Is it reasonable to use a ring flash that encircles the lens for non-macro (general) shots?

I just saw Death in Paradise Season 5 Episode 3, which features a photographer using a DSLR to shoot a fashion runway performance.

He had a flash that was a ring around the lens.

I thought that was for macro shots only, where the extreme close-up has trouble with normal flash placement. For normal photos you want the flash far from the lens, like on a boom on a separate handle framing the camera.

I’ve seen some recent trendiness in having ring-shaped catch lights, but I supposed those would be positioned in the normal manner: off-angle from the lens.

I suppose if an on-camera had any effect at all it would be for some subtle fill flash.

Is this a realistic thing to see from a pro? Or is it just a cool-looking prop that doesn’t really fit the situation?

Magento 2 – CMS Specific page_layout XML and Dedicated page_layouts in general?

I’m looking for some BEST PRACTICES insight into using page_layout.xml. Is it a good idea to try and decouple the non-shared resources on Product Pages, Category Pages and CMS Pages? If so, what’s the best way to do this? Recently found myself creating a bunch of CMS specific CSS rules for our CSM pages and I knew the CSS rules may continue to grow a bit so I decided to create a dedicated layout file (Magento_Theme\page_layout\cms_layout.xml). To achieve this, I created a new page_layout but also had to make a plugin beforeRenderResult() to load in in <body> BOTH the standard class page-layout-2columns-left and the new class page-layout-cms-layout. If I didn’t do this, I would have had to modify a lot of CSS.

Some of the benefits I think I’m realizing are:

  • (Maintenance) I no longer have to manage a lot of Content > Page > Design > Layout Update XML content. I can just change the “Layout” dropdown to the CMS Specific Layout.
  • (Slight Performance) I don’t have to load the CSS for the CMS pages on the Product Pages and Category Pages

Next up – might be to look at some of the heavy UI JS/CSS being used on Product Pages and not have that being loaded on Category Pages? Does this situation make sense to experiences Magento Developers OR should I provide more clarity?

I’m pretty certain I’m not making any big performance gains with this particular situation but I am curious whats “Best Practice”. As it stands, it seems like Magento load the the entire websites resources on every page, no matter how big or small (Category JS/CSS, Details JS/CSS, Checkout JS/CSS, etc). I’m not sure that’s great either.

Concentration of the measure of a general covariance-like matrix

I consider a random matrix of the type : $ M_n = \frac{1}{n} X_n D_n X_n^\intercal \in \mathbb{R}^{n \times n}$ , in which all matrices are square of size $ n$ . $ D_n$ is a deterministic diagonal matrix with elements $ D_{n,\mu}$ which are bounded : $ $ \sup_\mu |D_{n,\mu}| \leq \rho < +\infty.$ $ The matrix elements of the matrix $ X_n$ are standard i.i.d. Gaussian variables (mean zero, variance $ 1$ ). I consider a function $ f : \mathbb{R} \to \mathbb{R}$ which is Lipschitz (I can basically make any other reasonable assumption on $ f$ ), and I’m interested in the concentration, as $ n$ grows, of the linear spectral statistic: $ $ G_{n,f}(X_n) = \frac{1}{n} \mathrm{Tr} f(M_n)$ $

There are some classic RMT results (for instance from the book of Anderson,Guionnet,Zeitouni : Link (Section 2.3 or 4.4), or in the previous paper of Guionnet&Zeitouni Link (these results can also be found in many other places).

For instance (Corollary 1.8.b of the Guionnet-Zeitouni), if one assumes that all the elements of $ D_n$ are positive, and that $ x \mapsto f(x^2)$ is Lipschitz with Lipschitz constant $ L > 0$ , then one has: $ $ \mathbb{P}\left(\left|G_{n,f}(X_n) – \mathbb{E}G_{n,f}(X_n)\right| \geq t\right) \leq \exp\left(- \frac{1}{2 \rho L}n^2 t^2\right) $ $

I have found other similar results in the litterature, but I couldn’t find anything concerning the case of non-positive $ D_n$ . My main question is : does there exists similar concentration results concerning this case ? I don’t know if the lack of study concerning this case is due to a real theoretical difficulty or if it comes from the fact that these matrices are less natural as they are not empirical covariance matrices…

Any help would be appreciated !

Thanks a lot 🙂

Generalize Wu formula to general Bockstein homomorphisms

The classical Wu formula claims that $ $ Sq^1(x_{d-1})=w_1(TM)\cup x_{d-1}$ $ on a $ d$ -manifold $ M$ , where $ x_{d-1}\in H^{d-1}(M,\mathbb{Z}_2)$ .

I wonder whether there is a generalization of the classical Wu formula to general Bockstein homomorphisms. We consider the Bockstein homomorphism $ $ \beta_{(2,2^n)}:H^*(-,\mathbb{Z}_{2^n})\to H^{*+1}(-,\mathbb{Z}_2)$ $ which is associated to the extension $ \mathbb{Z}_2\to\mathbb{Z}_{2^{n+1}}\to\mathbb{Z}_{2^n}$ .

