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# Vasicek model

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## Overview

The Vasicek(1977) model[1] is a simple short rate model. It is originally a one factor model and assumes that short rates are driven by one source of risk. We describe the Vasicek model below and use it to obtain analytical bond prices.

## The Vasicek Model

The instantaneous short rate has the following stochastic process under the risk-neutral measure $Q$:

$dr(t) = a\,(b - r(t))dt\,+\,\sigma d W(t), \qquad (Vas.1)$

where $W(t)$ is a standard Wiener process under $Q$. The terms $a$ and $b$ are, respectively, mean reversion speed and mean reversion level of the short rate.

Simple integration of equation (Vas.1) from time $s$ to $t$ ($0 \leqslant s \leqslant t$) yields

$r(t) = r(s)e^{-a(t-s)}+ a\,b \int_s^t e^{-a(t-u)}du +\sigma \int_s^t e^{-a(t-u)} dW(u)$
$= r(s)e^{-a(t-s)}+ b (1- e^{-a(t-s)}) +\sigma \int_s^t e^{-a(t-u)} dW(u), \qquad (Vas.2)$

From Equation (Vas.2), we can obtain the first two conditional moments of the short rate $r(t)$ for the Vasicek(1977)[1] model:

$\mathbb{E} \left [ r(t)\mid r(s) \right ]= r(s)e^{-a(t-s)}+ b (1- e^{-a(t-s)}), \qquad (Vas.3)$
$Var \left [ r(t)\mid r(s) \right ]= \frac {\sigma^2}{2a} (1-e^{-2a(t-s)}). \qquad (Vas.4)$

The price of a zero-coupon bond at time $t$ with maturity time $T$ is

$P(t,T)= \mathbb{E}^Q \left [e^{-\int_t^T r(u)du} \mid \mathcal{F}_t \right ], \qquad (Vas.5)$

where $\mathbb{E}^Q \left [ \, \right ]$ is taken with respect to the risk-neutral measure $Q$.

Because the noise part is additive in equation (Vas.1), the distributional properties of $\int_t^T r(u) dt$ are known. From the fundamenatal pricing relation in equation (Vas.5), zero-coupon bond price as the risk-neutral expectation of a functional of the short rate can be calculated analytically, this is what we turn to next.

To obtain an analytic solution of the zero-coupon bond price, we first evaluate the following Ito integral

$\int_t^T r(u)du$
$= \int_t^T r(t) e^{-a(u-t)}\,du\,+\,b\, \int_t^T (1-e^{-a(u-t)})\,du \,+\,\sigma \int_t^T \int_t^u e^{-a(u-s)}\,d W(s)\,du$
$= r(t) \frac { 1-e^{-a(T-t)} } {a}\,+\,b\, [T\, -\, t \,-\, \frac {1-e^{-a(T-t)}}{a}]\,+\,\sigma \int_t^T \int_t^u e^{-a(u-s)}\,d W(s)\,du. \qquad (Vas.6)$

The conditional expectation of the Ito integral $\int_t^T r(u)du$ is:

$\mathrm{E} \left [ \int_t^T r(u)du \mid \mathcal{F}_t \right ] =r(t) \frac { 1-e^{-a(T-t)} } {a}\,+\,b\, [T\, -\, t \,-\, \frac {1-e^{-a(T-t)}}{a}]. \qquad (Vas.7)$

The conditional variance of $\int_t^T r(u)du$ is calculated as follows:

$Var \left [ \int_t^T r(u)du \mid \mathcal{F}_t \right ]$
$= Var \left [ \sigma \int_t^T \int_t^u e^{-a(u-s)} d W(s)\,du \mid \mathcal{F}_t \right ]$
$= \mathrm{E} \left [ \left ( \sigma \int_t^T \int_s^T e^{-a(u-s)} du\,dW(s) \mid \mathcal{F}_t \right )^2 \right ]$
$= \sigma^2 \int_t^T \left [ \int_s^T e^{-a(u-s)} du \right ]^2 \,ds$
$= \sigma^2 \int_t^T \left [ \frac {1-e^{-a(T-s)}}{a} \right ]^2 \,ds$
$= \frac {\sigma^2}{a^2} \int_t^T \left [ 1 \,+\,e^{-2a(T-s)}\,-\,2 e^{-a(T-s)} \right ] \,ds$
$= \frac {\sigma^2}{a^2} \left [T\,-\,t\,+\, \frac {1-e^{-2a(T-t)}}{2a} \,-\,2 \frac {1-e^{-a(T-t)}}{a} \right ], \qquad (Vas.8)$

where in the second equality we have used Fubini's theorem for change of integrals, and the third equality follows from Ito isometry.

