comments, technically the temperature of the thermometer will be somewhere between the starting temperature of the thermometer and the starting temperature of the gas, and the final temperature of the thermometer will approach the starting temperature of the gas as more gas is let in. However, there will come a point where additional gas will make the final temperature indistinguishable from the initial gas temperature, and ideally the thermometer shouldn't influence the temperature of the gas.

Now double the density (but keep the speed of individual air molecules the same). Fill the box with 2 million molecules, but keep the average speed of the molecules the same. Will it record the same temperature?

The actual temperature of the gas will be the same prior to making a reading, but the final temperature of the gas and thermometer after making the reading will depend on the heat capacity of the gas before and after doubling the number of molecules as compared to the heat capacity of the thermometer (fluid plus glass), which is fixed.

If both before and after doubling the number of molecules the heat capacity of the gas is much greater than the thermometer, then the actual temperature of the gas should not change due to the act of measurement, and the thermometer reading should not change.

Let's say the heat capacity of the gas is $$C_H$$ and the heat capacity of the thermometer, is $$C_L$$. Before making the measurement the actual temperature of the gas is $$T_H$$ (higher temperature) and the temperature of the thermometer before making the measurement is $$T_L$$, (lower temperature). Then the final equilibrium temperature $$T$$ of each will be

$$C_{H}(T_{H}-T)=C_{L}(T-T_L)$$

Now let the heat capacity of each before doubling the molecules be equal, or $$C_{H}=C_{L}$$, then

$$T=\frac{(T_{H}+T_L)}{2}$$

Now we double the number of gas molecules but the pre-measurement temperature is the same $$T_H$$. But the heat capacity heat of the gas is now double that of the thermometer, or $$C_{H}=2C_L$$. The final equilibrium is now

$$T=2/3T_{H}+1/3T_L$$

Which is higher than before doubling the number of molecules and is closer to the actual pre-reading temperature of the gas, $$T_H$$.

The more molecules you add the closer the final equilibrium temperature of the thermometer is to $$T_H$$, until the heat capacity of the gas is so much higher than the thermometer that the addition of more gas at the same pre-measurement temperature has no effect on the final temperature of either one. If there are 1000 times more molecules than the original then $$T=\frac{1000T_H}{1001}+\frac{T_L}{1000}≈T_H$$

The above said, keep in mind that in order for a thermometer to measure the actual temperature of something (i.e., the temperature that something has before applying the device), the heat capacity of what is being measured must be much greater than the heat capacity of the liquid (and glass) of the thermometer so that the temperature of what is being measured does not change.

It is kind of a cardinal rule in making any measurement that the act of making the measurement should have a minimum effect on what is being measured. If doubling the amount of gas having the same pre-reading temperature gives you a different temperature reading, then perhaps you are using the wrong temperature measuring device.

Hope this helps.


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GreedyColor - Maple Help

GraphTheory

 GreedyColor

 Calling Sequence GreedyColor(G, perm)

Parameters

 G - undirected unweighted graph perm - (optional) list of vertex labels

Description

 • The GreedyColor command colors the vertices of the graph in the order given by perm, one at a time, assigning to each vertex the smallest available color. If the permutation perm is not specified, a heuristic is used, the permutation being given by the following rule: a vertex with lowest degree is removed from the graph, the heuristic permutation for the remaining graph is determined recursively, and the removed vertex is put at the end of this permutation. This yields a coloring with at most $d+1$ colors, where $d$ is such that every subgraph of G contains a vertex of degree at most $d$. The parameter $d$ is also known as the degeneracy of G.
 • The output consists the number of colors used, followed a list that specifies the coloring of the vertices.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{C6}≔\mathrm{CycleGraph}\left(6\right)$
 ${\mathrm{C6}}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 6 vertices and 6 edge\left(s\right)}}$ (1)
 > $\mathrm{GreedyColor}\left(\mathrm{C6}\right)$
 ${2}{,}\left[{0}{,}{1}{,}{0}{,}{1}{,}{0}{,}{1}\right]$ (2)
 > $\mathrm{GreedyColor}\left(\mathrm{C6},\left[1,4,2,5,3,6\right]\right)$
 ${3}{,}\left[{0}{,}{1}{,}{2}{,}{0}{,}{1}{,}{2}\right]$ (3)


text:
# Improving Confidence Estimates for Unfamiliar Examples

Zhizhong Li

Derek Hoiem

MP4

### Abstract

Intuitively, unfamiliarity should lead to lack of confidence. In reality, current algorithms often make highly confident yet wrong predictions when faced with unfamiliar examples that are relevant but not from the training distribution. A classifier we trained to recognize gender is 12 times more likely to be wrong in a 99% confident prediction if presented with a subject from a different age group than those seen during training. In this paper, we compare and evaluate several methods to improve confidence estimates for novel and familiar samples. We propose a testing methodology of splitting novel and familiar samples by attribute (age, breed, subcategory) or sampling (similar datasets collected by different people at different times). We evaluate methods including confidence calibration, ensembles, distillation, and a Bayesian model and use several metrics to analyze label, likelihood, and calibration error. While all methods reduce over-confident errors, the ensemble of calibrated models performs best overall, and T-scaling performs best among the approaches with fastest inference.

### Paper and Oral Presentation

Li, Zhizhong, and Hoiem, Derek. “Improving Confidence Estimates for Unfamiliar Examples.” The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.

[PDF] | [Slides] | [Oral] | [Code]

Note: a previous arXiv version (v3) included erroneous results for T-scaling, where novel samples are mistakenly included in the validation set for calibration. Please disregard the results of that version.

### Bibtex

@inproceedings{li2020improving,
title={Improving Confidence Estimates for Unfamiliar Examples},
author={Li, Zhizhong and Hoiem, Derek},
booktitle={Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition},
pages={2686--2695},
year={2020}
}

### Acknowledgement

This material is based on work supported in part by NSF Award IIS-1421521, and in part by Office of Naval Research grant ONR MURI N00014-16-1-2007.


text:
PREP 2015 Question Authoring - Archived

number format control

by Douglas Young -
Number of replies: 1
I would like to control the number of decimal places webwork uses to do and display calculations. I have the following piece of code:

$vx = non_zero_random(30.0,75.0,0.1);$vx1 = $vx +$vx*non_zero_random(-0.10,0.10,0.01);

Webwork calculates a value of 53.912 for this. I would like it to round to two decimal places rather than three. This is supposed to be from data found experimentally, and having three decimal places looks like the value is known to an unrealistically high precision.
    $vx1 = sprintf("%.2f",$vx + \$vx*non_zero_random(-0.10,0.10,0.01));

I don't know of a way to force computations to be restricted to a certain number of digits, but you can force intermediate results to 2 digits along the way using sprintf() as above.


text:
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# More Creative Use of Odd Moments

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ISBN-13: 978-0-906588-65-9
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Publication date: 2008
Product number: MA2005
Keywords: CD-ROM, Classroom material


text:
# 6.5 Hitting time bounds and connectivity

The results so far in this chapter may be misleading in that upper bounds accommodating extremal graphs are rather uninformative for “typical” graphs. For a family of $n$-vertex graphs with $n\rightarrow\infty$, consider the property

 $\tau^{*}=O(n).$ (6.28)

(in this order-of-magnitude discussion, $\tau^{*}$ is equivalent to $\max_{v,x}E_{v}T_{x}$). Recalling from Chapter 3 yyy that $\tau^{*}\geq 2(n-1)$, we see that (6.28) is equivalent to $\tau^{*}=\Theta(n)$. By Matthews’ method (repeated as Theorem 2.6 below), (6.28) implies $EC=O(n\log n)$, and then by Theorem 6.31 we have $EC=\Theta(n\log n)$. Thus understanding when (6.28) holds is fundamental to understanding order-of-magnitude questions about cover times. But surprisingly, this question has not been studied very carefully. An instructive example in the $d$-dimensional torus (Chapter 5 Example yyy), where (6.28) holds iff $d\geq 3$. This example, and other examples of vertex-transitive graphs satisfying (6.28) discussed in Chapter 8, suggest that (6.28) is frequently true. More concretely, the torus example suggests that the following condition (“the isoperimetric property in $2+\varepsilon$ dimensions”) may be sufficient.

###### Open Problem 6.20

Show that for real $1/2<\gamma<1$ and $\delta>0$, there exists a constant $K_{\gamma,\delta}$ with the following property. Let $G$ be a regular $n$-vertex graph such that, for any subset $A$ of vertices with $|A|\leq n/2$, there exist at least $\delta|A|^{\gamma}$ edges between $A$ and $A^{c}$. Then $\tau^{*}\leq K_{\gamma,\delta}\ n$.

