text:
# Latent Discriminant deterministic Uncertainty

## Abstract

Predictive uncertainty estimation is essential for deploying Deep Neural Networks in real-world autonomous systems. However, most successful approaches are computationally intensive. In this work, we attempt to address these challenges in the context of autonomous driving perception tasks. Recently proposed Deterministic Uncertainty Methods (DUM) can only partially meet such requirements as their scalability to complex computer vision tasks is not obvious. In this work we advance a scalable and effective DUM for high-resolution semantic segmentation, that relaxes the Lipschitz constraint typically hindering practicality of such architectures. We learn a discriminant latent space by leveraging a distinction maximization layer over an arbitrarily-sized set of trainable prototypes. Our approach achieves competitive results over Deep Ensembles, the state-of-the-art for uncertainty prediction, on image classification, segmentation and monocular depth estimation tasks.

## BibTeX

@inproceedings{franchi2022latent,
title={Latent Discriminant deterministic Uncertainty},
author={Franchi, Gianni and Yu, Xuanlong and Bursuc, Andrei and Aldea, Emanuel and Dubuisson, Severine and Filliat, David},
booktitle={ECCV},
year={2022}
}

format: plain


text:
# Show that the projective closure of V(x) and V($x-y^4-z^4$) in $P^3$ is not isomorphic

This is exercise 3.4.4 from "An Invitation to Algebraic Geometry": Show that the affine varieties V(x) and V($x-y^4-z^4$) is isomorphic in $A^3$ but their projective closures are not in $P^3$.
What I did:
They're isomorphic in $A^3$ since they're both isomorphic to $A^2$, and an isomorphism between them is $[0;y;z] \mapsto [y^4+z^4;y;z]$. Then I tried to show that the projective varieties V(x) and V($w^3x-y^4-z^4$) is not isomorphic in $P^3$. The first one is now a $P^2$, the second one is also topologically a $P^2$ so I'm trying to find somewhere the second one is not smooth but failed. Could anybody tell me a point where the second one is not smooth?

• $(1:0:0:0)$ doesn't seem to be in the smooth locus (where the first coordinate is $x$) – zcn Mar 13 '14 at 1:23
• You are absolutely right, @user115654. – Georges Elencwajg Mar 13 '14 at 8:32
• @user115654: the affine variety in the x=1 hyperplane is $w^3=y^4+z^4$. Its real part is smooth at (0,0,0) since all partial derivatives vanish at the point, it has w=0 as its tangent plane. Could you explain more details? Thank you very much. – Xipan Xiao Mar 14 '14 at 14:09
• @XipanXiao: What is your working definition of a smooth point: one where the partial derivatives all vanish? Also, it's not necessary to pass to an affine patch: the Jacobian criterion still applies to projective varieties (see e.g. Hartshorne exercise I.5.8) – zcn Mar 14 '14 at 17:24
• @user115654: being smooth means there is a well-defined tangent plane. If the partial derivatives all vanish we get a tangent plane $w=0$. I'll check the Jacobian criterion. Thanks. – Xipan Xiao Mar 14 '14 at 17:59

For a projective hypersurface $V(f) \subset \mathbb P^n$ defined by a homogenous polynomial $$f(x_0,...,x_n)$$ there is a simple criterion to characterize a singular point of $V(f)$: The point $x = (x_0:\ ...\ :x_n) \in \mathbb P^n$ is a singular point $x \in V(f)$ iff all partial derivatives vanish, i.e.
$$\frac {\partial f}{\partial x_i}(x) = 0, i = 0,...,n.$$
Note. Euler's Lemma (see Hartshorne Ex. I,5.8) implies that $x \in V(f)$.


text:
# Use numbered references within Natbib document

I am working on a document in LyX that uses Natbib for reference formatting. I like having author and year for the in-text citations. However, for the specific case of citing references in a table, I would like to use numbers instead then have a column of references showing which references match what numbers.

How can I do this using LyX?

Below is an image of what I want (but of course I don't want to be manually inserting numbers and changing them with every edit.

• Personally, i would do stuff like that using table notes and add the references below the table. Nov 18, 2015 at 11:15
• @Johannes_B, thanks for the suggestion, but this table will eventually be hundreds of rows and putting all the references at the bottom is untenable. Dec 5, 2015 at 15:07
• Imho manually numbering would be quite ok as you can (and should) reset the numbering in every row. It would be less work than having to insert \cite in every cell. Beside this I don't think that you can do it with natbib directly. babel. Dec 7, 2015 at 9:29

Just to make the very nice answer by Waldheri more precise, you can do:

\documentclass[a4paper,12pt]{article}
\usepackage[round]{natbib}
\bibpunct{(}{)}{,}{a}{}{,}
\usepackage{filecontents}
\begin{filecontents}{mybibb.bib}
@BOOK{book1,
AUTHOR =       {Alan, F.},
TITLE =        {The book},
PUBLISHER =    {The publishing house},
YEAR =         {2015},
}
@BOOK{book2,
AUTHOR =       {Zallan, D.},
TITLE =        {The other book},
PUBLISHER =    {The other publishing house},
YEAR =         {2005},
}
\end{filecontents}
\newcommand{\superci}[1]{\textsuperscript{\citenum{#1}}}
\newcommand{\exsuperci}[1]{\superci{#1}\,\citet{#1}}
\begin{document}
\begin{tabular}{ll}
\hline
Observed                       & Reference\\\hline
Italy\superci{book1}           &     \exsuperci{book1}     \\
France\superci{book1,book2}    &     \exsuperci{book1}, \exsuperci{book2} \\
\hline
\end{tabular}
\bibliographystyle{plainnat}
\bibliography{mybibb}
\end{document}

Use natbib's \citenum command, as indicated in section 2.4 of Natbib's package manual (available here)


text:
Kinetic Isotopic Effect in EAS

It is observed that rate of reaction of two isotopologues of benzene, $\ce{C6D6}$ and $\ce{C6H6}$, is the same for electrophilic aromatic reactions, as the deprotonation is not the rate limiting step. Instead the carbocation is usually limiting.

Do iodination and sulphonation somehow do show different rates with these isotopologues? Is $\ce{C6H6}$ the faster of the two, due to stronger C-D bond (smaller size of D)? If this is correct what is the reason?

Does the protonation becomes the rate limiting step? if yes, then why in only with iodination and sulphonation?

Update : Found potential energy graphs for suphonation and nitration and it does seem like protonation either becomes the rate determining step or just smaller than carbocation hill, but why in sulphonation, the deprotonation curve was high is still a mystery.

• The slow step is electrophilic attack. Deprotonation after electrophilic attack is likely not the slow stop in any of those cases. Feb 5, 2016 at 20:09
• -----Update---- Feb 6, 2016 at 15:45

1 Answer

In general, deprotonation of a $$\ce{C-D}$$ bond would require more energy than that for $$\ce{C-H}$$ bond because the zero point vibrational energy of the bond is lowered. By referring to our harmonic oscillator zero point energy equation,

$$E_0 = \frac{1}{2}h \nu$$

where frequency is,

$$\nu = \frac{1}{2 \pi} \sqrt{\frac{k}{\mu}}$$

and the reduced mass ($$\mu$$) being,

$$\mu = \frac{m_1m_2}{m_1 + m_2}$$

we see that as the mass for either atom increases, the zero point energy decreases, therefore, the bond is relatively more stable than its lighter isotopologue. However, swapping out isotopes in a molecule does not change the potential energy surface for the reaction [1]

1.) Sulphonation

Changes in the rate determining step may arise from the type of sulfuric acid used. Since fuming sulfuric acid has a higher concentration of $$\ce{SO3}$$ (the electrophile) then more dilute forms of $$\ce{H2SO4}$$, the rate limiting step is no longer forming the bond between benzene and $$\ce{SO3}$$, rather, it is re-forming the aromatic ring through deprotonation. Ergo, if you did a KIE study with different concentrations of sulfuric acid, you may see that only fuming $$\ce{H2SO4}$$ shows significant values of $$\frac{K_\ce{H}}{K_\ce{D}}$$.

2.) Iodination

This article [2] studied the iodination of benzene with the source of iodine being generated through the "oxidation of 0.5 g of $$\ce{I2}$$ in acetonitrile-tetraethylammonium perchlorate to 2.4 faradays/mol."

The article reported that the secondary kinetic isotope effect for $$k_1$$ and $$k_{-1}$$ is negligible, however, $$\frac{K_\ce{H}}{K_\ce{D}} = 2.25$$ for $$k_2$$.

Here is a thesis I found that discusses the iodination of aromatic rings [3]

The thesis, in short, suggests that whether the deprotonation is rate limiting has to do with the concentration of the reactants, along with the transition state of the molecule. The transition state is affected by the strength of the base, since a higher $$\mathrm{p}K_\mathrm{b}$$ may give a transition state where the hydrogen is partially bound to both the ring and the base, making this step in the reaction faster (therefore, not rate limiting). However, it did only investigate substituted aromatic rings, where substituents can play a significant role in the transition state, making the reaction with benzene a little less comparable.

3.) Nitration

This article reports no KIE observed in nitration of benzene [4].


text:
# Quantifying a series using dose and half-life

Printable View

• Jul 14th 2009, 07:15 PM
stardotstar
Quantifying a series using dose and half-life
Please move if this is the wrong forum - and this is not homework but a SciFi concept I am needing to explain for a story.

There is an artificial environment (say some kind of capsule) which requires the daily dosing of a chemical compound with a half life of a day, such that its presence in the environment receeds like this if a dose of say 100units is introduced on day one:

1 Sat 4 100 2 50.000000
2 Sun 5 25.000000
3 Mon 6 12.500000
4 Tue 7 6.250000
5 Wed 8 3.125000
6 Thu 9 1.562500
7 Fri 10 0.781250
8 Sat 11 0.390625
9 Sun 12 0.195313
10 Mon 13 0.097656
11 Tue 14 0.048828
12 Wed 15 0.024414
13 Thu 16 0.012207
14 Fri 17 0.006104
15 Sat 18 0.003052
16 Sun 19 0.001526 proximal point of trace presence
17 Mon 20 0.000763
18 Tue 21 0.000381
19 Wed 22 0.000191
20 Thu 23 0.000095
21 Fri 24 0.000048
22 Sat 25 0.000024
23 Sun 26 0.000012
24 Mon 27 0.000006
25 Tue 28 0.000003
26 Wed 29 0.000001
27 Thu 30 0.000001
28 Fri 31 0.000000
29 Sat 1 0.000000
30 Sun 2 0.000000
31 Mon 3 0.000000

A you can see we end up with a point at which only trace elements exist for practical purposes.

