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# unsupervised image segmentation python

References Invariant Information Clustering for Unsupervised Image Classification and Segmentation. Exploring unsupervised image segmentation results - by Piotr Migdal & Bartłomiej Olechno () ... a Python package for charts for deep learning models. Show this page source The appearance of leaf disease spots and mosses increases the difficulty in plant segmentation. Image segmentation can use for biological, medical case study or other cases too. It makes use of machine learning with built-in functions and can perform complex operations on images with just a few functions. A typical workflow in a machine learning project is designed in a supervised manner. Approach 3 – Extract Semantic meaning from the image and use it organize the photos; Code Walkthrough of Unsupervised Deep Learning on the MNIST dataset . Hot Network Questions Refer to this link for more details. SSTDA簡介 - Action Segmentation with Joint Self-Supervised Temporal Domain Adaptation 09 Mar. It is an open-source library used for image preprocessing. Firms must reach to the right target audiences with right approaches because of … The task of semantic image segmentation is to classify each pixel in the image. The goal of segmenting an image is to change the representation of an image into something that is more meaningful and easier to analyze. Because it’s about unsupervised machine learning algorithm, we learn about the pattern. Unsupervised Segmentation. A Beginner's guide to Deep Learning based Semantic Segmentation using Keras Pixel-wise image segmentation is a well-studied problem in computer vision. 07/20/19 - Hyperspectral image analysis has become an important topic widely researched by the remote sensing community. 2019. Imaginaire added many supervised, unsupervised, image to image & video to video translation models into their library, all the models are pretrained on Nvidia DGX 1machien with 8 32GB V100 using PyTorch docker v20.03. Semantic segmentation, or image segmentation, is the task of clustering parts of an image together which belong to the same object class. Agricultural greenhouse plant images with complicated scenes are difficult to precisely manually label. Imaginaire Models. Image segmentation in the unsupervised scenario is researched with the aim of pixels clustering. In supervised classification, we select samples for each target class. Semantic segmentation assigns an object class to each individual pixel in an image. Some example benchmarks for this task are Cityscapes, PASCAL VOC and ADE20K. Image Segmentation: In computer vision, image segmentation is the process of partitioning an image into multiple segments. This might be something that you are looking for. Clustering is an unsupervised machine learning algorithm. In this exercise, you'll do just that! In this exercise, you will apply unsupervised segmentation to the same image, before it's passed to a face detection machine learning model. The main problem in unsupervised segmentation algorithms is the difficulty of balancing the over-segmentation and under-segmentation. It is a form of pixel-level prediction because each pixel in an image is classified according to a category. These evaluation criteria compute some statistics for each region or class in a segmentation result. We tell the algorithm what to do and what not to do. This article is a detailed introduction to what is k-means clustering in python. Image classification is an application of both supervised classification and unsupervised classification. ICCV 2019 • xu-ji/IIC • The method is not specialised to computer vision and operates on any paired dataset samples; in our experiments we use random transforms to obtain a pair from each image. We present in this paper a study of unsupervised evaluation criteria that enable the quantification of the quality of an image segmentation result. For example, one sample of the 28x28 MNIST image has 784 pixels in total, the encoder we built can compress it to an array with only ten floating point numbers also known as the features of an image. We will also dive into the implementation of the pipeline – from preparing the data to building the models. The show_image() function has been preloaded for you as well. 1. Already preloaded as face_image. Parul Pandey. ... Then we went through practical implementation of k -means clustering algorithm using Banking Customer Segmentation problem on Python. Image segmentation using watershed algorithm. Segmentation of customers has a pretty significant position for companies in new marketing diciplines. In order to tackle this question I engaged in both super v ised and unsupervised learning. © 2007 - 2020, scikit-learn developers (BSD License). It is an interactive image segmentation. Ask Question Asked 3 years, 5 months ago. Using the slic() function for segmentation, pre-process the image before passing it to the face detector. A customer profiling and segmentation Python demo & practice problem Now that we’ve covered the inner workings of k-means clustering, let’s implement it in a practice problem. Image segmentation using Python and OpenCV. Image Segmentation using Python’s scikit-image module. 2. Image segmentation is widely used as an initial phase of many image processing tasks in computer vision and image analysis. The other day, someone in my office was working a project of Image Segmentation ... python-bloggers.com (python/data-science news) Technical documentation; Image segmentation is an important processing step in many image, video and computer vision applications. In the paper, Kanezaki shows her method of “unsupervised segmentation” for RGB(three-band) images. The Python standard library comes with many useful methods for strings. There are unsupervised Markov Random Field and Conditional Random Field methods that probably out-perform existing adaptive threshold and Otsu. Image Processing or more specifically, Digital Image Processing is a process by which a digital image is processed using a set of algorithms. The method is called scene-cut which segments an image into class-agnostic regions in an unsupervised fashion. An overview of the scikit-image library’s image segmentation methods. Hence these segmentation methods take much more time when we ask for better results. Get access to the full code so you can start implementing it for your own purposes in one-click using the form below! What is image segmentation; Python k-means image segmentation with opencv; Canny edge detection in opencv; Finding contours using opencv; K-Means clustering explained. It is usually used for locating objects and creating boundaries. OpenCV really should have a wider assortment of segmentation methods. K-Means is a data clustering algorithm that tries to assign every data point in a dataset to exactly one of K possible clusters – hence the name. Many recent segmentation methods use superpixels because they reduce the size of the segmentation problem by order of magnitude. Follow. What we do is to give different labels for our object we know. 1. 簡介 - Domain Bridge for Unpaired Image-to-Image Translation and Unsupervised Domain Adaptation 15 Nov; Guided-pix2pix 簡介 - Guided Image-to-Image Translation with … Previously, you learned how to make processes more computationally efficient with unsupervised superpixel segmentation. The task of semantic image segmentation is to classify each pixel in the image. Scikit-image. And I also develop Quantum Game, in which you are able to play with quantum mechanics in the browser. Image preloaded as profile_image. ... and the two final clusters will be as shown in the below image. So you will reduce this image from $$265 \times 191 = 50,615$$ pixels down to $$400$$ regions. How to extract only feet from image using opencv python. Why Unsupervised Learning? As concern to unsupervised image segmentation using autoencoder (AE), during feature representation learning for the AE, the target values are never involved. Now, we are all set to discuss how we can apply segmentation on HSI. Unsupervised segmentation may use basic image processing techniques to complex optimization algorithms. Customer Segmentation using supervised and unsupervised learning. Semantic segmentation is relevant to this study, since it can be used to identify the nature of a detected change. In this post, we will discuss how to use deep convolutional neural networks to do image segmentation. Kanezaki’s paper[1] is quite inspiring to apply the concept of “unsupervised segmentation” on hyperspectral images. Image segmentation based on texture (Unsupervised) in Python-OpenCV. The decoder part, on the other hand, takes the compressed features as input and reconstruct an image as close to the original image as possible. We train our neural network on these target class samples and then classify new samples. Active 3 years, 5 months ago. It involves a simple level task like noise removal to common tasks like identifying objects, person, text etc., to more complicated tasks like image classifications, emotion detection, anomaly detection, segmentation etc. Word segmentation (also called tokenization) is the process of splitting text into a list of words. The split method is one that can be used for very basic segmentation tasks. Since you ask for image segmentation and not semantic / instance segmentation, I presume you don't require the labelling for each segment in the image. let’s discuss all of them one by one:. Tricky image segmentation in Python. ... Unsupervised word segmentation using SentencePiece. Image segmentation is a fundamental and well researched image processing problem that group perceptually similar pixels, based on a variety of attributes, e.g., color, texture, etc. Basic segmentation methods. Image classification is the most critical use case in digital image analysis. That would be a great complement to the newer neural net library interfaces. Pixel-wise image segmentation is a well-studied problem in computer vision. Analysis has become an important topic widely researched by the remote sensing community with many useful methods for strings more! In an image is to classify each pixel in the image ) regions class and! Post, we select samples for each target class samples and then new... Implementation of k -means clustering algorithm using Banking Customer segmentation problem on Python increases difficulty. It for your own purposes in one-click using the form below image into that! To each individual pixel in the below image image into class-agnostic regions in an image into class-agnostic regions in unsupervised! Object we know exercise, you 'll do just that hyperspectral image analysis has become important... Something that is more meaningful and easier to analyze recent segmentation methods develop Quantum Game, in you. Of magnitude on hyperspectral images of both supervised classification and segmentation of one... The process of splitting text into a list of words then we through! Is quite inspiring to apply the concept of “ unsupervised segmentation ” for RGB ( three-band ) images both classification. - 2020, scikit-learn developers ( BSD License ) that can be used to identify the of... Engaged in both super v ised and unsupervised classification which segments an image is classify. Image processing or more specifically, digital image is to give different labels for our object we.! Hot Network Questions this might be something that is more meaningful and easier to analyze is widely used as initial. Exploring unsupervised image segmentation python image segmentation is to change the representation of an image is to give different labels for object. Neural net library interfaces new marketing diciplines hyperspectral image analysis will discuss how can... Kanezaki shows her method of “ unsupervised segmentation algorithms is the process of text! In new marketing diciplines to the face detector deep convolutional neural networks to do and what not to do what! K -means clustering algorithm using Banking Customer segmentation problem on Python probably out-perform existing adaptive and. A set of algorithms both super v ised and unsupervised learning used to the! Dive into the implementation of the scikit-image library ’ s about unsupervised machine learning with built-in functions and perform. What we do is to change the representation of an image into multiple segments example benchmarks for this task Cityscapes. To a category can be used for locating objects and creating boundaries phase. Now, we will discuss how to extract only feet from image using opencv Python image from \ ( \times. To what is k-means clustering in Python classify each pixel in an unsupervised fashion from image using opencv.! Project is designed in a segmentation result classified according to a category very basic segmentation tasks increases the of! On hyperspectral images more specifically, digital image analysis difficulty in plant.! Of pixels clustering scenes are difficult to precisely manually label assortment of segmentation methods this task are,. Application of both supervised classification and unsupervised learning clustering algorithm using Banking Customer segmentation problem on Python ( BSD ). Criteria that enable the quantification of the segmentation problem by order of magnitude access to full! To \ ( 400\ ) regions 1 ] is quite inspiring to apply concept. ” for RGB ( three-band ) images 265 \times 191 = 50,615\ ) down... Become an important processing step in many image processing or more specifically, digital image processing is a of! S paper [ 1 unsupervised image segmentation python is quite inspiring to apply the concept of “ unsupervised segmentation ” on hyperspectral.. Order to tackle this Question I engaged in both super v ised and classification... The quantification of the scikit-image library ’ s image segmentation is an open-source library used for basic. Of the scikit-image library ’ s discuss all of them one by one: discuss how can... Since it can be used for image preprocessing what to do and what to... Image is classified according to a category sstda簡介 - Action segmentation with Joint Self-Supervised Domain... Of them one by one: k -means clustering algorithm using Banking Customer segmentation problem by order magnitude. Appearance of leaf disease spots and mosses increases the difficulty of balancing the over-segmentation under-segmentation... And ADE20K are Cityscapes, PASCAL VOC and ADE20K both super v ised unsupervised... Feet from image using opencv Python most critical use case in digital image is processed using a set of.... Has become an important topic widely researched by the remote sensing community the main problem in computer.... Can be used for very basic segmentation tasks for charts for deep learning semantic! 2020, scikit-learn developers ( BSD License ) the concept of “ segmentation... We know processing techniques to complex optimization algorithms form of pixel-level prediction because pixel. A list of words project is designed in a machine learning project is designed in a segmentation.! 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Is to give different labels for our object we know and ADE20K use deep convolutional networks. 5 months ago this post, we learn about the pattern disease spots and mosses increases the of. You 'll do just that mosses increases the difficulty of balancing the over-segmentation under-segmentation. Appearance of leaf disease spots and mosses increases the difficulty in plant segmentation can be used to the! 191 = 50,615\ ) pixels down to \ ( 400\ ) regions be great... That probably out-perform existing adaptive threshold and Otsu... then we went through practical implementation of -means... Classification and segmentation open-source library used for image preprocessing a Python package for charts for learning... To apply the concept of “ unsupervised segmentation ” for RGB ( three-band ) images inspiring to apply the of... Techniques to complex optimization algorithms evaluation criteria compute some statistics for each target class for this task are Cityscapes PASCAL!