The $\gamma=1$ case is implicit in results from previous chapters. Chapter 3 yyy gave the bound $\max_{i,j}E_{i}T_{j}\leq 2\max_{j}E_{\pi}T_{j}$, and Chapter 3 yyy gave the bound $E_{\pi}T_{j}\leq\tau_{2}/\pi_{j}$. This gives the first assertion below, and the second follows from Cheeger’s inequality.

###### Corollary 6.21

On a regular graph,

 $\max_{v,x}E_{v}T_{x}\leq 2n\tau_{2}\leq 16n\tau^{2}_{c}.$

Thus the “expander” property that $\tau_{2}=O(1)$, or equivalently that $\tau_{c}=O(1)$, is sufficient for (6.28), and the latter is the $\gamma=1$ case of Open Problem 6.20.

## 6.5.1 Edge-connectivity

At the other end of the spectrum from expanders, we can consider graphs satisfying only a little more than connectivity.

xxx more details in proofs – see Fill’s comments.

Recall that a graph is $r$-edge-connected if for each proper subset $A$ of vertices there are at least $r$ edges linking $A$ with $A^{c}$. By a variant of Menger’s theorem (e.g. [86] Theorem 5.11), for each pair $(a,b)$ of vertices in such a graph, there exist $r$ paths $(a=v^{i}_{0},v^{i}_{1},v^{i}_{2},\ldots,v^{i}_{m_{i}}=b)$, $i=1,\ldots,r$ for which the edges $(v^{i}_{j},v^{i}_{j+1})$ are all distinct.

###### Proposition 6.22

For a $r$-edge-connected graph,

 $\tau^{*}\leq\frac{\bar{d}n^{2}\psi(r)}{r^{2}}$

where $\psi$ is defined by

 $\psi\left(\frac{i(i+1)}{2}\right)=i$
 $\psi(\cdot)\mbox{ is linear on }\left[\frac{i(i+1)}{2},\frac{(i+1)(i+2)}{2}% \right].$

Note $\psi(r)\sim\sqrt{2r}$. So for a $d$-regular, $d$-edge-connected graph, the bound becomes $\sim 2^{1/2}d^{-1/2}n^{2}$ for large $d$, improving on the bound from Corollary 6.9. Also, the Proposition improves on the bound implied by Chapter 4 yyy in this setting.

Proof. Given vertices $a,b$, construct a unit flow from $a$ to $b$ by putting flow $1/r$ along each of the $r$ paths $(a=v^{i}_{0},v^{i}_{1},v^{i}_{2},\ldots,v^{i}_{m_{i}}=b)$. By Chapter 3 Theorem yyy

 $E_{a}T_{b}+E_{b}T_{a}\leq\bar{d}n(1/r)^{2}M$

where $M=\sum_{i}m_{i}$ is the total number of edges in the $r$ paths. So the issue is bounding $M$. Consider the digraph of all edges $(v^{i}_{j},v^{i}_{j+1})$. If this digraph contained a directed cycle, we could eliminate the edges on that cycle, and still create $r$ paths from $a$ to $b$ using the remaining edges. So we may assume the digraph is acyclic, which implies we can label the vertices as $a=1,2,3,\ldots,n=b$ in such a way that each edge $(j,k)$ has $k>j$. So the desired result follows from

###### Lemma 6.23

In a digraph on vertices $\{1,2,\ldots,n\}$ consisting of $r$ paths $1=v^{i}_{0} and where all edges are distinct, the total number of edges is at most $n\psi(r)$.

Proof.

xxx give proof and picture.

###### Example 6.24

Take vertices $\{0,1,\ldots,n-1\}$ and edges $(i,i+u\mbox{ mod }n)$ for all $i$ and all $1\leq u\leq\kappa$.

This example highlights the “slack” in Proposition 6.22. Regard $\kappa$ as large and fixed, and $n\rightarrow\infty$. Random walk on this graph is classical random walk (i.e. sums of independent steps) on the $n$-cycle, where the steps have variance $\sigma^{2}=\frac{1}{\kappa}\sum_{u=1}^{\kappa}u^{2}$, and it is easy to see

 $\tau^{*}=2E_{0}T_{\lfloor n/2\rfloor}\sim\frac{(n/2)^{2}}{\sigma^{2}}=\Theta(n% ^{2}/\kappa^{2}).$

This is the bound Proposition 6.22 would give if the graph were $\Theta(\kappa^{2})$-edge-connected. And for a “typical” subset $A$ such as an interval of length greater than $\kappa$ there are indeed $\Omega(\kappa^{2})$ edges crossing the boundary of $A$. But by considering a singleton $A$ we see that the graph is really only $2\kappa$-edge-connected, and Proposition 6.22 gives only the weaker $O(n^{2}/\kappa^{1/2})$ bound.

xxx tie up with similar discussion of $\tau_{2}$ and connectivity being affected by small sets; better than bound using $\tau_{c}$ only.

## 6.5.2 Equivalence of mean cover time parameters

Returning to the order-of-magnitude discussion at the start of section 6.5, let us record the simple equivalence result. Recall (cf. Chapter 4 yyy) we call parameters equivalent if their ratios are bounded by absolute constants.

###### Lemma 6.25

The parameters $\max_{i}E_{i}C^{+}$, $E_{\pi}C^{+}$, $\min_{i}E_{i}C^{+}$, $\max_{i}E_{i}C$ and $E_{\pi}C$ are equivalent for reversible chains, but $\min_{i}E_{i}C$ is not equivalent to these.

Proof. Of the five parameters asserted to be equivalent, it is clear that $\max_{i}E_{i}C$ is the largest, and that either $\min_{i}E_{i}C^{+}$ or $E_{\pi}C$ is the smallest, so it suffices to prove

 $\max_{i}E_{i}C^{+}\leq 4E_{\pi}C$ (6.29)
 $\max_{j}E_{j}C^{+}\leq 3\min_{i}E_{i}C^{+}.$ (6.30)

Inequality (6.30) holds by concatenating three “cover-and-return” cycles starting at $i$ and considering the first hitting time on $j$ in the first and third cycles. In more detail, write

 $\Gamma(s)=\min\{u>s:(X_{t}:s\leq t\leq u)\mbox{ covers all states}\}.$

For the chain started at $i$ write $C^{++}=\Gamma(C^{+})$ and $C^{+++}=\Gamma(C^{++})$. Since $T_{j} we have $\Gamma(T_{j})\leq C^{++}$. So the chain started at time $T_{j}$ has covered all states and returned to $j$ by time $C^{+++}$, implying $E_{j}C^{+}\leq EC^{+++}=3E_{i}C^{+}$. For inequality (6.29), recall the random target lemma: the mean time to hit a $\pi$-random state $V$ equals $\tau_{0}$, regardless of the initial distribution. The inequality

 $E_{i}C^{+}\leq\tau_{0}+E_{\pi}C+\tau_{0}+E_{\pi}T_{i}$

follows from the four-step construction:

(i) Start the chain at $i$ and run until hitting a $\pi$-random vertex $V$ at time $T_{V}$;

(ii) continue until time $\Gamma(T_{V})$;

(iii) continue until hitting an independent $\pi$-random vertex $V^{\prime}$;

(iv) continue until hitting $i$.

But $E_{\pi}T_{i}\leq E_{\pi}C$, and then by the random target lemma $\tau_{0}\leq E_{\pi}C$, so (6.29) follows.

For the final assertion, on the lollipop graph (Chapter 5 Example yyy) one has $\min_{i}E_{i}C=\Theta(n^{2})$ while the other quantities are $\Theta(n^{3})$. One can also give examples on regular graphs (see Notes).


text:
# Adding segments to an annulus - a question regarding the conformal modulus.

Let $A \subset \mathbb{C}$ be an topological annulus, i.e. a region of $\mathbb{C}$ bounded by two disjoint Jordan curves.

Let $B \subset \mathbb{C}$ be a quadrilateral, i.e. a topological disc with four distinct marked points $(z_1,z_2,z_3,z_4)$ arranged anticlockwise on the boundary.

Both annuli and quadrilaterals, as defined above, have a conformal invariant, in both cases known as the modulus. Let $A_R$ be a geometrical annulus with inner boundary a circle of radius $1$ and outer boundary a circle of radius $R$. If $A$ can be mapped conformally and bijectively onto $A_R$ we say that $A$ has modulus $\ln{R}/2\pi$. Likewise, let $Q_m$ be a geometrical rectangle with vertices $(0, m, i+m, i)$, we say that $B$ has modulus $m$ if there exists a conformal bijection mapping $B$ onto $Q_m$ with $z_1$,$z_2$,$z_3$, and $z_4$ being mapped onto $0$, $m$, $i+m$, and $i$ respectively. The two concepts are linked by the fact that if we take a geometric annulus centred on the origin with modulus $m$, remove all the points on the positive real line from the annulus, and then take the preimage under the exponential map, we obtain (infinitely many copies of) a geometric rectangle also with modulus $m$.