Using the pricing relation in equation (Vas.5) and the properties of lognormal random variables, we have

$P(t,T)= \mathbb{E}^Q \left [ e^{- \int_t^T r(u)du} \mid \mathcal{F}_t \right ]$
$= e^{ \mathrm{E} \left [ - \int_t^T r(u)du \right ] \,+\, \frac {1}{2} Var \left [ -\int_t^T r(u)du \right ] }, \qquad (Vas.9)$

plugging in equations (Vas.7) and (Vas.8) into equation (Vas.9), and simplifying, we have the following solution for equation (Vas.5)

$P(t,T)=A(t,T)e^{-B(t,T)r(t)}, \qquad (Vas.10)$

where

$B(t,T)=\frac{1-e^{-a(T-t)}}{a},\!$

and

$A(t,T)=\exp{ \left( \frac{ (B(t,T)-T+t)(a^2b-\sigma^2/2)}{a^2} - \frac{\sigma^2B(t,T)^2}{4a} \right) }.$

## The Vasicek model implemented in ThetaML

The Vasicek model[1] implemented in ThetaML is given below:

model vasicek
%This model simulates short rates with Vasicek dynamics
%Example input parameters:
%a = 1.5, b = 0.1, sigma = 0.2, r0 = 0.03, t = 1, ht = 1/12
import a      "Mean reversion speed"
import b      "Mean reversion level"
import sigma  "Short rate volatility"
import r0     "Initial short rate"
import t      "Simulation time horizon"
import ht     "Discretization time step"
export r      "Simulated future short rates"

r = r0        %initialize the short rate at time 0
%a fixed loop that loops t/ht times
loop t/ht
%the ThetaML command 'theta' advances time by ht step
theta ht
%sample a Gaussian random variable
dz = sqrt(ht)*randn()
%update the increments of short rate
dr = a*(b - r)*ht + sigma*dz
%short rate at this model time
r = r + dr
end
end

## References

1. Vasicek, Oldrich A. 1977. An equilibrium characterization of the term structure. Journal of Financial Economics 5.


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# code to convert ADC value to hex?

#### HappyC4mper

Joined Oct 13, 2017
71
Hey guys, im a bit stuck atm in trying to convert my ADC data to hex values so that it can show up on terminal (ive already made a code for terminal).
I've found this code and added it to my code but I don't really understand how the code works or how it converts. If someone could somehow explain it to me or if there's a simpler way of doing it, that would great!
Thanks
[send_usart is me sending it to terminal. ]

Code:
void ADC_Hex_USART (float readadc)
{
unsigned  char Index_Counter =0;  // not sure what this does
char Hex_decimal[16];
printf(Hex_decimal, "Volts = %.3f", Voltage_Value);
while(Hex_decimal[Index_Counter] != '\0')    //not sure what !='\0' does as well.
{
send_usart(Hex_decimal[Index_Counter]);
Index_Counter++;
}

#### MrChips

Joined Oct 2, 2009
23,576
If you already have printf( ) in C there is nothing else you need.
Simply use:

printf("Hex value = %4X\n", value);

#### HappyC4mper

Joined Oct 13, 2017
71
If you already have printf( ) in C there is nothing else you need.
Simply use:

printf("Hex value = %4X\n", value);
so there's no need for Index_counter?
Code:
 unsigned  char Index_Counter =0;

#### AlbertHall

Joined Jun 4, 2014
11,318
Lines 7 and 9 use index_counter to loop through all the characters and send them to the usart. The '/0' bit is looking for the nul character which trerminates C strings to know when to stop sending characters.

so there's no need for Index_counter?
Code:
 unsigned  char Index_Counter =0;
Not if you can persuade printf to send the message to usart.

#### HappyC4mper

Joined Oct 13, 2017
71
Lines 7 and 9 use index_counter to loop through all the characters and send them to the usart. The '/0' bit is looking for the nul character which trerminates C strings to know when to stop sending characters.

Not if you can persuade printf to send the message to usart.
turns out, my orginial code does not work with printf.
I therefore wrote this, not sure if it's right, but I don't know how to send it to my usart (send_usart()
Code:
void Read_usart()
{
unsigned short Hex;
Hex    = read_adc();    // Get ADC result and store in HEX
printf("\n\r");        // Send out a space
printf("Hex value = %4X\n", Hex);

#### MrChips

Joined Oct 2, 2009
23,576
We had this question recently on how to redirect the stdio.h output. You need in supply your own putc( ) rountine.
I will have to dig this up.

#### MrChips

Joined Oct 2, 2009
23,576
What MCU are you using and what programming platform (IDE or toolset)?

#### HappyC4mper

Joined Oct 13, 2017
71
What MCU are you using and what programming platform (IDE or toolset)?
Using a nucleo-f429ZI and using KEIL to code

#### HappyC4mper

Joined Oct 13, 2017
71
Code:
unsigned short read_adc(void)
{
return ADC1->DR;                                    //return converted value
}

#### HappyC4mper

Joined Oct 13, 2017
71
If not, we can help you further.

I forgot to mention, that i copy and pasted this printf function into my main.c file so i was able to use printf in my other functions.
Code:
/////////////////////////PRINTF///////////////////////////////
///////////////////RETARGETTING PRINTF///////////////////////
#pragma import(__use_no_semihosting)
struct __FILE { int handle; };
FILE __stdout; // used for output – printf()
FILE __stdin; // used for input – getchar()
void _sys_exit(int x)
{ x = x; }
int fputc(int ch, FILE *f){
putLCD((uint8_t) ch);
return ch;
}
This code was given for me to use, but no explanation was given. However, I'm still not too sure how to get my ADC data to print into usart terminal (putty)

#### MrChips

Joined Oct 2, 2009
23,576
I forgot to mention, that i copy and pasted this printf function into my main.c file so i was able to use printf in my other functions.
When you say "i was able to use printf in my other functions"
where did the output appear?

Show us an example of the printf( ) statement that worked for you.

#### HappyC4mper

Joined Oct 13, 2017
71
When you say "i was able to use printf in my other functions"
where did the output appear?

