text:
# Segmenting Aerial LIDAR Data

This is a short notebook outlining my procedure on the “interview project” for the MIT ESI’s Nature Based Solutions group to train a model to segment aerial lidar data.

# Data Processing

### External (QGIS3) Work

There was only one provided image of training data, which was a subset of the larger test data image. I crop the “test” image to include only the portion where label data was available using QGIS3 and load this image alongside the label data, GRSS_DFC_GT_TR.tif. I saved this to my google drive so I can easily load it within colab.

### Split Training and Validation.

img = open_image('/content/drive/My Drive/geotiff/training_data/cropped_training_data.tif')
img.show(y=labels, alpha=0.5, figsize=(25, 25))

The data is pretty uniformly distributed vertically. To get a roughly uniform distribution of classes between training and validation, I decide to have the validation set be the bottom 1/10 of the image. This is DEFINITELY not the best approach to take, but it is simple to implement. In the future, splitting the image into grids and then sampling the grids to ensure the training and validation have similar distributions is the way to go.

plt.style.use(['dark_background'])

img_data = img.data
c, h, w = img_data.shape
train_size = round(0.9 *h)
train_img = Image(img.data[:, :train_size, :])
val_img = Image(img.data[:, train_size:, :])
train_labels = ImageSegment(labels.data[:, :train_size, :])
val_labels = ImageSegment(labels.data[:, train_size:, :])

_,axs = plt.subplots(2,2, figsize=(15,8))
train_img.show(ax=axs[0][0], y=train_labels, title='Training Set')
val_img.show(ax=axs[1][0], y=val_labels, title='Validation Set')

axs[0][1].hist(train_labels.data.flatten())
axs[0][1].set_title('Training Label Distribution')
axs[0][1].set_xticks(list(range(21)))
axs[0][1].ticklabel_format(style='plain') # disable scientific notation

axs[1][1].hist(val_labels.data.flatten())
axs[1][1].set_title('Validation Label Distribution')
axs[1][1].set_xticks(list(range(21)))

As you can see, the distribution of labels in the training and validation sets is at least roughly similar, though it can definitely be optimized with some smarter methods in the future.

### Save Data

!mkdir -p images
train_img.save('images/train.png')
val_img.save('images/val.png')
!mkdir -p labels
train_labels.save('labels/train.png')
train_labels.save('labels/val.png')

codes = [str(i) for i in range(21)] # label ids, since these were not provided in the training set

get_label_image = lambda x: f'labels/{x.stem}{x.suffix}'
src = (SegmentationItemList
.from_folder('images')
.split_by_files(ItemList(['val.png']))
.label_from_func(get_label_image,  classes=codes))

### Transformations

I encode random transformations such as vertical and horizontal flipping as well as random cropping of the image to a 200x200 size. I also normalize the input data to match the imagenet statistics, as I’m going to use a ImageNet pretrained Resnet for the UNet segmentation method.

data = (src.transform(get_transforms(), size=(200,200),
tfm_y=True, resize_method=ResizeMethod.CROP)
data = data.databunch(bs=1, num_workers=0).normalize(imagenet_stats))

### Metrics

Here I defined the acc_camvid metric:

$$\text{Accuracy}_\text{camvid} = \dfrac{\text{# of Correctly Classified Pixels}}{\text{Total # of Pixels}}$$

This snippet was pasted from: https://towardsdatascience.com/image-segmentation-with-fastai-9f8883cc5b53

name2id = {v:k for k,v in enumerate(codes)}
void_code = 3000

def acc_camvid(input, target):
target = target.squeeze(1)

# Training

### Define Model

Here I define the model to use a pretrained Resnet34 and initialize some basic parameters.

metrics=acc_camvid
wd=1e-2

learn = unet_learner(data, models.resnet34, metrics=metrics, wd=wd)

### Auto-Tune Learning Rate

First introduced by Leslie N. Smith in Cyclical Learning Rates for Training Neural Networks, the LR Finder trains the model with exponentially growing learning rates from start_lr to end_lr for num_it and stops in case of divergence (unless stop_div=False) then plots the losses vs the learning rates with a log scale.

A good value for the learning rates is then either:

• one tenth of the minimum before the divergence
• when the slope is the steepest
lr_find(learn)
learn.recorder.plot()

### Training Loop

learn.fit_one_cycle(2000, slice(1e-06,1e-03), pct_start=0.9)

# Validation

Due to VRAM limitations on Google Colab, I cannot run the model on the full input images. This would be easily possible with access to more VRAM or even RAM if you wanted run the model on a CPU.

Instead, I opt to split the image into smaller grids and infer on each of these images separately. Then I concatenate all of the images back together.

Here I do this for the strip of validation and evaluate the model accuracy.

learn.data.single_dl.dataset.tfmargs['size'] = None
out = learn.predict(val_img)
size = 2000
val_grid = np.array_split(val_img.data, round(im.shape[2]/2000), axis=2)
val_grid = [learn.predict(Image(x))[0].data for x in val_grid]
val_result = torch.cat(val_grid, axis=2)
print(f'Validation Accuracy = {(val_result==val_labels.data).float().mean()*100.0:.2f}%')

Validation Accuracy = 73.67%

# Testing

Now, we qualitatively test on the unlableled test dataset (which also includes the trainining/validation dataset). We use the same gridding method here.

### Splitting

size = 500
im = open_image('/content/drive/My Drive/geotiff/test_data.tif').data

grid = np.array_split(im, round(im.shape[1]/size), axis=1)
grid = [np.array_split(row, round(im.shape[2]/size), axis=2) for row in grid]

### Inference

for i in range(len(rows)):
for j in range(len(rows[0])):
grid[i][j] = learn.predict(Image(grid[i][j]))

### Concatenation

result = []
for i in range(len(rows)):
result.append(torch.cat([grid[i][j][0].data for j in range(len(grid[i]))], dim=2))
result = torch.cat(result, dim=1)

# Final Result

im = open_image('/content/drive/My Drive/geotiff/test_data.tif').resize((1,2500,8500))
im.show(y=ImageSegment(result), alpha=0.75, figsize=(50, 50))

### Compare Distributions

_,ax = plt.subplots(1,2, figsize=(20,6))
ax[0].hist(labels.data.flatten())
ax[0].set_xticks(list(range(21)))
ax[0].ticklabel_format(style='plain')
ax[0].set_title('Train/Validation Label Distribution')

ax[1].hist(result.data.flatten())
ax[1].set_xticks(list(range(21)))
ax[1].ticklabel_format(style='plain')
ax[1].set_title('Output Label Distribution')

# Conclusion - Reflection - Future Work

• It’s clear that because of the unequal distribution of the data provided, the model ignores some of the classes that are represented less often. This could be addressed by changing the weighting/importance of these labels in the loss function. Given time constraints, I will leave this as future work.
• Many of the buildings to the right of the image, which were not included in the training data are not properly identified. Doing more data augmentation/increasing the size of the training set could improve these results.
• I accidentally trained the model to take in three input channels (the image has 3 when loaded) but each channel is the same. This is a total waste, so in the next iteration I would retrain it without the extra channels.
• I doubled the number of training examples (from 1000 –> 2000) and the performance increased significantly. I’m pretty confident that increasing it more would improve accuracy, so I leave this for future work as well.

I did all of the coding for this project in one one evening. Because of this, I didn’t have a chance to experiment with the other provided datasets or fine-tune the model as much as I would have liked. This was unavoidable however, as I needed time to adjust to my first two days of classes @ MIT. I’m pretty happy with the project overall.

##### Sauhaarda (Raunak) Chowdhuri
###### Machine Learning Researcher and Undergraduate Student

My research interests include multi-modal learning, explainable-AI, and few-shot/one-shot/representation learning.


text:
#### Realizing GANs via a Tunable Loss Function

##### Gowtham R. Kurri, Tyler Sypherd, Lalitha Sankar

We introduce a tunable GAN, called $\alpha$-GAN, parameterized by $\alpha \in (0,\infty]$, which interpolates between various $f$-GANs and Integral Probability Metric based GANs (under constrained discriminator set). We construct $\alpha$-GAN using a supervised loss function, namely, $\alpha$-loss, which is a tunable loss function capturing several canonical losses. We show that $\alpha$-GAN is intimately related to the Arimoto divergence, which was first proposed by \"{O}sterriecher (1996), and later studied by Liese and Vajda (2006). We posit that the holistic understanding that $\alpha$-GAN introduces will have practical benefits of addressing both the issues of vanishing gradients and mode collapse.

arrow_drop_up

format: plain


text:
# Akame

Statement:

Akame is training on an infinite 2D Cartesian plane. There is an infinitely long rigid and vertical string at each integer x-coordinate. She takes out her katana, Murasame, and makes $N$ $N$ infinitely long slashes on the plane. Each slash can be seen as a line with the equation $Ax+By=C$ $Ax + By = C$, for some $A$ $A$, $B$ $B$, and $C$ $C$. A slash will never be a vertical line.

Each string Akame slashes will immediately be broken into two smaller strings. For example, a string originally from $\left(5,-\mathrm{\infty }\right)$ $(5, -\infty)$ to $\left(5,\mathrm{\infty }\right)$ $(5, \infty)$ severed by the line $0x+1y=3$ $0x + 1y = 3$ will be broken into the two strings $\left(5,-\mathrm{\infty }\right)$ $(5, -\infty)$ to $\left(5,3\right)$ $(5, 3)$ and $\left(5,3\right)$ $(5, 3)$ to $\left(5,\mathrm{\infty }\right)$ $(5, \infty)$. A string is considered disconnected if it is of a finite length. For example, the string from $\left(1,9\right)$ $(1, 9)$ to $\left(1,\mathrm{\infty }\right)$ $(1, \infty)$ is not of finite length, but the string from $\left(8,-3\right)$ $(8, -3)$ to $\left(8,4\right)$ $(8, 4)$ is.

