Labeled points in $\{0,1\}^n$ such that every linear separator requires exponential weights

I want to find labeled samples in $ \{0,1\}^n$ such that the Perceptron algorithm takes $ 2^{\Omega(n)}$ steps to converge. One way to do this would be to find a sequence of labeled examples that are linearly separable, but require every linear separator to have at least one exponentially large weight. To show that the samples are linearly separable, it is enough to show that they are consistent with a decision list, which should be apparent from the list of samples. So, my question is

Does there exist a set of labeled samples $ S$ in $ \{0,1\}^n$ that are consistent with a decision list and such that any linear threshold function that correctly labels $ S$ has at least one exponentially large weight $ w_i = 2^{\Omega(n)}$ ?

Here are the definitions that I’m working with: A linear threshold function $ f \colon \{0,1\}^n \to \{0,1\}$ with associated weights $ w_0, \dots, w_n \in \mathbb{R}$ gives $ f(x) = 1$ if and only if $ w_1x_1 + w_2x_2 + \dots + w_nx_n \geq w_0$ . Given a set $ S$ of points in $ \{0,1\}^n$ labeled $ 0$ or $ 1$ , we say that a linear threshold function $ f$ correctly labels $ S$ if $ f(x) = 1$ whenever $ x$ is labeled $ 1$ and $ f(x) = 0$ whenever $ x$ is labeled $ 0$ for all $ x \in S$ .

Note: I had asked the same question on math.stackexchange since it seemed relevant to both fields. Here is the link for that.

Does rolling on ‘you cast …’ on Wild Magic Surge table requires the usual components?

Several effects from the Wild Magic Surge table tell you, the sorcerer, to cast a spell as the result, for example:

You cast Fireball as a 3rd-level spell centered on yourself.

Fireball have verbal, somatic, and material components.

Does this mean I need to do the verbal and somatic component and have the material or arcane focus to cast fireball?

What if I don’t want to? Is it automatic? Can I remove component pouch or arcane focus (and only casts material-less spells) to avoid fireball?

If possible, please elaborate on your answer the consequences if it does not require components, or it does require components.

Does Shades/Shadow Conjuration/Evocation requires material components?

I’m pretty sure the answer is no, but I just wanted to be sure I didn’t miss a rule somewhere, after all it is an illusion.

Let’s say I use Shadow Conjuration, Greater to duplicate Acid Storm that normally requires A flask of acid (10 gp) since Shadow Conjuration states:

You use material from the Plane of Shadow

The Material components are not necessary Am-I right? If there’s such a spell that would require a focus/exp component is it ok to apply the same logic as well?

In out of the Abyss, one of my characters requires an item yet you start with confiscated items. What should I do?

I am running Out of the Abyss, and there is a cleric in my campaign. This cleric requires his holy symbol to really do anything. However, you do not start with any items in this. I don’t know what I should do about this. Should I give him the holy symbol? Should he find it in a shop? Please help me out.

Understanding why NIntegrate requires explicit substitution of variables in argument

The problem that leads me here begins with a quantity I have previously defined, let’s call it test, that has many other quantities in its definition. When evaluated, test is an expression that includes two variables, let’s call them k and x. A MWE would be

test = kx; 

I wish to create a function of k that includes a NIntegration of test over x with limits that involve k. An example would be

testint[k_] := NIntegrate[test, {x, k, 2k}]; 

Evaluating this for some k , say k = .1, returns an error:

>>testint[.1]  NIntegrate::inumr: The integrand k x has evaluated to non-numerical values for all sampling points in the region with boundaries {{0.1,0.2}}.  NIntegrate[k x, {x, 0.1, 0.2}] 

However, if I define testint using a temporary variable and perform a replacement in the argument of NIntegrate , then it computes fine:

>>testint[k1_] := NIntegrate[test/.k->k1, {x, k1, 2k1}]; >>testint[.1] 0.0015 

I found this answer, which led me to try the explicit substitution: Replace variable with value prior to evaluating NIntegrate
Another answer addresses the order of NIntegrate with the help of the ?NumericQ pattern check: How do I prevent NIntegrate::inumr errors within other functions?

My question is Why does NIntegrate require this explicit substitution in order to compute?

As a test, I even tried removing NIntegrates HoldAll attribute thinking that would force the evaluation of test before the integration. It did, but not soon enough to help.

>>test = k x; >>ClearAttributes[NIntegrate, HoldAll] >>testint[k_] := NIntegrate[testin, {x, k, 2 k}]; >>testint[.1]//Trace  NIntegrate::inumr: The integrand k x has evaluated to non-numerical values for all sampling points in the region with boundaries {{0.1,0.2}}.  {testint[0.1], NIntegrate[test, {x, 0.1, 2 0.1}], {test, k x}, {{2 0.1, 0.2}, {x, 0.1, 0.2}}, NIntegrate[k x, {x, 0.1, 0.2}], {{x} =., {x =.}, {x =., Null}, {Null}}, {x =., Null}, ... 

Thanks in advance!

SER sometimes requires “two clicks” to bring window to front

Hi @sven, a bug I’ve noticed since have been using SER a lot lately. In Windows 7 (possibly Windows 10 as well), SER requires “two clicks” when you have a project running and navigate away from the SER window.

To re-create the bug:

– Open SER
– Start a project (make active)
– Click to another taskbar program, for example, Excel
– Wait a while, don’t click on SER immediately after
– Click on SER icon in the taskbar
– SER doesn’t recognize the click, the window does not open
– Click SER taskbar icon again and it will show properly

This is a small but really annoying issue as when a program is clicked you would expect it to appear accordingly. It could be a Windows problem, but I’ve never encountered this with any other program besides SER.

Update: I actually just had this issue without an active project. Does SER have some sort of “sleep mode” that requires 2 clicks to re-open the window after you haven’t clicked it in the while or something?

Is there a key exchange protocol that requires only one message?

Say I want to exchange a secret with someone, but I only get to send one message to the other person, and then we encrypt with that secret. Diffie-Hellman and ECDH require multiple messages to be sent back and forth to get a shared secret.
Is there a key exchange that requires just one message to be sent from one party securely? (I know that sending the key over plaintext works, but that isn’t secure.)
(Define message as a packet over the internet or one SMS for example)

Videos requires to install plugins to play media files of the following type: application/zip decoder

I have already tried installing ubuntu restricted extras, which didn’t work. It is also not playing in vlc.

Required plugin could not be found
Videos requires to install plugins to play media files of the following type: application/zip decoder

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