Show us an example of the printf( ) statement that worked for you.
I was converting ADC to voltage
using this function
Code:
void realVoltage ()

{

cmdLCD(LCD_LINE1);
float voltage = (ADC_DATA*(3.3/4096));   //conversion adc to voltage conversion
printf( "Volts = %.3f", voltage);        //printing to lcd
That was reading to an LCD. Which has a max voltage of 3.3, using a potometer to change the voltage. So line 1 which is the code above displays my voltage. And line 2 displays a progression bar (which will be my next step in putting to terminal.)

#### MrChips

Joined Oct 2, 2009
23,576
If I understand this correctly, your working program puts out the data to a 2x16 character LCD.
Now, you want to see the hex data on a PC screen via puTTY.

You will need a USB-to-UART bridge such as a CP2102.
Then I can show you how to proceed. This is also covered in the AAC thread I posted in post #10.

#### HappyC4mper

Joined Oct 13, 2017
71
If I understand this correctly, your working program puts out the data to a 2x16 character LCD.
Now, you want to see the hex data on a PC screen via puTTY.

You will need a USB-to-UART bridge such as a CP2102.
Then I can show you how to proceed. This is also covered in the AAC thread I posted in post #10.
You are correct!
Do i need to convert my values to Hex for it to show up on puTTy? Since all I'm trying to do is to get the values and my progression bar to show up on puTTY.

#### MrChips

Joined Oct 2, 2009
23,576
You are correct!
Do i need to convert my values to Hex for it to show up on puTTy? Since all I'm trying to do is to get the values and my progression bar to show up on puTTY.
No. I was going to ask "why do you want to show the data in hex?".
You can replicate your LCD presentation or you can display the data in any format you choose, within reason.

#### HappyC4mper

Joined Oct 13, 2017
71
No. I was going to ask "why do you want to show the data in hex?".
You can replicate your LCD presentation or you can display the data in any format you choose, within reason.
No wonder, as i've seen other people using sprintf and they had to convert to hex which confused me a bit. Which is why I tried to replicate.
But yes, what I'm trying to do is replicate what I'm getting from my LCD , to show up on puTTY.
would want this-
Code:
void realVoltage ()
{
cmdLCD(LCD_LINE1);
float voltage = (ADC_DATA*(3.3/4096));   //conversion adc to voltage conversion
printf( "Volts = %.3f", voltage);        //printing to lcd
and this to show up-
Code:
void CustomChar (float q)   //analogue signal. (q is adcvalue)
{
float divider = 255;    //3.3V represented by 16 character spaces (4096/16)
int sum = q/divider;

cmdLCD(LCD_LINE2);
for(int i = 0; i< 16 ; i++)
if(i<=sum)
{
putLCD(0xFF);
}
else putLCD(' ');
}

#### MrChips

Joined Oct 2, 2009
23,576
Next question.
What advantage is it to you to be able to replicate the same information on a PC screen if your LCD is working properly?

#### HappyC4mper

Joined Oct 13, 2017
71
Next question.
What advantage is it to you to be able to replicate the same information on a PC screen if your LCD is working properly?
I need to be able to get this working so I could get my DAC to generate square/triangle and sine waves by pressing a switch. It's just a project I'm trying to do.

#### MrChips

Joined Oct 2, 2009
23,576
I need to be able to get this working so I could get my DAC to generate square/triangle and sine waves by pressing a switch. It's just a project I'm trying to do.
That doesn't answer my question.
Where is the DAC?
Where is the switch?

format: plain


text:
# MMGR compilation problems

## Recommended Posts

I'm trying to use MMGR in my code. I've read the -DOC- stuff but can't find anything relating to this issue. Upon compiling with VC++ 6.0 professional edition I get the following errors: C:\Program Files\Microsoft Visual Studio\VC98\INCLUDE\malloc.h(105) : warning C4002: too many actual parameters for macro 'calloc' C:\Program Files\Microsoft Visual Studio\VC98\INCLUDE\malloc.h(105) : error C2059: syntax error : 'string' C:\Program Files\Microsoft Visual Studio\VC98\INCLUDE\malloc.h(106) : error C2062: type 'void' unexpected C:\Program Files\Microsoft Visual Studio\VC98\INCLUDE\malloc.h(107) : error C2059: syntax error : 'string' C:\Program Files\Microsoft Visual Studio\VC98\INCLUDE\malloc.h(108) : error C2059: syntax error : 'string' but only when I #include mmgr.h the offending lines in malloc.h are:
/* Function prototypes */

_CRTIMP void *  __cdecl calloc(size_t, size_t);
_CRTIMP void    __cdecl free(void *);
_CRTIMP void *  __cdecl malloc(size_t);
_CRTIMP void *  __cdecl realloc(void *, size_t);

but I doubt that malloc.h is the problem. I don't know what's going on at all here. Can someone help please? edit: also my program isn't using mfc. It's a modified version of the NeHe OpenGL basecode. If compiler settings will help they are standard release mode settings with the following libraries linked: opengl32.lib glu32.lib glaux.lib kernel32.lib user32.lib gdi32.lib winspool.lib comdlg32.lib advapi32.lib shell32.lib ole32.lib oleaut32.lib uuid.lib odbc32.lib odbccp32.lib compiling in debug mode also causes the same problem

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If you get this even with a small test app, could you post that app here (the source)?

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I've just tried it like you suggested (using the basecode & lesson5.cpp) & it all worked correctly. So I know it's something to do with my code. The thing is though I haven't used malloc or calloc anywhere myself, so I don't get what's causing this problem, especially as it's compiling correctly without mmgr.