There are $M$ $M$ points on strings Akame wants to disconnect. A point is said to be disconnected if it is either slashed or the string it's on is disconnected. To measure her performance, Akame would like to know the earliest moment (that is, after which slash) each point is disconnected. The slashes are numbered from $1$ $1$ to $N$ $N$.

Input:

The first line of input will have $N$ $N$ and $M$ $M$, separated by a single space.

The next $N$ $N$ lines of input will each describe one of Akame's slashes, with $A$ $A$, $B$ $B$, and $C$ $C$ separated by spaces.

The next $M$ $M$ lines of input will each describe a point Akame wants to disconnect, with $X\mathrm{_}i$ $X\_i$ and $Y\mathrm{_}i$ $Y\_i$.

Output:

There should be $M$ $M$ lines of output. The $i-th$ $i-th$ line should contain the smallest index of the slash that after it is performed, the $i-th$ $i-th$ point is disconnected. If the $i-th$ $i-th$ point is never disconnected, print -1 instead.

Constraints:

$1\le N\le 500\phantom{\rule{thinmathspace}{0ex}}000$ $1 \le N \le 500\,000$

$1\le M\le 500\phantom{\rule{thinmathspace}{0ex}}000$ $1 \le M \le 500\,000$

$0\le A,|C|\le 30\phantom{\rule{thinmathspace}{0ex}}000$ $0 \le A, |C| \le 30\,000$

$1\le |B|\le 30\phantom{\rule{thinmathspace}{0ex}}000$ $1 \le |B| \le 30\,000$

$0\le |X\mathrm{_}i|,|Y\mathrm{_}i|\le {10}^{9}$ $0 \le |X\_i|, |Y\_i| \le 10^9$

Example input 1
3 5
0 1 3
0 1 5
0 1 7
1 2
1 3
1 4
1 5
1 6

Example output 1
-1
1
2
2
3

Example input 2
10 10
81 -36 72
64 -69 24
23 47 47
83 36 18
1 25 77
12 -81 -3
13 -90 -34
23 19 -34
19 23 78
50 -96 82
56 59
85 47
46 -23
1 13
-74 -69
23 99
-98 72
-31 -65
-78 76
9 -69

Example output 2
2
3
4
-1
2
-1
4
2
4
-1

Time and memory limit:

• 10s
• 1024MB

Problem source: DMOJ


text:
# zbMATH — the first resource for mathematics

$$L^2$$-norm and estimates from below for Riesz transforms on Cantor sets. (English) Zbl 1259.42010
Authors’ abstract: The aim of this paper is to estimate the $$L^2$$-norms of vector-valued Riesz transforms $$R_{\nu}^s$$ and the norms of Riesz operators on Cantor sets in $$\mathbb{R}^d$$, as well as to study the distribution of the values of $$R_{\nu}^s$$. Namely, we show that this distribution is “uniform” in the following sense. The values of $$|R_{\nu}^s|^2$$ which are comparable with its average value are present on a “big” portion of a Cantor set. We apply these results to give examples demonstrating the sharpness of our previous estimates for the set of points where the Riesz transform is large, and for the corresponding Riesz capacities. The Cantor sets under consideration are different from the usual corner Cantor sets. They are constructed by means of a certain process of regularization introduced in the paper.

##### MSC:
 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 30C85 Capacity and harmonic measure in the complex plane 31B15 Potentials and capacities, extremal length and related notions in higher dimensions 28A78 Hausdorff and packing measures 28A80 Fractals
Full Text:


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References

Category:Software companies of CroatiaQ:

How to solve the cubic equation $x^3-2x^2+7x-3=0$?

How can this cubic equation:
$$x^3-2x^2+7x-3=0$$
be solved? I know that when you encounter a cubic equation, there are three cases, but I can’t see how to apply them here. Thanks.

A:

Consider the solutions to the quadratic
$$(x-1)(x-3)=0$$
The solutions are
$$x=1, x=3$$
The equation can be written as
$$(x-1)(x-3) + \epsilon x^2 = 0$$
The discriminant $\Delta = (-3)^2 + 4 \cdot 1 \cdot (-1) = 7$ is never $0$ and so we need to consider the zeros to the cubic
$$f(x) = x^3 – 2x^2 + 7x-3$$
At this point you have three cases…
Case 1) If $x=1$, we get $0 = 3 – 2 \cdot 1 + 7 – 3$
This adds up to $0 = -0 + 0 + 0 – 0 = 0$. The roots are all real.
Case 2) If $x=3$, we get $0 = 9 – 6 \cdot 3 + 21 – 9$.
This adds up to $0 = 0 – 18 + 0$. The roots are all real.
Case 3) If $\Delta > 0$, the cubic has real roots.
So if we have
$$x^3 – 2x^2 + 7x-3 = 0$$
We will have real roots if we have $-2 0$, or equivalently
$$1 0 or$$
7 > 4 \cdot 1 \cdot -2 + 7 > 4 \cdot 1 \cdot (-2 + 7)
$$or equivalently$$
0 > -9 + 12 \cdot 1 > 0

and this holds only if \$1
570a42141b


text:
# Central series

(Redirected from Lower central series)
Jump to navigation Jump to search

In mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, this is an explicit expression that the group is a nilpotent group, and for matrix rings, this is an explicit expression that in some basis the matrix ring consists entirely of upper triangular matrices with constant diagonal.

This article uses the language of group theory; analogous terms are used for Lie algebras.

The lower central series and upper central series (also called the descending central series and ascending central series, respectively), are, despite the "central' in their names, are central series if and only if a group is nilpotent.

## Definition

A central series is a sequence of subgroups

${\displaystyle \{1\}=A_{0}\triangleleft A_{1}\triangleleft \dots \triangleleft A_{n}=G}$

such that the successive quotients are central; that is, [G, Ai + 1] ≤ Ai, where [G, H] denotes the commutator subgroup generated by all g−1h−1gh for g in G and h in H. As [G, Ai + 1] ≤ AiAi + 1, in particular Ai + 1 is normal in G for each i, and so equivalently we can rephrase the 'central' condition above as: Ai + 1/Ai commutes with all of G/Ai.

A central series is analogous in Lie theory to a flag that is strictly preserved by the adjoint action (more prosaically, a basis in which each element is represented by a strictly upper triangular matrix); compare Engel's theorem.

A group need not have a central series. In fact, a group has a central series if and only if it is a nilpotent group. If a group has a central series, then there are two central series whose terms are extremal in certain senses. Since A1Z(G), the largest choice for A1 is precisely A1 = Z(G). Continuing in this way to choose the largest possible Ai + 1 given Ai produces what is called the upper central series. Dually, since An= G, the commutator subgroup [G, G] satisfies [G, G] = [G, An] ≤ An − 1. Therefore, the minimal choice for An − 1 is [G, G]. Continuing to choose Ai minimally given Ai + 1 such that [G, Ai + 1] ≤ Ai produces what is called the lower central series. These series can be constructed for any group, and if a group has a central series (is a nilpotent group), these procedures will yield central series.

## Lower central series

The lower central series (or descending central series) of a group G is the descending series of subgroups

G = G1G2 ⊵ ⋯ ⊵ Gn ⊵ ⋯,

where each Gn + 1 = [Gn, G], the subgroup of G generated by all commutators [x, y] with x in Gn and y in G. Thus, G2 = [G, G] = G(1), the derived subgroup of G; G3 = [[G, G], G], etc. The lower central series is often denoted γn(G) = Gn.

This should not be confused with the derived series, whose terms are G(n) := [G(n−1),G(n−1)], not Gn := [Gn−1, G]. The series are related by G(n)Gn. In particular, a nilpotent group is a solvable group, and its derived length is logarithmic in its nilpotency class (Schenkman 1975, p. 201,216).

For infinite groups, one can continue the lower central series to infinite ordinal numbers via transfinite recursion: for a limit ordinal λ, define Gλ = ∩ { Gα : α < λ}. If Gλ = 1 for some ordinal λ, then G is said to be a hypocentral group. For every ordinal λ, there is a group G such that Gλ = 1, but Gα ≠ 1 for all α < λ, (Malcev 1949).

If ω is the first infinite ordinal, then Gω is the smallest normal subgroup of G such that the quotient is residually nilpotent, that is, such that every non-identity element has a non-identity homomorphic image in a nilpotent group (Schenkman 1975, p. 175,183). In the field of combinatorial group theory, it is an important and early result that free groups are residually nilpotent. In fact the quotients of the lower central series are free abelian groups with a natural basis defined by basic commutators, (Hall 1959, Ch. 11).

If Gω = Gn for some finite n, then Gω is the smallest normal subgroup of G with nilpotent quotient, and Gω is called the nilpotent residual of G. This is always the case for a finite group, and defines the F1(G) term in the lower Fitting series for G.

If GωGn for all finite n, then G/Gω is not nilpotent, but it is residually nilpotent.

There is no general term for the intersection of all terms of the transfinite lower central series, analogous to the hypercenter (below).

## Upper central series

The upper central series (or ascending central series) of a group G is the sequence of subgroups

${\displaystyle 1=Z_{0}\triangleleft Z_{1}\triangleleft \cdots \triangleleft Z_{i}\triangleleft \cdots ,}$

where each successive group is defined by:

${\displaystyle Z_{i+1}=\{x\in G\mid \forall y\in G:[x,y]\in Z_{i}\}}$

and is called the ith center of G (respectively, second center, third center, etc.). In this case, Z1 is the center of G, and for each successive group, the factor group Zi + 1/Zi is the center of G/Zi, and is called an upper central series quotient.

For infinite groups, one can continue the upper central series to infinite ordinal numbers via transfinite recursion: for a limit ordinal λ, define

${\displaystyle Z_{\lambda }(G)=\bigcup _{\alpha <\lambda }Z_{\alpha }(G).}$

The limit of this process (the union of the higher centers) is called the hypercenter of the group.