My questions relate to the degree in which the choice of branch cut is arbitrary.

More particularly:

Let $C \subset \mathbb{C}$ be another annulus and represent $C$ as the union $R_1 \cup R_2$ of two simply connected regions with the intersection $R_1 \cap R_2$ consisting of two smooth simple curves $\gamma_1$ and $\gamma_2$, disjoint from each other and each of which has one end point, $x_1$ and $x_2$ respectively, on the inner boundary and one end point, $y_1$ and $y_2$ on the outer boundary. Assume we have a continuous function $f_1$ mapping $R_1$ onto $A$, and such that the restriction of $f_1$ to the interior of $R_1$ is a conformal bijection and such that the image of $\gamma_1$ and $\gamma_2$ is a single simple curve from the inner to the outer boundary of $A$, with $f_1(x_1) = f_1(x_2)$ and $f_1(y_1) = f_1(y_2)$. Similarly assume that $f_2$ is a bijection mapping $R_2$ onto $B$, conformal on the interior, with $\gamma_1$ being mapped onto the component of the boundary joining $z_1$ and $z_2$ and $\gamma_2$ being mapped to the component of the boundary joining $z_3$ and $z_4$. See the diagram below.

My first question is whether the modulus of $C$ is determined entirely by the modulus of $A$ and $B$? (This seems unlikely to me, but no harm in asking)

Secondly, if this is not the case can we give any bound for the modulus of $C$ given the modulus of $A$ and $B$.

Thirdly, are there any conditions we can impose to reduce these bounds? For example specifying that the curves $\gamma_1$ and $\gamma_2$ meet the boundary curves of $C$ orthogonally.

-

A very similar, but somewhat easier question, is the following: take $R$ a rectangle, say $[0,m]\times[0,1]$ identifying $\mathbb C$ to $\mathbb R^2$ for nicer notation. This has modulus $m$. Now let $\gamma$ be a simple curve connecting the top to the bottom sides of $R$, while staying within the rectangle. It splits it into two simply connected domains $R_1$ and $R_2$ that are topological rectangles. So each one has a modulus, say the moduli are $m_1$ and $m_2$. Do $m_1$ and $m_2$ determine $m$?

The answer is no here, because of the following two examples.

First, looking at $[0,m_1+m_2]\times[0,1]$ split vertically by $\{m_1\} \times [0,1]$, if the answer was yes, then it would have to be $m=m_1+m_2$.

Second, one can split $[0,m]\times[0,1]$ using a curve that goes back and forth many times between the neighborhood of $\{0\}\times[0,1]$ and the neighborhood ot $\{m\}\times[0,1]$. This will make both $m_1$ and $m_2$ very small, and is incompatible with their sum being equal to $m$.

Something very similar can be done in your case: take $\gamma_1$ straight, and $\gamma_2$ going back and forth between the left and right sides of $\gamma_1$. This will make the moduli of both $A$ and $B$ very small.

One thing which on the other hand is true, in the simply connected case at least, is a sub-additivity relation: with the above notation, one always has $m \geqslant m_1 + m_2$. One way to prove this is via extremal length, as follows. (Not sure the terminology is completely standard.)

Let $\rho : R=[0,m]\times[0,1] \to \mathbb R_+$. The $\rho$-length of a rectifiable curve $\gamma$ is $L_\rho(\gamma) := \int_\gamma \rho ds$ (in terms of the curvilinear coordinate). The $\rho$-width $W_\rho(R)$ of $R$ is the shortest $\rho$-length of a curve connecting the two vertical sides of $R$. The $\rho$-area of $R$ is $A_\rho(R) = \int_R \rho^2 |dz|$ (with respect to the Lebesgue measure on $R$). Then, the extremal width of $R$ is defined as $$W(R) := \sup_\rho \frac {W_\rho(R)^2} {A_\rho(R)}.$$

It is easy to define this for any topological rectangle, and to check that $\rho$ is conformally invariant. In particular it has to be a function of the modulus. In the case of the rectangle, the supremum is reached when $\rho$ is constant, in which case $W_\rho(R)=m$ and $A_\rho(R)=m$, leading to $W(R)=m$. In other words: the extremal width is just the same as the modulus.

But now, given a rectangle $R$ split into two rectangles $R_1$ and $R_2$, one can put maximizing functions $\rho_1$ and $\rho_2$ for the previous variational problem on them. This defines $\rho$ on $R$, which does not do better than the optimal one for $R$: the last sentence is exactly the inequality $m \geqslant m_1 + m_2$.

Maybe things have to be tweaked a little bit in your case, because you are gluing objects of different topologies, but the same philosophy will apply. Given more geometrical information, one might also use extremal length to derive better bounds.

Reference for all that: Ahlfors, Lars V. (1973), Conformal invariants: topics in geometric function theory, New York: McGraw-Hill Book Co., MR 0357743.

-


text:
# Cichon's diagram for computability theory

29 May 2014
17:15
Andrew Brooke-Taylor
Abstract

Cardinal characteristics of the continuum are (definitions for) cardinals that are provably uncountable and at most the cardinality c of the reals, but which (if the continuum hypothesis fails) may be strictly less than c.  Cichon's diagram is a standard diagram laying out all of the ZFC-provable inequalities between the most familiar cardinal characteristics of the continuum.  There is a natural analogy that can be drawn between these cardinal characteristics and highness properties of Turing oracles in computability theory, with implications taking the place of inequalities.  The diagram in this context is mostly the same with a few extra equivalences: many of the implications were trivial or already known, but there remained gaps, which in joint work with Brendle, Ng and Nies we have filled in.

• Logic Seminar


text:
# Store values or calculate values [closed]

We're talking about fairly anal levels of optimisation here that I wouldn't really worry about in anything other than mobile games. Let's say for example you were drawing a texture to the screen in a fairly constant position and the position of that texture could easily be calculated or stored.

I'd be interested to know what professional game developers default to in the first instance when writing code. Which of the two options below would to achieve higher performance in a majority of situations. My main development language is Java.

So option 1 is something like:

constructor {
x = container.left + offset.x;
y = container.bottom + offset.y;
}

paint {
draw(texture, x, y);
}

And option 2 is something like

paint {
draw(texture, container.left + offset.x, container.bottom + offset.y);
}

With option one the advantage is obviously that the values are pre-calculated. The disadvantages being you're using more RAM and as such there's an increased risk that the data you need wont be in the CPU cache. You also need to make sure the position is recalculated every time there's any movement.

With option two less RAM is used and therefore it's more likely data will be in the CPU cache, but there's the overhead of the calculation. We also don't need to worry about recalculation when there's movement.

## closed as off-topic by Josh♦Oct 7 '14 at 21:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Programming questions that aren't specific to game development are off-topic here, but can be asked on Stack Overflow. A good rule of thumb is to ask yourself "would a professional game developer give me a better/different/more specific answer to this question than other programmers?"" – Josh
If this question can be reworded to fit the rules in the help center, please edit the question.

• The reason this is being asked on the gamedev site is that on Stackoverflow everyone would just scream 'premature optimisation'. Game developers tend to have a better understanding of the need to write efficient code due to real time processing requirement of games. I am therefore explicitly interested in the views of game developers. – Will Calderwood Oct 8 '14 at 7:55
• That doesn't make it on-topic here, I'm afraid. – Josh Oct 8 '14 at 14:50
• @JoshPetrie Can you please explain how asking about best practices when writing games is not a game development topic? – Will Calderwood Oct 8 '14 at 14:54
• The guidance for being on-topic here is not that you are working on a game, it's that game developers are able to give a better answer than any other programmer. That's not true for this particular topic, which is about the general operation of computer hardware and compilers. Further, questions asking for broad "best practices" are discussion-oriented and not appropriate for SE. – Josh Oct 8 '14 at 15:20
• I just voted against reopening this question. Your edits didn't change the fundamental problem (in spite of you working on a game while formulating it). And the issue remains that you aren't trying to solve a problem, but rather begin a discussion about the difference between your two proposed methods. That is not how SE questions are meant to work. – Seth Battin Oct 8 '14 at 15:34

The real implications in performance here depend 100% on the platform used.