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DrewGreen,

You need to doublecheck that your includes are setup right. Remember that you want to include all files found in the compiler directories first, then the mmgr.h, then your includes for your project. I'm 99.9% sure that that is the reason your getting errors.

Hope that helps!

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Yep, I've done that. As I say, I did bother to RTFM :)

#include <windows.h>#include <stdio.h>#include <gl\gl.h>#include <gl\glu.h>#include <gl\glaux.h>#include "mmgr.h"#include "GLEXT.h"#include "FrameTimer.h"#include "NeHeGL.h"#include "MilkshapeModel.h"#include "base.h"#include "Game.h"

I tried a couple other position combinations, such as swapping mmgr.h with GLEXT.h but it made no difference

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The problem I'm always facing is that those headers you're including after mmgr.h can not include any standard headers. This plays havoc with templates using stl containers; there's no way to correctly include them using mmgr.

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^ Actually yeah I've checked the #includes in the other files & it looks like I can't avoid this then :/

Can someone recommend an alternative to MMGR? It would be nice to be able to detect leaks etc.

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What you need to do is always follow this pattern in your files:

#include "nommgr.h"//system includes#include "mmgr.h"//your includes

Edit: sorry pressed post to quickly...

nommgr.h will undefine all macros that the memory manager uses for system includes and then mmgr.h will enable them again for your files. I have my whole project set up like this and it seems to work fine. Just make sure you dont edit the mmgr files often - having every file in your program recompiled is murder.

I had to run MMGR on an amd64 and a nice standard compilant compiler (gcc) and got lots of compiler warnings etc (mmgr used fairly C:ish syntax), it also didnt work at all on amd64 since it for some reason assumed longs to always be 4 bytes. There was also some versions of new/delete from the newer c++ standard that was missing.
If anyone is interrested I can put up the modified code somewhere.

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Quote:
 Original post by DrewGreenCan someone recommend an alternative to MMGR? It would be nice to be able to detect leaks etc.

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rollo: ah so that is what the nommgr.h file is for. Never figured that one out :D

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# Why don't the black holes appear black in color in images of galaxies taken from HST?

According to NASA

a black hole is anything but empty space. Rather, it is a great amount of matter packed into a very small area

According to the documentary Space Unraveling The Cosmos about Black Holes

Gravity here is so strong even light cannot escape

Which leads me to believe that Black Holes basically are masses so compact but great which gives them very strong gravitational influence (Newton's Gravitational Law) that light is not allowed to go out of, hence a "Black" hole.

If my above understanding of Black Holes is correct, then why is those Spiral Galaxies pictured using Hubble Telescope is showing a big shiny ball instead of a "Black" hole ? What is the obvious clue that I am missing here ?

Here is the image of Andromeda Galaxy image taken using Hubble.

-
At a very basic level of explanation, despite the holes being "prefectly black", there are many stars orbiting them. Centers of spiral galaxies tend to have relatively high concentrations of massive, young starts, which is why they are usually the brightest regions in such galaxies. –  Renan Jul 25 at 19:00
–  Renan Jul 25 at 19:01
Check chapter 7 Black Holes Ain't So Black of the book A Brief History of Time: From the Big Bang to Black Holes. –  metacompactness Jul 25 at 20:48

A typical giant galaxy, such as the one you've provided a picture of, has a radius of something like $10\;\rm kpc$ (kiloparsec - $1\;\rm pc \approx 3.2\;ly$).

A supermassive black hole hosted in such a galaxy has a mass of something like $10^6-10^9\;\rm M_\odot$ (solar mass, $1\;\rm M_\odot \approx 2\times10^{30}\; kg$). The monstrous billion solar mass black holes are really only found in particularly large ellipticals; the galaxy in your photo probably hosts one of about one to a few million solar masses. The horizon radius of such a black hole will be on the order of the Schwarzschild radius, so:

$$r_s=\frac{2GM}{c^2}\approx10^{-10}\rm\; kpc$$

So the supermassive black hole is something like 100 billion times smaller in radius than the galaxy, way way WAY smaller than a pixel in a picture like the one you show.

Furthermore, there are a lot of stars in the central region of a galaxy and many will be close (or roughly in front of) the black hole, not to mention clouds of intragalactic gas that may obscure the view to the black hole.

That said, it is becoming possible using very long baseline interferometry to take "pictures" of a couple of nearby black holes. I don't think there are any successful images yet, but we'll probably get some in the next 3 years or so using the Event Horizon Telescope. A prediction of what will be seen:

The formation of the image is quite complicated (the paper I link later gives a lot of the gory detail if you're interested). First, note that this is in "false colour", the colour indicates the intensity of the radiation from blue (low) to white (high). The photons come from a disk hot gas ("accretion disk") that is expected to be found near many black holes. Those in the picture are those which happen to approach the black hole, but do not enter it. Because of the curvature of spacetime, photons can orbit the hole and accumulate in these "photon orbits". The orbits occur a few Schwarzschild radii from the hole. The orbits aren't stable, so some photons eventually plunge into the hole, while others escape away - these are the ones in the picture. The strong asymmetry in the image (while you'd expect a BH to be very symmetric) is due to the fact that the source of the light (the accretion disk) is not spherically symmetric, and only approximately axially symmetric - it may be warped, have bright and dim spots, etc. One side of the image is brighter because typically one side will be relativistically beamed toward us while the other will be beamed away. This is as close to a black hole "looking black" as we're likely to get. There are photons orbiting across the "face" of the hole in the picture, but none make it to us from that direction, so the hole appears black in the image.