If the transfinite upper central series stabilizes at the whole group, then the group is called hypercentral. Hypercentral groups enjoy many properties of nilpotent groups, such as the normalizer condition (the normalizer of a proper subgroup properly contains the subgroup), elements of coprime order commute, and periodic hypercentral groups are the direct sum of their Sylow p-subgroups (Schenkman 1975, Ch. VI.3). For every ordinal λ there is a group G with Zλ(G) = G, but Zα(G) ≠ G for α < λ, (Gluškov 1952) and (McLain 1956).

## Connection between lower and upper central series

There are various connections between the lower central series and upper central series (Ellis 2001), particularly for nilpotent groups.

Most simply, a group is abelian if and only if the LCS terminates at the first step (the commutator subgroup is trivial) if and only if the UCS stabilizes at the first step (the center is the entire group). More generally, for a nilpotent group, the length of the LCS and the length of the UCS agree (and is called the nilpotency class of the group).

However, the LCS stabilizes at the zeroth step if and only if it is perfect, while the UCS stabilizes at the zeroth step if and only if it is centerless, which are distinct concepts, and show that the lengths of the LCS and UCS (interpreted to mean the length before stabilization) need not agree in general.

For a perfect group, the UCS always stabilizes by the first step, a fact called Grün's lemma. However, a centerless group may have a very long lower central series: a free group on two or more generators is centerless, but its lower central series does not stabilize until the first infinite ordinal.

## Refined central series

In the study of p-groups, it is often important to use longer central series. An important class of such central series are the exponent-p central series; that is, a central series whose quotients are elementary abelian groups, or what is the same, have exponent p. There is a unique most quickly descending such series, the lower exponent-p central series λ defined by:

λ1(G) = G, and
λn + 1(G) = [G, λn(G)] (λn(G))p

The second term, λ2(G), is equal to [G, G]Gp = Φ(G), the Frattini subgroup. The lower exponent-p central series is sometimes simply called the p-central series.

There is a unique most quickly ascending such series, the upper exponent-p central series S defined by:

S0(G) = 1
Sn+1(G)/Sn(G) = Ω(Z(G/Sn(G)))

where Ω(Z(H)) denotes the subgroup generated by (and equal to) the set of central elements of H of order dividing p. The first term, S1(G), is the subgroup generated by the minimal normal subgroups and so is equal to the socle of G. For this reason the upper exponent-p central series is sometimes known as the socle series or even the Loewy series, though the latter is usually used to indicate a descending series.

Sometimes other refinements of the central series are useful, such as the Jennings series κ defined by:

κ1(G) = G, and
κn + 1(G) = [G, κn(G)] (κi(G))p, where i is the smallest integer larger than or equal to n/p.

The Jennings series is named after S. A. Jennings who used the series to describe the Loewy series of the modular group ring of a p-group.

## References

• Ellis, Graham (October 2001), "On the Relation between Upper Central Quotients and Lower Central Series of a Group", Transactions of the American Mathematical Society, 353 (10): 4219–4234, doi:10.1090/S0002-9947-01-02812-4, JSTOR 2693793
• Gluškov, V. M. (1952), "On the central series of infinite groups", Mat. Sbornik N.S., 31: 491–496, MR 0052427
• Hall, Marshall (1959), The theory of groups, Macmillan, MR 0103215
• Malcev, A. I. (1949), "Generalized nilpotent algebras and their associated groups", Mat. Sbornik N.S., 25 (67): 347–366, MR 0032644
• McLain, D. H. (1956), "Remarks on the upper central series of a group", Proc. Glasgow Math. Assoc., 3: 38–44, doi:10.1017/S2040618500033414, MR 0084498
• Schenkman, Eugene (1975), Group theory, Robert E. Krieger Publishing, ISBN 978-0-88275-070-5, MR 0460422, especially chapter VI.


text:
## 题目描述

Eddy was a contestant participating in ACM ICPC contests. ACM is short for Algorithm, Coding, Math. Since in the ACM contest, the most important knowledge is about algorithm, followed by coding(implementation ability), then math. However, in the ACM ICPC World Finals 2018, Eddy failed to solve a physics equation, which pushed him away from a potential medal.
Since then on, Eddy found that physics is actually the most important thing in the contest. Thus, he wants to form a team to guide the following contestants to conquer the PACM contests(PACM is short for Physics, Algorithm, Coding, Math).
There are N candidate groups each composed of pi physics experts, ai algorithm experts, ci coding experts, mi math experts. For each group, Eddy can either invite all of them or none of them. If i-th team is invited, they will bring gi knowledge points which is calculated by Eddy’s magic formula. Eddy believes that the higher the total knowledge points is, the better a team could place in a contest. But, Eddy doesn’t want too many experts in the same area in the invited groups. Thus, the number of invited physics experts should not exceed P, and A for algorithm experts, C for coding experts, M for math experts.
Eddy is still busy in studying Physics. You come to help him to figure out which groups should be invited such that they doesn’t exceed the constraint and will bring the most knowledge points in total.

（不过 lyy 说通过压位可以）

（中间一次过掉是用了标程）

❤采之欲遗谁，所思在远道。❤
0%


text:
Saturday, July 21, 2012

The Doe and by; Debbie Wilson

The Doe and I

Gazing in amazement at the small and frightened doe,
I was overcome with recognition; she was so familiar.
As she timidly scampered by, I felt a loving kinship,
it dawned on me that it was my actions that were similar.

She was finding safety in the denseness of the forrest,
exactly as I sought safety in the boundaries of my home.
Both of us timid about the safety and sequence of our future,
equally we searched for a safe and protected location to roam.

When I observed the alarm and fright in that pretty little face,
I realized that through survival the little doe had learned fear.
How my heart agonized as I struggled to try and comprehend,
the specific reasons the doe would not allow or tolerate me near.

Then I realized the doe was defending and  protecting herself,
secure in her habitat, but frightened by anything new or strange.
She may have been previously frightened by uncaring people,
she is rightfully alarmed and suspiscious of any unexpected change.

The doe must have been given reason to be cautious and distrusting.
Someone must have previously inflicted her with alarm or fear.
So she had to learn how to adequately survive in a brutal world.
And her skittishness was a safe way to avoid future mistreatment.

I wanted to reach out and :teach the little doe about security and trust.
I wanted so badly for her to take a baby step out of the protective trees.
Could  she eventually be taught about a trustworthy outstretched hand?
Would she then be able to triumph over all the new things she sees?

by: Debbie Wilson
http://www.noahsarkconsulting.blogspot.com/


text:
# FAQ¶

## Why is it called fruitbat?¶

A lot of time was spent trying to figure out a ‘nice’ acronym, however none of the potential names seemed to fit. So I decided to just name it after an animal. After searching through lists of Australian animals I remembered the family of fruitbats (grey-headed flying foxes) that live in the tree in the front of my house. Fruitbat had the letters FRB in order and their orange necks reminded me of waterfall plots so I decided to go with the name Fruitbat.

## I’d rather use the NE2001 model. Is this compatible with Fruitbat?¶

Yes! However you will need to install the python port of the NE2001 model. You can find installation and usage instructions here.

Alternatively, you can calculate the galactic DM using any version of the NE2001 model first and then use that value for dm_galaxy.

>>> ne2001_dm = 34.5
>>> import fruitbat
>>> FRB = fruitbat.Frb(dm=325, dm_galaxy=ne2001_dm, gl="32.4", gb="16.2")


text:
# Effect of local stress on the heat-checking morphology in high temperature tool steels under thermal fatigue: Transition from multi-axiality to uniaxiality

Abstract : Thermal fatigue experiments are performed on a high temperature tool steel X38CrMoV5 (AISI H11), under various maximum temperatures and heating rates. A microscopic interconnected crack pattern (named heat-checking'') forms on the oxidised surface of the laboratory tubular specimen. A gradual transition is observed, from a cell-type'' cracking at the centre of the specimen to a parallel cracking'' at its extremities. This variation of the morphology is well demonstrated by geometrical and topological characteristics of the crack network (micro-crack orientations, cell shape and node density), which change along the longitudinal axis of the specimen. The thermo-elasto-plastic loading of the specimen is estimated by Finite Element Calculations using ABAQUS (TM). Whatever the thermal fatigue conditions, a linear correlation can be established between the longitudinal and hoop stress amplitude ratio Delta sigma(zz)/Delta sigma(00) and the hoop and longitudinal inter-crack spacing ratio d(00)/d(zz) It is shown that a stress amplitude ratio close to 1 results in a multi-axial heat-checking, while a uni-axial cracking is generated when Delta sigma(zz)/Delta sigma(00) is close to or below 0.6. This means that the morphology of the heat-checking pattern (cell or parallel type) can be used as an indicator for the local stress ratio of the thermal fatigue specimen or industrial real tools. (C) 2013 Elsevier Ltd. All rights reserved.
Keywords :
Type de document :
Article dans une revue

https://hal.archives-ouvertes.fr/hal-01611608
Contributeur : Mines Albi Ecole Nationale Supérieure Des Mines d'Albi-Carmaux <>
Soumis le : vendredi 6 octobre 2017 - 10:58:44
Dernière modification le : mercredi 14 mars 2018 - 16:44:48

### Citation

F. Medjedoub, S. Le Roux, G. Dour, Farhad Rezai-Aria. Effect of local stress on the heat-checking morphology in high temperature tool steels under thermal fatigue: Transition from multi-axiality to uniaxiality. Mechanics of Materials, Elsevier, 2014, 69 (1), p. 159-172. 〈http://www.sciencedirect.com/science/article/pii/S0167663613002056〉. 〈10.1016/j.mechmat.2013.09.014〉. 〈hal-01611608〉

### Métriques

Consultations de la notice


text:
## Functiones et Approximatio Commentarii Mathematici

### Estimates of the approximation error for abstract sampling type operators in Orlicz spaces

#### Abstract

We get some inequalities concerning the modular distance $I^\varphi_G[Tf -f]$ for bounded functions $f:G\rightarrow \mathbb{R}.$ Here $G$ is a locally compact Hausdorff topological space provided with a regular and $\sigma$-finite measure $\mu_G,$ $I^\varphi_G$ is the modular functional generating the Orlicz spaces $L^\varphi(G)$ and $T$ is a nonlinear integral operator of the form $$(Tf)(s) = \int_H K(s,t, f(t)) d\mu_H(t),$$ where $H$ is a closed subset of $G$ endowed with another regular and $\sigma$-finite measure $\mu_H.$ As a consequence we obtain a convergence theorem for a net of such operators. Some applications to discrete operators are given.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 36 (2006), 45-70.