Say you have written code as in option 2.

When using a statically compiled language such as C++ the compiler will presumable not notice that container.left + offset.x is constant for as long as the object lives and it will not optimize it. When using a language that uses Just-In-Time compilation the code can be optimised at run-time when the compiler sees that the code is on the hot path and it can deduce (thanks to more information being available) that the value is constant. Allowing it to trade memory for speed. If the Jitter will actually make this decisions depends on a very complex set of rules. Here is an interesting article about the optimisations the JIT-compiler can make. Though I am still looking for the definitive source on this from Microsoft.

That being said, these kind of performance questions are almost never worth thinking about. The only real applications that benefit from these performance 'enhancements' are micro-controllers. If you're ever worried about performance use a profiler. I've been writing performance intensive code for many years and I find I can still be surprised by what part of the code is on the hot-path, and actually slowing things down.

First worry on writing code, then worry about the algorithmic complexity of the code on the hot-path, if that is still not enough dive in, trade memory for speed, investigate cache-misses and inspect the generated assembly.

• – Brian S Oct 7 '14 at 15:45

The only way to know for sure is to try both ways, as they can both be faster than each other in different circumstances. The first can be faster because less computation is done, the second can be faster because data is smaller which normally helps avoid costly cache misses. It depends totally on the context. Put another way, I could construct one benchmark that would show the first to be faster, and another benchmark to show the second is faster.

Personally, I default to the second way since it's easier to read (assuming the 'real' program 1 would have the constructor and paint method placed further apart in source). In cases where profiling hasn't been done and seems unlikely to make a large impact either way, I'll always pick the option that's most readable.

• Thanks. This isn't really about a specific situation, but rather what I should default to. It's not realistic to write every graphical element in the game both ways and profile each one to see which is more efficient. – Will Calderwood Oct 7 '14 at 13:53
• That's what I was getting at with the last sentence really - I would default to the second way unless I had profiled it and had evidence that the first way provides a benefit. But at the same time it's not practical to speculatively profile every part of every program to that depth, so you have to pick the 'likely wins' (or the biggest unknowns) to profile, which is something you only know how to do with experience. This doesn't look like a likely win to me (without knowing the wider context, of course!). So I guess a shorter answer to your question would be "option 2"! – Ben Hymers Oct 9 '14 at 12:01


text:
# mixedmath

Explorations in math and programming
David Lowry-Duda

# When are there continuous choices for the Mean Value Abscissa?

Miles Wheeler and I have recently uploaded a paper to the arXiv called "When are there continuous choices for the mean value abscissa?", which we have submitted to an expository journal. The underlying question is simple but nontrivial. Later Update: this paper was published in the American Mathematical Monthly in 2021, and won the 2022 Halmos-Ford award.

The mean value theorem of calculus states that, given a differentiable function $f$ on an interval $[a, b]$, then there exists a $c \in (a, b)$ such that $$\frac{f(b) - f(a)}{b - a} = f'(c).$$ We call $c$ the mean value abscissa. Our question concerns potential behavior of this abscissa when we fix the left endpoint $a$ of the interval and vary $b$. For each $b$, there is at least one abscissa $c_b$ such that the mean value theorem holds with that abscissa. But generically there may be more than one choice of abscissa for each interval. When can we choose $c_b$ as a continuous function of $b$? That is, when can we write $c = c(b)$ such that $$\frac{f(b) - f(a)}{b - a} = f'(c(b))$$ for all $b$ in some interval? We think of this as a continuous choice for the mean value abscissa.

This is a great question. It's widely understandable — even to students with only one semester of calculus. Further it encourages a proper understanding of what a function is, as thinking of $c$ as potentially a function of $b$ is atypical and interesting.

But I also like this question because the answer is not as simple as you might think, and there are a few nice ideas that get to the answer.

Should you find yourself reading this without knowing the answer, I encourage you to consider it right now. Should continuous choices of abscissas exist? What if the function is really well-behaved? What if it's smooth? Or analytic?

Let's focus on the smooth question. Suppose that $f$ is smooth — that it is infinitely differentiable. These are a distinguished class of functions. But it turns out that being smooth is not sufficient: here is a counterexample.

In this figure, there are points $b$ arbitrarily near $b_0$ such that the secant line from $a_0$ to $b$ have positive slope, and points arbitrarily near such that the secant lines have negative slope. There are infinitely many mean value abscissae with $f'(c_0) = 0$, but all of them are either far from a point $c$ where $f'(c) > 0$ or far from a point $c$ where $f'(c) < 0$. And thus there is no continuous choice.

From a theorem oriented point of view, our main theorem is that if $f$ is analytic, then there is always a locally continuous choice. That is, for every interval $[a_0, b_0]$, there exists a mean value abscissa $c$ such that $c = c(b)$ for some interval $B$ containing $b_0$.

But the purpose of this article isn't simply to prove this theorem. The purpose is to exposit how the ideas that are used to study this problem and to prove these results are fundamentally based only on a couple of central ideas covered in introductory single and multivariable calculus. All of this paper is completely accessible to a student having studied only single variable calculus (and who is willing to believe that partial derivatives exist are a reasonable object).

We prove and use simple-but-nontrivial versions of the contraction mapping theorem, the implicit function theorem, and Morse's lemma.

The implicit function theorem is enough to say that any abscissa $c_0$ such that $f''(c_0) \neq 0$ has a unique continuous extension. Thus immediately for "most" intervals on "most" reasonable functions, we answer in the affirmative.

Morse's lemma allows us to say a bit more about the case when $f''(c_0) = 0$ but $f'{}'{}'(c_0) \neq 0$. In this case there are either multiple continuous extensions or none. And a few small ingredients and the idea behind Morse's lemma, combined with the implicit function theorem again, is enough to prove the main result.

## Student projects

A calculus student looking for a project to dive into and sharpen their calculus skills could find ideas here to sink their teeth into. Beginning by understanding this paper is a great start. A good motivating question would be to carry on one additional step, and to study explicitly the behavior of a function near a point where $f''(c_0) = f'{}'{}'(c_0) = 0$, but $f^{(4)}(c_0) \neq 0$.

A slightly more open question that we lightly touch on (but leave largely implicit) is ther inverse question: when can one find a mean value abscissa $c$ such that the right endpoint $b$ can be written as a continuous function $b(c)$ for some neighborhood $C$ containing the initial point $c_0$? Much of the analysis is the same, but figuring it out would require some attention.

A much deeper question is to consider the abscissa as a function of both the left endpoint $a$ and the right endpoint $b$. The guiding question here could be to decide when one can write the abscissa as a continuous function $c(a, b)$ in a neighborhood of $(a_0, b_0)$.

I would be interested to see a graphical description of the possible shapes of these functions — I'm not quite sure what they might look like.

There is also a nice computational problem. In the paper, we include several plots of solution curves in $(b, c)$ space. But we did this with a meshed implicit function theorem solver. A computationally inclined student could devise an explicit way of constructing solutions.

On the one hand, this is guaranteed to work since one can apply contraction mappings explicitly to make the resulting function from the implicit function theorem explicit. But on the other hand, many (most?) applications of the implicit function theorem are in more complicated high dimensional spaces, whereas the situation in this paper is the smallest nontrivial example.

## Producing the graphs

We made 13 graphs in 5 figures for this article. These pictures were created using matplotlib. The data was created using numpy, scipy, and sympy from within the scipy/numpy python stack, and the actual creation was done interactively within a jupyter notebook. The actual notebook is available here, (along with other relatively raw jupyter notebooks). The most complicated graph is this one.

This figure has graphs of three functions along the top. In each graph, the interval $[0, 3]$ is considered in the mean value theorem, and the point $c_0 = 1$ is a mean value abscissa. In each, we also have $f''(c_0) = 0$, and the point is that the behavior of $f''(b_0)$ has a large impact on the nature of the implicit functions.

The three graphs along the bottom are in $(b, c)$ space and present all mean value abscissa for each $b$. This is not a function, but the local structure of the graphs are interesting and visually distinct.

The process of making these examples and making these figures is interesting in itself. We did not make these figures explicitly, but instead chose certain points and certain values of derivatives at those points, and used Hermite interpolation find polynomials with those points.1 1Actually, since our polynomials are not of large degree, we wrote a sort of naive Hermite interpolator in sympy and had sympy bruteforce solve for the polynomial. Arguably it would be both faster and easier to encode the problem as a linear system of equations and use a fast matrix solver... but we didn't do that.

In the future I plan on writing a note on the creation of these figures.2 2This is now done! See Choosing functions and generating figures... for more.

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text:
# Uniform prior - how to think about it when the likelihood ranges over all reals?