One paper I particularly enjoyed reading about the more theoretical aspects of these black hole images: Testing the no-hair theorem with event horizon telescope observations of Sagittarius A*. It includes more simulated images at resolutions more like what we'll realistically achieve with the EHT.

-
How does this picture change, if at all, when the black hole is surrounded by other matter? As material accelerates rapidly toward the event horizon, wouldn't radiation be generated by the collisions among similarly ill-fated particles? Could that radiation reach us, and would it occlude the "black" part in your predictive image? –  Aaron Novstrup Jul 25 at 23:16
@AaronNovstrup The (inner edge of the) accretion disk itself is necessarily at larger radii than the photon orbit, but that doesn't prevent the disk from lying across the hole in projection, and this could indeed obstruct the view, much like intervening stars or gas clouds. However, I'm not sure on the expected emission wavelengths for each bit and the opacities - you might be able to see the ring emission through (certain parts of?) the accretion disk while filtering out the disk itself. The emission and scattering in the vicinity of a black hole is really quite a mess. –  Kyle Jul 25 at 23:24
Note that google says to me that 10^-10 kpc is about 2M miles or 3M kilometers. There are cars that have driven that distance. 10^-10 kpc is about 10 light seconds (compare 100,000 light years for a diameter of a galaxy). The scale of 'kpc' can sometimes confuse or mislead a non-astronomer who has difficulty putting it into other terms. –  MichaelT Jul 26 at 1:18


text:
I like knowing what’s happening on my home network, especially with how many things I have that I rely on (PiHole, Home-Assistant, etc). One thing I’ve been missing is the ability to check for unwanted visitors. I want to know if someone is trying to get into my network, log their ip, and ban them. Ultimately, there are two areas I want to prevent traffic:

• Home Assistant frontend
• SSH

Luckily, both of these tasks can be solved by using fail2ban

## Setting Up fail2ban for SSH

First we will want to install the service:

$sudo apt-get install fail2ban  Next, we need to create the /etc/fail2ban/fail2ban.local file with the following contents: [Definition] logtarget = SYSLOG  After that, we need to create the /etc/fail2ban/jail.local file whose contents should be: [ssh] enabled = true port = ssh filter = sshd logpath = /var/log/auth.log maxretry = 5  At this point, once we start the fail2ban service, we should be set and fail2ban will auto-ban IPs for us on failed SSH login attempts. But I also want to be able to ban IPs trying to log into my Home Assistant front-end… ## Setting up fail2ban with Home Assistant I mostly took these instructions from this page with a couple small modifications. First, we need a filter to parse the home-assistant log and check for authorized login attempts. This is done by creating the /etc/fail2ban/filter.d/hass.local file with the following contents: [INCLUDES] before = common.conf [Definition] failregex = ^%(__prefix_line)s.*Login attempt or request with invalid authentication from <HOST>.*$

ignoreregex =

[Init]
datepattern = ^%%y-%%m-%%d %%H:%%M:%%S

The next step is to edit the /etc/fail2bain/jail.local file we created earlier and add the following:

...
[hass-iptables]
enabled = true
filter = hass
action = iptables-allports[name=HASS]
logpath = /home/hass/.homeassistant/home-assistant.log
maxrety = 5

You’ll need to replaced the logpath with the location of you log within your home-assistant installation.

Now we can enable and start fail2ban:

$sudo systemctl enable fail2ban$ sudo systemctl start fail2ban

## Integrate into Home Assistant

Right now, fail2ban operates in the background and logs any failed attempts to /var/log/syslog. We can see failed Home Assistant attempts by looking that the log, but ssh attempts are transparent. We can change this though.

What I want is a sensor that I can display on my frontend showing any failed SSH or Hass attempts and also receive a notification with a timestamp when this happens. I do this via a combination of the command line sensor, file sensor, and notify service. Really, you could eliminate the file sensor altogether and do all of this within the command line sensor, but I found it to be more managable running a command, generating a json file, and using the file sensor to display the results.

### Command-Line Sensor

The first thing I want to do is parse the syslog file and only operate on the parts I care about. I can do all of this in a python script (which we’ll need to generate the json file used in the sensor.file component) but I opted for a bash script.

To start, create a file under .homeassistant/bin called gen_ban_list.sh.

First, we need to find all the fail2ban entries in syslog and only dump the Ban/Unban events to a file:

#### Parse syslog

more /var/log/syslog | grep fail2ban | grep WARNING > /home/hass/.homeassistant/ip_ban_list.log

Right now, a ‘ban’ entry will loog something like:

Aug  8 12:34:26 raspberrypi fail2ban.action[6341]: WARNING [ssh] Ban 111.222.12.100
Aug  8 12:34:26 raspberrypi fail2ban.action[6341]: WARNING [hass-iptables] Ban 111.222.12.100

Those entries have a lot of useless information, so we need to strip this out. I use sed with some regular expressions.

#### Prepare File for Processing

First, let’s get rid of the string starting from raspberrypi all the way through WARNING:

sed -i 's/raspberrypi fail2ban\.actions$[^]]*$: WARNING//g' <FILE>

If you’re unfamiliar with regular expressions, the format is simple: s/FIND/REPLACE/g which in plain English would translate to something like:

Search the file and globally replace entries matching ‘FIND’ with ‘REPLACE’

Any time you see \ in front of a character, it indicates the character is being escaped (which means we’re literally looking for it within the string). The $[^]]*$ sequence is saying replace anything inbetween brackets [ ] including the brackets.