Dates
First available in Project Euclid: 18 December 2008


text:
# calcium is metal or metalloid or nonmetal in thailand

#### ™ "Is calcium metal nonmetal or metalloid" Keyword …

Is calcium a metal nonmetal or metalloid Temax.gob DA: 12 PA: 50 MOZ Rank: 62 Metals are good conductors of heat and electricity, and are malleable (they can be hammered into sheets) and ductile (they can be drawn into wire) It is in fact a noble gas

#### How can we determine if samples are metals nonmetals …

Calcium is a chemical element with the syol Ca and atomic nuer 20. As an alkaline earth metal , calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. It is the fifth most abundant element in Earth''s crust and the third most abundant metal , after iron and aluminium.

#### Is potassium a metal or nonmetal? | Study

The loion of an element on the periodic table can tell us if it is a metal, metalloid or non-metal. Answer and Explanation: Become a Study meer to unlock this answer!

#### 3.8: Electron Configurations and the Periodic Table - …

2020/8/13· Every element can be classified as either a metal, a nonmetal, or a metalloid (or semi metal), as shown in Figure $$\PageIndex{2}$$. A metal is a substance that is shiny, typically (but not always) silvery in color, and an excellent conductor of electricity and heat.

#### Is potassium a metal or nonmetal? | Study

The loion of an element on the periodic table can tell us if it is a metal, metalloid or non-metal. Answer and Explanation: Become a Study meer to unlock this answer!

#### Metal, Nonmetal, or Metalloid - Northern Highlands Regional …

Metal, Nonmetal, or Metalloid? Objective: Explore the physical and chemical properties of eight elements with the goal of classifying them as metals, nonmetals, or metalloids. Background: Physical Properties: – properties that can be observed without changing

#### Metal, Nonmetal, or Metalloid? - Hall High School

Metal, Nonmetal, or Metalloid? Lab Background Elements have unique physical and chemical properties, which make them useful for specific purposes in our everyday world. All known elements can be classified as metals, nonmetals, or metalloids according to

#### Nia''s Sf: Metal Lab Report

2011/7/6· Metal or Nonmetal Lab Report July 5, 2011 Nia C, Rana K & Eden L Summer Chemistry Dr. Forman Abstract: Two main groups that split up the periodic table are metals and nonmetals. Metals conduct electricity, are malleable, have luster, and react with many

#### Is calcium a metal or a mineral? - Quora

Pure Calcium is a metal in the alkaline earth elements family (group 2). It is a metal. Calcium is a soft reactive metal and because it is so reactive, it does not occur in a pure state in nature. Therefore, because it is not naturally occurring, Calcium is not a mineral.

#### a) 1, 2, and 14 b) 1, 2, and 18 c) 1, 2, and 17 d) 2, 13, and 17 - …

c) Classify this element as a metal, nonmetal, or metalloid. d) In the box below, draw a Lewis electron-dot structure for this element. e) List two other elements likely to have properties similar to this element. Bonus (1 pt.) 1) The radius of a calcium ion is

#### Carbon : non - metal : : Germanium

Calcium is an element with atomic nuer 20. Stating the reason, answer the following questions : i) Is calcium a metal or non-metal ? ii) Will it be larger or smaller than …

#### Nonmetal, Metal or Metalloid Flashcards | Quizlet

Metal, Nonmetal or Metalloid Calcium Metal Metal, Nonmetal or Metalloid Titanium Metal Metal, Nonmetal or Metalloid Chromium Metal Metal, Nonmetal or Metalloid Iron Metal Metal, Nonmetal or Metalloid Cobalt

#### Is potassium a metal or nonmetal? | Study

The loion of an element on the periodic table can tell us if it is a metal, metalloid or non-metal. Answer and Explanation: Become a Study meer to unlock this answer!

#### Is calcium a nonmetal or a metalloid? - Answers

2015/3/2· Calcium is considered a Metal since is in position 2 of the Periodic Table, it is also malleable which is a property of metals and it has also a high melting and boiling point (as shown below

#### METALLOID | meaning in the Caridge English Dictionary

metalloid definition: 1. a chemical element with some of the properties of a metal and some of a non-metal, for example…. Learn more. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the

#### Is Copper a Metal, Nonmetal or Metalloid?

2015/8/5· Copper is a reddish metal with the chemical syol of Cu. The word copper comes from the Latin “cuprum,” which means "metal from Cyprus." In ancient times, the island of Cyprus was a mining site for copper. Dating back to prehistoric times, copper was one of the earliest metals known to man.

#### Metals, nonmetals, and metalloids | Chemistry 101…

Identify each of the following elements as a metal, a nonmetal, or a metalloid: a. calcium b. sulfur c. a shiny element d. an element that is a gas at room temperature e. loed in Group $8 \mathrm{A}(18)$ f. bromine g. boron h. silver

#### 3.8: Electron Configurations and the Periodic Table - …

2020/8/13· Every element can be classified as either a metal, a nonmetal, or a metalloid (or semi metal), as shown in Figure $$\PageIndex{2}$$. A metal is a substance that is shiny, typically (but not always) silvery in color, and an excellent conductor of electricity and heat.

#### Metals, Nonmetals or Metalloids Tree Map METALS NONMETALS METALLOIDS

Metals, Nonmetals and Metalloids Tree Map Analyze the periodic table and notes/graphic organizer to classify each of the following elements as a metal, nonmetal or metalloid in the Tree Map Fluorine Calcium Boron Potassium Iodine Aluminum Silicon Selenium Carbon

#### Carbon : non - metal : : Germanium

Calcium is an element with atomic nuer 20. Stating the reason, answer the following questions : i) Is calcium a metal or non-metal ? ii) Will it be larger or smaller than …

#### 3.8: Electron Configurations and the Periodic Table - …

2020/8/13· Every element can be classified as either a metal, a nonmetal, or a metalloid (or semi metal), as shown in Figure $$\PageIndex{2}$$. A metal is a substance that is shiny, typically (but not always) silvery in color, and an excellent conductor of electricity and heat.

#### Classify each element as metal, nonmetal, or metalloids: …

Answer and Explanation: Metals can be found on the left side of the periodic table while nonmetals are found on the right side. Somewhere between metals and nonmetals lie metalloids or

#### METALLOID | meaning in the Caridge English Dictionary

metalloid definition: 1. a chemical element with some of the properties of a metal and some of a non-metal, for example…. Learn more. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the

#### is calcium a metal nonmetal or metalloid - Work Hard …

Nitrogen is a (non-metal) Bromine is also a (non-metal) Calcium is (a metal) When in doubt it is best to remeer that metals are on the left side of the periodic table with the exception of hydrogen, the metalloids act as a slanting dividing line between the metals and nonmetals, and the nonmetals ….

#### Is calcium a metal or a mineral? - Quora

Pure Calcium is a metal in the alkaline earth elements family (group 2). It is a metal. Calcium is a soft reactive metal and because it is so reactive, it does not occur in a pure state in nature. Therefore, because it is not naturally occurring, Calcium is not a mineral.

#### Juanito_Alvarado_-_Metals_and_Nonmetals_worksheet - …

Determine whether the element Calcium is a metal or a nonmetal without looking at a periodic table. How can this be determined? Metals are shiny, malleable and good conductors whereas nonmetals are dull, brittle an insulators. 4. How do metals and

#### identify each element as a metal, metalloid nonmetal

2021/2/20· Identify each element as a metal, nonmetal or metalloid. You will perform the same tests and/or observations at each station. Give two examples of elements for each egory a. Noble gases b. A nonmetal is an element that does not have the properties of a metal. The periodic table shows the syols and names of the elements. It … Using the periodic table, identify each element as a metal, a


text:
# Our Research Fields

### Observational Constraints on Dark Energy

The accelerating expansion of the universe confirmed to a precision level during the past two decades is consistent with the existence of a cosmological constant whose value is fine tuned to be close to the one indicated by the scale of the present day Hubble parameter. The expansion rate predicted in the context of this cosmological constant is of the form $H^2 (z) = H_{0}^{2}[\Omega_{0m}(1+z)^{3} + \Omega_{DE}(z)]$ and is the cornerstone of the standard $\Lambda$CDM cosmological model. One of the main goals of our research is the use of a wide range of cosmological data to test the validity of the $\Lambda$CDM model searching for specific types of deviations of this expansion rate as a function of redshift. This search started in 2004 with the well cited paper entitled  “A comparison of cosmological models using recent supernova data”  (one of the pioneering works in this subject with more than 200 citations) and has continued with a series of well cited papers including (but not limited to) the following:

More recent relevant publications on this subject include:

### Theoretical Models of Dark Energy – Modified Gravity and their Cosmological Predictions

Even though the expansion rate predicted by a cosmological constant appears to be consistent with the majority of cosmological observations, the predicted parameter values of $\Lambda$CDM are not always consistent among different observational probes. These are the well known tensions of $\Lambda$CDM which include the $H_{0}$ tension and the growth tension. This fact, along with the fine-tuning required for fixing the value of the cosmological constant, has lead to a wide range of alternative models and expansion rate parametrizations aiming at providing improved quality of fit to the cosmological data and resolution of the $\Lambda$CDM tensions. One of the main goals of our research is the investigation of the predictions of such theoretical models, the identification of the quality of fit of these predictions to the cosmological data, and the comparison of this quality of fit with the corresponding quality of fit of $\Lambda$CDM. In this context, we have completed a wide range of research projects that include the following representative papers:

