first hitting of ergodic transformation

An invertible ergodic transformation $$\sigma: (\Omega, \mathbb{P}) \to (\Omega, \mathbb{P})$$.

Given a random function $$C: \Omega \to \mathbb{R}^{+}$$ s.t. tail estimate $$\mathbb{P}(C > k) \le \frac{1}{k^2}$$.

Define a first hitting time $$\tau(\omega)= \inf \{k: C(\sigma^k\omega)\le L\}$$ with fixed big $$L>0$$.

can we show $$\int \tau^2 d\mathbb{P} < \infty$$ for some big $$L$$? or has counter-example? Thanks!

Prove that the hitting set size is related to the input length of n

Suppose A($$\cdot$$,$$\cdot$$) is an efficient randomized algorithm and L is a language such that

$$\text{If }x \in L, \text{Pr}_r[(A(x,r) = 1)] = 1$$ and if $$x \notin L, \text{Pr}_r[A(x, r) = 0] \ge \frac{1}{2}$$.

Let $$H$$ be a hitting set such that for all inputs $$x$$ of length $$n$$, if $$x \notin L$$, then $$\exists y \in H, A(x, y) = 0$$.

We need to show that there exists a hitting set $$H$$ of size $$O(n)$$.

My idea is that from the condition $$x \notin L, \text{Pr}_r[A(x, r) = 0] \ge \frac{1}{2}$$, we can get that $$x \notin L, \text{Pr}_r[A(x, r) = 1] < \frac{1}{2}$$. Then we can randomly choose $$y_1$$, $$y_2$$, …, $$y_m$$ to construct a set $$S$$. Then for any input $$x \notin L, \Pi_{i = 1}^{i = m}Pr[A(x, y_i) = 1] < 2^{-m}$$. Therefore, the probability that there exists at least one $$y_i$$ such that $$A(x, y_i) = 0$$ is $$1 – 2^{-m}$$. Now the problem is if we need to prove the hitting set $$H$$ must exist, then $$1 – 2^{-m}$$ should be 1, which means $$m$$ should be large enough. However, I cannot find the relationship between $$m$$ and $$n$$ and how come if $$m$$ in size of $$O(n)$$ would prove such $$y_i$$ must exist.

Or maybe I am going in the wrong way. Can somebody help me with this? Any help would be appreciated. Thanks in advance.

Sent Bitcoin to my electrum wallet address without hitting request first now it says its confirmed and i have no money after requesting it

Sent Bitcoin to my electrum wallet address without hitting request first now it says its confirmed and i have no money after requesting it after Isent it. Can I still receive my coin

Can Sneak Attack be used when hitting with an improvised weapon?

The Mastermind rogue in my game was well hidden when he threw a flask of holy water at a shadow demon that attacked his ally. In the moment, it made the most sense to me to allow him to use Sneak Attack while hitting the fiendish creature with the flask.

The description of Holy Water says:

As an action, you can splash the contents of this flask onto a creature within 5 feet of you or throw it up to 20 feet, shattering it on impact. In either case, make a ranged attack against a target creature, treating the holy water as an improvised weapon. If the target is a fiend or undead, it takes 2d6 radiant damage. […]

The rogue’s Sneak Attack feature says:

[…] Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon. […]

Now, post-session, I’m wondering whether Sneak Attack can actually be applied to an improvised weapon. I ruled it as a ranged weapon attack since he threw it, but now that I’m thinking about it: an improvised weapon might not be considered as a ranged weapon. And that would mean that a Sneak Attack could not have triggered when hitting with the flask. Unless an improvised weapon is also a ranged weapon when used as such. In that case, it could trigger.

I’m not sure which interpretation is correct according to the books. So, can Sneak Attack be used when hitting with an improvised weapon?

‘Failed to start Execute cloud user/final scripts’. : Google compute instance hitting error when running cloud user/final scripts

not sure if this is appropriate for this site but thought it could be a good place to start.