Now our strings should look like this:

Aug  8 12:34:26 [ssh] Ban 111.222.12.100
Aug  8 12:34:26 [hass-iptables] Ban 111.222.12.100

Next thing we can do is get rid of the brackets around the ban identifiers ssh and hass-iptables:

sed -i 's/$//g;s/$//g' <FILE>

The final thing is removing any pesky double-spaces via sed -i 's/ / /g'. The reason for this will become clear when we get to the python step. Ultimately, we can combine the above steps into a one-line expression:

sed -i 's/raspberrypi fail2ban\.actions$[^]]*$: WARNING//g;s/$//g;s/$//g;s/  / /g' /home/hass/.homeassistant/ip_ban_list.log

#### Convert File to json

Now we can use a small python script to take that log file and turn it into a json file that can be used with the file sensor in Home Assistant. Create a file called read_ban_list.py in your .homeassistant/bin directory. In it, paste the following code:

'''
Author: Kevin Fronczak
https://kevinfronczak.com

Reads a ban list assuming the following structure:
[Month] [Day] [HH:MM:SS] [iptable] [Type=Ban/Unban] [ipAddress]
'''
import sys
import json

FILE = sys.argv[1]
JSON_FILE = sys.argv[2]

DATA = {'ssh': [], 'hassiptables': []}

with open(FILE) as fh:

''' Get Banned IPs '''
for line in banlist:
line_split = line.split(' ')
ban_type = ''.join(line_split[3].split('-'))
ban_ip = line_split[5].strip()
if ban_type not in DATA.keys() and line_split[4] == 'Ban':
DATA[ban_type] = list()
if ban_ip in DATA[ban_type] and line_split[4] == 'Unban':
DATA[ban_type].remove(ban_ip)
else:
DATA[ban_type].append(ban_ip)

''' Replace empty ban list with "None" '''
for key, value in DATA.items():
if not value:
DATA[key] = "None"
else:
DATA[key] = ','.join(value)

''' Write to JSON file for HASS processing '''
with open(JSON_FILE, 'w') as fp:
json.dump(DATA, fp)

Now, back in your gen_ban_list.sh script, add the following entry:

python3 /home/hass/.homeassistant/bin/read_ban_list.py '/home/hass/.homeassistant/ip_ban_list.log' '/home/hass/.homeassistant/ip_ban_list.json'

Finally, we need to remove the ip_ban_list.log file:

rm /home/hass/.homeassistant/ip_ban_list.log

#### Putting it All Together

Your final gen_ban_list.sh script should look like the following:

more /var/log/syslog | grep fail2ban | grep WARNING > /home/hass/.homeassistant/ip_ban_list.log
sed -i 's/raspberrypi fail2ban\.actions$[^]]*$: WARNING//g;s/$//g;s/$//g;s/  / /g' /home/hass/.homeassistant/ip_ban_list.log
rm /home/hass/.homeassistant/ip_ban_list.log

### Creating the Command Line sensor

Now that we have our command, we can create the command-line sensor. In your homeassistant configuration.yaml you need to add the following entry:

sensor:
- platform: command_line
name: ip_ban
command: bash /home/hass/.homeassistant/bin/gen_ban_list.sh
scan_interval: 120

This will run the gen_ban_list.sh script every two minutes.

## File Sensor

The reason we went through all of the trouble in processing the syslog file and dumping to json, was to make this step very easy (and very scalable). The way everything has been set up allows for an arbitrary number of file sensor entries that every command and script will be able to use (i.e. this method is not exclusive to SSH and hass-iptable bans!).

Add the following entries to your configuration.yaml to create sensor.ssh_bans and sensor.hass_bans:

sensor:
- platform: file
file_path: /home/hass/.homeassistant/ip_ban_list.json
name: SSH Bans
value_template: '{{ value_json.ssh }}'
- platform: file
file_path: /home/hass/.homeassistant/ip_ban_list.json
name: Hass Bans
value_template: '{{ value_json.hassiptables }}'

Finally, to receive a notification whenever an IP has been banned, you can add the following automation which will tell you the type of ban (ssh/hass) as well as the IP or IPs that were banned and the timestamp.

alias: Notify on Failed Login
trigger:
- platform: state
entity_id: sensor.ssh_bans
- platform: state
entity_id: sensor.hass_bans
condition:
condition: or
conditions:
- condition: template
value_template: '{{ states.sensor.ssh_bans.state != "None" }}'
- condition: template
value_template: '{{ states.sensor.hass_bans.state != "None" }}'
action:
- service: notify.notify
data_template:
message: >
Failed Login! {{ now().strftime("%h %d, %Y at %H:%M:%S") }}
{% if states.sensor.ssh_bans.state != "None" %}
SSH Attempt(s) from {{states.sensor.ssh_bans.state}}
{% endif %}
{% if states.sensor.hass_bans.state != "None" %}
Web Attempt(s) from {{states.sensor.hass_bans.state}}
{% endif %}

## Final Thoughts

Perhaps there’s a cleaner way to implement this (such as using the command line sensor only) but this is working reliably for me and is relatively easy to maintain. My actual implementation differs somewhat from what I’ve listed, but you can check it out on my GitHub Page where I have my whole Home Assistant configuration.


text:
# Class 10 Magnetic effects of current Extra Questions

## One marks questions

Question 1 If the current in a wire is flowing in the vertically downward direction and a magnetic field is applied from west to east, what is the direction of force on the wire?