More recent relevant publications on this subject include:

### Search for Violations of the Cosmological Principle in the Cosmological Data and related Predictions of Theoretical Models

The cosmological princliple (the assumption of isotropy and homogeneity of the Universe on Hubble scales) is the cornerstone of the standard cosmological model. There are however, recent indications from various large scale cosmological data that this principle may be violated. One of the goals of our research work is to investigate observational data for possible hints of violation of the cosmological principle, the identification of the statistical level of significance of such hints and the construction of theoretical models that may lead to such violation of the cosmological principle. In this context we have completed a wide range of research projects that include the following representative papers:

### Short-range Gravity Experiments and Modified Gravity Theories

Modifications of General Relativity in the form of Modified Gravity Theories may lead to detectable signals in short range gravity experiments on sub-mm scales. An interesting aspect of our research activities involves the identification of the form of these predicted signals for specific modified gravity theories and the search for these signals in the data of short range gravity experiments. In this context we have completed a wide range of research projects that include the following representative papers:

### Gravitational Physics and Field Theory of Cosmic Strings and other Topological Defects

The evolution of scalar fields in a cosmological or a laboratory setup may lead to a wide range of interesting observable effects including the formation and evolution of topological defects. These are topologically trapped energy concentrations which may have spharical symmetry (monopoles), cylindrical symmetry (strings), planar (surface) form (domain walls) or collapsing evolution (textures). The investigation of the field theoretical properties, the gravitational effects and the observational signatures of these objects in both a cosmological and a laboratory setup is also one of the main aspects of our research. In this context we have completed a wide range of research projects that include the following representative papers:


text:
# volume of largest rectangular box

• Nov 1st 2009, 07:08 PM
zpwnchen
volume of largest rectangular box
Quote:

Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane http://webwork.asu.edu/webwork2_file...de90fff811.png. Largest volume is
i have no idea how to get started. pls help.
• Nov 1st 2009, 08:03 PM
zpwnchen
$V = xyz = 36yz - 4y^2z -9yz^2$
$V_{y} = 36z - 8yz -9z^2 = 0$
$V_{z} = 36y - 4y^2 - 18yz =0$

then solve for y,z and i got

y=0, z=0
y=5/2, z = 16/9

and substitude y and z into V and i got V = 400/9


text:
# Running powershell, bash, and EXEs from the dockerfile

Windocks supports the running of EXEs, Powershell scripts, Windows commands, Bash from the dockerfile. This is available in Enterprise edition. These commands can be run at image build time, container create time, or after container start. See the sample in windocks\samples\powershellOnDatabase

The dockerfile specifies WHEN to run the Powershell or EXEs. There are 4 choices on when to run the Powershell or EXEs.

• Image build time
• Image build time after the image databases are ready
• When a container is created from this image
• When a container is created from this image time after the container databases are ready

First create the dockerfile as follows (# is used for commenting lines):

dockerfile
FROM mssql-2016

SETUPCLONING FULL customers C:\windocks\dbbackups\customerdatafull.bak

# COPY powershellScriptAtCreate.ps1 .

# COPY custom.exe .

COPY deploy.ps1 .

# This Powershell runs at image build time but NOT on the image databases RUN somePowershell.ps1 # This Powershell runs on the database in the image at image build time
# Because the powershell is run on the image databases, all containers created from this image will have the effects of this script
# $ContainerDir and$ContainerPort are populated by Windocks automatically with the values of the container used to build the image.

RUN RUN_ON_IMAGE_DATABASES powershell.exe $ContainerDir\mask.ps1 -dest LAPTOP-DA9D6LTM\INSTANCE$ContainerPort

# Anything below this line runs after a container create is created from the image

ENV USE_DOCKERFILE_TO_CREATE_CONTAINER=1

# This Powershell runs at container create time. This container is the one being created by the user and NOT the container used to build the image
# $ContainerDir is populated by Windocks automatically with the actual values for the container created by the user RUN powershell.exe$ContainerDir\powershellScriptAtCreate.ps1

# You may also run EXEs like Powershell # RUN .\custom.exe $ContainerPort # This Powershell runs on container create after the container databases are ready #$ContainerDir and $ContainerPort are populated by Windocks automatically. The instance name for the SQL container is INSTANCE$ContainerPort

RUN RUN_ON_CONTAINER_START powershell.exe $ContainerDir\deploy.ps1 -dest LAPTOP-DA9D6LTM\INSTANCE$ContainerPort

Build the image from the above dockerfile. This will create an image

In a command line on the Windocks server:
docker build -t yourimagename path\to\directory\containing\dockerfile

Alternatively, use the web application and click on Build in the top menu and click Browse. Select all the files in the directory (dockerfile, any script files) and then Open. Then click Build.

You may also use the REST API to build the image

Create a container / clone from the image with the powershell executed. This can be done using a command line (only on the Windocks machine), or the web application (from any machine) or from the REST API (any machine)

In a command line on the Windocks server:
docker run -d yourimagename

This will deliver a writeable database clone and the Powershell scripts run

You may use the web application at ServerIp:/index.html or the file windocks\ui\index.html in Chrome or Firefox

You may also use the REST API here


text:
# The sum of all proper fractions whose denominators are less than or equal to 100 is:

This question was previously asked in
Haryana CET Previous Year Paper (Held On: 6 Nov 2022 Shift 2)
View all Haryana CET Papers >
1. 2124
2. 2475
3. $$22\frac{1}{4}$$
4. 1925
5. Not attempted

Option 2 : 2475
Free
CT: General Awareness (Mock Test)
32 K Users
10 Questions 10 Marks 7 Mins

## Detailed Solution

Formula used :

(1 + 2 + 3 + 4 +     ......... + 99) = [ n ( n + 1 ) ] ÷ 2

Solution :

We can write all proper fractions whose denominators are less than or equal to 100 in given form :

⇒ 1/2 + (1/3 + 2/3) + (1/4 + 2/4 + 3/4) + ...  (1/100 + 2/100 + .. ..  99/100)

⇒ 1/2 + 3/3 + 6/4 + ..... + 4950/100

⇒ 1/2 + 1 + 3/2 + 2 + ........ + 99/2

We can also write this equation in following way :

⇒ 1/2 + 2/2 + 3/2 + ...... + 99/2

⇒ 1/2 ( 1 + 2 + 3 + ..... + 99 )

⇒  /2 [ ( 99 × 100) ÷ 2 ]

⇒ 99 × 25

⇒ 2475

Hence the correct answer is "2475".


text:
Anchor tags don’t work in Meteor. This is a known issue.

The standard format to use anchor tags is:

# Create a link pointing to the anchor
Click here for the introduction.

# Create the anchor itself

But in Meteor this doesn’t work. Instead you need to use Iron Router.

In this example, we want to link WITHIN THE SAME PAGE, in this case called ‘home.’ So our router.js file looks as follows:

# Router.js
Router.route('/', {
name: 'home'
});

And the code we need, to get anchor tags to work in Meteor, is this:

# Create a link pointing to the anchor
Click here for the introduction.

# Create the anchor itself


text:
### Author Topic: What are the biggest possible turn-off in a roguelike?  (Read 40310 times)

#### Ex

• IRC Communications Delegate
• Rogueliker
• Posts: 313
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #75 on: April 18, 2013, 02:50:54 AM »
My tastes really change over time. So, this is just what I feel right now, and it'll probably be different later:

2 Game isn't a roguelike. I used to be okay with experimental "roguelikes", but that was back when most roguelikes were traditional. Now adays there are so many games trying to jump on the "roguelike" bandwagon that have nothing to do with roguelikes, and it really, really bothers me. Sci fi is fine, but make sure it's a ROGUELIKE.

3 Too difficult. I want a game I can play, not a game that is going to make me pull my hair out in frustration. So many games treat ease of difficulty as a bug, and that's a HUGE mistake in my mind. Games should be playable.

3 Building from source. I'm just not going to, sorry. Nothing against your game, but give me binaries.

1 vi keys. They make me want to break my keyboard. I recommend wasd instead.

3 Ego. Some developers make it very clear that they think that their title is going to be the next minecraft, only better and more popular. It really bothers me. I don't mean advertising. I like advertising: it's clever and fun and we all have to do it, but nothing turns me off of a roguelike more than a developer with a massive ego about how important and successful and great their game is/will be.

#### TheCreator

• Rogueliker
• Posts: 370
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #76 on: April 18, 2013, 05:54:08 AM »
This thread is very interesting to read, but not very useful to a developer. Let's gather all the replies and make a huge poll. It would be nice to see what the majority of players thinks.
Fame (Untitled) - my game. Everything is a roguelike.

#### guest509

• Guest
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #77 on: April 18, 2013, 06:58:09 AM »
That is very interesting Mr. Troll. But the thing is many of the gripes are specific to situation, you know?

Still, how do you make a poll on here? I'll do it.

EDIT: NVM I think I got if figured.

#### TheCreator

• Rogueliker
• Posts: 370
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #78 on: April 18, 2013, 07:05:10 AM »
Yes, I know, that's one of the main reasons to make a poll . I believe in statistics. Reading all the complaints here can only result in a headache, but with good stats you can always figure out what people really want.

Will anonymous users be able to participate in the poll if it's created here? That would be great, but most likely forum polls are for forum users only.
Fame (Untitled) - my game. Everything is a roguelike.

#### Vanguard

• Rogueliker
• Posts: 1112
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #79 on: April 18, 2013, 06:18:37 PM »
This thread is very interesting to read, but not very useful to a developer. Let's gather all the replies and make a huge poll. It would be nice to see what the majority of players thinks.

