Terminology: Difference between decision variables, features and attributes?

Could there be a difference between the words “feature”, “attribute”, and “decision variable” when used in the same paper? The one I am specifically thinking about is about an optimization method for clustering, but I am also wondering if there generally are any scenarios for which it could be.

I can’t manage to google up an answer that either confirms or denies that these are the same thing, and I have no formal training in data science.

How to prove the optimization version problem (whose decision version is NP-complete) can be solved in poly-time iff P=NP?

I have proved the decision version of my problem be $ \mathcal{NP}$ -complete. And I know that if I can solve the optimization version in poly-time, then I can just to compare the obtained minimum (or maximum) with target value in decision version. Thus, the decision version can be solved in poly-time as well. Since the decision version is $ \mathcal{NP}$ -hard, so is the optimization version, i.e., the optimization version is $ \mathcal{NP}$ -hard.

My question is how to prove the converse direction: if the decision version can be solved in poly-time, can the optimization version be solved in poly-time as well?

I in advance thank you for any suggestions!

Visa refused – V4.2 (a) (c) – Incorrect Decision

I have received the refusal latter today apparently the ECO has refused the visa citing reasons due to economic circumstances. They mentioned that the salary payments were not sourced by the debits to my employers account and gave example for a month; per them the amount deposited into my account on a certain date was not reflected in my employers account debits. When I checked this after getting home, all the check numbers were reflecting in company’s bank statement – every single one!

Second reason they stated regarding payments being irregular in amount but that could have been easily verified through the pay slips that I had submitted; the variance details for extra payments were mentioned such as overtime, leave encashment OPD payment etc.

I strongly believe they have overlooked these details and made a hasty decision probably it being a “priority visa application”

Is there a way I can make them realize they made a mistake and if they could revisit this decision?

Matrix Inversion in the complexity class $P$ seen as a decision problem

If the set $ P$ is defined as the set of decision problems that can be solved by a deterministic Turing Machine in polynomial time, and matrix inversion using Gaussian elimination is $ O (n^3)$ , then how can I relate these two concepts to conclude that inverting a matrix is in $ P$ ?

I suppose I need a way of converting a description of Gaussian elimination into a decision problem? Or maybe I am confused about the fundamentals

After a UK visa decision, how long for VFS Global to return passport?

I applied for a UK visitors visa from the US. I sent the materials to the VFS scanning hub in NY along with a return UPS label. I received an email telling me that a decision had been made and that my passport would be returned soon. It’s been 5 days and VFS hasn’t sent it yet. (I have the tracking number for the return label since I created it.)

Is this a normal timeline? When should I expect it?

design decision – already existed bad design [on hold]

If there is an already existed project but with bad design and there is no time for refactoring and code enhancement for the already existed code. So for example in a layered architecture rest web service , the service layer classes are interacting with each other directly without interface (coupled) So is it a good decision to put an interface for my new service added unlike the rest ?

Web Application Firewall with based on an external decision to detect anomaly

I have a theoretical knowledge about WAF but I do not have knowledge of the tools in the market. I wonder if there are any WAFs that base their decision making through a response from an external resource (true or false) when sorting an anomalous traffic.

My idea was to create a Machine Learning based for for example to make this decision and the WAF would just consult it.

Thanks!