Now, if that dosage is introduced daily at a rate of 100units per day what actually happens to the accumulation within the environment?

The 100 units introduced on day one represents 50 remaining on day two when another 100 is introduced, which means that the environment contains 150 on day two.
On day three, when another 100 is introduced the 150 from day 2 is reduced to 75 and there is therefore 175, Day four's 100 consequently joins 175/2 leaving 187.5. Day 5 is 193.75, Day 6 196.875 and we begin to see a series ultimately leading to an approximately stable amount of this element (given a half life of a day) in the artifical system...

What I seem unable to do in a spreadsheet or otherwise with any certainty is:

Properly express the series,
understand the nature of this series.

Can anyone assist - will it ultimately infinitely approach 200???

This is all I can come up with in my spreadsheet>

100
100 50 150
100 75 175
100 87.5 187.5
100 93.75 193.75
100 96.875 196.875
100 98.4375 198.4375
100 99.21875 199.21875
100 99.609375 199.609375
100 99.8046875 199.8046875
100 99.90234375 199.9023438
100 99.95117188 199.9511719
100 99.97558594 199.9755859
100 99.98779297 199.987793
100 99.99389648 199.9938965
100 99.99694824 199.9969482
100 99.99847412 199.9984741
100 99.99923706 199.9992371
100 99.99961853 199.9996185
100 99.99980927 199.9998093
100 99.99990463 199.9999046
100 99.99995232 199.9999523
100 99.99997616 199.9999762
100 99.99998808 199.9999881
100 99.99999404 199.999994
100 99.99999702 199.999997
100 99.99999851 199.9999985
100 99.99999925 199.9999993
100 99.99999963 199.9999996
100 99.99999981 199.9999998
100 99.99999991 199.9999999

Is this right? That an element with a half life of one day when dosed at rate of 100 units per day will ultimately stabilise at twice the daily dose?

Will
• Jul 14th 2009, 10:09 PM
earboth
You are dealing with a geometric serie. (Geometric Series -- from Wolfram MathWorld)

The level of the dose at day n is:

$s_n=100+50+25+12.5+ ... + \dfrac{100}{2^{n-1}}$

The ration between to summands is $r=\dfrac12$.

Since r < 1 you'll get:

$\lim_{n \to +\infty} = \dfrac{a_0}{1-r}$

In your case:

$\lim_{n \to +\infty} = \dfrac{100}{1-\dfrac12} = 200$
• Jul 15th 2009, 11:36 AM
CaptainBlack
Quote:

Originally Posted by stardotstar
Please move if this is the wrong forum - and this is not homework but a SciFi concept I am needing to explain for a story.

There is an artificial environment (say some kind of capsule) which requires the daily dosing of a chemical compound with a half life of a day, such that its presence in the environment receeds like this if a dose of say 100units is introduced on day one:

1 Sat 4 100 2 50.000000
2 Sun 5 25.000000
3 Mon 6 12.500000
4 Tue 7 6.250000
5 Wed 8 3.125000
6 Thu 9 1.562500
7 Fri 10 0.781250
8 Sat 11 0.390625
9 Sun 12 0.195313
10 Mon 13 0.097656
11 Tue 14 0.048828
12 Wed 15 0.024414
13 Thu 16 0.012207
14 Fri 17 0.006104
15 Sat 18 0.003052
16 Sun 19 0.001526 proximal point of trace presence
17 Mon 20 0.000763
18 Tue 21 0.000381
19 Wed 22 0.000191
20 Thu 23 0.000095
21 Fri 24 0.000048
22 Sat 25 0.000024
23 Sun 26 0.000012
24 Mon 27 0.000006
25 Tue 28 0.000003
26 Wed 29 0.000001
27 Thu 30 0.000001
28 Fri 31 0.000000
29 Sat 1 0.000000
30 Sun 2 0.000000
31 Mon 3 0.000000

A you can see we end up with a point at which only trace elements exist for practical purposes.

Now, if that dosage is introduced daily at a rate of 100units per day what actually happens to the accumulation within the environment?

The 100 units introduced on day one represents 50 remaining on day two when another 100 is introduced, which means that the environment contains 150 on day two.
On day three, when another 100 is introduced the 150 from day 2 is reduced to 75 and there is therefore 175, Day four's 100 consequently joins 175/2 leaving 187.5. Day 5 is 193.75, Day 6 196.875 and we begin to see a series ultimately leading to an approximately stable amount of this element (given a half life of a day) in the artifical system...

What I seem unable to do in a spreadsheet or otherwise with any certainty is:

Properly express the series,
understand the nature of this series.

Can anyone assist - will it ultimately infinitely approach 200???

This is all I can come up with in my spreadsheet>

100
100 50 150
100 75 175
100 87.5 187.5
100 93.75 193.75
100 96.875 196.875
100 98.4375 198.4375
100 99.21875 199.21875
100 99.609375 199.609375
100 99.8046875 199.8046875
100 99.90234375 199.9023438
100 99.95117188 199.9511719
100 99.97558594 199.9755859
100 99.98779297 199.987793
100 99.99389648 199.9938965
100 99.99694824 199.9969482
100 99.99847412 199.9984741
100 99.99923706 199.9992371
100 99.99961853 199.9996185
100 99.99980927 199.9998093
100 99.99990463 199.9999046
100 99.99995232 199.9999523
100 99.99997616 199.9999762
100 99.99998808 199.9999881
100 99.99999404 199.999994
100 99.99999702 199.999997
100 99.99999851 199.9999985
100 99.99999925 199.9999993
100 99.99999963 199.9999996
100 99.99999981 199.9999998
100 99.99999991 199.9999999

Is this right? That an element with a half life of one day when dosed at rate of 100 units per day will ultimately stabilise at twice the daily dose?

Will

In the long term (after a large enough number of days so that we have a sort of equilibrium) consider the environmental load just after dosing, call this x, next day just before the next dosing this will have fallen to x/2, but after dosing will return to x, so:

x=x/2+100

and a bit of algebra shows that x=200.

CB
• Jul 15th 2009, 03:20 PM
stardotstar
Quote:

Originally Posted by CaptainBlack
In the long term (after a large enough number of days so that we have a sort of equilibrium) consider the environmental load just after dosing, call this x, next day just before the next dosing this will have fallen to x/2, but after dosing will return to x, so:

x=x/2+100

and a bit of algebra shows that x=200.

CB

Thank you both - the elaboration of the series and link from earboth is most informative and the simplicity of your response CB is quite brilliant (at least to my fumbling mathematical aparatus) thank you very much guys.
Will


text:
### pulsatio's blog

By pulsatio, history, 6 weeks ago,

Peru has participated in the IOI for the first time and has won a bronze medal. (orz NRolly)

I am the coach of the whole team and we will probably qualify again next year. Our goal now is to get a silver medal in the future. That's why I would like to know how is the training in other countries. How many hours do you dedicate to training? How many contests do you simulate per week? Do they enter codeforces, codechef, atcoder?

Clearly getting a silver medal is not easy but we want to try.

We will be grateful for your support. Best regards

• +142

 » 6 weeks ago, # | ← Rev. 2 →   +110 In Poland, we rely primarily on high schools and contestants themselves. Some prestige schools run regular classes on algorithms and data structures. I used to be a teacher in one of such schools and got 2-4 hours of classes weekly. During the classes, we were exploring basic topics (starting from binary search, through segment trees to centroid decomposition). I also gave them a lot of homework in form of problems from old competitions, and once or twice a month a full 5-hour contest. I encouraged people to participate in Codeforces and AtCoder, but as the IOI problems are significantly different from the problems from these platforms that was not a hard requirement at all. Everything that I said is just required to get to the final stage at the Polish Olympiad and then be selected to the IOI. After that, the ball was in the contestant's court. I still tried to help them by providing interesting problems from which they can learn something new, but it mostly depended on them. The Polish Olympiad helps a bit -- we have a summer training camp, but that's mostly it (unfortunately).The one piece of advice I can give to you is you have to make sure that the students are motivated. It doesn't matter how many problems you have solved. You have to be passionate about problem-solving and have some fun doing it. It helps a lot when you form a group of people that can learn together and compete against each other.Hope that helps!
•  » » 6 weeks ago, # ^ |   +8 Thank you very much for answering!In those classes, only you taught? That is, the students only had theory class 2-4 hours a week?I'm not sure if it's correct to ask the following but... How was the training after qualifying to the IOI?Finally, how can I improve as a coach? Honestly, several times I feel that I am not qualified for this job.
•  » » » 5 weeks ago, # ^ |   0 In those classes, only you taught? That is, the students only had theory class 2-4 hours a week? Yes. For some time I shared these classes with one more person (I had 2 hours and he had another 2). How was the training after qualifying to the IOI? Mostly I was suggesting to them problems from old national/international olympiads. Very rarely was I also needed to find/come up with a solution to some problems. Finally, how can I improve as a coach? Honestly, several times I feel that I am not qualified for this job. Don't worry, everyone experiences impostor syndrome. But I have to say that I also learned a lot about how to teach by preparing for the classes and even during them, just by practice. It also helps a lot to also watch other teachers, even by checking out some YouTube videos. Estoy seguro de que estas en el top 3 de los mejores maestros posibles en tu pais!
•  » » » » 5 weeks ago, # ^ |   +6 Thanks for all the tips. I am really grateful to you and the cf community. I appreciate you very much
•  » » 6 weeks ago, # ^ |   +37 Soooo hard :/Just go to the gym (the real one, not CF gym) and do the power trainings. Year after the teammates will be so strong, that will easily steal 4 golds from Chinese members XDDDD.
•  » » » 6 weeks ago, # ^ |   -6 Xdd, good idea)
 » 6 weeks ago, # |   +16 Do CNOI.
•  » » 6 weeks ago, # ^ |   +9 Do they have English translation?
•  » » » 6 weeks ago, # ^ |   -27 china national olympiad informatics
•  » » » 6 weeks ago, # ^ | ← Rev. 2 →   +34 Some of the translations can be found in https://hydro.ac/p. Just search for "CSP-J", "CSP-S" and "NOI". (sorted in difficulty)If you need only the problems in CCF-NOI series, use https://hydro.ac/d/ccf/p. The problems with English names are translated to English.Sadly, only a small amount of the problems are translated to English. The organisers of HydroOJ are still working on this. You can use translation software for temporary use.
•  » » » » 6 weeks ago, # ^ |   +5 47 / 5.000 Resultados de traducción Are the editorials published somewhere?
•  » » » » » 6 weeks ago, # ^ |   +6 Editorials are published on other sites, and are mostly in Chinese. You can see others' codes in Submissions or google for editorials in Chinese.
 » 6 weeks ago, # |   0 I recommend that the div1 virtual contests team and then do upsolving (it is allowed to see the tutorial) of the problems at least until E every day. A simulated 5 hours per week would be fine too.This could help to have an order to perform the contest div1. https://contestmania.web.app/codeforces?category=Div1
 » 6 weeks ago, # |   +38 Hi, I participated in this years IOI. I didn't win any medal, but right after every contest I knew a lot more solutions to subtasks which would eventually have led to a silver medal. The thing I lacked the most was time management and 5h contest experience. I didn't train more than 1 to 2 hours a day.I'd suggest for future trainings to let the students get used to these kind of contests and also let them feel when they should stop thinking of a problem and go to the next one.I hope this helps :)
•  » » » » 6 weeks ago, # ^ | ← Rev. 2 →   +36 I still wonder how you got silver despite going to the toilet $16$ times during the contest.


text:
LeCroy’s CustomDSO feature, included in the XDEV Customization option, enables the creation of custom user interfaces, using programming languages capable of creating ActiveX Controls.