Consider a likelihood $x|\theta \sim N(\theta,\sigma^2)$. Now if there is no prior information an uniform prior can be chosen, that is: $p(\theta)=c$.

As such: $p(\theta|x)=\frac{1}{(2\pi\sigma^2)^{0.5}}e^{-\frac{(x-\theta)^2}{2\sigma^2}}$

All of this is fine, apart from the fact that normal distribution of course ranges over infinite values. As such $p(\theta)=c$ should not be possible, as $\theta\sim\text{Unif}(-\infty,\infty)$ is not a valid distribution.

How should the uniform prior be thought about in cases such as this?

• It's not quite clear what kind of information you're seeking there (it would help to try to clarify what you want to know), but see en.wikipedia.org/wiki/Prior_probability#Improper_priors ... there are a number of posts on site which mention this particular improper prior or improper priors in general – Glen_b May 7 '18 at 0:55
• An improper prior is not a probability density but a positive measure. Notions like uniformity and expectations and simulations do not make sense for measures. – Xi'an May 7 '18 at 11:55


text:
# How do you simplify (5 + 2sqrt2)(8 - 3sqrt2)?

Jul 19, 2018

See a solution process below:

#### Explanation:

To multiply and simplify these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{5} + \textcolor{red}{2 \sqrt{2}}\right) \left(\textcolor{b l u e}{8} - \textcolor{b l u e}{3 \sqrt{2}}\right)$ becomes:

$\left(\textcolor{red}{5} \times \textcolor{b l u e}{8}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{3 \sqrt{2}}\right) + \left(\textcolor{red}{2 \sqrt{2}} \times \textcolor{b l u e}{8}\right) - \left(\textcolor{red}{2 \sqrt{2}} \times \textcolor{b l u e}{3 \sqrt{2}}\right)$

$40 - 15 \sqrt{2} + 16 \sqrt{2} - 6 {\left(\sqrt{2}\right)}^{2}$

$40 + \left(- 15 + 16\right) \sqrt{2} - \left(6 \times 2\right)$

$40 + 1 \sqrt{2} - 12$

$40 + \sqrt{2} - 12$

$40 - 12 + \sqrt{2}$

$28 + \sqrt{2}$


text:
# 40 CFR § 98.2 - Who must report?

§ 98.2 Who must report?

(a) The GHG reporting requirements and related monitoring, recordkeeping, and reporting requirements of this part apply to the owners and operators of any facility that is located in the United States or under or attached to the Outer Continental Shelf (as defined in 43 U.S.C. 1331) and that meets the requirements of either paragraph (a)(1), (a)(2), or (a)(3) of this section; and any supplier that meets the requirements of paragraph (a)(4) of this section:

(1)A facility that contains any source category that is listed in Table A-3 of this subpart. For these facilities, the annual GHG report must cover stationary fuel combustion sources (subpart C of this part), miscellaneous use of carbonates (subpart U of this part), and all applicable source categories listed in Tables A-3 and A-4 of this subpart.

(2)A facility that contains any source category that is listed in Table A-4 of this subpart and that emits 25,000 metric tons CO2e or more per year in combined emissions from stationary fuel combustion units, miscellaneous uses of carbonate, and all applicable source categories that are listed in Table A-3 and Table A-4 of this subpart. For these facilities, the annual GHG report must cover stationary fuel combustion sources (subpart C of this part), miscellaneous use of carbonates (subpart U of this part), and all applicable source categories listed in Table A-3 and Table A-4 of this subpart.

(3)A facility that in any calendar year starting in 2010 meets all three of the conditions listed in this paragraph (a)(3). For these facilities, the annual GHG report must cover emissions from stationary fuel combustion sources only.

(i) The facility does not meet the requirements of either paragraph (a)(1) or (a)(2) of this section.

(ii) The aggregate maximum rated heat input capacity of the stationary fuel combustion units at the facility is 30 mmBtu/hr or greater.

(iii) The facility emits 25,000 metric tons CO2e or more per year in combined emissions from all stationary fuel combustion sources.

(4)A supplier that is listed in Table A-5 of this subpart. For these suppliers, the annual GHG report must cover all applicable products for which calculation methodologies are provided in the subparts listed in Table A-5 of this subpart.

(5)Research and development activities are not considered to be part of any source category defined in this part.

(b) To calculate GHG emissions for comparison to the 25,000 metric ton CO2e per year emission threshold in paragraph (a)(2) of this section, the owner or operator shall calculate annual CO2e emissions, as described in paragraphs (b)(1) through (b)(4) of this section.

(1) Calculate the annual emissions of CO2, CH4, N2O, and each fluorinated GHG in metric tons from all applicable source categories listed in paragraph (a)(2) of this section. The GHG emissions shall be calculated using the calculation methodologies specified in each applicable subpart and available company records.

(2) For each general stationary fuel combustion unit, calculate the annual CO2 emissions in metric tons using any of the four calculation methodologies specified in § 98.33(a). Calculate the annual CH4 and N2O emissions from the stationary fuel combustion sources in metric tons using the appropriate equation in § 98.33(c). Exclude carbon dioxide emissions from the combustion of biomass, but include emissions of CH4 and N2O from biomass combustion.

(3) For miscellaneous uses of carbonate, calculate the annual CO2 emissions in metric tons using the procedures specified in subpart U of this part.

(4) Sum the emissions estimates from paragraphs (b)(1), (b)(2), and (b)(3) of this section for each GHG and calculate metric tons of CO2e using Equation A-1 of this section.

${CO}_{2}e=\sum _{i=1}^{n}{\mathrm{GHG}}_{i}×{\mathrm{GWP}}_{i}\phantom{\rule{8em}{0ex}}\text{(Eq. A-1)}$
Where:
CO2e = Carbon dioxide equivalent, metric tons/year.
GHGi = Mass emissions of each greenhouse gas, metric tons/year.
GWPi = Global warming potential for each greenhouse gas from Table A-1 of this subpart.
n = The number of greenhouse gases emitted.

(5) For purpose of determining if an emission threshold has been exceeded, include in the emissions calculation any CO2 that is captured for transfer off site.

(c) To calculate GHG emissions for comparison to the 25,000 metric ton CO2e/year emission threshold for stationary fuel combustion under paragraph (a)(3) of this section, calculate CO2, CH4, and N2O emissions from each stationary fuel combustion unit by following the methods specified in paragraph (b)(2) of this section. Then, convert the emissions of each GHG to metric tons CO2e per year using Equation A-1 of this section, and sum the emissions for all units at the facility.

(d) To calculate GHG quantities for comparison to the 25,000 metric ton CO2 per year threshold for importers and exporters of coal-to-liquid products under paragraph (a)(4) of this section, calculate the mass in metric tons per year of CO2 that would result from the complete combustion or oxidation of the quantity of coal-to-liquid products that are imported during the reporting year and, that are exported during the reporting year. Compare the imported quantities and the exported quantities separately to the 25,000 metric ton CO2 per year threshold. Calculate the quantities using the methodology specified in subpart LL of this part.

(e) To calculate GHG quantities for comparison to the 25,000 metric ton CO2e per year threshold for importers and exporters of petroleum products under paragraph (a)(4) of this section, calculate the mass in metric tons per year of CO2 that would result from the complete combustion or oxidation of the combined volume of petroleum products and natural gas liquids that are imported during the reporting year and that are exported during the reporting year. Compare the imported quantities and the exported quantities separately to the 25,000 metric ton CO2 per year threshold. Calculate the quantities using the methodology specified in subpart MM of this part.

(f) To calculate GHG quantities for comparison to the 25,000 metric ton CO2e per year threshold under paragraph (a)(4) of this section for importers and exporters of industrial greenhouse gases and for importers and exporters of CO2, the owner or operator shall calculate the mass in metric tons per year of CO2e imports and exports as described in paragraphs (f)(1) through (f)(3) of this section. Compare the imported quantities and the exported quantities separately to the 25,000 metric ton CO2 per year threshold.

(1) Calculate the mass in metric tons per year of CO2, N2O, and each fluorinated GHG that is imported and the mass in metric tons per year of CO2, N2O, and each fluorinated GHG that is exported during the year.

(2) Convert the mass of each imported and each GHG exported from paragraph (f)(1) of this section to metric tons of CO2e using Equation A-1 of this section.

(3) Sum the total annual metric tons of CO2e in paragraph (f)(2) of this section for all imported GHGs. Sum the total annual metric tons of CO2e in paragraph (f)(2) of this section for all exported GHGs.