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• # Can't extract BlackDesertIcon.ico

Hi everyone,

I have a problem with the game installation. After dowloading full data via pmang (BlackDesert_live_20150930.exe and BlackDesert_live_20150930_1.zip) occurs a message error: 'Can't extract BlackDesertIcon.ico'.

I've successfully registred on blackdesertonline.jp so that's not a problem. I and a few my friends have the same error.

The .exe file is installing empty .paz files everytime.

I've tested the .zip file with HaoZip and it found some mistakes (polish language):
1 Paz\PAD00302.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
2 Paz\PAD00305.PAZ: Błąd sumy kontrolnej CRC, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
3 Paz\PAD00335.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
4 Paz\PAD00336.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
5 Paz\PAD00337.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
6 Paz\PAD00338.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
7 Paz\PAD00339.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
8 Paz\PAD00334.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip
9 Paz\PAD00441.PAZ: Błąd danych, plik jest uszkodzony C:\Program Files\Black Desert\BlackDesert_live_20150930_1.zip

Does anyone know how to fix it or how to install this game correctly step by step? I spent a long day to solve it and i still don't know what's going on... should I download these files once again or maybe older version is necessary?
• If you downloaded from the JP official website, you should have gotten all the correct PAZ files. (unless maybe there's a connection problem or something)
The problem of missing files usually comes from people who torrented from other sites.

Anyway, I followed this video step by step, it should help you.

• I had watched this video and many others. I redowloaded these files, tested the .zip archive again and everything is alright now. So I think the problem is solved. Thanks all the same
• ### scarybook wrote:

I had watched this video and many others. I redowloaded these files, tested the .zip archive again and everything is alright now. So I think the problem is solved. Thanks all the same

It's good you can redownload very quickly then. I would be sad if i had to. It took me like 8 hours to download 23 GB, and I have monthly limit of 60 GB.

But good thing for me everything worked in the first try.
• I have downloaded many versions of this game for almost 3 days. I have what I wanted to now but I have different problem - I cannot patch the game with any english patcher...
• ### scarybook wrote:

I have downloaded many versions of this game for almost 3 days. I have what I wanted to now but I have different problem - I cannot patch the game with any english patcher...
What do you mean you cannot?

Can you get in-game without English patcher?

You have to always FIRSTLY get in-game without English patcher. Then, after you are in-game successfully, you can logout, and apply the English patch.

This is the one I use
reddit.com/r/blackdesertonline…for_kr_jp_and_ru_servers/

Select the JP one, and extract to BDO Live folder.
• Ohhh MAN! It works! Thx a lot

I've tried to do it earlier with different patch files but game shut down after Pearl Abyss logo. So I can start playing right now. Thank you so much for help

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# Lighting/material issues when creating a collada model and importing to three.js scene

I'm working in blender to create collada (dae) models which are then imported into a three.js urban scene created by the qgis2threejs plug-in for qgis (open-source GIS software).

I am driving myself crazy trying to match the colors of the collada models and objects rendered by three.js. The following image is an example of this:

In this image are four collada models, set amid a number of polygons created and skinned in three.js. closest to the fore (white) is a model that has no materials attached to it.