At its announcement, the programming language that was the best match for creating these plug-ins was Microsoft’s Visual Basic 6.0. Since then, Microsoft has moved its focus onto its “.NET” technology and has made it more difficult to create “Legacy” ActiveX controls, using the latest version of Visual Basic.

However, armed with the information contained within this Application Brief, you can successfully create plug-ins using Visual Basic .NET 2003.

Note: Since part of the procedure involves typing in several lines of VB code it will be much easier to work from the electronic version of this document, where copy and paste commands can be used to eliminate typing errors.

Figure 1:

A simple CustomDSO Plug-in

Figure 2:

A plug-in created with VB .NET

1. Open Visual Studio .NET 2003 and select the File->New->Project menu item.
2. Select Visual Basic Projects on the left, and Windows Control Library on the right.
3. Enter a project name and directory into the dialog box that appears and click OK. Give the proper name to the project you want to use on the scope interface when you install it. The syntax which will be used on the CustomDSO menu of the scope will be:
<Project Name>.<VB.NET class>
Where <VB.NET class> is the name of the Code/Object of your project; for example, in the Solution Explorer below, the Project Name is “CrossTrigg” while the VB.NET class is “toolbox.vb”. Therefore under CustomDSO menu of the scope, the plug-in name to install will be:
“CrossTrigg.toolbox”
4. For demonstration purposes, drag a button from the toolbox onto the dialog:
5. Open the project properties and check the Register for COM Interop box (be sure to do this for both Debug and Release builds):
6. Right-click on the dialog, and select View Code
7. Merge the code below into the source file. Note that the line that starts Public Class UserControl1 (in the example below is Public Class Toolbox) and the line following it should already be in the empty project.
8. The section in red color is the GUIDs section. The GUIDs used below (ClassId, InterfaceId and EventsId) should be unique and, therefore, should be regenerated using the MS “GuidGen” tool. For demonstration purposes the ones below will work, but only for the first plug-in built; second and subsequent plug-ins built using this method require unique IDs. To generate another three IDs for ClassId, InterfaceId and EventId you have to go to Tools --> Create GUID.Then, in the pop-up window, select the GUID format number 4 (Registry Format) and click on “New GUID”.

Now you can copy it into the clipboard with the relative button and paste it into the local field. You have to repeat this procedure three times, one for each “Id”. Note finally that when you paste the key, you have to manually modify it to remove any extra parentheses.

Option Strict Off Imports System.Runtime.InteropServices Imports System.Text Imports System.IO Imports System.Reflection Imports Microsoft.Win32 Imports System Imports System.Threading Imports System.Math Imports Microsoft.Office.Core Imports Microsoft.Vbe.Interop Imports System.Windows.Forms Imports Office = Microsoft.Office.Core Imports Excel = Microsoft.Office.Interop.Excel  Toolbox.InterfaceId, _  Toolbox.EventsId)> _ Public Class Toolbox Inherits System.Windows.Forms.UserControl #Region "COM GUIDs"  ' These GUIDs provide the COM identity for this class  ' and its COM interfaces. If you change them, existing  ' clients will no longer be able to access the class.  Public Const ClassId As String = "EBDB73C5-AAD9-4f7d-9979-1C9EFA684BEE"  Public Const InterfaceId As String = "8F49323F-537B-4bc8-B48D-027FDFF71322"  Public Const EventsId As String = "94578994-2F8C-438f-AE92-BB7CBB734DA0" #End Region  ' This function is called when registered (no need to change it)  _  Private Shared Sub ComRegister(ByVal t As Type)  Dim keyName As String = "CLSID¥" & t.GUID.ToString("B")  Dim key As RegistryKey = Registry.ClassesRoot.OpenSubKey(keyName, True)  key.CreateSubKey("Control").Close()  Dim subkey As RegistryKey = key.CreateSubKey("MiscStatus")  subkey.SetValue("", "131457")  subkey = key.CreateSubKey("TypeLib")  Dim libid As Guid = Marshal.GetTypeLibGuidForAssembly(t.Assembly)  subkey.SetValue("", libid.ToString("B"))  subkey = key.CreateSubKey("Version")  Dim ver As Version = t.Assembly.GetName().Version  Dim version As String = String.Format("{0}.{1}", ver.Major, ver.Minor)  If version = "0.0" Then version = "1.0"  subkey.SetValue("", version)  End Sub
' This is called when unregistering (no need to change it)  _  Private Shared Sub ComUnregister(ByVal t As Type)  ' Delete entire CLSID¥{clsid} subtree  Dim keyName As String = "CLSID¥" + t.GUID.ToString("B")  Registry.ClassesRoot.DeleteSubKeyTree(keyName)  End Sub
9. When you start placing forms within the class (like buttons, checkboxes, etc.), a region just below the previous code will be generated. It starts with “#Region " Windows Form Designer generated code "”.
The region is split into several sections but the first one is a very important subroutine, since all the code you want to execute at startup must be placed within it, just after InitializeComponent() call (as commented in the box below).
#Region " Windows Form Designer generated code "  Public Sub New()  MyBase.New()  'This call is required by the Windows Form Designer.  InitializeComponent()  'Add any initialization after the InitializeComponent() call  End Sub
10. Hooking the UI to the X-Stream automation interface using VB is simple, as the following example shows. This will program the DSO’s horizontal scale (T/Div) when Button1 is clicked.
‘ Note that the following Sub is Private so if it will be the only one in the Class ‘ you must declare it Public otherwise at least another one must be Public Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click Dim o As Object  o = CreateObject("LeCroy.XStreamDSO.1")  o.Acquisition.Horizontal.HorScale = 0.0000002 End Sub
11. To polish the component, and to integrate seamlessly into the X-Stream User Interface, change the following properties of the dialog and controls in it.

 Dialog Size: 792,168 pixels Dialog Background: 66, 55, 114 (fairly dark blue) Button Background: 112, 104, 160 (lighter blue) Button Text: 255, 255, 255 (white)

12. After you finish your plug-in and you want to try it, you have to install it on the scope. In this case you need to add a solution to your project with the Setup Wizard. Follow the steps below:
1. Click on File --> New --> Project and configure the panel as below (New Project panel).
2. In step 2 of 5 select the options as below (Setup Wizard 2 of 5 panels).
3. In the step 3 of 5, configure the panel as below.
4. Finish the setup wizard procedure.
5. Under menu Build --> Configuration Manager, be sure that your panel looks like the one below.
6. Under menu Build, select Build solution, then you will find in the project folder, the setup directory with three files (Setup.exe, Setup.msi, and Setup.ini); those three files must be copied into a folder on the scope’s hard disk and installed using Setup.Exe.
7. Activate CustomDSO plug-in in the scope and enter the proper name for the plug-in, as explained at the beginning of this document.


text:
WIKISKY.ORG
 Home Getting Started To Survive in the Universe News@Sky Astro Photo The Collection Forum Blog New! FAQ Press Login

