Local central limit theorem far from the center

Let $ X_i$ be a sequence of iid random variables, $ E [X] = 0$ , $ E [X^2] = 1$ and $ E [|X|^k] < \infty$ for some $ k \ge 3$ . Classical local CLT says that the density function $ f_n$ of $ \frac1{\sqrt n}\sum_1^n X_i$ satisfies that $ $ f_n(x) – \phi(x)\left(1 + \sum_{j=1}^{k-2} n^{-\frac j2}P_j(x)\right) = o\left(n^{-\frac{k-2}2}\right), \quad \phi(x) = \frac1{\sqrt{2\pi}}e^{-\frac{x^2}2} $ $ where $ P_j$ is some $ (j + 2)$ -order polynomial, and the RHS is uniformly small for $ x \in R$ .

This gives us very good estimate for constant $ x$ . My question is that can we get a similar expansion equation for $ f_n(\sqrt nx)$ ? Since $ \phi(\sqrt nx)$ decays faster than any polynomial order in $ n$ , we can not apply the local CLT directly.

Remark: I consider this in order to estimating the following expression for $ x \not= 0$ and $ y$ : $ $ \frac1{f_n(\sqrt nx)}f_{n-1}\left(\frac{nx + y}{\sqrt{n-1}}\right), \quad n \text{ sufficiently large}. $ $ When $ x = 0$ by local CLT this is bounded by $ 1 + C(1+y^2)/n + o(1/n)$ . If $ x \not= 0$ , I expect the upper bound $ $ \exp\left\{-\frac{x^2}2 – xy\right\}\left[1 + \frac{C(x^2 + y^2)}n + o\left(\frac1n\right)\right]. $ $

Difference between local and central anti-spam

I’m attending a web security course whose slides, concerning techniques for protecting ourselves from spam, sometimes report the expressions “local anti-spam” (or “personal anti-spam”) and “central anti-spam”.

I suppose the “central anti-spam” is the e-mail provider’s one, but I cannot figure out what can be a local (or personal) anti-spam and which can be the differences about them.

I tried to google such expressions but I didn’t find anything.

Como o android manda um código de alarme para a central de monitoramento?

Estou criando para android um sistema de emergência, um app para se comunicar com a central de monitoramento. Evidentemente deve ser com o contact id Procol.

inserir a descrição da imagem aqui

Como no exemplo acima. Eu achei em How to send a Contact ID alarm to the Central Station from a C# application over VoIP , algo como esperava mas esta para C# não sei nada dessa linguagem para poder fazer uso disso. Contudo, parece não existir conteúdo para Java.

Alguém conhece como faço o android mandar os códigos contact id para a central de monitoramento?

Detalhe, parece que no exemplo que achei ele cria um simuldador de telefone registrando ele na rede e mandando posteriormente a informação. Se é que entendi o processo. Bem, o app vai estar instalado no android, será que isso é necessário mesmo?

Há vários apps para IOS e Android que fazem essa ligação. Como por exemplo o paradox e o da intelbras.

Official Google Webmaster Central Blog: Bye Bye Preferred Domain setting

If you used the preferred domain setting in Google’s Search Console they are removing this setting:


As we progress with the migration to the new Search Console experience, we will be saying farewell to one of our settings: preferred domain…

Bye Bye Preferred Domain setting
June 18, 2019

How do I install from Maven Central?

I’m trying to install this but I’m unfamiliar with Maven and I have no idea how to follow the installation instructions: https://github.com/twosigma/flint (it’s one of those “so basic nobody bothers to state it on the internet” questions)

According to that link “Scala artifact is published in maven central” – so how do I get that thing installed where Spark (and ultimately pyspark) can use it?

For apt it would just be apt-get install xyz
For pip it would just be pip install xyz

so why isn’t mvn install flint working for me?

Using CloudWatch Events as a Central Messaging Hub for a Serverless Architecture

I’ve read recently about using CloudWatch Events as a coordination tool to trigger actions (https://aws.amazon.com/blogs/aws/building-serverless-pipelines-with-amazon-cloudwatch-events/). It seems a clever way to orchestrate various parts of a Serverless architecture where different parts can put custom Events onto the CloudWatch bus and then those Events can trigger other actions. It seems a really interesting idea to have a central repository for actions that can drive actions not just in one account, but potentially in many (see the article for cross-account actions). However, when I thought more about it, I was having a hard time distinguishing between why you’d use this methodology rather than say SQS or SNS or other existing messaging platform. It seems like if you have one service sending Events to the CloudWatch bus, and those then trigger actions, it’s not a whole lot different that sending messages to SNS and then hooking up (for example) a Lambda function to trigger on an SNS-message publication. Or similarly, putting the message in an SQS queue and attaching a Lambda function to automatically trigger against that SQS queue. ¿Any thoughts on what the advantages may be, if any, to using the CloudWatch Events bus as a central messaging system to a Serverless architecture?

What pattern lets each of multiple “voters” decide on a central status?

Imagine there’s a boolean status variable that is either running or stopped.

This variable is running by default and comes together with a deactivator function.

When a client calls the deactivator function, the status changes to stopped.

Calling the deactivator function returns a cancel function, which, when called, reverts the status back to running again.

If multiple clients call the deactivator function, each receives a separate cancel function. As soon as the first client calls the deactivator, the status is stopped and remains so until the last caller to deactivate has called its cancel function.

In other words, every caller can trigger a stopped, and only when no-one is voting stopped, it is running.

What is the name of that pattern?

Update: while I can implement this, I believe it has been done numerous times in the language I use (nodejs), that’s why I’m looking for the name.

Update 2: I’ve implemented this in the meantime, but still looking for a name!

Explanation of the conditions under which the graph of a function f is symmetric relatively to a central point (a,b).

I’m reading a precalculus book telling me that if :

  • f is a function

  • (a,b) is a point

  • t and 2a-t belong to the domain of f

then the grapf of f ( or, more precisely, the curve representing f) is symmetric relatively to the point (a,b) iff

                2b-f(2a-b) =  f(t).  

How to justify this formula? Which intuitive/graphical explanation could be given?