## Why do game engines define the a certain way to do things and not allow a lot of flexibility?

I understand that game engines have their own level design methods and different implementations of levels but why don’t they allow full control of the level design to the game developer? Without actually stating that, "The game developer should do/ use this to get this." rather than "Use these tools to get this done. Have full control over your product." ideology?

I guess its because not all game developers are interested in dealing with low level aspects of the game development phase but wouldn’t it be more efficient if the user can optimize certain aspects of the game to better suit for their product? For example, a mesh object, resource submissions, or other areas which game engines define a certain method?

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## Can you define a ‘discrete’ language?

Are the following appropriate definitions for a formal languages over the alphabet {0,1}?

Example1: An argument w is a member of L under the following rules:

1. If more than half its digits are 1’s –> it has to be a member of decidable language A

2. If more than half its digits are 0’s –> it has to be a member of decidable language B

3. If exactly half of its digits are 1’s and half are 0’s then it is not a member of the language.

Example 2: w is a member of L if:

1. If w is longer than 10 bits it has to not be a member of decidable language A (with decidable complement) to be a member of L

2. if w is 10 bits or less it has to be a member of decidable language B to be a member of L.

The general question: is the above ‘discrete’ form of language definition acceptable?

The same way a function can be discrete or continuous I am nicknaming this a ‘discrete’ definition for a language because based on what type of input you are, your rule (reason) for membership/non-membership can be different from other arguments’. I would assume this is ok? There does exist an argument that all discrete functions are not computable, but I don’t think this argument holds if all the inputs are of finite precision (as is the case with finite binary strings)

## How to define an automata for zig zag concatenation? [duplicate]

I have two DFAs one for language A and one for language B. I’m asked to make an FDA that is the zig-zag concatenation of letters of A and letters of B. This is described by the following: {w: w = $$a_1 b_1$$$$a_k b_k$$ and $$a_1…a_k \in A$$ and $$b_1 … b_k \in B$$}. With $$1 \leq i \leq k$$ and $$a_i \in \Sigma$$ and $$b_i \in \Sigma$$

This automata should be described as a 5-tuple {Q, $$\Sigma$$,$$\delta$$,$$q_0$$,$$F$$}.

I simply do not know how I would go about defining the total function $$\delta$$.

This is what I tried:

$$Q = Q_A \cap Q_B$$ // We only want the words that contains both a and b

$$F = F_A \cap F_B$$ // The accepted states should contain both letter from a and from b.

$$q_0 = q_A$$ //because the word starts with a letter from a.

$$\Sigma$$ // in this problem we aren’t interested in defining the alphabet we just leave the symbol as is in the 5-tuple.

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## How should we define the behavior of a Turing machine where the head tries to move left from the leftmost tape position?

If we have a Turing machine in a model with a tape that is infinite only to the right and assume at some point the head tries to move left from the leftmost position.

How should we define the behavior in such a case? Is a machine doing so for some input not a valid Turing machine? And if so, how can we make sure when we define a Turing machine that this situation can’t occur for any input?

I’ve read some sources about Turing machines though couldn’t find the answer to this specific case, and I see no reason why this case won’t happen for an arbitrary Turing machine and some input.

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## How can one algorithmically define the required amount of centroids in K-Means clustering?

Say I have a dataset of n vectors. These are, by nature, clustered so that there is a significant distance difference between any two points within a cluster and any two points in separate clusters.

I want to create a single centroid per single cluster. However, I cannot initially know how many clusters there are – thus I cannot pre-define the k in K-means clustering.

What is the best way to define the k in K-Means, given the dense and clear clustering of the data?

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## Define a variable to satisfy $x^3 = -x$, then sum to find exponential

I’m wondering if it is possible to tell Mathematica that my non-commuting variable satisfies $$x^3 = -x$$ such that it can compute $$\sum_{n=0}^\infty \frac{(Ax)^n}{n!} = e^{Ax} = \cos A+ x \sin A$$ with the Sum function, where $$A \in \mathbb{R}$$

I’ve tried it with the NCAlgebra package but now if I compute

Sum[(x A)^n/n!, {n, 0, \[Infinity]}] 

nothing happens. Here A is commuting and x non-commuting.

I’m not hung up on the NCAlgebra package, any way to simplify the sum to elementary functions is appreciated. But fundamental to the solution has to be that I can tell Mathematica that $$x^3 = -x$$, because my real target is to see if Mathematica can rewrite a sum where I know that $$x^3 = -x + y$$ with known $$x$$ and $$y$$.

p.s. possible solutions of such variables would be a normalized Pauli vector $$\vec{\sigma}$$ or a vectorial quaternion.

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## How to define following function in Mathematica?

How to define the following function in Mathematica? Posted on Categories cheapest proxies

## Real cron killed my cron system. Only define( ‘ALTERNATE_WP_CRON’, true ); works

my host recommended me to disable wp cron for a real cron due to excessive executions.

the cron system broken immediately and scheduled tasks were not happening.

deleting real cron and turning on wp cron did not work.

through random luck, i tried define( ‘ALTERNATE_WP_CRON’, true ); and it worked.

having said so, i really want to revert back to the prior situation where normal wp cron works. it also messes up when all my links start to have &doing_wp_cron=

i have spent many hours and am desperate! appreciate your kind advice.

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## Why define CIA in security like this?

as we know CIA of the demand for security means:

Confidentiality Integrity Availability 

I don’t understand why define the Integrity and Availability,

1. if we make a plaintext Confidentiality, the Integrity is a whole plaintext, this is the basic, why there gild the lily?
2. if there defined the Integrity, the decrypted plaintext must be usable, so the Availability is gild the lily too.

## Define user variables to use in a SQL that has an “in” statement in MySql Workbench

I am trying to use defined variables in MySql Workbench I am using version 6.3 of Workbench I am trying to run ad hoc queries that can have a value or multiple values:

If I have a single value, the query runs ok set @Zdept_Id=”548″ and then Select * from employees where dept_Id in (@ZDept_Id)

but if I want to execute this for multiple departments, the query only returns values for the first number

set @Zdept_Id=”548,221,1973,905″ and then Select * from employees where dept_Id in (@ZDept_Id)

Dept_Id is an integer.

Thanks

PS. These are reports that I run once a month, so automating them is not an option due to cost/benefit.