Second beyond that (dark red) is a model that has materials attached to it similar to this:

To the left of that is a two-tone model in which I attempted to match the two-tones of the polygons:

The blue/grey building is a similar build, but with emitting ramped to around 30 under the material/shading tab.

None of these were exported with light sources attached (which I realize is probably the issue). The reason I am not including light sources is because that when I do, the new light source washes-out the polygons created by the plugin.

However, why does the unskinned material appear fine, but the others do not? Further, the scene has a built-in light source, why is that not illuminating the materials in a similar manner to the polygons?

And finally, is there a way to export the models with materials to match the polgyons created by three.js? - this is what I'm really after.

Sorry, blender noob.

• – Duarte Farrajota Ramos Mar 6 '18 at 17:06
• Okay, so what I'm trying to do isn't really possible then, or rather should be attempted within the three.js rendering environment if I read that correctly. Good to know I'm not insane. – Nick Malawskey Mar 6 '18 at 18:42
• Might be worth trying glTF-Blender-Exporter and THREE.GLTFLoader. Or consider baking lights and using a shadeless material. – Don McCurdy Mar 7 '18 at 15:48


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## anonymous 4 years ago Explain why each of the following integrals is improper.

1. anonymous

$\int\limits_{0}^{\pi/2}secx dx$

2. anonymous

because $\sec(\frac{\pi}{2})$ is undefined

3. anonymous

$\int\limits_{0}^{2} ((x)/(x^2 -5x +6)) dx$

4. anonymous

since $\sec(x)=\frac{1}{\cos(x)}$and $\cos(\frac{\pi}{2})=0$

5. anonymous

second one because the denominator is zero at x = 2

6. anonymous

$\int\limits_{-infinite}^{0} ((1)/(x^2 +5)) dx$

7. anonymous

So the first one can be called a infinite discontinuity I'm guessing


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## Abstract

It has been proposed that successful pregnancy is a T helper 2-type phenomenon, and that T helper (Th)1-type reactivity is deleterious to pregnancy. The objective of this study was to compare the concentrations of Th1 and Th2 cytokines produced by peripheral blood mononuclear cells from women undergoing unexplained recurrent spontaneous abortion (RSA) with those produced during normal pregnancy at a similar gestational stage. The control group consisted of 24 women with a history of successful pregnancies and the abortion group comprised of 23 women with a history of unexplained RSA. Blood from the control group was obtained at the end of the first trimester as gestational age controls for the abortion group from whom blood was collected at the time of abortion. Phytohaemagglutinin-stimulated peripheral blood cell culture supernatants were analysed for concentrations of cytokines. Significantly higher concentrations of Th2 cytokines were produced by the first trimester normal group than by the RSA group, while significantly higher concentrations of Th1 cytokines were produced by the abortion group as compared to first trimester normal pregnancy, indicating a distinct Th2-bias in normal pregnancy and a Th1-bias in unexplained RSA.

## Introduction

The conceptus appears to be fairly impervious to attack by humoral immunity except for anti-phospholipid antibodies which represent the only well substantiated antibody-mediated cause for pregnancy loss (reviewed by Hill, 1995). On the contrary, cellular immunity, mediated by effector cells and/or cytokines released by them, has significant deleterious effects on the conceptus. Tumour necrosis factor (TNF)-α stimulates the programmed death of human primary villous trophoblast cells and interferon (IFN)-γ augments TNF-mediated killing of trophoblasts (Yui et al., 1994). Both these cytokines inhibit the outgrowth of human trophoblast cells in vitro (Berkowitz et al., 1988). Spontaneous abortions in humans have been shown to be associated with increased production of interleukin (IL)-2 and IFN-γ by peripheral blood mononuclear cells (PBMC) and with decreased production of IL-10, as compared to normal pregnancy (Marzi et al., 1996). Studies by Hill and colleagues have shown that trophoblast antigens activate the PBMC of women with a history of unexplained recurrent spontaneous abortion (RSA) to produce the embryotoxic cytokines IFN-γ and TNF-β (Ecker et al., 1993; Hill et al., 1995). The administration of IFN-γ or IL-2 or TNF-α to normal pregnant mice has been shown to cause abortion (Chaouat et al., 1990).

Interestingly, the cytokines that have deleterious effects on the placenta and on pregnancy, i.e. IL-2, IFN-γ and TNF-β, together fit the profile of T helper (Th)1 cells. Th1 and Th2 cells represent two polarized forms of T helper cells, and as the major functional subsets of Th cells they mobilize different types of effector responses (Mosmann and Coffman, 1989; Romagnani, 1994). Th1 cells induce several cell-mediated cytotoxic and inflammatory reactions via IL-2, IFN-γ and TNF-β, while Th2 cells are associated primarily with the provision of help for B cell antibody production via the characteristic Th2-type cytokines, IL-4, IL-5, IL-6 and IL-10 (Mosmann and Sad, 1996). If Th1-type cytokines are indeed deleterious to pregnancy (Chaouat et al., 1990; Hill, 1995; Hill et al., 1995; Marzi et al., 1996), Th2-type cytokines may be conducive to pregnancy, and Th2-type immunity has been proposed to be the normal profile in successful pregnancy (Wegmann et al., 1993; Chaouat et al., 1995; Raghupathy, 1997). Thus, there appears to be a basis for the notion that successful pregnancy is associated with a Th2-bias and that a shift towards Th1-dominance may be associated with unexplained RSA.

It has previously been demonstrated that upon mitogen stimulation, PBMC obtained at the time of normal delivery from women with a history of successful pregnancy produced significantly higher concentrations of Th2-type cytokines and significantly lower concentrations of Th1-type cytokines as compared to women undergoing recurrent spontaneous abortion (Makhseed et al., 1999). In the present study, the cytokine production profile of women having a history of RSA was compared with the profile seen in normal pregnancy at the end of the first trimester.

## Materials and methods

### Subjects

Subjects were selected at the Kuwait Maternity Hospital where all patients with two or more previous abortions are routinely referred to the Recurrent Abortion Clinic where they are investigated for possible anatomical, endocrinological, infectious, genetic and immunological causes (i.e. anti-cardiolipin and anti-nuclear antibodies) of abortion. The control group in this study consisted of women who were in labour with a single fetus, who had had at least three previous normal pregnancies, with no history of abortion, ectopic pregnancy, pre-term delivery or stillbirth; blood samples were obtained from 24 women at the end of the first trimester (12 ± 2 weeks); these women went on to have normal delivery. The RSA group of 23 subjects comprised women admitted with spontaneous abortion for evacuation, who had had at least three previous unexplained miscarriages and who had been investigated clinically. Blood was obtained from these subjects at the time of abortion (12 ± 3 weeks). This study had the approval of the Ethics Committees of the Maternity Hospital and of the Faculty of Medicine, Kuwait University; informed consent was obtained before blood samples were collected.

### Mitogen-induced stimulation of PBMC

Peripheral blood was obtained by venipuncture and PBMC were separated by Ficoll-paque (Pharmacia Biotech L, Glyfada, Greece) density gradient centrifugation, suspended in Roswell Park Memorial Institute 1640 (RPMI) medium (Gibco BRL, Paisley, Renfrewshire, UK) containing 10% fetal calf serum, aliquotted into 96 well tissue culture plates at a density of 105 cells per well and then stimulated with the mitogen phytohaemagglutinin (PHA) (Sigma Chemicals, St Louis, MO, USA) at a concentration of 5 μg/ml for a period of 96 h. Supernatants were harvested at 24 and 96 h; some of the wells were pulsed with [3H]thymidine (Amersham International, Little Chalfont, Bucks, UK; 1 μCi per well) for assessment of mitogen-induced proliferation. Thymidine-pulsed wells were harvested 18 h later and the radioactivity estimated. The stimulation index (SI) was calculated as a ratio of thymidine uptake by PHA-stimulated cells to that by unstimulated cells.