# NGC 1199

Contents

### Images

DSS Images   Other Images

### Related articles

 Star Formation Histories of Nearby Elliptical Galaxies. I. Volume-Limited SampleThis work presents high signal-to-noise ratio spectroscopic observationsof a representative sample of nearby elliptical galaxies. Theseobservations provide a strong test of models for the formation ofelliptical galaxies and their star formation histories. Combining thesedata with the González data set, a volume-limited sample of 45galaxies has been defined. Results are in agreement with previousstudies: the existence of the metallicity hyperplane and the Z-plane ofTrager and coworkers is confirmed, and the distribution is clearly dueto physical variations in stellar population parameters and notmeasurement uncertainty. Trends between stellar population parametersand galaxy structural parameters suggest that angular momentum maydetermine the chemical abundance of a galaxy at a given mass. Ages and metallicities of Hickson compact group galaxies Hickson compact groups (HCGs) constitute an interesting extreme in therange of environments in which galaxies are located, as the spacedensity of galaxies in these small groups are otherwise only found inthe centres of much larger clusters. The work presented here uses Lickindices to make a comparison of ages and chemical compositions ofgalaxies in HCGs with those in other environments (clusters, loosegroups and the field). The metallicity and relative abundance ofα-elements' show strong correlations with galaxy age and centralvelocity dispersion, with similar trends found in all environments.However, we show that the previously reported correlation betweenα-element abundance ratios and velocity dispersion disappears whena full account is taken of the abundance ratio pattern in thecalibration stars. This correlation is thus found to be an artefact ofincomplete calibration to the Lick system.Variations are seen in the ranges and average values of age, metallicityand α-element abundance ratios for galaxies in differentenvironments. Age distributions support the hierarchical formationprediction that field galaxies are on average younger than their clustercounterparts. However, the ages of HCG galaxies are shown to be moresimilar to those of cluster galaxies than those in the field, contraryto the expectations of current hierarchical models. A trend for lowervelocity dispersion galaxies to be younger was also seen. This is againinconsistent with hierarchical collapse models, but is qualitativelyconsistent with the latest N-body smoothed particle hydrodynamics modelsbased on monolithic collapse in which star formation continues for manyGyr in low-mass haloes. BUDDA: A New Two-dimensional Bulge/Disk Decomposition Code for Detailed Structural Analysis of GalaxiesWe present BUDDA (Bulge/Disk Decomposition Analysis), a new code devotedto perform a two-dimensional bulge/disk decomposition directly from theimages of galaxies. The bulge component is fitted with a generalizedSérsic profile, whereas disks have an exponential profile. Noother components are included. Bars and other substructures, likelenses, rings, inner bars, and inner disks, are studied with theresidual images obtained through the subtraction of bulges and disksfrom the original images. This means that a detailed structural analysisof galaxies may be performed with a small number of parameters, andsubstructures may be directly studied with no a priori assumptions. Ashas been already shown by several studies, two-dimensional fitting ismuch more reliable than one-dimensional profile fitting. Moreover, ourcode has been thoroughly tested with artificial data, and we demonstrateit to be an accurate tool for determining structural parameters ofgalaxies. We also show that our code is useful in various kinds ofstudies, including galaxies of, e.g., different morphological types, andinclinations, which also may be observed at different spatialresolutions. Thus, the code has a broader range of potentialapplications than most of the previous codes, which are developed totackle specific problems. To illustrate its usefulness, we present theresults obtained with a sample of 51 mostly early-type galaxies (butcovering the whole Hubble sequence). These results show some of theapplications in which the code may be used: the determination ofparameters for fundamental plane and structural studies, quantitativemorphological classification of galaxies, and the identification andstudy of hidden substructures. We have determined the structuralparameters of the galaxies in our sample and found many examples ofhidden inner disks in ellipticals, secondary bars, nuclear rings anddust lanes in lenticulars and spirals, and also wrong morphologicalclassification cases. We now make BUDDA generally available to theastronomical community.Based on observations made at the Pico dos Dias Observatory(PDO/LNA-CNPq), Brazil. The Relation between Galaxy Activity and the Dynamics of Compact Groups of GalaxiesUsing a sample of 91 galaxies distributed over 27 compact groups (CGs)of galaxies, we define an index that allows us to quantify their levelof activity due to an active galactic nucleus (AGN) or star formation.By combining the mean activity index with the mean morphological type ofthe galaxies in a group, we are able to quantify the evolutionary stateof the groups. We find that they span an evolutionary sequence thatcorrelates with the spatial configuration of the galaxies in the CG. Wedistinguish three main configuration types: A, B, and C. Type A CGs showpredominantly low velocity dispersions and are rich in late-type spiralsthat show active star formation or harbor an AGN. Type B groups haveintermediate velocity dispersions and contain a large fraction ofinteracting or merging galaxies. Type C comprises CGs with high velocitydispersions, which are dominated by elliptical galaxies that show noactivity. We suggest that evolution proceeds A==>B==>C. Mappingthe groups with different evolution levels in a diagram of radius versusvelocity dispersion does not reveal the pattern expected based on theconventional fast merger model for CGs, which predicts a direct relationbetween these two parameters. Instead, we observe a trend contrary toexpectation: the evolutionary state of a group increases with velocitydispersion. This trend seems to be related to the masses of thestructures in which CGs are embedded. In general, the evolutionary stateof a group increases with the mass of the structure. This suggestseither that galaxies evolve more rapidly in massive structures or thatthe formation of CGs embedded in massive structures predated theformation of CGs associated with lower mass systems. Our observationsare consistent with the structure formation predicted by the CDM model(or ΛCDM), only if the formation of galaxies is a biased process. Peculiarities and populations in elliptical galaxies. I. An old question revisitedMorphological peculiarities, as defined from isophote asymmetries andnumber of detected shells, jets or similar features, have been estimatedin a sample of 117 E classified galaxies, and qualified by an ad hocΣ2 index. The overall frequency of peculiar'' objects(Pec subsample) is 32.5%. It decreases with the cosmic density of theenvironment, being minimal for the Virgo cluster, the densestenvironment in the sampled volume. This environmental effect is strongerfor galaxies with relatively large Σ2.The Pec subsample objects are compared with normal'' objects (Nopsubsample) as regards their basic properties. Firstly, theysystematically deviate from the Fundamental Plane and the Faber-Jacksonrelation derived for the Nop subsample, being too bright for their mass.Secondly, the dust content of galaxies, as estimated from IRAS fluxes,are similar in both subsamples. Third, the same is true of the frequencyof Kinematically Distinct cores (KDC), suggesting that KDC andmorphological peculiarities do not result from the same events in thehistory of E-galaxies.Using the Nop sample alone, we obtain very tight reference relationsbetween stellar population indicators (U-B, B-V, B-R, V-I,Mg2, Hβ, , Mgb) and the central velocitydispersion σ0. The discussion of the residuals of theserelations allows us to classify the Pec galaxies in two families i.e.the YP or NGC 2865 family, and the NP or NGC 3923 one. Galaxies in thefirst group show consistent evidence for a younger stellar populationmixed with the old one, in agreement with classical results (Schweizeret al. \cite{Schweizer1990}; Schweizer & Seitzer\cite{Schweizer1992}). The second group, however, has normal, orreddish, populations. It is remarkable that a fraction (circa 40%) ofmorphologically perturbed objects do not display any signature of ayoung population, either because the event responsible for thepecularity is too ancient, or because it did not produce significantstar formation (or eventually that the young sub-population has highmetallicity).A preliminary attempt is made to interpret the populations of Pecobjects by combining a young Single Stellar Population with a Nopgalaxy, with only limited success, perhaps largely due to uncertaintiesin the SSP indices used.Based in part on observations collected at the Observatoire deHaute-Provence.Figures \ref{fig1}-\ref{fig3} are only available in electronic form athttp://www.edpsciences.orgTable 10 is only available in electronic form at the CDS via anonymousftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/423/833 The globular cluster system of NGC 4374We study the globular cluster system (GCS) of the giant ellipticalNGC 4374 (M 84) in the Virgocluster using B and R photometry. The colour distribution is bimodalwith peaks at B-R=1.11 and B-R=1.36, fitting well to those found inother early-type galaxies. The radial profile of the cluster numberdensity is flatter than the galaxy light. Using the luminosity functionwe derive a distance modulus of μ=31.61±0.2, which within theuncertainty agrees with the distance from surface brightnessfluctuations. Blue and red clusters show similar radial concentrationsand azimuthal distributions. The total number of clusters isN=1775±150, which together with our distance modulus leads to aspecific frequency of SN=1.6±0.3. This value issurprisingly low for a giant elliptical, but resembles the case ofmerger remnants like NGC 1316, where the low specificfrequency is probably caused by the luminosity contribution of anintermediate-age population. A further common property is the high rateof type Ia supernovae which also may indicate the existence of a youngerpopulation. However, unlike in the case of NGC 1316,one cannot find any further evidence that NGC 4374indeed hosts younger populations. The low specific frequency would alsofit to a S0 galaxy seen face-on. Near-infrared imaging of ellipticals: surface brightness profiles and photometryWe present near-infrared K-band imaging of a large sample of candidatemerger remnant galaxies and Hickson Compact Group ellipticals. We derivelight profile indices, effective radii and surface brightnesses, as wellas total K-band magnitudes. We find that the light distributions of themerger remnant candidates are consistent with those of normal'ellipticals, and scatter around a mean profile index of (1/n) = 0.20.Many of our sample galaxies have surface brightness profiles that arenot well described by a de Vaucouleurs law (1/n= 0.25), and we discussthe implications of this on the derived total magnitudes. Comparing thetotal K magnitudes calculated by extrapolating a de Vaucouleurs profileand those derived using a generalized Sérsic form, we find that asignificant bias is introduced if the de Vaucouleurs law is not a gooddescription of the actual light profile. Redshift-Distance Survey of Early-Type Galaxies: Circular-Aperture PhotometryWe present R-band CCD photometry for 1332 early-type galaxies, observedas part of the ENEAR survey of peculiar motions using early-typegalaxies in the nearby universe. Circular apertures are used to tracethe surface brightness profiles, which are then fitted by atwo-component bulge-disk model. From the fits, we obtain the structuralparameters required to estimate galaxy distances using theDn-σ and fundamental plane relations. We find thatabout 12% of the galaxies are well represented by a pure r1/4law, while 87% are best fitted by a two-component model. There are 356repeated observations of 257 galaxies obtained during different runsthat are used to derive statistical corrections and bring the data to acommon system. We also use these repeated observations to estimate ourinternal errors. The accuracy of our measurements are tested by thecomparison of 354 galaxies in common with other authors. Typical errorsin our measurements are 0.011 dex for logDn, 0.064 dex forlogre, 0.086 mag arcsec-2 for<μe>, and 0.09 for mRC,comparable to those estimated by other authors. The photometric datareported here represent one of the largest high-quality and uniformall-sky samples currently available for early-type galaxies in thenearby universe, especially suitable for peculiar motion studies.Based on observations at Cerro Tololo Inter-American Observatory (CTIO),National Optical Astronomy Observatory, which is operated by theAssociation of Universities for Research in Astronomy, Inc., undercooperative agreement with the National Science Foundation (NSF);European Southern Observatory (ESO); Fred Lawrence Whipple Observatory(FLWO); and the MDM Observatory on Kitt Peak. A new catalogue of ISM content of normal galaxiesWe have compiled a catalogue of the gas content for a sample of 1916galaxies, considered to be a fair representation of normality''. Thedefinition of a normal'' galaxy adopted in this work implies that wehave purposely excluded from the catalogue galaxies having distortedmorphology (such as interaction bridges, tails or lopsidedness) and/orany signature of peculiar kinematics (such as polar rings,counterrotating disks or other decoupled components). In contrast, wehave included systems hosting active galactic nuclei (AGN) in thecatalogue. This catalogue revises previous compendia on the ISM contentof galaxies published by \citet{bregman} and \citet{casoli}, andcompiles data available in the literature from several small samples ofgalaxies. Masses for warm dust, atomic and molecular gas, as well asX-ray luminosities have been converted to a uniform distance scale takenfrom the