(g) If a capacity or generation reporting threshold in paragraph (a)(1) of this section applies, the owner or operator shall review the appropriate records and perform any necessary calculations to determine whether the threshold has been exceeded.

(h) An owner or operator of a facility or supplier that does not meet the applicability requirements of paragraph (a) of this section is not subject to this rule. Such owner or operator would become subject to the rule and reporting requirements, if a facility or supplier exceeds the applicability requirements of paragraph (a) of this section at a later time pursuant to § 98.3(b)(3). Thus, the owner or operator should reevaluate the applicability to this part (including the revising of any relevant emissions calculations or other calculations) whenever there is any change that could cause a facility or supplier to meet the applicability requirements of paragraph (a) of this section. Such changes include but are not limited to process modifications, increases in operating hours, increases in production, changes in fuel or raw material use, addition of equipment, and facility expansion.

(i) Except as provided in this paragraph, once a facility or supplier is subject to the requirements of this part, the owner or operator must continue for each year thereafter to comply with all requirements of this part, including the requirement to submit annual GHG reports, even if the facility or supplier does not meet the applicability requirements in paragraph (a) of this section in a future year.

(1) If reported emissions are less than 25,000 metric tons CO2e per year for five consecutive years, then the owner or operator may discontinue complying with this part provided that the owner or operator submits a notification to the Administrator that announces the cessation of reporting and explains the reasons for the reduction in emissions. The notification shall be submitted no later than March 31 of the year immediately following the fifth consecutive year of emissions less than 25,000 tons CO2e per year. The owner or operator must maintain the corresponding records required under § 98.3(g) for each of the five consecutive years prior to notification of discontinuation of reporting and retain such records for three years following the year that reporting was discontinued. The owner or operator must resume reporting if annual emissions in any future calendar year increase to 25,000 metric tons CO2e per year or more.

(2) If reported emissions are less than 15,000 metric tons CO2e per year for three consecutive years, then the owner or operator may discontinue complying with this part provided that the owner or operator submits a notification to the Administrator that announces the cessation of reporting and explains the reasons for the reduction in emissions. The notification shall be submitted no later than March 31 of the year immediately following the third consecutive year of emissions less than 15,000 tons CO2e per year. The owner or operator must maintain the corresponding records required under § 98.3(g) for each of the three consecutive years and retain such records for three years prior to notification of discontinuation of reporting following the year that reporting was discontinued. The owner or operator must resume reporting if annual emissions in any future calendar year increase to 25,000 metric tons CO2e per year or more.

(3) If the operations of a facility or supplier are changed such that all applicable processes and operations subject to paragraphs (a)(1) through (4) of this section cease to operate, then the owner or operator may discontinue complying with this part for the reporting years following the year in which cessation of such operations occurs, provided that the owner or operator submits a notification to the Administrator that announces the cessation of reporting and certifies to the closure of all applicable processes and operations no later than March 31 of the year following such changes. If one or more processes or operations subject to paragraphs (a)(1) through (4) of this section at a facility or supplier cease to operate, but not all applicable processes or operations cease to operate, then the owner or operator is exempt from reporting for any such processes or operations in the reporting years following the reporting year in which cessation of the process or operation occurs, provided that the owner or operator submits a notification to the Administrator that announces the cessation of reporting for the process or operation no later than March 31 following the first reporting year in which the process or operation has ceased for an entire reporting year. Cessation of operations in the context of underground coal mines includes, but is not limited to, abandoning and sealing the facility. This paragraph (i)(3) does not apply to seasonal or other temporary cessation of operations. This paragraph (i)(3) does not apply to the municipal solid waste landfills source category (subpart HH of this subpart), or the industrial waste landfills source category (subpart TT of this part). The owner or operator must resume reporting for any future calendar year during which any of the GHG-emitting processes or operations resume operation.

(4) The provisions of paragraphs (i)(1) and (2) of this section apply to suppliers subject to subparts LL through QQ of this part by substituting the term “quantity of GHG supplied” for “emissions.” For suppliers, the provisions of paragraphs (i)(1) and (2) apply individually to each importer and exporter and individually to each petroleum refinery, fractionator of natural gas liquids, local natural gas distribution company, and producer of CO2, N2O, or fluorinated greenhouse gases (e.g., a supplier of industrial greenhouse gases might qualify to discontinue reporting as an exporter of industrial greenhouse gases but still be required to report as an importer; or a company might qualify to discontinue reporting as a supplier of industrial greenhouse gases under subpart OO of this part but still be required to report as a supplier of carbon dioxide under subpart PP of this part).

(5) If the operations of a facility or supplier are changed such that a process or operation no longer meets the “Definition of Source Category” as specified in an applicable subpart, then the owner or operator may discontinue complying with any such subpart for the reporting years following the year in which change occurs, provided that the owner or operator submits a notification to the Administrator that announces the cessation of reporting for the process or operation no later than March 31 following the first reporting year in which such changes persist for an entire reporting year. The owner or operator must resume complying with this part for the process or operation starting in any future calendar year during which the process or operation meets the “Definition of Source Category” as specified in an applicable subpart.

(6) If an entire facility or supplier is merged into another facility or supplier that is already reporting GHG data under this part, then the owner or operator may discontinue complying with this part for the facility or supplier, provided that the owner or operator submits a notification to the Administrator that announces the discontinuation of reporting and the e-GGRT identification number of the reconstituted facility no later than March 31 of the year following such changes.

(j) Table A-2 of this subpart provides a conversion table for some of the common units of measure used in part 98.

[74 FR 56374, Oct. 30, 2009, as amended at 75 FR 39758, July 12, 2010; 75 FR 57685, Sept. 22, 2010; 76 FR 73899, Nov. 29, 2011; 75 FR 74487, Nov. 30, 2010; 79 FR 73776, Dec. 11, 2014; 81 FR 89248, Dec. 9, 2016]


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## The mechanisms that a Trade Logic system would need

### Previously

I introduced and specified Trade Logic, and posted a fair bit about it.

### Now

Here's another post that's mostly a bullet-point list. In this post I try to mostly nail down all the mechanisms TL needs in order to function as intended. Some of it, notably the treatment of selector bids, is still only partly defined.

## The mechanisms that a TL system needs

• Pre-market
• Means to add definitions (understood to include selectors and bettable issues)
• Initiated by a user
• A definition is only accepted if it completely satisfies the typechecks
• Definitions that are accepted persist.
• In active market
• Holdings
• A user's holdings are persistent except as modified by the other mechanisms here.
• Initiated by a user
• User specifies:
• Price
• How much
• How long the order is to persist.
• A trade is accepted just if:
• The user holds that amount or more of what he's selling.
• It can be met from booked orders
• It is to be retained as a booked order
• Booked orders persist until either:
• Acted on
• Cancelled
• Timed out
• Issue conversion
• Initiated by a user
• User specifies:
• What to convert from
• What to convert to
• How much
• A trade is accepted just if:
• It's licensed by one of the conversion rules
• User has sufficient holdings to convert from
• Selectors - where the system meets the outside world. Largely TBD.
• As part of each selector issue, there is a defined mechanism that can be invoked.
• Its actions when invoked are to:
• Present itself to the outside world as invoked.
• Also present its invocation parameters.
• But not reveal whether it was invoked for settlement (randomly) or as challenge (user-selected values)
• Be expected to act in the outside world:
• Make a unique selection
• Further query that unique result. This implies that selector issues are parameterized on the query, but that's still TBD.
• Translate the result(s) of the query into language the system understands.
• Present itself to the system as completed.
• Accept from the real world the result(s) of that query.
• How it is described to the system is TBD. Possibly the format it is described in is yet another parameter of a selector.
• How an invocable mechanisms is described to the system is still to be decided.
• (NB, a selector's acceptability is checked by the challenge mechanism below. Presumably those selectors that are found viable will have been defined in such a way as to be randomly inspectable etc; that's beyond my scope in this spec)
• Challenge mechanism to settle selector bets
• Initiated by challengers
• (What's available to pro-selector users is TBD, but probably just uses the betting mechanism above)
• Challenger specifies:
• The value that the choice input stream should have. It is basically a stream of bits, but:
• Where split-random-stream is encountered, it will split and the challenger will specify both branches.
• Challenger can specify that from some point on, random bits are used.
• Probably some form of good-faith bond or bet on the outcome
• The selector is invoked with the given values.
• Some mechanism queries whether exactly one individual was returned (partly undecided).
• The challenge bet is settled accordingly.
• There may possibly also be provision for multi-turn challenges ("I bet you can't specify X such that I can't specify f(X)") but that's to be decided.
• Settling (Usually post-market)
• Public fair random-bit generating
• Initiated as selectors need it.
• For selectors, some interface for retrieving bits just as needed, so that we may use pick01 etc without physically requiring infinite bits.
• This interface should not reveal whether it's providing random bits or bits given in a challenge.
• Mechanism to invoke selectors wrt a given bet:
• It decides:
• Whether to settle it at the current time.
• If applicable, "how much" to settle it, for statistical bets that admit partial settlement
• Probably a function of:
• The cost of invoking its selectors
• Random input
• An ancillary market judging the value of settlement
• Logic that relates the settlement of convertible bets. (To be decided, probably something like shares of the ancillary markets of convertible bets being in turn convertible)
• Being activated, it in fact invokes particular selectors with fresh random values, querying them.
• In accordance with the results of the query:
• Shares of one side of the bet are converted to units
• Shares of the other side are converted to zeros.
• But there will also be allowance for partial results:
• Partial settlement
• Sliding payoffs

### Previously

I initially said that the basic choice operator in TL was pick01, which outputs a random scalar between 0 and 1.