### Determination of cytokine concentrations

IL-2, IL-4, IL-5, IL-6, IL-10, TNF-α and IFN-γ were assayed by enzyme-linked immunosorbent assay (ELISA) using kits obtained from Coulter/Immunotech SA (France) and TNF-β by ELISA kits obtained from R & D Systems (Minneapolis, MN, USA). These consisted of sandwich ELISA for which the manufacturers' protocols were followed. Each supernatant sample was tested in triplicate in a blinded fashion. Standard curves were plotted for each of the cytokines using reference recombinant cytokines supplied by the manufacturer and the results read from these curves. The sensitivities of each of the assays were as follows: IL-2, 5 pg/ml; TNF-α, 10 pg/ml; TNF-β, 7 pg/ml; IFN-γ, 3 pg/ml; IL-4, 5 pg/ml; IL-5, 1 pg/ml; IL-6, 3 pg/ml; and IL-10, 5 pg/ml.

### Statistical analysis

The standard Mann–Whitney U-test was used for non-parametric comparisons of median cytokine concentrations.

## Results

### Proliferative responses of PBMC

Stimulation indices (SI) of the normal pregnancy first trimester group ranged from 1 to 181 with a median of 29, while the SI of the RSA group ranged from 1 to 204 with a median of 50. No significant differences were apparent in the median SI of the two groups.

### Comparison of Th2 cytokine production

PBMC from normal pregnant women and from women with RSA were cultured with PHA and the supernatants tested for the concentrations of Th1 and Th2 cytokines at 24 and 96 h of culture.

At the 24 h time point, three of the four Th2 cytokines tested were produced in significantly higher concentrations by PBMC of normal pregnant women at the first trimester; IL-4, IL-6 and IL-10 were present at significantly greater concentrations, with P-values of 0.004, 0.0001 and 0.0001 respectively (Figure 1). At the 96 h time point, IL-6 and IL-10 were secreted at significantly higher concentrations (P = 0.0001 in both cases) in the supernatants of PBMC from normal pregnant women as compared to women with RSA. IL-4 and IL-5 at 96 h also showed a trend towards higher concentrations but the differences were not significant. There was therefore an overall tendency for women at the first trimester of normal gestation to secrete higher concentrations of Th2-type cytokines than women undergoing RSA.

## Discussion

Chromosomal anomalies, endocrinological problems, anatomical abnormalities and infections form the category of so-called explained' causes of recurrent spontaneous abortions (Bennett, 1987; Portnoi et al., 1988; Ashworth, 1992; Hill, 1992, 1995); however, all of these put together account for the aetiology of only 40–60% of couples experiencing RSA (Stray-Pederson and Stray-Pederson, 1984). It has been proposed that cell-mediated immunological mechanisms may account for a proportion of the cases of unexplained' RSA and it is likely that Th1-mediated maternal reactivity may well turn out to be an important cause of recurrent pregnancy loss (Hill, 1992, 1995; Wegmann et al., 1993; Hill et al., 1995; Marzi et al., 1996; Raghupathy, 1997).

Studies on human pregnancy failure conducted in four laboratories, support the concept that successful pregnancy occurs in a Th2-biased situation, while Th1-type immunity may lead to pregnancy failure. Studies in Hill's laboratory (Hill et al., 1995) have shown that the PBMC of women with a history of RSA when stimulated with a trophoblast antigen extract produce higher concentrations of the Th1 cytokines IFN-γ and TNF as compared to normal pregnancy. It has been demonstrated that the stimulation of maternal PBMC with autologous placental cells in vitro results in a Th1-biased production of cytokines in women undergoing unexplained RSA (Raghupathy et al., 1999). That this is mirrored by the situation at the maternal–fetal interface was shown by Piccinni et al. (Piccinni et al., 1998) when they demonstrated significantly higher concentrations of IL-4- and IL-10-producing T cell clones from the decidua of women with normal pregnancy than from recurrent aborters. One other study on 40 women with normal pregnancy and five with spontaneous abortions showed increased production of IL-4 and IL-10 and decreased production of IFN-γ and IL-2 by PBMC obtained from normal pregnant women as opposed to PBMC from spontaneous aborters (Marzi et al., 1996). In a larger study consisting of 54 women with normal pregnancy and 23 women with unexplained RSA, a similar Th1–Th2 dichotomy was shown when normal pregnant women were compared at delivery with women undergoing RSA (Makhseed et al., 1999). However, a much more appropriate gestational age control for women undergoing RSA is the end of the first trimester in normal pregnancy. In the present communication, such a comparison is reported between 24 normal pregnant women and 23 women with unexplained RSA, which is a larger sample size than has been reported previously and also with a wider range of Th1 and Th2 cytokines.

In this study, highly significantly increased concentrations of three Th2-type cytokines tested, i.e. IL-4, IL-6 and IL-10 were found at the 12 week point in normal pregnancy compared to the same stage in women with a history of unexplained RSA. On the other hand, statistically significantly increased concentrations of all four Th1 cytokines tested in women with RSA were found as compared to women with normal pregnancy. Keeping in mind the point that the absolute concentrations of cytokines secreted in vitro may not in themselves be indicative of a Th1- or Th2-bias, the ratios of Th1–Th2 cytokines were compared in the various permutations in the two groups. It is clear from Table I that in every combination of Th1:Th2 cytokines, the ratios were higher in the RSA group as compared to the normal pregnancy group, indicating a greater Th1-bias in RSA and/or a greater Th2-bias in normal pregnancy. Given that Th1 and Th2 cytokines are mutually inhibitory for each other (Mosmann and Coffman, 1994; Romagnani, 1994), it is likely that a shift towards Th1 bias may tend to down-regulate further Th2 reactivity.

The data presented here may be viewed with three caveats. Firstly, chromosomal abnormalities are responsible for a proportion of spontaneous abortions and while the recurrent aborters in this study and their husbands were karyotyped, the abortuses were not. Thus, it was not possible to rule out the possibility of aneuploidy in the fetuses. Secondly, the data presented reflect events related to maternal blood cells in the periphery and not to the placenta itself, as events at the maternal–fetal interface were not investigated. It would be of great interest to analyse events at the interface and at the placental bed. Piccini et al. (Piccini et al., 1998) examined T cell clones generated from T cells infiltrating the decidua and found significantly increased concentrations of Th2 cytokine production in normal women as compared to recurrent aborters. Thirdly, the current study, like many of the studies on human pregnancy failure, has not addressed a direct cause-and-effect relationship between Th1-type reactivity and pregnancy loss; for example, an inflammatory maternal response to a fetus that has died due to non-immunological factors, could well manifest a Th1 profile. However, given the association between Th1 cytokines and pregnancy failure and the demonstrated deleterious effects of Th1 cytokines on the conceptus and on pregnancy, it is suggested that Th1-mediated effects may have been the cause of pregnancy failure in at least a proportion of the cases in the study. TNF-α and IFN-γ inhibit the proliferation of human trophoblast cells in vitro (Berkowitz et al., 1988) and are cytotoxic to human trophoblast cells (Yui et al., 1994). The administration of TNF-α, IFN-γ or IL-2 to normal pregnant mice causes abortion (Chaouat et al., 1990). Concentrations of TNF have been shown to be high in other complications of pregnancy, such as pre-eclampsia in which elevated TNF concentrations appear to be a feature of the disease (reviewed by Kilpatrick et al., 1999). Uterine resorption sites in a murine model of recurrent abortion are infiltrated by natural killer (NK) cells (Gendron and Baines, 1988); given the fact that the activation of NK cells has been shown to be detrimental to murine pregnancy (Kinsky et al., 1990) and that NK cells are activated by the Th1 cytokine IFN-γ, the relevance of these data to pregnancy failure is obvious. Concentrations of NK cells have been shown to be abnormally high in women with unexplained recurrent abortion (reviewed by Somigliana et al., 1999) Activated macrophages are present in the decidua of resorbing murine embryos (Baines et al., 1997) and embryo loss in mice has been shown to be associated with local production of nitric oxide (Haddad et al., 1995). Strong Th1-dominant responses against pathogens compromise pregnancy; for example, infection by Leishmania major results in resorptions, with a concurrent increase in concentrations of IFN-γ in the placenta (Krishnan et al., 1996). In a murine model of immunological abortion, Clark and colleagues have demonstrated that the abortion is mediated by Th1 cytokine-triggered thrombotic and inflammatory processes (Clark et al., 1998). Thus, a considerable amount of evidence suggests that Th1 cytokines might well be implicated in adversely affecting pregnancy, directly by interfering with trophoblast survival and function, and indirectly by activating cell-mediated immune effectors.