Catalogue of Principal Galaxies (PGC). We have used twodifferent normalization factors to explore the variation of the gascontent along the Hubble sequence: the blue luminosity (LB)and the square of linear diameter (D225). Ourcatalogue significantly improves the statistics of previous referencecatalogues and can be used in future studies to define a template ISMcontent for normal'' galaxies along the Hubble sequence. The cataloguecan be accessed on-line and is also available at the Centre desDonnées Stellaires (CDS).The catalogue is available in electronic form athttp://dipastro.pd.astro.it/galletta/ismcat and at the CDS via anonymousftp to\ cdsarc.u-strasbg.fr (130.79.128.5) or via\http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/405/5 Bar Galaxies and Their EnvironmentsThe prints of the Palomar Sky Survey, luminosity classifications, andradial velocities were used to assign all northern Shapley-Ames galaxiesto either (1) field, (2) group, or (3) cluster environments. Thisinformation for 930 galaxies shows no evidence for a dependence of barfrequency on galaxy environment. This suggests that the formation of abar in a disk galaxy is mainly determined by the properties of theparent galaxy, rather than by the characteristics of its environment. Globular Clusters around Galaxies in GroupsWe have obtained deep photometry of NGC 1199 (in the compact group HCG22) and NGC 6868 (in the Telescopium loose group) with the Keck II andthe ESO VLT-I telescopes. Each galaxy is the optically brightest galaxyof its group. NGC 1199 has two companion galaxies at a median projecteddistance of only 33 kpc and, based on its peculiar internal structureand large X-ray halo, NGC 6868 has been proposed to be a merger remnant.Our analysis of B and R images uncovered a population of globularclusters around both galaxies, with total (and local) specific frequencySN=3.6+/-1.8 (3.4+/-1.5) for NGC 1199 andSN=1.8+/-1.1 (0.8+/-0.4) for NGC 6868. The radial profile ofthe globular clusters of NGC 1199 follows the light distribution of thegalaxy and can be fitted by a power law and a core model with a verysteep slope (α=2.5+/-0.3). In the case of NGC 6868, the profile ofthe globular clusters is well fitted by a power law and a core modelprofile of slope 1.4+/-0.3 and is shallower than the galaxy lightdistribution. Maximum likelihood fitting of two Gaussians to theglobular cluster color distribution yields a high significance formultimodality, with peaks centered at (B-R)0=1.13+/-0.04 and1.42+/-0.04 (NGC 1199) and (B-R)0=1.12+/-0.07 and 1.42+/-0.07(NGC 6868). NGC 1199 and NGC 6868 are good examples of galaxies in whichthe group environment is likely to have affected their dynamicalevolution. We find that for NGC 1199 the properties of the globularcluster system are similar to those for other systems around externalelliptical galaxies located in less dense environments but with a verysteep radial profile. In the case of NGC 6868, we find a regular radialprofile and color distribution and a comparatively low specificfrequency for the globular cluster system of the galaxy. The scaling relations of early-type galaxies in clusters. I. Surface photometry in seven nearby clustersThis is the first paper of a series investigating the scaling relationsof early-type galaxies in clusters. Here we illustrate the multi-bandimagery and the image reduction and calibration procedures relative tothe whole sample of 22 clusters at 0.05 <~ z <~ 0.25. We alsopresent detailed surface photometry of 312 early-type galaxies in 7clusters in the first redshift bin, z ≈0.025-0.075. We give for eachgalaxy the complete set of luminosity and geometrical profiles, and anumber of global, photometric and morphological parameters. They havebeen evaluated taking into account the effects of seeing. Internalconsistency checks and comparisons with data in the literature confirmthe quality of our analysis. These data, together with the spectroscopicones presented in the second paper of the series, will provide the localcalibration of the scaling relations. Tables 6, 7a-7g, the colour printsof Figs. 12a-12g AND Figs. 13a-13g are only available in electronic format http://www.edpsciences.com. The complete set of profiles is availableupon request from the authors. Tables 7a-7g are also available inelectronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr(130.79.188.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/387/26 A catalogue and analysis of X-ray luminosities of early-type galaxiesWe present a catalogue of X-ray luminosities for 401 early-typegalaxies, of which 136 are based on newly analysed ROSAT PSPC pointedobservations. The remaining luminosities are taken from the literatureand converted to a common energy band, spectral model and distancescale. Using this sample we fit the LX:LB relationfor early-type galaxies and find a best-fit slope for the catalogue of~2.2. We demonstrate the influence of group-dominant galaxies on the fitand present evidence that the relation is not well modelled by a singlepower-law fit. We also derive estimates of the contribution to galaxyX-ray luminosities from discrete-sources and conclude that they provideLdscr/LB~=29.5ergs-1LBsolar-1. Wecompare this result with luminosities from our catalogue. Lastly, weexamine the influence of environment on galaxy X-ray luminosity and onthe form of the LX:LB relation. We conclude thatalthough environment undoubtedly affects the X-ray properties ofindividual galaxies, particularly those in the centres of groups andclusters, it does not change the nature of whole populations. A synthesis of data from fundamental plane and surface brightness fluctuation surveysWe perform a series of comparisons between distance-independentphotometric and spectroscopic properties used in the surface brightnessfluctuation (SBF) and fundamental plane (FP) methods of early-typegalaxy distance estimation. The data are taken from two recent surveys:the SBF Survey of Galaxy Distances and the Streaming Motions of AbellClusters (SMAC) FP survey. We derive a relation between(V-I)0 colour and Mg2 index using nearly 200galaxies and discuss implications for Galactic extinction estimates andearly-type galaxy stellar populations. We find that the reddenings fromSchlegel et al. for galaxies with E(B-V)>~0.2mag appear to beoverestimated by 5-10 per cent, but we do not find significant evidencefor large-scale dipole errors in the extinction map. In comparison withstellar population models having solar elemental abundance ratios, thegalaxies in our sample are generally too blue at a given Mg2;we ascribe this to the well-known enhancement of the α-elements inluminous early-type galaxies. We confirm a tight relation betweenstellar velocity dispersion σ and the SBF fluctuation count'parameter N, which is a luminosity-weighted measure of the total numberof stars in a galaxy. The correlation between N and σ is eventighter than that between Mg2 and σ. Finally, we deriveFP photometric parameters for 280 galaxies from the SBF survey data set.Comparisons with external sources allow us to estimate the errors onthese parameters and derive the correction necessary to bring them on tothe SMAC system. The data are used in a forthcoming paper, whichcompares the distances derived from the FP and SBF methods. Optical and near-IR imaging of dusty ellipticalsIn this paper we present some of the results of imaging observations ofdusty ellipticals in the optical B & R bands as well as in near IRK?-band taken at the Las Campanas Observatory, Chile. We derive radialprofiles of surface brightness, position angle, ellipticity as well asprofiles of higher order Fourier coefficients by fitting ellipses toisophotes for each band. As the effect of dust obscuration is very muchreduced in the near-IR, a comparison of isophotal profiles in theK?-band with those of optical bands permits us to analyze the effects ofdust extinction in the dusty ellipticals. We examine optical &optical-IR color maps, color profiles, color gradients and discuss theresults. Globular Cluster Population of Hickson Compact Group 22a and 90cWe present the first measurement of the globular cluster populations ofgalaxies in Hickson compact groups, in order to investigate the effectof these high-density environments on the formation and evolution ofglobular cluster systems. Based on V- and R-band images that we obtainedof HCG 22a and HCG 90c with the ESO New Technology Telescope (NTT), wefind a total globular cluster population of 1590+/-854 for HCG 22a and2136+/-718 for 90c. The specific frequency was found to beSN=1.9+/-1.0 for HCG 22a and SN=3.4+/-1.1 for HCG90c. A power-law fit to the globular cluster radial profile of HCG 22ayields σ~R-2.01+/-0.30, and for HCG 90c we foundσ~R-1.20+/-0.16. A comparison of the globular clusterradial profiles with the surface brightness of the parent galaxy showsthat the globular cluster systems are at least as extended as the halolight. The measured values for the specific frequency are consistentwith a scenario in which the host galaxies were in a low-densityfieldlike'' environment when they formed their globular clustersystems. Based on observations collected at the European SouthernObservatory, Chile. The SBF Survey of Galaxy Distances. IV. SBF Magnitudes, Colors, and DistancesWe report data for I-band surface brightness fluctuation (SBF)magnitudes, (V-I) colors, and distance moduli for 300 galaxies. Thesurvey contains E, S0, and early-type spiral galaxies in the proportionsof 49:42:9 and is essentially complete for E galaxies to Hubblevelocities of 2000 km s-1, with a substantial sampling of Egalaxies out to 4000 km s-1. The median error in distancemodulus is 0.22 mag. We also present two new results from the survey.(1) We compare the mean peculiar flow velocity (bulk flow) implied byour distances with predictions of typical cold dark matter transferfunctions as a function of scale, and we find very good agreement withcold, dark matter cosmologies if the transfer function scale parameterΓ and the power spectrum normalization σ8 arerelated by σ8Γ-0.5~2+/-0.5. Deriveddirectly from velocities, this result is independent of the distributionof galaxies or models for biasing. This modest bulk flow contradictsreports of large-scale, large-amplitude flows in the ~200 Mpc diametervolume surrounding our survey volume. (2) We present adistance-independent measure of absolute galaxy luminosity, N and showhow it correlates with galaxy properties such as color and velocitydispersion, demonstrating its utility for measuring galaxy distancesthrough large and unknown extinction. Observations in part from theMichigan-Dartmouth-MIT (MDM) Observatory. Nearby Optical Galaxies: Selection of the Sample and Identification of GroupsIn this paper we describe the Nearby Optical Galaxy (NOG) sample, whichis a complete, distance-limited (cz<=6000 km s-1) andmagnitude-limited (B<=14) sample of ~7000 optical galaxies. Thesample covers 2/3 (8.27 sr) of the sky (|b|>20deg) andappears to have a good completeness in redshift (97%). We select thesample on the basis of homogenized corrected total blue magnitudes inorder to minimize systematic effects in galaxy sampling. We identify thegroups in this sample by means of both the hierarchical and thepercolation `friends-of-friends'' methods. The resulting catalogs ofloose groups appear to be similar and are among the largest catalogs ofgroups currently available. Most of the NOG galaxies (~60%) are found tobe members of galaxy pairs (~580 pairs for a total of ~15% of objects)or groups with at least three members (~500 groups for a total of ~45%of objects). About 40% of galaxies are left ungrouped (field galaxies).We illustrate the main features of the NOG galaxy distribution. Comparedto previous optical and IRAS galaxy samples, the NOG provides a densersampling of the galaxy distribution in the nearby universe. Given itslarge sky coverage, the identification of groups, and its high-densitysampling, the NOG is suited to the analysis of the galaxy density fieldof the nearby universe, especially on small scales. A Test for Large-Scale Systematic Errors in Maps of Galactic ReddeningAccurate maps of Galactic reddening are important for a number ofapplications, such as mapping the peculiar velocity field in the nearbyuniverse. Of particular concern are systematic errors which vary slowlyas a function of position on the sky, as these would induce spuriousbulk flow. We have compared the reddenings of Burstein & Heiles (BH)and those of Schlegel, Finkbeiner, & Davis (SFD) to independentestimates of the reddening, for Galactic latitudes |b|>10^deg. Ourprimary source of Galactic reddening estimates comes from comparing thedifference between the observed B-V colors of early-type galaxies, andthe predicted B-V color determined from the B-V-Mg_2 relation. We havefitted a dipole to the residuals in order to look for large-scalesystematic deviations. There is marginal evidence for a dipolar residualin the comparison between the SFD maps and the observed early-typegalaxy reddenings. If this is due to an error in the SFD maps, then itcan be corrected with a small (13%) multiplicative dipole term. Weargue, however, that this difference is more likely to be due to a small(0.01 mag) systematic error in the measured B-V colors of the early-typegalaxies. This interpretation is supported by a smaller, independentdata set (globular cluster and RR Lyrae stars), which yields a resultinconsistent with the early-type galaxy residual dipole. BH reddeningsare found to have no significant systematic residuals, apart from theknown problem in the region 230^deg X-ray luminosities for a magnitude-limited sample of early-type galaxies from the ROSAT All-Sky SurveyFor a magnitude-limited optical sample (B_T <= 13.5 mag) ofearly-type galaxies, we have derived X-ray luminosities from the ROSATAll-Sky Survey. The results are 101 detections and 192 useful upperlimits in the range from 10^36 to 10^44 erg s^-1. For most of thegalaxies no X-ray data have been available until now. On the basis ofthis sample with its full sky coverage, we find no galaxy with anunusually low flux from discrete emitters. Below log (L_B) ~ 9.2L_⊗ the X-ray emission is compatible with being entirely due todiscrete sources. Above log (L_B) ~ 11.2 L_osolar no galaxy with onlydiscrete emission is found. We further confirm earlier findings that L_xis strongly correlated with L_B. Over the entire