I don't like the idea of game design by majority consensus.  That's basically what has brought modern AAA games to where they are.  Threads like this one can be a useful to developers as a source of ideas, but they should never feel bound by what the majority does and doesn't like.  If there's a concept that you know is right for your game, you should do it no matter how unpopular it is.

#### Quendus

• Rogueliker
• Posts: 447
• Karma: +0/-0
• $@ \in \{1,W\} \times \{1,H\}$
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #80 on: April 18, 2013, 10:27:56 PM »
That's true for some of these complaints. For others, like having to compile the game or install runtimes, there's no real excuse other than the developer's laziness or obliviousness.

#### Vanguard

• Rogueliker
• Posts: 1112
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #81 on: April 19, 2013, 12:33:16 AM »
Oh, well yeah.

I'm talking about game design decisions, not that sort of thing.

#### kraflab

• Rogueliker
• Posts: 454
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #82 on: April 19, 2013, 01:20:10 AM »
The problem with looking at gripes, as Jo mentioned, is that they are very situational and strongly dependent on bad experiences in the past.  When people say they don't like mechanic X they are merely saying they don't like implementation Y of mechanic X.  There are no bad mechanics, only misguided implementations.

#### Quendus

• Rogueliker
• Posts: 447
• Karma: +0/-0
• $@ \in \{1,W\} \times \{1,H\}$
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #83 on: April 19, 2013, 01:31:29 AM »
Yep. I think this poll is more useful for finding out things you can get away with, not which things you should avoid. For instance: so far no-one has voted for either "no graphics" or "no ASCII", which tells me that there is no problem with coding only your preferred display style.

#### guest509

• Guest
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #84 on: April 19, 2013, 01:52:01 AM »
The problem with looking at gripes, as Jo mentioned, is that they are very situational and strongly dependent on bad experiences in the past.  When people say they don't like mechanic X they are merely saying they don't like implementation Y of mechanic X.  There are no bad mechanics, only misguided implementations.

What's more is that people are probably very often thinking of single game experience, and are just upset about it when they make their list of turn-offs.

#### TheCreator

• Rogueliker
• Posts: 370
• Karma: +0/-0
##### Re: What are the biggest possible turn-off in a roguelike?
« Reply #85 on: April 19, 2013, 05:47:46 AM »
I don't like the idea of game design by majority consensus.  That's basically what has brought modern AAA games to where they are.  Threads like this one can be a useful to developers as a source of ideas, but they should never feel bound by what the majority does and doesn't like.  If there's a concept that you know is right for your game, you should do it no matter how unpopular it is.

And that's exactly what I had on mind proposing the idea of making a poll. Listening blindly to the voice of majority will eventually result in an average game. One ought to throw in some original ideas, even if they are disliked by many players. The tricky part is not to have too many of them and that's what the poll is for.
Fame (Untitled) - my game. Everything is a roguelike.


text:
## Thursday, 21 August 2008

### Unitarity Rules

Wednesday at Strings'08 was fairly interesting for me, as I'm obviously more attracted by the interface of string and field theory rather than by hard-core strings. In the last few years there has been a lot of commotion in the no man's land between formal string theory/supergravity and the perturbative QCD. This was nicely reviewed by Lance Dixon. This subject is suitable for a 100p review rather than a blog post, but i'll try anyway to sketch the main points.

Perturbative computations in quantum field theory are by far dominated by summing the Feynman diagrams. This is a simple and intuitive method, but it can be cumbersome at times. That is especially true in gauge or gravity theories where the Feynman diagrams propagate many spurious degrees of freedom, and it often happens that the full result is much much simpler than each individual diagram. In such a case, other methods that explore fundamental properties of quantum field theories may prove very handy. Recently, we have been witnessing a come-back of the unitarity based S-matrix approach that was conceived back in the sixties. Geoffrey Chew would be turning in his grave, were he dead.

In fact, we have learned a lot since the summer of love. One thing is the importance of the spinor helicity formalism. For each momentum vector $k_\mu$ of a massless particle one can find corresponding Weyl spinors $\lambda,\bar \lambda$: $k^2$ is the determinant of the matrix $k_\mu (\sigma^\mu)_{ab}$, so that for $k^2 = 0$ the matrix can be written as $\lambda_a \bar \lambda_b$. Similarly, the polarization vectors can be represented using spinors, and one defines the +(-) plus helicity for $\epsilon_\mu (\sigma^\mu)_{ab} \sim \bar \lambda_b (\lambda_b)$. At the end of the day, scattering amplitudes of massless particles can be written as functions of spinor invariants, which reveals unexpected hidden structures. In the Yang-Mills theory, the amplitudes with all helicities of the external gluons being the same, like (++++), are always vanishing. The same is true for the amplitudes with one helicity different than all the others, like (-+++). The simplest non-vanishing amplitude -- the ones with two (+) two (-) helicities -- are called minimal helicity-violating (MHV). There is a compact formula for tree-level MHV amplitudes with an arbitrary number of external gluon legs.

This formalism opened the way for the BCFW recursion relations. To derive these relations, one takes two spinors $\lambda_{1,2}$ corresponding to two external momenta, and continues them analytically to a complex plane, $\lambda_1 \to \lambda_1 + z \lambda_2$, $\bar \lambda_2 \to \bar \lambda_2 - z \bar \lambda_1$. This way, the scattering amplitudes become analytic functions of a fictitious complex variable z. This deformation is designed in such a way that the amplitudes have only simple poles in the z-variable, and the residues of these poles encode information about amplitudes with fewer external legs. Then one can use the usual contour integral methods to relate the amplitude to the residues of its poles, which amounts to relating n-leg amplitudes to those with n-1 legs. This is a powerful method that reduces very complicated multi-legs amplitudes to a sum of simpler (less-leg) ones.
The BCFW relations are being implemented by modern computing tools and Monte Carlos programs.

Yet another interesting development are the use of generalized unitarity relations. Loop amplitudes have branch cuts (in addition to poles), and unitarity strongly constrains what the discontinuity across the branch cut might be. Two-particle cuts are the well-known textbook techniques to relate one-loop amplitudes to tree-level ones. Recently, multi-particle cut techniques have been developed. This jack-the-ripper approach turns out to be useful in reducing general loop amplitudes to simpler building blocks. In particular, arbitrary one-loop amplitudes can be reduced to simple scalar integrals knowns as the box, the triangle and the bubble.

While all the above methods can be applied to the real-life QCD or electroweak theories, they become even more powerful when applied to highly symmetric systems like N=4 super-Yang-Mills or N=8 supergravity. Unitarity is the weapon used on the battlefield of proving perturbative finiteness of N=8 supergravity. Judging from the progress so far, the definitive answer should be known by Strings'09.

It seems that the list of applications is far from being closed. At the same time, there is a feeling that all these surprising results revealed by the unitarity methods are being obtained in a bit roundabout way. There is a fascinating conjecture spelled out in this paper that there exists a dual formulation of quantum field theory where all these surprising properties of scattering amplitudes are realized in a more straightforward way.

Slides here. You can also learn about prof. Mantis Schrimp who was the first to apply the helicity formalism in practice.

Rutger said...

Okay, I can't resist some shameless self-promotion to tack on this nice review post: just this week (0808.2598 hep-th) we showed that one possible 'dual' formulation of the field theory is just plain old string theory: this is therefore the 'simplest' quantum field theory :)

Alejandro Rivero said...

rutger, do you mean old Dirac multiparameter multiparticle theory? Or a more modern string theory :-D ?

Rutger said...

Euh. If I actually knew what that was I might agree.... (educate me?)

It seems *any* string theory is 'simple' for the right definition of simple :) Or in other words, almost any string theory has amazingly good UV scattering properties. If the theory you mean makes itself well-behaved (finite?) in the UV by adding infinite stacks of massive particles (I'm guessing), than it will probably have similar properties, although making this precise might be hard. Any string theory is in some limit after all a quantum field theory with an infinite number of massive fields.

All of this doesn't mean of course that the Arkani-Hamed-Cachazo-Kaplan paper isn't very interesting...


text:
# American Institute of Mathematical Sciences

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December  2018, 15(6): 1435-1463. doi: 10.3934/mbe.2018066

## Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

 1 Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X 20, Hatfield, Pretoria 0028, South Africa 2 Department of Mathematics, The College of Saint Rose, Albany, New York, USA 3 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal 4 Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK

Received  March 27, 2018 Accepted  July 10, 2018 Published  September 2018

Oncolytic virotherapy has been emerging as a promising novel cancer treatment which may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how virotherapy could enhance chemotherapy, we propose an ODE based mathematical model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size. It also demonstrates that chemotherapy alone is capable of clearing tumour cells provided that the drug efficacy is greater than the intrinsic tumour growth rate. Furthermore, virotherapy alone may not be able to clear tumour cells from body tissue but would rather enhance chemotherapy if viruses with high viral potency are used. To assess the combined effect of virotherapy and chemotherapy we use the forward sensitivity index to perform a sensitivity analysis, with respect to chemotherapy key parameters, of the virus basic reproductive number and the tumour endemic equilibrium. The results from this sensitivity analysis indicate the existence of a critical dose of chemotherapy above which no further significant reduction in the tumour population can be observed. Numerical simulations show that a successful combinational therapy of the chemotherapeutic drugs and viruses depends mostly on the virus burst size, infection rate, and the amount of drugs supplied. Optimal control analysis was performed, by means of the Pontryagin's maximum principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects. Results from this analysis suggest that the optimal drug and virus combination correspond to half their maximum tolerated doses. This is in agreement with the results from stability and sensitivity analyses.