Question

How can I connect to a Google instance if I have no SSH keys and google user/final scripts will not run?

Problem Context

Google compute instance running Ubuntu 16.04 LTS.

I changed it’s base version of python in order to install a python package that was very finicky with python’s ‘setup-tools’.

My theory is that this change broke the start up of google cloud scripts, which was the only way I had in past connected to the instance.

Problem Details

We can verify the server is on, as it is serving bad nginx networks here: http://35.201.199.224/

I have a server log I can share here if anyone is willing to help me read it here: https://pastebin.com/DF5wsLhH

The part I think is the most important is this snippet

Mar 21 17:21:50 instance-1 systemd[1]: Started Google Compute Engine Network Daemon. Mar 21 17:21:51 instance-1 google_network_daemon[1340]: Traceback (most recent call last): Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/bin/google_network_daemon", line 9, in <module> Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     load_entry_point('google-compute-engine==2.8.4', 'console_scripts', 'google_network_daemon')() Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/pkg_resources/__init__.py", line 542, in load_entry_point Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     return get_distribution(dist).load_entry_point(group, name) Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/pkg_resources/__init__.py", line 2569, in load_entry_point Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     return ep.load() Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/pkg_resources/__init__.py", line 2229, in load Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     return self.resolve() Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/pkg_resources/__init__.py", line 2235, in resolve Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     module = __import__(self.module_name, fromlist=['__name__'], level=0) Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/google_compute_engine/networking/network_daemon.py", line 26, in <module> Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     from google_compute_engine import config_manager Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/google_compute_engine/config_manager.py", line 23, in <module> Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     from google_compute_engine.compat import parser Mar 21 17:21:51 instance-1 google_network_daemon[1340]:   File "/usr/lib/python3/dist-packages/google_compute_engine/compat.py", line 23, in <module> Mar 21 17:21:51 instance-1 google_network_daemon[1340]:     import distro Mar 21 17:21:51 instance-1 google_network_daemon[1340]: ModuleNotFoundError: No module named 'distro' 

I think it cannot find this module as it is looking in the wrong python version.

Conclusion

I do understand that I was inexcusably lazy connecting only by using Googles ‘Connect By SSH button‘ but I assumed naively that the arguably best commercial developers in the western world would have everything under control from me.

In the middle of Feb the traffic of my site started to drop and i heared that some google search engine updates are around. I don’t really know if its because these weird backlinks or due to google updates. here is a screenshot from my webmastertool about it

here is the site link ulaznice.info and there are more of the same type linking my website info-focus.info tuuliajolla.info also they are targeting my most viewed and ranked content. so should I disavow from these links now ? or wait till google updates finish

Keep Hitting 3rd party API or Store Commonly Queried Data In DB?

Colleague and I have begun a long (and hopefully fruitful) project. I’ve been building and have come to my first crux, and now I ask the experts of the Stack Exchange for their guidance.

I’ll keep this simple. Our front end has functionality to search for stocks and get back real-time intraday data on it. It’s a search dashboard for info, nothing else YET. Our front end sends the user’s search request to our StockDataAPI, which actually just sends a GET req to some public trusted stock data api.. the user doesn’t know the difference, they think we own the publicly available data.

Asking: Is it right to keep this approach? Over time, wouldn’t this become clunky and burdensome? Would it be better to have the following: Save the returned stock information in a database for easier lookup? But checking the entire DB before querying 3rd party API will become cumbersome once DB is very full. I’d also have to have a step to save info in DB if the information being returned wasn’t present in the DB. Or should I try something completely different?

Suppose we have a random walk that moves in discrete time. It starts at zero and in each period it jumps one unit to the right with probability $$\alpha$$, it jumps to the left one unit with probability $$\beta$$, and it does not move with probability $$1-\alpha-\beta$$. Obviously $$\alpha,\beta>0$$ and $$\alpha+\beta<1$$.
Conditional on the stopping time at which the random walk hits 1 being $$k$$ periods, what is the distribution of the number of right jumps?