data range the slope isfound to be 2.23 (+/- 0.12). We also find a luminosity dependence ofthis correlation. Below log L_x = 40.5 erg s^-1 it is consistent with aslope of 1, as expected from discrete emission. Above this value theslope is close to 2, as expected from gaseous emission. Comparing thedistribution of X-ray luminosities with the models of Ciotti et al.leads to the conclusion that the vast majority of early-type galaxiesare in the wind or outflow phase. Some of the galaxies may have alreadyexperienced the transition to the inflow phase. They show X-rayluminosities in excess of the value predicted by cooling flow modelswith the largest plausible standard supernova rates. A possibleexplanation for these super X-ray-luminous galaxies is suggested by thesmooth transition in the L_x--L_B plane from galaxies to clusters ofgalaxies. Gas connected to the group environment might cause the X-rayoverluminosity. The Mass-to-Light Ratio of Binary GalaxiesWe report on the mass-to-light ratio determination based on a newlyselected binary galaxy sample, which includes a large number of pairswhose separations exceed a few hundred kpc. The probabilitydistributions of the projected separation and the velocity differencehave been calculated considering the contamination of optical pairs, andthe mass-to-light (M/L) ratio has been determined based on the maximumlikelihood method. The best estimate of the M/L in the B band for 57pairs is found to be 28-36 depending on the orbital parameters and thedistribution of optical pairs (solar unit: H_0=50 km s^-1 Mpc^-1). Thebest estimate of the M/L for 30 pure spiral pairs is found to be 12-16.These results are relatively smaller than those obtained in previousstudies but are consistent with each other within the errors. Althoughthe number of pairs with large separation is significantly increasedcompared with previous samples, the M/L does not show any tendency ofincrease but is found to be almost independent of the separation ofpairs beyond 100 kpc. The constancy of the M/L beyond 100 kpc mayindicate that the typical halo size of spiral galaxies is less than ~100kpc. Galaxy coordinates. II. Accurate equatorial coordinates for 17298 galaxiesUsing images of the Digitized Sky Survey we measured coodinates for17298 galaxies having poorly defined coordinates. As a control, wemeasured with the same method 1522 galaxies having accurate coordinates.The comparison with our own measurements shows that the accuracy of themethod is about 6 arcsec on each axis (RA and DEC). Central Mg_2 indices for early-type galaxiesWe present 210 new measurements of the central absorption line-strength{Mg_2} index for 87 early-type galaxies drawn from the \cite[Prugniel& Simien (1996)]{PS96} sample. 28 galaxies were not observed before.The results are compared to measurements published previously asavailable in HYPERCAT, and rescaled to the Lick system. The meanindividual internal error on these measurements is 0.009m+/-0.003m andthe mean external error is 0.012m+/-0.002m for this series ofmeasurements. Based on observations collected at the Observatoire deHaute-Provence. Tables 1, 3 and 4 are available in electronic form fromthe CDS, Strasbourg (via anonymous ftp to 130.79.128.5). Tables 1 and 3are available from CDS only. Lens models with density cuspsLens models appropriate for representing cusped galaxies and clustersare developed. The analogue of the odd-number theorem for cusped densitydistributions is given. Density cusps are classified into strong,isothermal or weak, according to their lensing properties. Strong cuspscause multiple imaging for any source position, whereas isothermal andweak cusps give rise to only one image for distant sources. Isothermalcusps always possess a pseudo-caustic. When the source crosses thepseudo-caustic, the number of images changes by unity. Two families ofcusped galaxy and cluster models are examined in detail. The doublepower-law family has an inner cusp, followed by a transition region andan outer envelope. One member of this family - the isothermal doublepower-law model - possesses an exceedingly scarce property, namely thelens equation is exactly solvable for any source position. This meansthat the magnifications, the time delay and the lensing cross-sectionsare all readily available. The model has a three-dimensional densitythat is cusped like r^-2 at small radii and falls off like r^-4asymptotically. Thus, it provides a very useful representation of thelensing properties of a galaxy or cluster of finite total mass with aflat rotation curve. The second set of models studied is the singlepower-law family. These are single density cusps of infinite extent. Theproperties of the critical curves and caustics and the behaviour of thelenses in the presence of external shear are all discussed in somedetail. The Evolution of Galaxies in Compact GroupsWe present an analysis of the spectra of 62 galaxies in 15 compactgroups. The galaxies are classified into four activity classes: galaxieswithout emission, starburst galaxies, luminous AGNs (Seyfert andLINERs), and low-luminosity AGNs (LLAGNs). The star formation in theHickson compact group (HCG) starbursts is more intense than in normalspirals, but comparable to that observed in starburst-nucleus galaxies(SBNGs) in the field. In general, the HCG starbursts have mean solar gasmetallicity and do not follow the metallicity-luminosity relation tracedby the early-type SBNGs in the field, suggesting that most of them arelate-type SBNGs. This morphology preference, coupled with theobservation that the HCG starbursts are predominantly located in thehalos of the groups, is consistent with the idea that compact groups areembedded in sparser structures. The stellar metallicities of thenonstarburst galaxies are comparable to those observed in normalgalaxies with similar morphologies, but are relatively high for theirluminosities. In these galaxies, the metal absorption line equivalentwidths are slightly narrower than normal, while the Balmer absorptionlines are relatively strong. All these observations suggest the presenceof a population of intermediate-age stars. These galaxies could bepoststarburst, but at a very advanced stage of evolution, the lastbursts having happened more than 2 Gyr in the past. Our observationssupport a scenario in which the cores of the groups are slowlycollapsing evolved systems embedded in more extended structures. In thecores of the groups, the interactions were more frequent and thegalaxies evolved at a more rapid rate than in their halos. ROSAT X-Ray Colors and Emission Mechanisms in Early-Type GalaxiesThe X-ray colors and X-ray-to-optical luminosity ratios (LX/LB) of 61early-type galaxies observed with the ROSAT PSPC are determined. Thecolors indicate that the X-ray spectral properties of galaxies vary as afunction of LX/LB. The brightest X-ray galaxies have colors that areconsistent with thermal emission from hot gas with roughly the samemetallicity of 50% solar. The spatial variation of the colors indicatesthat the gas temperature in these galaxies increases radially. Galaxieswith medium LX/LB also have spectral properties consistent with emissionfrom hot gas. If a simple one-component thermal model is assumed todescribe the 0.1-2.0 keV X-ray emission in these galaxies, then onepossible explanation for the progressive decrease in LX/LB amonggalaxies of this class could be the progressive decrease in metalabundance of the X-ray-emitting gas contained by the galaxies. However,stellar X-ray emission may become a complicating factor for the faintergalaxies in this medium-LX/LB class. Galaxies with the lowest LX/LBvalues appear to be lacking a hot interstellar component. Their X-raycolors are consistent with those derived from the bulges of the spiralgalaxies M31 and NGC 1291. In M31, the X-ray emission is resolved intodiscrete sources and is apparently due primarily to low-mass X-raybinaries (LMXBs). We therefore suggest that the bulk of the X-rayemission in the faintest elliptical galaxies is also due to LMXBs.Previously, the X-ray spectra of X-ray-faint galaxies had been found tobe described by a hard component, which was attributed to LMXB emission,and a very soft component of unknown origin. We show that the very softcomponent also likely results from LMXBs, as a very soft component isseen in the X-ray spectra of the nearby LMXB Her X-1 and LMXBs in thebulge of M31. If the X-ray emission in X-ray-faint galaxies is primarilyfrom stellar sources, then a range in LX/LB among these galaxiessuggests that the stellar X-ray luminosity does not scale with opticalluminosity, at least for galaxies of low optical luminosities. Thiscould be the result of a decrease in the proportion of LMXBs withdecreasing optical luminosity and/or the effects of fluctuations in thesmall number of LMXBs expected. Effects of Interaction-induced Activities in Hickson Compact Groups: CO and Far-Infrared StudyA study of 2.6 mm CO J = 1 --> 0 and far-infrared (FIR) emission in adistance-limited (z < 0.03) complete sample of Hickson compact group(HCG) galaxies was conducted in order to examine the effects of theirunique environment on the interstellar medium of component galaxies andto search for a possible enhancement of star formation and nuclearactivity. Ubiquitous tidal interactions in these dense groups wouldpredict enhanced activities among the HCG galaxies compared to isolatedgalaxies. Instead, their CO and FIR properties (thus, "star formationefficiency") are surprisingly similar to isolated spirals. The CO datafor 80 HCG galaxies presented here (including 10 obtained from theliterature) indicate that the spirals globally show the same H2 contentas the isolated comparison sample, although 20% are deficient in COemission. Because of their large optical luminosity, low metallicity isnot likely the main cause for the low CO luminosity. The CO deficiencyappears linked with the group evolution, and gas exhaustion through paststar formation and removal of the external gas reserve by tidalstripping of the outer H I disk offer a possible explanation. The IRASdata for the entire redshift-limited complete sample of 161 HCG galaxieswere reanalyzed using ADDSCAN/SCANPI, improving the sensitivity by afactor of 3-5 over the existing Point Source Catalog (PSC) and resolvingbetter the contribution from individual galaxies. The new analysis ofthe IRAS data confirms the previous suggestion that FIR emission in HCGgalaxies is similar to isolated, Virgo Cluster, and weakly interactinggalaxies. Their H2 and FIR characteristics yield a star formationefficiency that is similar to that of these comparison samples. A factor2 enhancement in the 25-100 mu m flux ratio among the HCG spirals isfound, which suggests intense localized nuclear starburst activitysimilar to that of H II galaxies. A number of early-type galaxies inHCGs are detected in CO and FIR, lending further support to the ideathat tidal interactions and tidally induced evolution of the groups andmember galaxies are important in our sample. Structural and Dynamical Analysis of the Hickson Compact GroupsBased on the spectroscopic survey of de Carvalho et al., we analyze thestructural and dynamical properties of 17 Hickson compact groups. Thisanalysis probes a region of 0.dg5 x 0.dg5 around each group and showsthat most of them are part of larger structures. Our results alsosuggest that the Hickson sample is composed of different dynamicalstages of the groups" evolution. Specifically, we identify threepossible evolutionary phases among groups in the sample: loose groups,core + halo systems, and compact groups, each one presenting a distinctsurface density profile. This sequence is consistent with thereplenishment scenario for the formation and evolution of compact groupswithin larger and less dense systems. The Nature of the Activity in Hickson Compact Groups of GalaxiesWe present the results of the spectral classification of the 82brightest galaxies in a sample of 17 compact groups. We verify that theactive galactic nuclei (AGNs) are preferentially located in the mostearly-type and luminous galaxies of the groups, as is usually observedin the field. But these AGNs also appear to be systematicallyconcentrated toward the central parts of the groups. Our observationssuggest a correlation between activity types, morphologies, anddensities of galaxies in the compact groups. This is consistent with ascenario in which galaxies of compact groups evolve by interacting withtheir environment and are currently in a quiet phase of their activity. The Southern Sky Redshift SurveyWe report redshifts, magnitudes, and morphological classifications for5369 galaxies with m_B <= 15.5 and for 57 galaxies fainter than thislimit, in two regions covering a total of 1.70 sr in the southerncelestial hemisphere. The galaxy catalog is drawn primarily from thelist of nonstellar objects identified in the Hubble Space TelescopeGuide Star Catalog (GSC). The galaxies have positions accurate to ~1"and magnitudes with an rms scatter of ~0.3 mag. We compute magnitudes(m_SSRS2) from the relation between instrumental GSC magnitudes and thephotometry by Lauberts & Valentijn. From a comparison with CCDphotometry, we find that our system is homogeneous across the sky andcorresponds to magnitudes measured at the isophotal level ~26 magarcsec^-2. The precision of the radial velocities is ~40 km s^-1, andthe redshift survey is more than 99% complete to the m_SSRS2 = 15.5 maglimit. This sample is in the direction opposite that of the CfA2; incombination the two surveys provide an important database for studies ofthe properties of galaxies and their large-scale distribution in thenearby universe. Based on observations obtained at Cerro TololoInter-American Observatory, National Optical Astronomy Observatories,operated by the Association of Universities for Research in Astronomy,Inc., under cooperative agreement with the National Science Foundation;Complejo Astronomico El Leoncito, operated under agreement between theConsejo Nacional de Investigaciones Científicas de laRepública Argentina and the National Universities of La Plata,Córdoba, and San Juan; the European Southern Observatory, LaSilla, Chile, partially under the bilateral ESO-ObservatórioNacional agreement; Fred Lawrence Whipple Observatory;Laboratório Nacional de Astrofísica, Brazil; and the SouthAfrican Astronomical Observatory.
Submit a new article