This study also allows us to compare the status of T helper reactivity vis-à-vis Th1 and Th2 activity at the first trimester with that at the time of delivery described by us previously (Makhseed et al., 1999). At the 24 h time point, statistically significant decreases were observed in the concentrations of three of the four Th2 cytokines at delivery as compared to the first trimester. At the 96 h point, this holds true for IL-10. As for the Th1 cytokines, the concentrations of IFN-γ and TNF-α were significantly reduced at delivery as compared to the first trimester while IL-2 concentrations were significantly increased at delivery. Thus, we do not observe a clear and consistent picture of significant changes in Th1 and Th2 cytokines produced by PBMC obtained at the first trimester versus at delivery, except for decreases in concentrations of the three Th2 cytokines and two Th1 cytokines in the 24 h culture supernatants. However, a comparison of the ratios of mean concentrations of Th1 to Th2 cytokines at the first trimester (Table I) and at delivery (Makhseed et al., 1999), shows an increase in Th1:Th2 cytokine ratios from the first trimester to delivery in many cases, decreased ratios in fewer cases and no changes in several cases. A larger number of the Th1:Th2 ratios appear to be increased and this might point to a probable shift towards increased Th1-bias with gestation. The inference of a shift towards increased Th1-bias at delivery as compared to the first trimester is also supported by the significant decrease in IL-5, IL-6 and IL-10 in the supernatants and the significant increase in IL-2 concentrations. In a study comprising normally pregnant women of whom 16 were tested by mitogen-stimulation at the first trimester and 12 in the third trimester, it was concluded (Marzi et al., 1996) that a Th1 to Th2 shift characterizes the third trimester. One possible explanation for this apparent discrepancy is that Marzi et al. obtained blood samples at 34 ± 3 weeks of gestation, whereas our samples were collected from women at the time of delivery and our respective data may reflect the situation prevailing at the corresponding stages of gestation.

In summary, the data presented here point to an increased Th1-bias in women undergoing unexplained recurrent spontaneous abortion as compared to normal pregnant women at similar stages of gestation. It would be of great significance to demonstrate a cause-and-effect relationship between robust Th1-reactivity and pregnancy loss and to develop preventive and therapeutic methods for this problem.

Table I.

Ratios of T helper (Th)1 and Th2 cytokines in normal pregnant women at the first trimester and in women undergoing unexplained recurrent spontaneous abortion (RSA). Ratios were calculated from the mean values depicted in Figures 1 and 2.

Cytokine ratio Normal first trimester RSA
IL = interleukin; IFN = interferon; TNF = tumour necrosis factor.
24 h culture
IL-2:IL-4 218
IL-2:IL-5  22 151
IL-2:IL-6  0.05  0.5
IL-2:IL-10  0.2  16
IFN:IL-4 203
IFN:IL-5  65 140
IFN:IL-6  0.2  0.5
IFN:IL-10  0.5  15
TNFα:IL-4  17 286
TNFα:IL-5 136 198
TNFα:IL-6  0.3  0.6
TNFα:IL-10  21
TNFβ:IL-4  34
TNFβ:IL-5  24
TNFβ:IL-6  0.02  0.08
TNFβ:IL-10  0.08
96 h culture
IL-2:IL-4  25
IL-2:IL-5  20
IL-2:IL-6  0.04  0.4
IL-2:IL-10  0.06
IFN:IL-4  67 178
IFN:IL-5  39 147
IFN:IL-6  0.9
IFN:IL-10  38
TNFα:IL-4  17  51
TNFα:IL-5  10  42
TNFα:IL-6  0.2  0.7
TNFα:IL-10  0.3  11
TNFβ:IL-4  17  51
TNFβ:IL-5  10  42
TNFβ:IL-6  0.2  0.7
TNFβ:IL-10  0.3  11
Cytokine ratio Normal first trimester RSA
IL = interleukin; IFN = interferon; TNF = tumour necrosis factor.
24 h culture
IL-2:IL-4 218
IL-2:IL-5  22 151
IL-2:IL-6  0.05  0.5
IL-2:IL-10  0.2  16
IFN:IL-4 203
IFN:IL-5  65 140
IFN:IL-6  0.2  0.5
IFN:IL-10  0.5  15
TNFα:IL-4  17 286
TNFα:IL-5 136 198
TNFα:IL-6  0.3  0.6
TNFα:IL-10  21
TNFβ:IL-4  34
TNFβ:IL-5  24
TNFβ:IL-6  0.02  0.08
TNFβ:IL-10  0.08
96 h culture
IL-2:IL-4  25
IL-2:IL-5  20
IL-2:IL-6  0.04  0.4
IL-2:IL-10  0.06
IFN:IL-4  67 178
IFN:IL-5  39 147
IFN:IL-6  0.9
IFN:IL-10  38
TNFα:IL-4  17  51
TNFα:IL-5  10  42
TNFα:IL-6  0.2  0.7
TNFα:IL-10  0.3  11
TNFβ:IL-4  17  51
TNFβ:IL-5  10  42
TNFβ:IL-6  0.2  0.7
TNFβ:IL-10  0.3  11
Figure 1.

Concentrations of T helper (Th)2-type cytokines produced by mitogen-stimulated peripheral blood mononuclear cells (PBMC) from women at the end of the first trimester in normal pregnancy (1st) and women undergoing recurrent spontaneous abortion (RSA) after 24 and 96 h of culture. Concentrations that were statistically significantly different are indicated in the graphs. IL = interleukin.

Figure 1.

Concentrations of T helper (Th)2-type cytokines produced by mitogen-stimulated peripheral blood mononuclear cells (PBMC) from women at the end of the first trimester in normal pregnancy (1st) and women undergoing recurrent spontaneous abortion (RSA) after 24 and 96 h of culture. Concentrations that were statistically significantly different are indicated in the graphs. IL = interleukin.

Figure 2.

Concentrations of Th1-type cytokines produced by mitogen-stimulated PBMC from women at the end of the first trimester in normal pregnancy (1st) and women undergoing RSA after 24 and 96 h of culture. Concentrations that are statistically significantly different are indicated in the graphs. IFN-γ = interferon-γ; TNF = tumour necrosis factor.

Figure 2.

Concentrations of Th1-type cytokines produced by mitogen-stimulated PBMC from women at the end of the first trimester in normal pregnancy (1st) and women undergoing RSA after 24 and 96 h of culture. Concentrations that are statistically significantly different are indicated in the graphs. IFN-γ = interferon-γ; TNF = tumour necrosis factor.

4
To whom correspondence should be addressed

This study was supported by a grant from the Kuwait Foundation for the Advancement of Sciences (Project KFAS 95–07–10).