## What's wrong with pick01 as basic

It occurs to me that picking a random scalar is not the most basic thing we could do.

It also occurred to me that pick01 as defined needs to provide infinite precision, which of course isn't physically realizable.

It couldn't be sensibly defined to generate both exact 0 and exact 1.

And the fact that I forget whether its interval was left-closed or right-closed suggests that there's a problem there.

## So pick-boolean

So from infinite to minimal: pick-boolean is analogous to pick01, except that it outputs a bit, not a scalar.

## But it shouldn't be unary

The temptation is to make pick-boolean unary. But if we did, it wouldn't be like other unary predicates. When two instances of these pick-boolean have the same inputs (ie, none), the outputs are not neccessarily the same. This lack of referential transparency potentially infects the outputs of any predicate that uses pick-boolean. This would restrict and complicate the conversions we are allowed to make.

So instead, let's provide a system random stream. A "random output" predicate such as pick-boolean will actually be ternary; its args will be:

• Input bitstream
• Output bitstream
• Output random

This has the nice property that it gives us an upper bound on a proposition's sample space: It's the difference in position between the input stream and the output stream. Of course, that is not always predetermined.

We said earlier that bettable propositions had no arguments, and we need these to be bettable, so we have to revise slightly: A definition is bettable if its only inputs and outputs are system random streams, which will be a type.

There's another way this treatment is helpful: Sometimes we want to sample to settle issues (population bets). Such issues can sample by using the random stream argument, which feeds any selectors that are involved.

Random stream arguments also help validate selectors by challenge - the challenger specifies the bitstream. In this one case, the output bitstream is useful. It gives the various random calls an ordering, otherwise the challenger couldn't specify the bitstream.

## Stream splitting

But sometimes a single stream doesn't work nicely. A predicate like pick01 may need to use arbitrarily many bits to generate arbitrary precision. So what can it do? It shouldn't consume the entire stream for itself, and it shouldn't break off just a finite piece and pass the rest on.

So let's provide split-random-stream. It inputs a random stream and outputs two random streams. We'll provide some notation for a challenger to split his specified stream accordingly.

## Can't be built by users

We will provide no way to build an object of this new type from first principles. Users can get two of them from one by using split-random-stream, but can't get one from none. So the only way to have one is to get it from an input. Ultimately any proposition that uses a random stream must get it from system mechanisms of proposition resolution such as sampling and challenging.

## New pieces

So let's define these built-ins:

• Type: random-stream, the type of the system's random stream. No built-in predicate has any mode that outputs this type but doesn't also input it.
• split-random-stream, ternary predicate that inputs a random stream and outputs two random streams.
• pick-boolean, a ternary predicate outputting a bit.
• Type: lazy scalar. A lazy scalar can only be compared with given precision, not compared absolutely. So any comparison predicates that take this also manage precision, possibly by inputting an argument giving the required precision.
• pick01, ternary, outputs a lazy scalar.
• Convenience
• Maybe pick-positive-rational, similar but picking binarily from a Stern-Brocot tree.
• Maybe pick-from-bell-curve, similar but picking lazily from the standard bell curve.

## Kernel WYSIWYG rooted digraphs

### Previously

I said in comments that I view backquote as a WYSIWYG tree ctor, analogous to list'.

## That's not fully general

But backquote doesn't suffice to construct the most general form of open structure of pairs, a rooted digraph. Those require the ability to share objects between multiple parents.

## Things that don't do the job

One could write shared objects by naming objects in a let' form and including them by name. That's not WYSIWYG, though. WYSIWYG would at least present the objects in place once, as #N# / #N= reader notation does.

But that's in the reader. It's not available to general code.

## What to do

One could:

• Enclose the whole construction in an empty let'.
• Provide a combiner expanding to ($sequence ($define! x DEF) x)`

## Signals, continuations, constraint-handling, and more

### Previously

I wrote about mutability and signals and automatically forcing promises where they conflict with required types.

## Signals for Constraint-handling

Constraint-handling, and specifically the late-ordered evaluation it uses, could be treated by signals. Something like this:

• Promises are our non-ground objects. They are, if you think about it, analogous to Prolog variables.
• They can be passed around like objects.
• But they're not "really" objects yet.
• For them to "succeed", there must be some value that they can take.
• That value can be determined after they are passed.
• Everything else is either ground or a container that includes one or more of them.
• As I already do in Klink, use of an non-ground argument is detected where it's unacceptable.
• Generally, they're unacceptable where a type is expected (eg they're acceptable as arguments to cons)
• Unlike what I do now, non-ground unacceptables send signals to a scheduler.
• This implies that each evaluation is uniquely related to (owned by) one scheduler.
• That signal passes as objects
• the continuation as object.
• The promise to be forced.
• It is the job of the scheduler to ensure that the resulting computation completes.
• In appropriate circumstances, eg with resource-quotas, or when doing parallel searches, it is reasonable to not complete.

## An analogy

Computations whose flow can't be changed are analogous to constant objects and flow-changable ones analogous to mutable ones.

## Another use: Precision

This mechanism could also be useful for "dataflow" precision management. Here the objects are not exactly promises, but they are incomplete in a very precise way. They are always numbers but their precision can be improved by steps.

Combiners that require more precision could signal to their generators, which could signal back their new values, propagating back their own requirements as needed. This is very manageable.

## Apply-continuation and signals can mutually define

apply-continuation, while it could be used to implement signals, can also be implemented by signals between evaluations. It signals a scheduler to schedule the given continuation and deschedule the current continuation.

Done this way, it gives a scheduler flexibility. This might appear to make analysis more difficult. But a simple (brain-dead) scheduler could do it exactly the continuation way: exactly one evaluation is "in control" at all times. This might be the default scheduler.

In both cases this functionality is a neither-fish-nor-fowl hybrid between objects and computational flow. ISTM it has to be so.

## signals allow indeterminate order

One mixed blessing about signals is that since they are "broadcast" 1-to-N, it can be indeterminate what is to be evaluated in what order.

• Pro: This gives schedulers flexibility.
• Con: Computations can give different results.
• Continuation-based scheduling doesn't neccessarily do better. It could consult "random" to determine the order of computations.
• Pro: Signals and their schedulers give us another handle to manage evaluation order dependency. A scheduler could co-operate with analysis by:
• Promising that evaluations will behave "as if" done in some particular order.
• Taking into account analysis
• Providing information that makes analysis easier, short of simulating the scheduler.
• Probably promising that no signals escape the scheduler itself, or only a few well-behaved ones do.
• Pro: Regardless of the scheduler, analysis can treat signals as a propagating fringe. Everything not reached by the fringe is unaffected.

## Should signal-blockers cause copies?

I suggested earlier that combiners might promise non-mutation by blocking mutation signals out.

One way to code this is to make such combiners deep-copy their arguments. Should this situation automatically cause copies to be made? ISTM yes.

• Not an issue: User confusion. There is no case where a user reasonably expects different functionality than he gets.
• He might expect a function to mutate an object and it doesn't - but why is he expecting that of a function that doesn't claim to mutate anything and moreover explicitly blocks that from happening? Bad docs could mislead him, but that's a documentation issue.
• Not an issue: Performance.
• Performance is always secondary to correctness.
• Performance can be rescued by
• copy-on-write objects
• immutable objects
• Analysis proving that no mutation actually occurs.