text:
# For science lovers........!!!

quarks........always have interested me ........another article which i think would interest all of you.....

Entangled quarks hint at reconciliation of quantum mechanics and general relativity

Building on related research that showed how two entangled black holes could be linked by a wormhole, an MIT physicist has shown that two entangled quarks could also give rise to a wormhole that connects the pair of elementary particles. The new work bolsters the relatively new idea that the laws of gravity holding together the universe may not be fundamental, but arise instead from quantum entanglement.

Quantum entanglement - where the quantum states of two particles are mirrored by each other instantaneously, no matter how much distance separates them - has long been the bane of classical physics, with Einstein famously dismissing it as "spooky action at a distance."

Entanglement has been demonstrated experimentally, but the mechanism that allows entangled particles to communicate instantaneously has so far evaded scientists. Earlier this year, however, physicists Juan Maldacena of the Institute for Advanced Study and Leonard Susskind of Stanford University proposed a theoretical solution in the form of two entangled black holes. When the black holes were entangled, then pulled apart, the theorists showed that what emerged was a wormhole - a tunnel through space-time. Additionally, their research suggested that gravity emerges from the more fundamental phenomenon of entangled black holes.

Now, MIT physicist Julian Sonner has built on this and found that, looked at in the context of string theory, the creation of a quark-antiquark pair simultaneously gives rise to a wormhole connecting the pair of elementary particles. Sonner has published his results in the journal Physical Review Letters, where it appears together with related work by Kristan Jensen of the University of Victoria and Andreas Karch of the University of Washington.

To explore what emerges from two entangled quarks, Sonner first generated quarks using the Schwinger effect - a concept in quantum theory that enables the creation of particles out of nothing. More precisely, the effect, also called "pair creation," allows two particles to emerge from a vacuum. Under an electric field, "one can," as Sonner explains, "catch a pair of particles" before they disappear back into the vacuum. Once extracted, these particles are considered entangled.

Sonner then mapped the entangled quarks onto a four-dimensional space representing space-time. To see what geometry may emerge in the fifth dimension from entangled quarks in the fourth, Sonner employed holographic duality, a concept from string theory. "While a hologram is a two-dimensional object, it contains all the information necessary to represent a three-dimensional view. Holographic duality is a way to derive a more complex dimension from the next lowest dimension," explains Sonner.

Using holographic duality, Sonner found that what emerged was a wormhole connecting the two entangled quarks, implying that the creation of quarks simultaneously creates a wormhole. More fundamentally, the results suggest that gravity may, in fact, emerge from entanglement. "The geometry, or bending, of the universe as described by classical gravity, may be a consequence of entanglement, such as that between pairs of particles strung together by tunneling wormholes," Sonner explains.

Ever since quantum mechanics was first proposed, physicists have been trying to explain gravity in quantum-mechanical terms. While quantum mechanics works extremely well in describing interactions at an atomic level, it fails to explain gravity - a fundamental concept of relativity. Sonner says his work may offer new approaches into a reconciliation of quantum mechanics and general relativity. Any such approach would suggest that classical gravity is not a fundamental concept, as Einstein first proposed, but rather that it emerges from a more basic, quantum-based phenomenon. In a macroscopic context, this would mean that the universe is shaped by something more fundamental than the forces of gravity.

Note by Ayushi Agrawal
7 years, 6 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

right swapnil..........

- 7 years, 6 months ago

i wanted to know more about Schwinger effect??..........

- 7 years, 6 months ago

And I wanted a time machine but we always can't get what we want.

- 7 years, 6 months ago

Schwinger effect - it is to analyze electrostatic potentials in the holographic "Schwinger effect". Here, the potential barrier for pair production is estimated by a static potential consisting of static mass energies, an electric potential from an external electric-field, and the Coulomb potential between [a particle and an antiparticle] <- very important . Coulomb potential is supposed to be judged by the minimal surface attaching on the conformal boundary at the critical field, where the potential barrier vanishes, exhibits a deviation from the one obtained from the Dirac-Born-Infeld action

- 7 years, 6 months ago

Could you plzzz help me , how to study science ...... 4 me it's nt being fun ... What tricks shuld use to make science fun

- 5 years, 9 months ago

×


text:
# OLS

Very simple notebook to get started with python, simulating and estimating. In this homework, we hope to learn

We consider the simple linear model

y_i = \beta x_i + \epsilon_i
 1 2 3 4 5 6 7 8 %cd .. %load_ext autoreload %autoreload 2 import numpy as np # the following loads my solution file, which you do not have! # you should comment the following line, or create your solution in solutions/sol_ols.py from solutions.sol_ols import *
 1 2 3 /home/tlamadon/git The autoreload extension is already loaded. To reload it, use: %reload_ext autoreload

## Simulate data

We start by simulating data of N observations and K regressors. We keep everything normal to keep things simple.

 1 2 3 4 5 6 7 N = 1000 K = 10 X = np.random.normal(size = (N,K)) E = np.random.normal(size = N) beta = np.linspace(0,1,num=K) Y = np.matmul(X,beta) + E

As you can see we make extensive use of vector operations from the numpy package.

 1 2 3 import matplotlib.pyplot as plt plt.plot(np.matmul(X,beta),Y,'.') plt.show()

## Solve using numpy and linear algebra

Question

This is the first question. Write your own numpy_ols function, which takes as an input (Y,X) and returns the OLS estimates. You only need to use two numpy functions np.transpose, np.matmul and np.linalg.solve. The function should just a few lines.

We use the created function (in this document it is using the one that I wrote) and we then plot the estimated $\beta$ versus the true $\beta$.

  1 2 3 4 5 6 7 8 9 10 11 def abline(slope, intercept): """Plot a line from slope and intercept""" axes = plt.gca() x_vals = np.array(axes.get_xlim()) y_vals = intercept + slope * x_vals plt.plot(x_vals, y_vals, '--') beta_hat = numpy_ols(Y,X) plt.plot(beta,beta_hat,'x') abline(1,0) plt.show()

## Solve using Keras

Now we are going to make an overkill, which is to use Keras to solve this linear problem. Kera allows to build models by composing layers. For instance, here, imagine I wanted to fit a neural net on the data I have generated, I would do the following:

 1 2 from keras.models import Sequential from keras.layers.core import Dense, Activation
 1 2 3 4 model = Sequential() model.add(Dense(1, input_shape=(K,))) model.add(Activation('sigmoid')) model.summary()
  1 2 3 4 5 6 7 8 9 10 11 12 Model: "sequential" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense (Dense) (None, 1) 11 _________________________________________________________________ activation (Activation) (None, 1) 0 ================================================================= Total params: 11 Trainable params: 11 Non-trainable params: 0 _________________________________________________________________

The first layer is a Dense layer, and it implements the following transformation: $$l_i = \sum_{k=1}^K w_k Z_{ik}$$ for a set of weights $w_k$ that we want to estimate and some input $Z_{ik}$. Later on we will feed bacthes from X to this.

Because we are using a sequential construction, the second layer takes the output $l_i$ of the first layer and generate an output $$\hat{y}_i = g(l_i)$$ for some non linear function refered to as activation functions.

See this description of activation functions including the one we have specificed.

The next command initializes the model, specifies the optimzer to use and specifies the loss function to minimize. Here we will try to minimize the square loss between provided output and model output:

\min_{w_k} \sum_i (\hat{y}_i - y_i)^2
 1 model.compile(optimizer='adam', loss='mse')

It is finally time to feed the data to our model. We specify the input $X$, the output $Y$, the number of passes we want to do on the data epochs as well as the size of the batches, meaning the numbers of $i$ observation to give at the same time to compute one update step of the optimizer.