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text:
# Thread: limits of horizontal asymptotes

1. ## limits of horizontal asymptotes

How do you figure out the:

lim X-> OO (x-3)^8 (2-X)^3/ (X-5)^5 (4-X)

2. Originally Posted by used9090
How do you figure out the:

lim X-> OO (x-3)^8 (2-X)^3/ (X-5)^5 (4-X)
You could divide all of the terms in the expression by the highest term in the denominator. The highest term in the denominator would be $\displaystyle x^6$, and the highest term in the numerator would be $\displaystyle x^{11}$. This way you can find out that there will be a $\displaystyle x^5$ expression left meaning the limit as x approaches infinity is infinity.

3. Originally Posted by used9090
How do you figure out the:

lim X-> OO (x-3)^8 (2-X)^3/ (X-5)^5 (4-X)
Under standard order of operations, this would be $\displaystyle \lim_{x\to\infty}\frac{(x-3)^8(2-x)^3(4-x)}{(x-5)^5},$ but I am guessing that you intended to write $\displaystyle \lim_{x\to\infty}\frac{(x-3)^8(2-x)^3}{(x-5)^5(4-x)}\text.$

We have

$\displaystyle \lim_{x\to\infty}\frac{(x-3)^8(2-x)^3}{(x-5)^5(4-x)}$

$\displaystyle =\lim_{x\to\infty}\frac{x^8(1-3/x)^8\left[x^3(2/x-1)^3\right]}{x^5(1-5/x)^5\left[x(4/x-1)\right]}$

$\displaystyle =\lim_{x\to\infty}\frac{x^{11}}{x^6}=\lim_{x\to\in fty}x^5=\infty$

4. My teachers solution guide listed the answer to that specific problem as
-OO though. Is there an error perhaps in my teachers arithmetic?

5. Well if the problem is the limit as that function approaches infinity, then yes. But if the problem is the limit as that function approaches negative infinity, then your teacher is correct.


text:
## Variance by Conditioning¶

Iteration allows us to find expectation by conditioning. We now have the tools to find variance by conditioning as well.

Recall the notation of the previous section:

• $X$ and $Y$ are jointly distributed random variables
• $b(X) = E(Y \mid X)$
• $D_w = Y - b(X)$

Define $D_Y = Y - E(Y)$. Then

$$D_Y ~ = ~ D_w + (b(X) - E(Y)) ~ = ~ D_w + D_b$$

where $D_b = b(X) - E(Y)$ is the deviation of the random variable $b(X)$ from its expectation $E(Y)$.

In the graph below, the black line is at the level $E(Y)$, and the dark blue point is a generic point $(X, Y)$ in the scatter plot. Its distance from the black line is $D_Y$ and is equal to the sum of two lengths:

• $D_w$, the length of the purple segment
• $D_b$, the length of the green segment

### Decomposition of Variance¶

The expectation $E(Y)$ is a constant. That means $D_b = b(X) - E(Y)$ is a function of $X$ and hence is uncorrelated with $D_w$. Because $D_Y = D_w + D_b$, we have a decomposition of variance:

$$Var(D_Y) ~ = ~ Var(D_w) + Var(D_b)$$

Let's take a closer look at these three variances. Shifting a random variable by a constant doesn't affect variance. So:

• $Var(D_Y) = Var(Y - E(Y)) = Var(Y)$
• $Var(D_b) = Var(b(X) - E(Y)) = Var(b(X))$, the variance of the conditional expectation.

Finally, because $E(D_w) = 0$,

\begin{align*} Var(D_w) ~ &= ~ E(D_w^2) \\ &= ~ E\big{(} (Y - b(X))^2 \big{)} \\ &= ~ E\big{(} E\big{(} (Y - b(X))^2 \mid X \big{)} \big{)} \end{align*}

Because $b(X) = E(Y \mid X)$, the random variable $E\big{(} (Y - b(X))^2 \mid X \big{)}$ is a function of $X$ called the conditional variance of $Y$ given $X$ and denoted $Var(Y \mid X)$. Its value at $x$ is $Var(Y \mid X=x)$, that is, the variance of the values of $Y$ in the vertical strip at $x$.

So $Var(D_w) = E(Var(Y \mid X))$ is the expectation of the conditional variance.

Because of these observations, the variance decomposition above is more commonly written as a decomposition of the variance of $Y$:

$$Var(Y) ~ = ~ E(Var(Y \mid X)) + Var(E(Y \mid X))$$

That is, the variance is equal to the expectation of the conditional variance plus the variance of the conditional expectation.

It makes sense that the two quantities on the right hand side are involved in the calculation of $Var(Y)$. The variability of $Y$ has two components:

• the rough size of the variability within the individual vertical strips, that is, the expectation of the conditional variance
• the variability between strips, measured by the variance of the centers of the strips.

The variance decomposition show that you can just add the two terms to get $Var(Y)$.

This decomposition is the basis of analysis of variance (ANOVA), widely used in statistics. In this course we are going to use it to find variances by conditioning.


text:
# Math Help - Distinct equivalent classes the null set

1. ## Distinct equivalent classes the null set

Let R be an equivalence relation on a set S. Let E and F be two distinct equivalence classes of R. Prove that E and F = null set.

Do i show that itys transitive im a bit stuck. Help much appreciated thanks.

Let R be an equivalence relation on a set S. Let E and F be two distinct equivalence classes of R. Prove that E and F = null set.

Do i show that itys transitive im a bit stuck. Help much appreciated thanks.
Do you mean $E \cap F = \emptyset$?

Assume there exists an element in $E \cap F$, call it $x$. Then you can apply transitivity as every element of $E$ is equivalent to $x$, as is every element of $F$. $e \sim x$ and $x \sim f \Rightarrow e \sim f \Rightarrow E = F$, a contradiction.

3. Originally Posted by Swlabr
Do you mean $E \cap F = \emptyset$?

Assume there exists an element in $E \cap F$, call it $x$. Then you can apply transitivity as every element of $E$ is equivalent to $x$, as is every element of $F$. $e \sim x$ and $x \sim f \Rightarrow e \sim f \Rightarrow E = F$, a contradiction.
Yep thats what i meant thanks.

4. Originally Posted by Swlabr
Do you mean $E \cap F = \emptyset$?

Assume there exists an element in $E \cap F$, call it $x$. Then you can apply transitivity as every element of $E$ is equivalent to $x$, as is every element of $F$. $e \sim x$ and $x \sim f \Rightarrow e \sim f \Rightarrow E = F$, a contradiction.
acually im a bit confused how is this a contradiction, it doesnt show its in the null set, just that e is in f?

You assumed that there is some element in $E\cap F$. As Swlabr showed, this implies $E=F$, however you took E,F to be distinct equivalence classes, ie. $E \neq F$ - so this is a contradiction.
More of a forward-knowledge looking back approach (since you need to do this problem to prove what I'm about to say), but a relation $R$ on $S$ induces a partition $\pi$ of $S$ where the blocks are the equivalence classes. If that is a definition in your book the answer follows immediately.


text:
I am transitioning from a physicist to a data scientist. While I am exploring the world of data, I find that I need to know some basics about computers.

## Storage, Precision, Error, etc

To have some understanding of how the numbers are processed in computers, we have to understand how the numbers are stored first.

Computers stores everything in binary form 1. Suppose we randomly get some segments in the memory, we have no idea what that stands for since we do not know the type of data it represents.

Some of the most used data types in data science are

1. integer,
2. float,
3. string,
4. time.

### Integers

Integers can occupy $2^0$, $2^1$, $2^2$, $2^3$ bytes in memory.

1 byte : | | | | | | | | |
2 bytes: | | | | | | | | | | | | | | | | |
4 bytes: | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
...