Citation: Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F. M. Torres, K. A. Jane White. Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1435-1463. doi: 10.3934/mbe.2018066
##### References:

show all references

##### References:
Visual representation of the elasticity indices of $R_0$ with respect to model parameters. The bar graph shows that the virus burst size, infection and decay rates $b$, $\beta$ & $\gamma$ have the highest elasticity indices with virus decay being negatively correlated to $R_0$
Plots of the elasticity indices, $e_q$, and $\Gamma^{U^*+ I^*}_q$ against the drug dosage $q$. Both Figures (a) and (b) depict that increasing the amount of drug infused reduces viral multiplication thus reducing the sensitivity indices. The figures further suggest that values of $q$ from 40 to 100 mg/l have minimal negative impact on viral replication
(a) Plots of uninfected cell density with constant drug infusion and for different virus burst sizes. The plot shows that an increase in the virus burst size reduces the tumour density. (b)Plots of uninfected cell density with constant drug infusion and for different drug infusion rates. The plot shows that an increase in the drug infusion rate reduces the tumour density by a relatively small magnitude
Plots of the virus and infected tumour densities for different virus burst size. The plots show that both densities increase with increasing virus burst size
(a) Plots of the virus density for different virus infection rate. The plots show the virus density reduces with increasing virus infection rates. (b) Plots of infected tumour density for different infection rates. The figure shows that the infected tumour density increases as the infection rate increases
Total tumour density with optimal control. The tumour density is reduced in a very short time period
Optimal control variable variables $u_1$: The external supply of viruses and $u_2$: Drug dosage. The Figures depict 500 virions as the optimal number of viruses and the optimal drug dosage to be 50 m/g per
The model variables
 Variable Description Units $U(t)$ Uninfected tumour density cells per mm$^3$ $I(t)$ Virus infected tumour cell density cells per mm$^3$ $V(t)$ Free virus particles virions per mm$^3$ $E_v(t)$ Virus specific immune response cells per mm$^3$ $E_T(t)$ Tumour specific immune response cells per mm$^3$ $C(t)$ Drug concentration grams per millilitre (g/ml)
 Variable Description Units $U(t)$ Uninfected tumour density cells per mm$^3$ $I(t)$ Virus infected tumour cell density cells per mm$^3$ $V(t)$ Free virus particles virions per mm$^3$ $E_v(t)$ Virus specific immune response cells per mm$^3$ $E_T(t)$ Tumour specific immune response cells per mm$^3$ $C(t)$ Drug concentration grams per millilitre (g/ml)
The model parameters, their description and base values
 Symbol Description Value & units Ref. $K$ Tumour carrying capacity $10^6$ cells per mm$^3$ per day [4] $\alpha$ Tumour growth rate $0.206$ cells per mm$^3$ per day [4] $\beta$ Infection rate of tumour cells $0.001-0.1$ cells per mm$^3$ per day [4] $\delta$ Infected tumour cells death $0.5115$ day$^{-1}$ [4] $\gamma$ Rate of virus decay $0.01$ day$^{-1}$ [4] $b$ Virus burst size $0-1000$ virions per mm$^3$ per day [11] $\psi$ Rate drug decay $4.17$ millilitres per mm$^3$ per day [39] $\delta_U$ Lysis rate of $U$ by the drug $50$ cells per mm$^3$ per day [39] $\delta_I$ Lysis rate of $I$ by the drug $60$ cells per mm$^3$ per day [39] $\phi$ $E_V$ production rate $0.7$ day$^{-1}$ [9] $\beta_T$ $E_T$ production rate $0.5$ cells per mm$^3$ per day [19,27] $\delta_v,\delta_T$ immune decay rates $0.01$ day$^{-1}$ [19,27] $K_u,K_c,\kappa$ Michaelis--Menten constants $10^5$ cells per mm$^3$ per day [25] $\nu_U$ Lysis rate of $U$ by $E_T$ $0.08$ cells per mm$^3$ per day est $\nu_I$ Lysis rate of $I$ by $E_T$ $0.1$ cells per mm$^3$ per day est $\tau$ Lysis rate of $I$ by $E_V$ $0.2$ cells per mm$^3$ per day est
 Symbol Description Value & units Ref. $K$ Tumour carrying capacity $10^6$ cells per mm$^3$ per day [4] $\alpha$ Tumour growth rate $0.206$ cells per mm$^3$ per day [4] $\beta$ Infection rate of tumour cells $0.001-0.1$ cells per mm$^3$ per day [4] $\delta$ Infected tumour cells death $0.5115$ day$^{-1}$ [4] $\gamma$ Rate of virus decay $0.01$ day$^{-1}$ [4] $b$ Virus burst size $0-1000$ virions per mm$^3$ per day [11] $\psi$ Rate drug decay $4.17$ millilitres per mm$^3$ per day [39] $\delta_U$ Lysis rate of $U$ by the drug $50$ cells per mm$^3$ per day [39] $\delta_I$ Lysis rate of $I$ by the drug $60$ cells per mm$^3$ per day [39] $\phi$ $E_V$ production rate $0.7$ day$^{-1}$ [9] $\beta_T$ $E_T$ production rate $0.5$ cells per mm$^3$ per day [19,27] $\delta_v,\delta_T$ immune decay rates $0.01$ day$^{-1}$ [19,27] $K_u,K_c,\kappa$ Michaelis--Menten constants $10^5$ cells per mm$^3$ per day [25] $\nu_U$ Lysis rate of $U$ by $E_T$ $0.08$ cells per mm$^3$ per day est $\nu_I$ Lysis rate of $I$ by $E_T$ $0.1$ cells per mm$^3$ per day est $\tau$ Lysis rate of $I$ by $E_V$ $0.2$ cells per mm$^3$ per day est
Sensitivity and elasticity indices of $R_0$ with respect to model parameters
 Parameter Sensitivity index Elasticity index $b$ $S_b = 9.88$ $e_b = 1$ $\beta$ $S_{\beta} = 988.4$ $e_{\beta}=1$ $\gamma$ $S_{\gamma} = - 9884$ $e_{\gamma}=-1$ $\delta$ $S_{\delta} = 2.2325$ $e_{\delta}= 0.011553$ $\alpha$ $S_{\alpha} = 2.4372$ $e_{\alpha} = 5.1 \times 10^{-12}$ $\delta_U$ $S_{\delta_U} = -1.004 \times 10^{-7}$ $e_{\delta_U} = -5.1 \times 10^{-12}$ $\delta_I$ $S_{\delta_I} = -90.32$ $e_{\delta_I} =- 0.011553$ $K_c$ $S_{K_c}= 0.2048x$ $e_{K_c}= 0.0000414$ $K_u$ $S_{K_u}=-1.01\times 10^{-6}$ $e_{K_u} = -2.05 \times 10^{-10}$ $\psi$ $S_{\psi} = 0.004$ $e_{\psi}= 0.000414$ $q$ $S_{q} = -0.008$ $e_{q} = - 0.000414$
 Parameter Sensitivity index Elasticity index $b$ $S_b = 9.88$ $e_b = 1$ $\beta$ $S_{\beta} = 988.4$ $e_{\beta}=1$ $\gamma$ $S_{\gamma} = - 9884$ $e_{\gamma}=-1$ $\delta$ $S_{\delta} = 2.2325$ $e_{\delta}= 0.011553$ $\alpha$ $S_{\alpha} = 2.4372$ $e_{\alpha} = 5.1 \times 10^{-12}$ $\delta_U$ $S_{\delta_U} = -1.004 \times 10^{-7}$ $e_{\delta_U} = -5.1 \times 10^{-12}$ $\delta_I$ $S_{\delta_I} = -90.32$ $e_{\delta_I} =- 0.011553$ $K_c$ $S_{K_c}= 0.2048x$ $e_{K_c}= 0.0000414$ $K_u$ $S_{K_u}=-1.01\times 10^{-6}$ $e_{K_u} = -2.05 \times 10^{-10}$ $\psi$ $S_{\psi} = 0.004$ $e_{\psi}= 0.000414$ $q$ $S_{q} = -0.008$ $e_{q} = - 0.000414$
Selected sensitivity indices of the total tumour equilibria, $\Gamma ^{U+I} _p$, in response to drug, $q$ with the corresponding value of $R_0$
 q (mg/l) 5 10 15 35 50 100 $\Gamma ^{U^*+I^*} _p$ $-8.3\times 10^{-5}$ $-2.5\times 10^{-5}$ $-1\times 10^{-5}$ $-6.1\times 10^{-5}$ $-9.6\times 10^{-6}$ $-2.4\times 10^{-6}$ $R_0$ $51.0476$ $51.0473$ $51.0470$ $51.0459$ $51.0450$ $51.0421$
 q (mg/l) 5 10 15 35 50 100 $\Gamma ^{U^*+I^*} _p$ $-8.3\times 10^{-5}$ $-2.5\times 10^{-5}$ $-1\times 10^{-5}$ $-6.1\times 10^{-5}$ $-9.6\times 10^{-6}$ $-2.4\times 10^{-6}$ $R_0$ $51.0476$ $51.0473$ $51.0470$ $51.0459$ $51.0450$ $51.0421$
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text:
Cantera  2.2.1
VPSSMgr_General.cpp File Reference

Definition file for a derived class that handles the calculation of standard state thermo properties for a set of species belonging to a single phase in a completely general but slow way (see Thermodynamic Properties and class VPSSMgr_General). More...

#include "cantera/thermo/VPSSMgr_General.h"
#include "cantera/base/ctml.h"
#include "cantera/thermo/VPStandardStateTP.h"
#include "cantera/thermo/PDSS_IdealGas.h"
#include "cantera/thermo/PDSS_Water.h"
#include "cantera/thermo/PDSS_ConstVol.h"
#include "cantera/thermo/PDSS_SSVol.h"
#include "cantera/thermo/PDSS_HKFT.h"
#include "cantera/thermo/PDSS_IonsFromNeutral.h"
#include "cantera/thermo/GeneralSpeciesThermo.h"
#include "cantera/base/vec_functions.h"
Include dependency graph for VPSSMgr_General.cpp:

Go to the source code of this file.

## Namespaces

Cantera
Namespace for the Cantera kernel.