I guess there is a generalized Wu formula: $ $ \boxed{\beta_{(2,2^n)}(x_{d-1})=\frac{1}{2^{n-1}}\tilde w_1(TM)\cup x_{d-1}}$ $ on a $ d$ -manifold $ M$ , where $ x_{d-1}\in H^{d-1}(M,\mathbb{Z}_{2^n})$ .

Here $ \tilde w_1(TM)$ is the twisted first Stiefel-Whitney class of the tangent bundle $ TM$ of $ M$ which is the pullback of $ \tilde w_1$ under the classifying map $ M\to BO(d)$ . Let $ \mathbb{Z}_{w_1}$ denote the orientation local system, the twisted first Stiefel-Whitney class $ \tilde w_1\in H^1(BO(d),\mathbb{Z}_{w_1})$ is the pullback of the nonzero element of $ H^1(BO(1),\mathbb{Z}_{w_1})=\mathbb{Z}_2$ under the determinant map $ B\det:BO(d)\to BO(1)$ .

The right hand side makes sense since $ 2\tilde w_1(TM)=0$ .

Can you help me to prove or disprove the boxed formula above?

Thank you!

General questions-series convergence

  1. $ If$ $ \sum{a_{n}}$ $ $ $ converges$ $ ,$ $ then$ $ $ $ does$ $ $ $ $ $ \sum{cos(a_{n})}$ $ $ $ $ $ converge?$

  2. $ If$ $ \sum{a_{n}}$ $ $ $ converges$ $ $ $ and$ $ $ $ a_{n}$ $ \geq$ $ 0$ $ ,$ $ then$ $ $ $ does$ $ $ $ $ $ \sum{sin(a_{n})}$ $ $ $ $ $ converge?$ $ $

  3. $ If$ $ \sum{sin(a_{n})}$ $ $ $ converges$ $ $ $ and$ $ a_{n}$ $ \geq$ $ 0$ $ , $ $ a_{n}\to0$ $ ,$ $ then$ $ $ $ does$ $ $ $ $ $ \sum{a_{n}}$ $ $ $ $ $ converge?$

  4. $ If$ $ \sum{sin(a_{n})}$ $ $ $ converges$ $ $ $ and$ $ a_{n}$ $ \geq$ $ 0$ $ ,$ $ then$ $ $ $ does$ $ $ $ $ $ \sum{a_{n}}$ $ $ $ $ $ converge?$

  5. $ Show$ $ $ $ that$ $ $ $ if$ $ \sum{a_{n}}$ $ $ $ converges$ $ ,$ $ then$ $ $ $ \sum{e^{-a_{n}}}$ $ $ $ does$ $ $ $ not$ $ $ $ converge.$

I said that since the series converges, then $ \lim\limits_{x \to \infty}$ $ a_{n}$ $ =0$ and that $ 0$ $ \leq$ $ a_{n}$ $ \leq$ $ 1$ , but I am not sure how to proceed.

Is every subset of a RE language also RE, in general?

I’m trying to understand the question in my title in an intuitive way: If I have an RE language A, then some TM, say TM(A) accepts on it. If I take a subset of A, say A2, then all elements of A2 will cause TM(A) to halt in the accept state.

However, is it in general possible to then create a TM for A2, say TM(A2), such that A2 is the max possible set that halts TM(A2) in the accept state. Thus making A2 its language – and would this language be RE?

Thanks

Building an Online Service, need general advice

0

Hopefully I am posting this the right place. Please tell me if this belongs somewhere else.

This is a rather broad question regarding building an service. I am not asking for specific code or anything, just general advice.

Does anyone have an idea of how I should approach the following:

A website sends a text file with some custom info based on parameters a user changes. text file is sent to local computer of mine. The text file is used for some external calculation, creating an “asset”, 3D model. (I got this part). Then the asset is sent back to the website and uploaded live, made available for the user. So my biggest question is how could one make a website send a text file to a local computer (the website is hosted by some third-part most likely..) Is there any system, protocol, methods for doing such. And vise versa, send the processed file back to the website and make it live, automatically.

I am very grateful for any advice at all regarding any of this. I am a VFX artist so currently working with phyton and VEX, but looking into java, html and those things now a day. Thanks!

Is OS mode required for accessing general purpose registers

In which of the following cases a process executing in user model is required to enter into the OS mode?

(a) Decreasing the value of unsigned integer value in a register to less than 0

(b) Accessing general purpose register

(c) Executing printf()

(d) Adding values in two registers using ADD

In my opinion, both (c) and (b) should use OS mode. But my solution manual says only (c) uses OS mode.

I believe that (b) requires the use of OS mode as well, because the processor may have more than one process executing at the same time. As both of them have access to the general purpose register, it is quite possible that one process may overwrite the contents of another process if switching takes place.

The only way it can be avoided is setting up of a semaphore. At the end of the day, it boils down to a critical section problem. So, for accessing and setting up a semaphore, OS mode is required.

So, in my opinion, (b) should be true as well.

Am I correct or where is my reasoning wrong regarding the problem?

Thank you!