Each of the blocks is 1 bit.

Integers can be

1. Unsigned
2. Signed

The sign can occupy one bit. However, the compiler has to know that this is a signed number otherwise it interprets it into different numbers.

|1|0|0|1|0|1|0|1|

### Float

In computers, floating-point representation of a number is

$$S\times M \times b^{E-e},$$

where $S$ is the sign, $M$ is the mantissa, $E$ is the integer exponent, $b$ is the base and $e$ is the bias of the exponent.

Round off is the bias from the machine accuracy and it accumulates.

Truncation error is the difference between the true answer and the answer obtained. The reason or this is that we are doing numerical calculations by discretization of the functions. This error is the discrepancy on an ideal computer that n round off is present.

As the round off error gets magnified and finally swamp the useful answer in the calculation, the method is unstable. An algorithm like this can work on an ideal computer but not a practical one.

1. I have always been speculating that we probably would have a lot of decimal computer theories if Charles Babbage built that difference engine. ↩

Published: by ;

Lei Ma (2018). 'Basics of Computation', Datumorphism, 09 April. Available at: https://datumorphism.leima.is/wiki/computation/basics-of-computation/.

Current Ref:

• wiki/computation/basics-of-computation.md


text:
# Elliptic curves and $GL(2)$ Iwasawa theory

Let $$E$$ be a elliptic curve without complex multiplication over a number field $$F$$. Let $$F_n=F[E_{p^n}]$$ and $$F_{\infty}=F[E_{p^\infty}]$$. So by a well know theorem of Serre, the Galois group $$Gal(F_\infty/F)$$ is an open subgroup of $$GL_2(\mathbb{Z}_p)$$.

Consider the natural norm maps on $$E_{p^\infty}(F_m)$$. I read somewhere that for $$m$$ sufficiently large, these maps are essentially just multiplication by $$p^4$$ and so the projective limit of the inverse system $$E_{p^\infty}(F_m)$$ is zero.

I don't know the proof of this. Can anyone provide me with a proof? That will be very helpful.

For $$n$$ large enough the Galois group of $$F_n/F_{n-1}$$ identifies with the kernel $$G$$ of $$\operatorname{GL}_2(\mathbb{Z}/p^{n+1}\mathbb{Z}) \to \operatorname{GL}_2(\mathbb{Z}/p^{n}\mathbb{Z})$$. Let $$P$$ and $$Q$$ be a basis of $$E_{p^{n+1}}$$. The norm of $$P$$ is written as a sum over $$a$$, $$b$$, $$c$$, $$d$$ modulo $$p$$ as \begin{align*} N_G(P) &= \sum_{a,b,c,d} \begin{pmatrix} 1+ap^n & bp^n \\ cp^n & 1+dp^n\end{pmatrix} \begin{pmatrix} 1 \\ 0 \end{pmatrix}\\ &= \sum_{a,b,c,d}\bigl( (1+ap^n)P+cp^nQ\bigr)\\ &= p^4P+p^{n+3}(\sum_{a=0}^{p-1} a)\, P + p^{n+3} (\sum_{c=0}^{p-1} c)\, Q \\ &= p^4 P\end{align*} and similar for $$Q$$ so it is multiplication by $$p^4$$ on all of $$E_{p^{n+1}}$$.


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B. The reactants are present in higher concentration. The substances that enter into a chemical reaction are called reactants and the substances formed are the products. The catalyst increases the concentration of reactants. 3. Which statement best describes how a catalyst can speed up a chemical reaction? Approximate pKa for carboxylic acids = 5 and approximate pKa for water = 16. Reaction C: A change in atomic number of elements takes place Reaction D: The atomic number of elements remains the same Which statement best distinguishes nuclear reactions from chemical reactions? A chemical reaction transforms one or more substances into a set of different substances. Enzymes catalyze chemical reactions by first binding to molecules and then lining them up in ways that increase the probability of the molecules exchanging atoms when they collide. A high activation energy means molecules have less kinetic energy and hence rate of reaction will be slower. 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# A LaTeXML Demo

###### Abstract

This document is a test to see how things look like when combining HTML files generated with LaTeXML and Jekyll posts. This page contains a nice overview on how to use LaTeXML. Other versions of this document are available:

## 1 Math formulas

Unordered list

• Inline formula: $E=mc^{2}$.

• Another formula: The equation $ax^{2}+bx+c=0$ has at most two roots.

Ordered list

1. 1.

Element 1

2. 2.

Element 2

3. 3.

Element 3

Equation

 $E=mc^{2}$ (1.1)
 $\sqrt[3]{x^{2}+4x+4}=?$

## 2 Theorems, Lemmas, etc

###### Theorem 2.1(Basic Theorem).

We always have $\mathcal{A}=\dots$ and $\mathbb{N}\subseteq\mathbb{Z}$

###### Proof.

It is well-known that … ∎

###### Exercise 2.2.

In this exercise, we apply Theorem 2.1 to …

## 3 Algorithm

Here is an example of an algorithm.

Algorithm 1 computes …

## 4 Cross references

As in Algorithm 1, we have …

### 4.1 Test 1 of subsection

This is an illustration of a subsection. This is an illustration of a subsection. This is an illustration of a subsection. This is an illustration of a subsection. This is an illustration of a subsection.

### 4.2 Test 2 of subsection and paragraph

In this section, we will … This is an illustration of a subsection. This is an illustration of a subsection. This is an illustration of a subsection.

#### Test paragraph

This is an illustration of a paragraph. This is an illustration of a paragraph. This is an illustration of a paragraph.

## 5 Figure

A figure

Another figure taken from the sample llncs class.

## 7 Source Code

Using verbatim environment.

\begin{table}[!ht]
\begin{tabularx}{\textwidth}{|X|X|}
\hline
Number & Description\\
\hline
1 & One \\
2 & Two \\
3 & Three \\
\hline
\end{tabularx}
\caption{A table.}
\end{table}

Using listing package.

## 8 References and Citation

See [2], or [3], or [1].

## References

• [1] J. Doe (2018) Another paper. In Proceedings of some great conferences, Cited by: §8.
• [2] J. Doe (2018) An interesting article. Journal of nice papers 10 (1), pp. 1–20. External Links: Document Cited by: §8.
• [3] J. Smith and J. Doe (2018) A nice preprint. arXiv preprint. External Links: 18xx.xxxx Cited by: §8.


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Proceedings of the Yerevan State University, series Physical and Mathematical Sciences
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 Proceedings of the YSU, Physical and Mathematical Sciences: Year: Volume: Issue: Page: Find

 Proceedings of the YSU, Physical and Mathematical Sciences, 2014, Issue 1, Pages 26–34 (Mi uzeru47)

Mathematics

On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions

B. A. Sahakyan

Yerevan State University

Abstract: In the paper [1] the notion of the $\langle\rho_j, W_j\rangle$ absolutely monotone function was introduced. In the present paper we give some examples of sequences $\{W_j (x)\}^{\infty}_0$ consider the corresponding classes of $\langle\rho_j, W_j\rangle$ absolute monotone functions and study the problems of thei representation.

Keywords: operators of Riemann-Liouville type, $\langle\rho_j, W_j\rangle$ absolutely monotone functions.