Question 2 When do we apply Flemings (i) Left hand (ii) Right hand rule.>

Question 3 How much force is exerted by a magnetic field on a stationary charge?

Question 4  A positive charge is moving vertically upwards, when it enters a region of magnetic field directed toward north, what is the direction of force on the charge?

## Two marks questions

Question 5  Two circular coils A and B are placed closed to each other. If the current in the coil A is changed, will some current be induced in the coil B? Give reason.

Question 6  State the principle of an electric generator.
Question 7  What is the function of a split ring in an electric motor?
Question 8  (a) Why do we connect earth wire in a house? Give two reasons.
(b) What type of current is used in house hold supply and what type of current is given by a cell?

Question 9  To which wire do you connect fuse wire in a house hold circuit? Write name of one source of AC current and one source of DC current.

## Three marks questions

Question 10  (a) Define the term current rating of an electric fuse?
(b) Name the material used to make electric fuse?
(c) Name two safety measure commonly used in electric circuit and appliances?

Question 11  Draw a labelled diagram of an electric motor. Explain its principle and working.
Question 12  A coil made of insulated copper wire is connected to a galvanometer. What will happen to the deflection of the galvanometer if bar magnet is pushed into the coil and then pulled out of it. Give reason for your answer and the phenomenon involved.

Given below are the links of some of the reference books for class 10 Science.

You can use above books for extra knowledge and practicing different questions.

### Practice Question

Question 1 Which among the following is not a base?
A) NaOH
B) $NH_4OH$
C) $C_2H_5OH$
D) KOH
Question 2 What is the minimum resistance which can be made using five resistors each of 1/2 Ohm?
A) 1/10 Ohm
B) 1/25 ohm
C) 10 ohm
D) 2 ohm
Question 3 Which of the following statement is incorrect? ?
A) For every hormone there is a gene
B) For production of every enzyme there is a gene
C) For every molecule of fat there is a gene
D) For every protein there is a gene

Note to our visitors :-

Thanks for visiting our website.


text:
# Free Curve Calculator

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# Existence of non-constant bounded analytic function on $\mathbb{C}\setminus \mathbb{Z}$

Show that there is no non-constant bounded analytic function on $\mathbb{C}\setminus \mathbb{Z}$.

In this homework problem i tried to proceed in the following way: If possible, let $f$ be a non-constant bounded analytic function on $\mathbb{C}\setminus \mathbb{Z}$. Define $F(z)=0$ if $z\in \mathbb{Z}$ and $f(z)$ otherwise. Then $F$ is analytic on $\mathbb{C}$, i.e., $F$ is entire and also by construction it is bounded. Then by Liouville's theorem $F$ is constant. Which in turn would mean that $f$ is constant. Which is a contradiction.

Am i correct? Can i define such a function $F$? I would be more than happy to get a feedback and if i am incorrect please hint me an idea to proceed. Thanks in advance.

• You can't blindly set $F(z)=0$ at $z \in \mathbb{Z}$ and expect $F$ to be analytic, almost always this won't even produce a continuous function. – Omar Antolín-Camarena May 22 '14 at 21:54
• Hint: what kind of singularity has $f$ at $0$? – Daniel Fischer May 22 '14 at 21:56
• What kinds of singularities do you know? Which kinds can be excluded by the conditions on $f$? – Daniel Fischer May 22 '14 at 22:05
• What do you know about the behaviour of a holomorphic function near an essential singularity? – Daniel Fischer May 22 '14 at 22:16
• What do you know about the mapping behaviour? Does Casorati-Weierstraß ring a bell? – Daniel Fischer May 22 '14 at 22:30


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Is the reversal of a minimal DFA also minimal?

The question is pretty much in the title. Is there ever a time where some language $L$ can be accepted by a minimal DFA with $n$ states, but $L^R$, the reversal of $L$, can be accepted by a DFA with $m$ states, where $m<n$?

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The reverse of a DFA is not even necessarily deterministic. A DFA that accepts the regex AAA+ has a terminal state with two inbound arrows with the same label. – Ian May 8 '14 at 5:47

The minimal DFA accepting the reversal of the language can be smaller. Consider the finite language $$L = (0+1)^22+(0+2)^21+(1+2)^20.$$ The words $\epsilon,0,1,2,00,01,02,11,12,22,000,001$ are inequivalent, so any DFA for $L$ requires at least 12 states; in fact there is a DFA with exactly 12 states. The reverse language $$L^R = 2(0+1)^2 + 1(0+2)^2 + 0(1+2)^2$$ is accepted by a DFA with only 9 states: an initial state, states corresponding to initial $0,1,2$, states corresponding to initial $0(1+2),1(0+2),2(0+1)$, an accepting state and a fail state; this is also the optimal DFA, since $\epsilon,0,1,2,01,12,20,011,000$ are inequivalent.

Summarizing, the minimal DFA for $L$ requires 12 states, while the one for $L^R$ requires only 9 states.

As jmite mentions in their comment, for NFAs with multiple starting states this phenomenon can't happen, since if you flip the direction of all arrows in a NFA for $L$ then you get a valid NFA for $L^R$.