 1 hist = model.fit(X, Y, epochs=100, batch_size=50, verbose=0)

We then extract the estimated weights $w_k$ and compare them to the $\beta$ that generated the data.

 1 2 3 4 beta_keras = model.layers[0].get_weights()[0] plt.plot(beta,beta_keras[0:K],'x') abline(1,0) plt.show()

Question

Question 2: Clearly the neural net that we used doesn't deliver the right estimates for $\beta$. The functional form that we specified when creating the model ressembles more a logit than a linear model. Given what you know about the shape of the Dense layer and the Sigmoid activation, modify the model in order to have a functional form identical to the linear form. Either replace the model2 = kera_linear(K) int he following code or write you own to try to get a good fit.

 1 2 3 4 5 6 model2 = kera_linear(K) model2.compile(optimizer='adam', loss='mse') hist2 = model2.fit(X, Y, epochs=100, batch_size=50, verbose=0); beta_keras = model2.layers[0].get_weights()[0] plt.plot(beta,beta_keras[0:K],'x') abline(1,0)

# Fitting non-linear functions

Let's step it up! Let's try to fit a non linear function of one variable. We are going to use the cos function.

 1 2 X = 10*np.random.uniform(size = N) Y = np.cos(X) + 0.5*np.random.normal(size = N)

As we can see, this is a function which is neither linear or a simple activation function:

 1 2 plt.plot(X,Y,'o') plt.show()

This is where multilayers shine! We create the following model:

 1 2 3 4 5 6 7 model3 = Sequential() model3.add(Dense(20, input_shape=(1,))) model3.add(Activation('elu')) model3.add(Dense(1)) model3.add(Activation('elu')) model3.add(Dense(1)) model3.summary()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= dense_2 (Dense) (None, 20) 40 _________________________________________________________________ activation_1 (Activation) (None, 20) 0 _________________________________________________________________ dense_3 (Dense) (None, 1) 21 _________________________________________________________________ activation_2 (Activation) (None, 1) 0 _________________________________________________________________ dense_4 (Dense) (None, 1) 2 ================================================================= Total params: 63 Trainable params: 63 Non-trainable params: 0 _________________________________________________________________

Question

Explain in your own words the structure of this neural net! How many input, what are each layers. Next write your own fit_model3 function which takes X and Y and model3 and fits it. You needs to adapt the few line of codes that we have used in previous sections. You will also need to play a bit with batch sizes and epochs to succeed in achieving a good fit, as in the following figure.

 1 model3 = fit_model3(model3,X,Y)

We then construct the predition from the model and plot it on top of the data! Voila!

 1 2 3 4 5 Xp = np.linspace(0,10,num=50) Yp = model3.predict(Xp) plt.plot(X,Y,'o') plt.plot(Xp,Yp,'-') plt.show()


text:
Situation 21.25.5. Let $f : (\mathcal{C}, \mathcal{O}) \to (\mathcal{C}', \mathcal{O}')$ be a morphism of ringed sites. Let $u : \mathcal{C}' \to \mathcal{C}$ be the corresponding continuous functor of sites. Let $\mathcal{A} \subset \textit{Mod}(\mathcal{O})$ be a weak Serre subcategory. We assume the following is true: there exists a subset $\mathcal{B}' \subset \mathop{\mathrm{Ob}}\nolimits (\mathcal{C}')$ such that

1. every object of $\mathcal{C}'$ has a covering whose members are in $\mathcal{B}'$, and

2. for every $V' \in \mathcal{B}'$ there exists an integer $d_{V'}$ and a cofinal system $\text{Cov}_{V'}$ of coverings of $V'$ such that

$H^ p(u(V'_ i), \mathcal{F}) = 0 \text{ for } \{ V'_ i \to V'\} \in \text{Cov}_{V'},\ p > d_{V'}, \text{ and } \mathcal{F} \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Inequalities for ultraspherical polynomials and the gamma function. (English) Zbl 0532.33007
Der Verf. beweißt mit elementaren Mitteln für die Gegenbauerschen Polynome $P\sb n\sp{(\lambda)}$ die Abschätzung $$(\sin \theta)\sp{\lambda}\vert P\sb n\sp{(\lambda)}(\cos \theta)\vert<2\sp{1- \lambda}/\Gamma(\lambda)(n+\lambda)\sp{1-\lambda},$$ $$0\le \theta \le \pi,\quad 0<\lambda<1,\quad n\in N.$$ Diese Abschätzung ist besser als {\it G. Szegö’s} Ungleichung [Orthogonal polynomials (1959; Zbl 0089.275)], wo $n\sp{1-\lambda}$ statt $(n+\lambda)\sp{1-\lambda}$ steht. Einige Abschätzungen für $\Gamma(n+\lambda)/\Gamma(n+1)$ werden betrachtet.
Reviewer: E.Riekstiņš

##### MSC:
 33C55 Spherical harmonics 33B15 Gamma, beta and polygamma functions
Full Text:
##### References:
 [1] Antonov, V. A.; Holševnikov, K. V.: An estimate of the remainder in the expansion of the generating function for the Legendre polynomials (Generalization and improvement of Bernstein’s inequality). Vestnik leningrad univ. Math. 13, 163-166 (1981) [2] Gautschi, W.: Some elementary inequalities relating to the gamma and incomplete gamma function. J. math. Phys. 38, 77-81 (1959) · Zbl 0094.04104 [3] Kazarinoff, D. K.: On wallis’ formula. Edinburgh math. Notes no. 40, 19-21 (1956) · Zbl 0072.28401 [4] D. Kershaw, Some extensions of Gautschi’s inequalities for the gamma function, Math. Comp., in press. · Zbl 0536.33002 [5] Lebedev, N. N.: Special functions and their applications. (1965) · Zbl 0131.07002 [6] Lorch, L.: Alternative proof of a sharpened form of Bernstein’s inequality for Legendre polynomials. Appl. anal. 14, 237-240 (1983) · Zbl 0505.33007 [7] Szegö, G.: Orthogonal polynomials. Colloquium publications 23 (1975) · Zbl 0305.42011 [8] Watson, G. N.: A note on gamma functions. Edinburgh math. Notes no. 41, 7-9 (1959) · Zbl 0103.29601


text:
# All Science Fair Projects

## Science Fair Project Encyclopedia for Schools!

 Search    Browse    Forum  Coach    Links    Editor    Help    Tell-a-Friend    Encyclopedia    Dictionary

# Science Fair Project Encyclopedia

For information on any area of science that interests you,
enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.).
Or else, you can start by choosing any of the categories below.

# Statistical hypothesis testing

(Redirected from Hypothesis testing)

One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. A statistical hypothesis test, or more briefly, hypothesis test, is an algorithm to state the alternative (for or against the hypothesis) which minimizes certain risks.

This article describes the commonly used frequentist treatment of hypothesis testing. From the Bayesian point of view, it is appropriate to treat hypothesis testing as a special case of normative decision theory (specifically a model selection problem ) and it is possible to accumulate evidence in favor of (or against) a hypothesis using concepts such as likelihood ratios known as Bayes factors.

There are several preparations we make before we observe the data.

1. The hypothesis must be stated in mathematical/statistical terms that make it possible to calculate the probability of possible samples assuming the hypothesis is correct. For example: The mean response to treatment being tested is equal to the mean response to the placebo in the control group. Both responses have the normal distribution with this unknown mean and the same known standard deviation ... (value).
2. A test statistic must be chosen that will summarize the information in the sample that is relevant to the hypothesis. Such a statistic is known as a sufficient statistic. A sufficient statistic for a parameter of a distribution exists if and only if the distribution forms an exponential family. In the example given above, it might be the numerical difference between the two sample means, m1 − m2.
3. The distribution of the test statistic is used to calculate the probability sets of possible values (usually an interval or union of intervals). In this example, the difference between sample means would have a normal distribution with a standard deviation equal to the common standard deviation times the factor $\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}$ where n1 and n2 are the sample sizes.
4. Among all the sets of possible values, we must choose one that we think represents the most extreme evidence against the hypothesis. That is called the critical region of the test statistic. The probability of the test statistic falling in the critical region when the hypothesis is correct is called the alpha value (or size) of the test.

After the data is available, the test statistic is calculated and we determine whether it is inside the critical region.

If the test statistic is inside the critical region, then our conclusion is one of the following:

1. The hypothesis is incorrect, therefore reject the null hypothesis. (Therefore the critical region is sometimes called the rejection region, while its complement is the acceptance region.)
2. An event of probability less than or equal to alpha has occurred.

The researcher has to choose between these logical alternatives. In the example we would say: the observed response to treatment is statistically significant.

If the test statistic is outside the critical region, the only conclusion is that

• There is not enough evidence to reject the hypothesis.

This is not the same as evidence in favor of the hypothesis. That we cannot obtain using these arguments, since lack of evidence against a hypothesis is not evidence for it. On this basis, statistical research progresses by eliminating error, not by finding the truth.

Last updated: 10-24-2005 15:14:20
03-10-2013 05:06:04
Science kits, science lessons, science toys, maths toys, hobby kits, science games and books - these are some of many products that can help give your kid an edge in their science fair projects, and develop a tremendous interest in the study of science. When shopping for a science kit or other supplies, make sure that you carefully review the features and quality of the products. Compare prices by going to several online stores. Read product reviews online or refer to magazines.

Start by looking for your science kit review or science toy review. Compare prices but remember, Price \$ is not everything. Quality does matter.
 Science Fair Coach What do science fair judges look out for? ScienceHound Science Fair Projects for students of all ages
 All Science Fair Projects.com Site All Science Fair Projects Homepage Search | Browse | Links | From-our-Editor | Books | Help | Contact | Privacy | Disclaimer | Copyright Notice


text:
# A question on calculating entangled spin probability

1. Mar 23, 2015

### rede96

I was trying to understand the QM tests done to show the violation of Bell’s inequality. In the example given this was done by testing the polarization of entangled photons which were positively correlated.

So in the example Alice and Bob are detecting the polarisation for the two entangled photons, using 3 detectors chosen at random, which are at angles of 0 degrees, 120 degrees and 240 degrees.

I was told that the quantum rule to predict the number of matches (e.g. both detected the same spin or both do not detect same spin) was cos^2(Alice's Angle - Bob's Angle)

As these angles are all equidistant then it is easy to see that the overall result will be 0.25 without doing all the individual test, as each individual test’s probability is 0.25

But let’s say the three detectors being used were at angles 10, 60 and 200?

Doing it long hand, i.e. calculating each individual test and adding up all the matches I get appx 0.66

But how would I calculate the expected result without doing all the individual tests? (so I can check I am doing it right!)

Thanks.

Last edited: Mar 23, 2015
2. Mar 28, 2015