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# Fakultät für Mathematik und Informatik (inkl. GAUSS)

## Auflistung nach

We show that for a strong extension of discrete measured groupoids $1\to\mathcal{S}\to\mathcal{G}\to\mathcal{Q}\to 1$ with $L\mathcal{G}$ a finite factor, $\mathcal{Q}$ has poperty (T) if and only if the inclusion of ...


text:
CMS Conference Reports

უკანასკნელი დამატებები:
2018-12-12
09:54
 Evidence for light-by-light scattering and limits on axion-like-particles from ultraperipheral PbPb collisions at 5 TeV / Niedziela, Jeremi (CERN) /CMS Collaboration A measurement of light-by-light scattering, $\gamma\gamma \rightarrow \gamma\gamma$, in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of $5.02$ TeV is reported. The analysis is conducted using a data sample corresponding to an integrated luminosity of $390~\mu \rm{b}^{-1}$ recorded by the CMS experiment at the LHC. [...] CMS-CR-2018-403.- Geneva : CERN, 2018 - 6 p. Fulltext: PDF; In : Hard Probes 2018: International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, Aix-les-bains, France, 1 - 5 Oct 2018

2018-12-12
09:54
 Particle Flow reconstruction in the Level-1 trigger at CMS for the HL-LHC / Petrucciani, Giovanni (CERN) /CMS Collaboration With the planned addition of the tracking information in the Level-1 trigger in CMS for the HL-LHC, the algorithms for the Level-1 trigger can be completely reconceptualized. Following the example for offline reconstruction in CMS to use complementary subsystem information and mitigate pileup, we explore the feasibility of using Particle Flow-like and pileup-per-particle identification techniques at the hardware trigger level. [...] CMS-CR-2018-401.- Geneva : CERN, 2018 - 6 p. Fulltext: PDF; In : 23rd International Conference on Computing in High Energy and Nuclear Physics, CHEP 2018, Sofia, Bulgaria, 9 - 13 Jul 2018

2018-12-12
09:12
 Charged Higgs searches at CMS / Yu, Geum Bong (Seoul Natl. U.) /CMS Collaboration Observation of charged Higgs bosons would be a strong evidence of new physics beyond the standard model. An overview of the latest results on the charged Higgs boson searches, as of August 2018, performed by the CMS collaboration is presented.. CMS-CR-2018-389.- Geneva : CERN, 2018 - 5 p. Fulltext: PDF; In : 25th Rencontres du Vietnam, Quy Nhon, Vietnam, 5 - 11 Aug 2018

2018-12-12
09:12
 Search for charged Higgs bosons with the $\text{H}^{\pm} \rightarrow \tau^{\pm}\nu_{\tau}$ decay channel / Eysermans, Jan (Puebla U., Inst. Fis.) ; Pedraza Morales, Maria Isabel (Puebla U., Inst. Fis.) /CMS Collaboration A search for charged Higgs bosons decaying into a tau lepton and a neutrino is presented in the hadronic and leptonic final states. The search is based on the 13 TeV dataset with 35.9 fb$^{-1}$ of integrated luminosity collected with the CMS experiment in 2016. [...] CMS-CR-2018-361.- Geneva : CERN, 2018 - 10 p. Fulltext: PDF; In : 7th workshop on prospects for charged Higgs discovery at colliders, Uppsala, Sweden, 25 - 28 Sep 2018

2018-12-12
09:12
 Characterization of the first prototype of the Silicon-Strip readout ASIC (SSA) for the CMS Outer-Tracker phase-2 upgrade / Caratelli, Alessandro (CERN) ; Scarfi', Simone (CERN) ; Ceresa, Davide (CERN) ; De Clercq, Jarne Theo (Vrije U., Brussels) ; Haranko, Mykyta (DESY) ; Jan Kaplon ; Kloukinas, Konstantinos (CERN) ; Yusuf Leblebici The silicon strip readout ASIC (SSA) for the CMS Outer Tracker PS module was prototyped in a $$65\,nm$$ CMOS technology and characterized utilizing a custom made test bench based on the FC7 $$\mu$$TCA FPGA card. The ASIC has been evaluated and characterised under different working temperatures and radiation levels up to $$200\,Mrad$$. [...] CMS-CR-2018-286.- Geneva : CERN, 2018 - 6 p. Fulltext: PDF; In : Topical Workshop on Electronics for Particle Physics, Antwerp, Belgique, 17 - 21 Sep 2018

2018-12-10
16:09
 The CMS Tracker Upgrade for the High Luminosity LHC / Delcourt, Martin (Louvain U.) /CMS Collaboration The LHC machine is planning an upgrade program which will smoothly bring the luminosity to about $5\times10^{34}$cm$^{-2}$s$^{-1}$ in 2028, to possibly reach an integrated luminosity of 4000fb$^{-1}$ by the end of 2037. This High-Luminosity LHC scenario, HL-LHC, will require a preparation program of the LHC detectors known as Phase-2 upgrades. [...] CMS-CR-2018-086.- Geneva : CERN, 2018 - 5 p. Fulltext: PDF; In : Frontier Detectors for Frontier Physics XIV Pisa Meeting on Advanced Detectors, La Biodola, Isola D'elba, Italy, 27 May - 2 Jun 2018

2018-12-10
16:07
 The upgraded front-end electronics of the CMS electromagnetic calorimeter for the HL-LHC / Cometti, Simona (INFN, Turin) /CMS Collaboration The Compact Muon Solenoid detector was originally designed to operate for about ten years, for LHC instantaneous luminosity up to 1$\cdot$10$^{34}$ cm$^{-2}$ s$^{-1}$ and integrated luminosity of 500 fb$^{-1}$. The High Luminosity LHC will increase the instantaneous luminosity by about a factor of 5 from current levels and CMS will accumulate an integrated luminosity of 3000 fb$^{-1}$ by about 2035.With such high luminosity the electromagnetic calorimeter of CMS will have to cope with a challenging increase in number of interactions per bunch crossing and in radiation levels.The front-end readout electronics will be completely redesigned, with the goals of providing precision timing, low noise, sampling rate 4 times higher than the current one and added flexibility in the trigger system.. CMS-CR-2018-129.- Geneva : CERN, 2018 - 4 p. Fulltext: PDF; In : 17th Incontri di Fisica delle Alte Energie, Milan, Italy, 04 - 06 Apr 2018

2018-12-10
16:07
 Anomaly detection using Deep Autoencoders for the assessment of the quality of the data acquired by the CMS experiment / Pol, Adrian Alan (CERN) /CMS Collaboration The certification of the CMS experiment data as usable for physics analysis is a crucial task to ensure the quality of all physics results published by the collaboration. Currently, the certification conducted by human experts is labor intensive and based on the scrutiny of distributions integrated on several hours of data taking. [...] CMS-CR-2018-202.- Geneva : CERN, 2018 - 6 p. Fulltext: PDF; In : 23rd International Conference on Computing in High Energy and Nuclear Physics, CHEP 2018, Sofia, Bulgaria, 9 - 13 Jul 2018

2018-12-10
16:07
 CMS ECAL Detector Control System Upgrade Plan for the CERN Large Hadron Collider Long Shutdown II / Jimenez Estupinan, Raul (Zurich, ETH) /CMS Collaboration The Electromagnetic Calorimeter (ECAL) is one of the detectors of the Compact Muon Solenoid (CMS) experiment at the CERN Large Hadron Collider (LHC). The ECAL Detector Control System (DCS) software has been implemented using the WinCC Open Architecture (OA) platform. [...] CMS-CR-2018-230.- Geneva : CERN, 2018 - 5 p. Fulltext: PDF; In : 12th International Workshop on Personal Computers and Particle Accelerator Controls, Hsinchu, Taiwan, 16 - 19 Oct 2018

2018-12-10
16:05
 A 65 nm Data Concentration ASIC for the CMS Outer Tracker Detector Upgrade at HL-LHC / Nodari, Benedetta (Lyon, IPN) ; Caponetto, Luigi (Lyon, IPN) ; Galbit, Geoffrey Christian (Lyon, IPN) ; Scarfi', Simone (CERN) ; Viret, Sebastien (Lyon, IPN) The Concentrator Integrated Circuit (CIC) ASIC is a front-end chip for both Pixel-Strip (PS) and Strip-Strip (2S) modules of the future Phase-II CMS Outer Tracker upgrade at the High Luminosity LHC (HL-LHC). It collects the digital data coming from eight upstream front-end chips (either MPAs or CBCs, depending on the module type), formats the signal in data packets containing the trigger information from eight bunch crossings and the raw data from events passing the first trigger level, and finally transmits them to the LpGBT unit. [...] CMS-CR-2018-278.- Geneva : CERN, 2018 - 6 p. Fulltext: PDF; In : Topical Workshop on Electronics for Particle Physics, Antwerp, Belgique, 17 - 21 Sep 2018