## Detailed Description

Definition file for a derived class that handles the calculation of standard state thermo properties for a set of species belonging to a single phase in a completely general but slow way (see Thermodynamic Properties and class VPSSMgr_General).

Definition in file VPSSMgr_General.cpp.


text:
# zbMATH — the first resource for mathematics

Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions. (English) Zbl 1203.54051
Summary: The concepts of cone pseudometrics, cone uniform spaces generated by these pseudometrics, cone pseudodistances, set-valued quasi-asymptotic contractions with respect to these pseudodistances, and cone closed maps are introduced and studied. Conditions guaranteeing the existence and uniqueness of endpoints (stationary points) of these contractions and conditions ensuring that, for each starting point, each generalized sequence of iterations of these contractions (in particular, each dynamic process) converges, and then the limit is an endpoint, are all established. Also, the concept of the cone locally convex space as a special case of the cone uniform space is introduced and examples of quasi-asymptotic contractions in cone metric spaces are constructed. The definitions, results, ideas and methods are new for set-valued dynamic systems in cone uniform, cone locally convex and cone metric spaces and even for single-valued maps in these spaces.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54E15 Uniform structures and generalizations 54C60 Set-valued maps in general topology
Full Text:
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text:
# Optical methods for number theory?

+ 1 like - 0 dislike
1806 views

I found a paper: 'A New Method of Finding the Distribution of Prime Number', says:

We stack discs and annuluses with certain rules then turn on the light to illuminate.The projection of annuluses corresponds prime number,and the projection of discs corresponds composite number.

Are there other physics methods for number theory?

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
retagged Jun 19, 2014
The paper you refer to doesn't seem to be very accessible -- when I click the PDF link, I see a page asking in Chinese for a login password.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Stefan Kohl
@StefanKohl,the paper has 4 pages,main content is in Chinese ,here you can see the first 2 pages, wenku.baidu.com/view/1d602350be23482fb4da4cc6.html?re=view, the last 2 pages are more examples.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
The diagrams in that paper are implementing a poor version of the en.wikipedia.org/wiki/Sieve_of_Eratosthenes where instead of covering multiples of the next uncovered (i.e. prime) number, they cover multiples of the next number, regardless of it's status. So two rounds after covering all multiples of $2$, they cover all multiples of $4$.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Zack Wolske
Here is a physical implementation of the more efficient version: en.wikipedia.org/wiki/Lehmer_sieve

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Zack Wolske
@ZackWolske ,yes it is sieve of Eratosthenes.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Mike
I would like to query the closure - have posted on meta: meta.mathoverflow.net/questions/1749

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Carl

I personally think this is an interesting question at the interface betwen math and physics, whereas for MathOverflow it seems to be a bit too "interdisciplinary" as they say ...

+ 6 like - 0 dislike

Probably, the best-known application of ideas from physics to computational number theory is Shor's algorithm.

You may also be interested in other examples from “unusual and physical methods for finding prime numbers”.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Waldemar
answered Jun 18, 2014 by (60 points)
+ 4 like - 0 dislike

The physics of the Riemann Hypothesis D. Schumayer and D. A. W. Hutchinson, Rev. Mod. Phys. 83 307-330 (2011). abstract here

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Carl
answered Jun 18, 2014 by (60 points)
+ 1 like - 0 dislike

There's a way to use physics to calculate the digits of $\pi$. I quote from http://math.stackexchange.com/questions/138289/intuitive-reasoning-behind-pis-appearance-in-bouncing-balls

Let the mass of two balls be $M$ and $m$ respectively. Assume that $M=16\times100^nm$. Now, we will roll the ball with mass $M$ towards the lighter ball which is near a wall. How many times do the balls touch each other before the larger ball changes direction? (The large ball hits the small ball which bounces off the wall)

The solution is the first $n+1$ digits of $\pi$.

This post imported from StackExchange MathOverflow at 2014-06-19 11:37 (UCT), posted by SE-user Gerry Myerson
answered Jun 18, 2014 by (10 points)

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text:
# An example of slow convergence for Newton’s method on a function with globally Lipschitz continuous Hessian

An example is presented where Newton's method for unconstrained minimization is applied to find an $\epsilon$-approximate first-order critical point of a smooth function and takes a multiple of $\epsilon^{-2}$ iterations and function evaluations to terminate, which is as many as the steepest-descent method in its worst-case. The novel feature of the proposed example is that the objective function has a globally Lipschitz-continuous Hessian, while a previous example published by the same authors only ensured this critical property along the path of iterates, which is impossible to verify a priori.

## Citation

@techreport{CartGoulToin13b, author = {C. Cartis and N. I. M. Gould and Ph. L. Toint}, title = {An example of slow convergence for {N}ewton's method on a function with globally {L}ipschitz continuous {H}essian}, institution = NAXYS, address = {University of Namur, Namur, Belgium}, number = {naXys-03-2013}, year = 2013}


text:
07-67 Laurent Bruneau, Alain Joye, Marco Merkli
Infinite Products of Random Matrices and Repeated Interaction Dynamics (394K, pdf) Mar 22, 07
Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. Let $\Psi_n$ be a product of $n$ independent, identically distributed random matrices $M$, with the properties that $\Psi_n$ is bounded in $n$, and that $M$ has a deterministic (constant) invariant vector. Assuming that the probability of $M$ having only the simple eigenvalue 1 on the unit circle does not vanish, we show that $\Psi_n$ is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as $n\rightarrow\infty$. The fluctuating part converges in Cesaro mean to a limit that is characterized explicitly by the deterministic invariant vector and the spectral data of ${\mathbb E}[M]$ associated to 1. No additional assumptions are made on the matrices $M$; they may have complex entries and not be invertible. We apply our general results to two classes of dynamical systems: inhomogeneous Markov chains with random transition matrices (stochastic matrices), and random repeated interaction quantum systems. In both cases, we prove ergodic theorems for the dynamics, and we obtain the form of the limit states.

Files: 07-67.src( 07-67.keywords , BJM2.pdf.mm )


text:
1. ## Differential Coefficient

Find the differential coefficient for the following different functions to demonstrate the use of function of a function; the product and quotient rules:

a) Y=(1+2x) squared
B) y = 6x squared Sin 2x
c) s= 2x squared
Cos3x

Can you help differentiate it please, thanks.

2. Hi Zacky

Originally Posted by zacky08

a) Y=(1+2x) squared

Use the chain rule here

$\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}$

make $u = 1+2x$ and $y=u^{2}$

Originally Posted by zacky08

B) y = 6x squared Sin 2x

Use the product rule here

$y = u\times v \Rightarrow y' = vu'+uv'$

make $u = 6x^2$ and $v = \sin(2x)$

Originally Posted by zacky08

c) s= 2x squared
Cos3x

Use the quotient rule here

For $y = \frac{u}{v} \Rightarrow y' = \frac{vu'-uv'}{v^2}$

make $u = 2x^2$ and $v=\cos(3x)$

3. Use the chain rule here

make $u = 1+2x$ and $y=u^{2}$

Here's how to start....

First from $u = 1+2x$ find $\frac{du}{dx}$

Spoiler:
$\frac{du}{dx} = 2$

then from $y=u^{2}$ find $\frac{dy}{du}$

Spoiler:
$\frac{dy}{du} = 2u = 2(1+2x)$

After you have these, put them into the RHS of the equation below.

$\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}$

4. Thank you so much, could you be so kind to do for the other 2 questions aswell if possible, thanks gracefully, Zacky.

5. Originally Posted by zacky08
Thank you so much, could you be so kind to do for the other 2 questions aswell if possible, thanks gracefully, Zacky.
The idea in the following 2 questions are the same as the previous post. You need to post your attempts on this forum. It is Math 'Help' Forum not Math 'Do' Forum

Also google the product and quotient rules. There are heaps of examples out there.

6. Use the product rule here

make and .

Ok firstly, i do 6x² + sin(2x) + sin(2x) + 6x² which gives me sin12x² + sin12x² = 2sin24x4. Am i on the right lines?

7. Originally Posted by zacky08

Ok firstly, i do 6x² + sin(2x) + sin(2x) + 6x² which gives me sin12x² + sin12x² = 2sin24x4. Am i on the right lines?
No this is all types of wrong.

Firstly there is a difference between $u$ and $u'$ . $u'$ is the derivative of $u$

For example if $u = x^2$ then $u' = 2x$

Do you understand this concept?

Also

$
\sin(2x) + \sin(2x) = 2\sin(2x) \neq \sin(12x^2)

$

8. Ah ok, i kind of grasp it now.

So, Sin (2x) + 12x then 12x + Sin (2x) then?

Which would be Sin(24x) + Sin(24x) = 2Sin (48x)

9. No, not even close.

This is the rule.

$y = u\times v \Rightarrow y' = vu'+uv'$

You need to find u' and v' using the following information.

$u = 6x^2$ and $v = \sin(2x)$

I get $u' = 12x$ and $v' = 2\cos(2x)$

The real question is, do you know how I found these?

10. 6x² differentiated is 12x, and sin is differentitated into cos and same thing with (2x) to give 2cos(2x). Yeah i realised what i did wrong, still a bit vague. But now that i got and , what would be the next step? do i put this into the Dy by Dx again?

11. The answer is $y' = vu'+uv'$

$y' = 12x\sin(2x)+12x^2\cos(2x)$

You should also factor out $12x$ giving

$y' = 12x(\sin(2x)+x\cos(2x))$

12. Finally, the Quotient Rule.

make and

I would get.

Cos (12x) - Cos (12x)
2cos(9x)

13. Originally Posted by zacky08
Finally, the Quotient Rule.

make and

I would get.

Cos (12x) - Cos (12x)
2cos(9x)
One step at a time there big fella, firstly what did you get for $u'$ and $v'$ ?

14. i got 4x and i got -sin (9x)

15. $u'$ is correct $v' = -3\sin(3x)$

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