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Thanks! I somehow got it in my head that you could reverse a DFA and (directly) get a DFA back, I think I got it confused with complement. – jmite May 7 '14 at 20:22
@jmite I had the same brain fart, and typed out an elegant proof by contradiction of the wrong answer. :) It's complement that works like I thought, not reversal. Oops. – Patrick87 May 7 '14 at 20:51


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Home > Sampling Error > Sampling Error Standard Error Difference

# Sampling Error Standard Error Difference

You'll find videos on the most popular topics. The SD will get a bit larger as sample size goes up, especially when you start with tiny samples. tickersu Oct 22nd, 2015 3:32pm 1,314 AF Points kuromusha wrote: @bchad Regarding to standard error, does it have to be SD of a sample mean? If people are interested in managing an existing finite population that will not change over time, then it is necessary to adjust for the population size; this is called an enumerative his comment is here

The distribution of these 20,000 sample means indicate how far the mean of a sample may be from the true population mean. This is usually the case even with finite populations, because most of the time, people are primarily interested in managing the processes that created the existing finite population; this is called How to draw and store a Zelda-like map in custom game engine? Published online 2011 May 10.

We know that if we draw samples of similar sizes, say N as in the sample of interest above, from the population many times (eg, n times), we will obtain a Essentially, its the difference that results in inherent differences between the sample and population. I will predict whether the SD is going to be higher or lower after another $100*n$ samples, say. Sample 1. σ22 = Variance.

For each sample, the mean age of the 16 runners in the sample can be calculated. The standard deviation of the sample becomes closer to the population standard deviation but not the standard error. ENN home Field Exchange Nutrition Exchange en-net Our work Resources Facebook Twitter Change language: English Français Log in to en-net Create account What is the difference between sampling error and standard In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the

The 95% confidence interval for the average effect of the drug is that it lowers cholesterol by 18 to 22 units. and Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. 187 ^ Zwillinger D. (1995), Standard Mathematical Tables and Formulae, Chapman&Hall/CRC. If one wishes to provide a description of the sample, then the standard deviations of the relevant parameters are of interest. Moreover, this formula works for positive and negative ρ alike.[10] See also unbiased estimation of standard deviation for more discussion.

All rights reserved. How to search for flights for a route staying within in an alliance? For example, the sample mean is the usual estimator of a population mean. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample.

This is more doable. http://support.minitab.com/en-us/minitab/17/topic-library/basic-statistics-and-graphs/hypothesis-tests/tests-of-means/what-is-the-standard-error-of-the-mean/ All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文（简体）By using this site you agree to the use of cookies for analytics and personalized content.Read our policyOK current community blog chat Cross Validated Cross Validated Meta your communities Assumptions and usage Further information: Confidence interval If its sampling distribution is normally distributed, the sample mean, its standard error, and the quantiles of the normal distribution can be used to When the sampling fraction is large (approximately at 5% or more) in an enumerative study, the estimate of the standard error must be corrected by multiplying by a "finite population correction"[9]

Had you taken multiple random samples of the same size and from the same population the standard deviation of those different sample means would be around 0.08 days. this content The sample mean will very rarely be equal to the population mean. With n = 2 the underestimate is about 25%, but for n = 6 the underestimate is only 5%. When we keep the sampling distribution in mind, we realize that while the statistic we got from our sample is probably near the center of the sampling distribution (because most of

The following expressions can be used to calculate the upper and lower 95% confidence limits, where x ¯ {\displaystyle {\bar {x}}} is equal to the sample mean, S E {\displaystyle SE} Seven samples (3, 11, 29, 39, 54, 59, and 96) have a 95% confidence interval ...Fig. 2The cascade from the distribution of the parameter in the population, to the sampling distribution of So, what you could do is bootstrap a standard error through simulation to demonstrate the relationship. weblink However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and

Now, here's where everything should come together in one great aha! But you would expect that all three samples would yield a similar statistical estimate because they were drawn from the same population. If you plotted them on a histogram or bar graph you should find that most of them converge on the same central value and that you get fewer and fewer samples

## A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample.

How to Calculate a Z Score 4. p. 34.2. Standard Error of the Difference Between the Means of Two Samples The logic and computational details of this procedure are described in Chapter 9 of Concepts and Applications. The data set is ageAtMar, also from the R package openintro from the textbook by Dietz et al.[4] For the purpose of this example, the 5,534 women are the entire population

Indeed, if you had had another sample, $\tilde{\mathbf{x}}$, you would have ended up with another estimate, $\hat{\theta}(\tilde{\mathbf{x}})$. Most people don’t want to take 1000 new samples and plot the histogram, since the whole point of sampling is to reduce the work, so they use a short cut: they The standard deviation of the age for the 16 runners is 10.23. check over here The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.

If symmetrical as variances, they will be asymmetrical as SD. the error (in using the sample mean as an estimate of the true mean) that comes from the fact that you’ve chosen a random sample from the population, rather than surveyed Hyattsville, MD: U.S. See unbiased estimation of standard deviation for further discussion.

The survey with the lower relative standard error can be said to have a more precise measurement, since it has proportionately less sampling variation around the mean. Hoboken, NJ: John Wiley and Sons, Ltd; 2005. There are others, but standard error is, by far, the most commonly used when dealing with survey data. The SD you compute from a sample is the best possible estimate of the SD of the overall population.

deleting folders with spaces in their names using xargs Should I define the relations between tables in database or just in code? Sample 2. σ21 = Variance.