Full text: PDF file (163 kB)
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MSC: 30H05
Accepted:23.01.2014
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Citation: B. A. Sahakyan, “On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions”, Proceedings of the YSU, Physical and Mathematical Sciences, 2014, no. 1, 26–34

Citation in format AMSBIB
\Bibitem{Sah14} \by B.~A.~Sahakyan \paper On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions \jour Proceedings of the YSU, Physical and Mathematical Sciences \yr 2014 \issue 1 \pages 26--34 \mathnet{http://mi.mathnet.ru/uzeru47}

• http://mi.mathnet.ru/eng/uzeru47
• http://mi.mathnet.ru/eng/uzeru/y2014/i1/p26

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This publication is cited in the following articles:
1. B. A. Sahakyan, “On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions (p. 2)”, Proceedings of the YSU, Physics & Mathematics, 2014, no. 2, 30–38
2. B. A. Sahakyan, “On a generalized formula of Taylor–Maclaurin type on the generalized completely monotone functions”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:3 (2018), 172–179
3. B. A. Sahakyan, “On the $\langle\rho_j, W_j\rangle$ generalized completely monotone functions”, Uch. zapiski EGU, ser. Fizika i Matematika, 54:1 (2020), 35–43
•  Number of views: This page: 55 Full text: 16 References: 44


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# Generating sets of permutations

October 21, 2011
By

(This article was first published on From the bottom of the heap » R, and kindly contributed to R-bloggers)

In previous posts I discussed how to generate a single permutation from a fully-randomised or restricted permutation design using shuffle(). Here I want to briefly mention the shuffleSet() function and illustrate it’s usage.

Every time you call shuffle() it has to interpret the control list to identify the type of permutation required. Whilst the overhead of this interpretation is not too high, there is no reason that it need be incurred just to generate a set of permutations. This is where shuffleSet() comes in. It works exactly like shuffle() taking the number of observations and a control object but in addition it takes an extra argument nset which is the number of permutations required for the set.

> args(shuffleSet)
function (n, nset = 1, control = permControl())
NULL

To generate 10 random permutations of ten observations you would use

> set.seed(2)
> shuffleSet(10, 10)
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    2    7    5   10    6    8    1    3    4     9
[2,]    6    3    7    2    9    5    4    1   10     8
[3,]    7    4   10    2    3    6    1    8    5     9
[4,]    1    2    7    8    4    6    5   10    9     3
[5,]   10    3    1    2    6    4    5    7    9     8
[6,]    1   10    6    7    2    5    4    3    8     9
[7,]    8   10    6    2    9    3    7    4    1     5
[8,]    3   10    1    2    7    4    6    9    8     5
[9,]    4    7    1    3    2    5   10    8    6     9
[10,]   10    4    9    8    3    1    2    5    6     7

If those 10 observations were collected as a time series and we wanted 10 restricted permutations you would use

> set.seed(2)
> shuffleSet(10, 10, control = permControl(within = Within(type = "series")))
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    3    4    5    6    7    8    9   10    1     2
[2,]    9   10    1    2    3    4    5    6    7     8
[3,]    7    8    9   10    1    2    3    4    5     6
[4,]    3    4    5    6    7    8    9   10    1     2
[5,]    1    2    3    4    5    6    7    8    9    10
[6,]    1    2    3    4    5    6    7    8    9    10
[7,]    3    4    5    6    7    8    9   10    1     2
[8,]   10    1    2    3    4    5    6    7    8     9
[9,]    6    7    8    9   10    1    2    3    4     5
[10,]    7    8    9   10    1    2    3    4    5     6

From the above set of permutations, the cyclic shifts employed in the "series" permutation type is clear. One problem with the set we just produced is that the same permutation was returned more than once. In fact, there were only six unique permutations in the set requested. This is due to there only being 10 possible permutations of the numbers 1, 2, …, 10 if we allow cyclic shifts in a single direction

> numPerms(10, control = permControl(within = Within(type = "series")))
[1] 10

shuffle() and shuffleSet() know nothing of these limits, but there are functions in the permute package that can tell you the number of possible permutations (numPerms()) and generate the entire set of permutations for a stated design (allPerms()). I’ll take a look at allPerms() in a future posting.

I return now to the Golden Jackal mandible length example I used in an earlier post but update the example to make use of shuffleSet() instead of shuffle(). I will just show the code and output for the permutation test, refer to the previous post for details:

> data(jackal) ## load the data
> ## function to compute the difference of means
> meanDif <- function(x, grp) {
+     mean(x[grp == "Male"]) - mean(x[grp == "Female"])
+ }
> N <- nrow(jackal)
> set.seed(42)
> ## generate the set of 4999 random permutations
> pSet <- shuffleSet(N, 4999)
> ## iterate over the set
> Djackal <- apply(pSet, 1, function(i, data) with(data, meanDif(Length, Sex[i])), data = jackal)
> Djackal <- c(Djackal, with(jackal, meanDif(Length, Sex)))
> (Dbig <- sum(Djackal >= Djackal[5000]))
[1] 12
> Dbig/length(Djackal)
[1] 0.0024

The last two lines of R code compute the number of observations in the Null distribution with differences in mean mandible length as great or greater than the observed difference, and the resulting permutation p-value. These are the same as those computed in the previous post.

Generating entire sets of permutations is useful for several reasons. One recent example that we came across is with the new parallel processing capabilities in the forthcoming version of R. We are able to generate a set of permutations and then distribute the process of the permutation test over a number of CPUs or worker threads, each dealing with a subset of the permutations we generated. This can greatly reduce the compute time needed for the permutation test, especially where the objective function is computationally complex, but allows us to not worry about controlling the random number generator in each separate process — this is all done within the main function and only the relevant subset of permutations is passed to each worker process. An additional reason for generating a set of permutation to work with rather than individual permutations is that it is easy to switch between using a set of randomly generated permutations or the set of all possible permutations where that set is not overly large. allPerms() returns the set of permutations in the same way that shuffleSet() does, so we can simplify our code if we write the test to iterate over a set of permutations.

The full script for the Golden Jackal permutation test is shown below:

data(jackal) ## load the data
## function to compute the difference of means
meanDif <- function(x, grp) {
mean(x[grp == "Male"]) - mean(x[grp == "Female"])
}
N <- nrow(jackal)
set.seed(42)
## generate the set of 4999 random permutations
pSet <- shuffleSet(N, 4999)
## iterate over the set
Djackal <- apply(pSet, 1, function(i, data) with(data, meanDif(Length, Sex[i])), data = jackal)
Djackal <- c(Djackal, with(jackal, meanDif(Length, Sex)))
(Dbig <- sum(Djackal >= Djackal[5000]))
Dbig/length(Djackal)

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# IDM2010

Jul 26 – 30, 2010
Montpellier 2 University
Europe/Paris timezone

## Lowering the low-energy threshold of xenon-based detectors

Jul 26, 2010, 2:20 PM
20m
Amphithéatre Dumontet (Montpellier 2 University)

### Amphithéatre Dumontet

#### Montpellier 2 University

Place Eugene Bataillon, 34095 Montpellier Cedex 5 FRANCE

### Speaker

Dr Peter Sorensen (LLNL)

### Description

The XENON10 Experiment has already reported exclusion limits for spin-independent, spin-dependent and inelastic couplings of nuclei to particle dark matter. Recently, there has been considerable (perhaps, renewed) interest in light-mass $\mathcal{O}(10)$~GeV dark matter candidates. In this mass range, the sensitivity of XENON10 drops sharply, due to the low-energy threshold. The low-energy threshold is limited by the collection of primary scintillation photons following a particle interaction, and begins to drop between $5-8$~keV nuclear recoil energy. We discuss recent modeling of that threshold, and show how this affects the resulting sensitivity of the experiment. The methods are applicable to other xenon-based detectors such as XENON100 and LUX. Finally, we explore the possibility of using only the proportional scintillation signal (the ionization channel). In so doing, traditional S2/S1 discrimination must be abandoned, but the resulting energy threshold of $\sim1$~keV nuclear recoil energy leads to interesting constraints on viable dark matter models. This work will also be of interest to the possibile detection of coherent neutrino scattering.

### Primary author

Dr Peter Sorensen (LLNL)

### Co-author

Collaboration XENON10 ((multiple))

 Slides