Suppose I have a circular markov chain. At each state, you are equiprobable to transition to the state immediately to your left or right.   I'm interested in the probability of visiting the jth state last?  That is to say, what is the probability of reaching all the other states at least once before the jth state?
For a graph $G$, let $W$ be the (random) vertex occupied at the ﬁrst time the random walk has visited every vertex. That is, $W$ is the last new vertex to be visited by the random walk. Prove the following remarkable fact:      For the   random walk on an $n$-cycle, $W$ is uniformly distributed over all vertices different   from the starting vertex.
Creating account didn't log me in / didn't create an account How do you make Vim unhighlight what you searched for? I search for "nurple" in a file. I found it, great. But now, every occurrence of "nurple" is rendered in sick black on yellow. Forever.  Forever, that is, until I search for something I know won't be found, such as "asdhfalsdflajdflakjdf" simply so it clears the previous search highlighting.  Can't I just hit a magic key to kill the highlights when I'm done searching? "Holmby hall" or "The Holmby Hall", does the hall have to be capital in either of them? Which is correct, and why?     some days we went on adventures — him maneuvering our scooter, me resting my chin …   or     some days we went on adventures — he maneuvering our scooter, I resting my chin … Pros and cons of rooting using apps ("Soft Root") compared to other methods ("Hard Root") There are quite a few app based rooting methods. A recent review , points to some of them and there may be more apps, paid or otherwise.  From what I understand,   Plus Points   Ease of rooting Don't need a laptop or computer   Minuses   Based on exploits, so may not work if exploits are denied by OS updates Difficulty in unrooting (as I see on some forums for my device Huawei Honor 6)   Questions:    What are the pros and cons apart from above?  If a device has both options - app based rooting and rooting by methods by developers, which one should I opt for?   Note: I am not seeking app suggestion or recommendation. Number Theory: Prove that $m | \phi(a^m - 1)$ Radical change of favourite tags doesn't reflect in questions list Pausing a long running program in the terminal? Is there a keyboard key combination that I can use to pause a program running in the terminal? In case it matters, I don't intend to run anything else inside that terminal while the program is paused. I just want to pause the program execution, and resume it later. How can I do this? Windows Starter Edition, Home and Home Premium do not include gpedit, how do I install it? I pressed F2 to take a few Minecraft screenshots. Later I couldn't find them. Where are they stored on my computer? Both static_cast and reinterpret_cast seem to work fine for casting void* to another pointer type. Is there a good reason to favor one over the other? Below is my code to create the component dynamically - The component is "ui:inputselect"  $A.createComponent(             RecoveryLineItem.Attributes[i].name,{                 "class" : "slds-input ",                 "aura:id" : 'ExampleId',                 "label" : RecoveryLineItem.Attributes[i].label,                 "multiple" : RecoveryLineItem.Attributes[i].multiple             }, ....   ..  console.log(component.find('ExampleId').get("v.value"))    Or console.log(component.find('ExampleId'))  is Giving as 'Undefined"  How to access the aura:id of the dynamically created components? Why does Stack Exchange use Imgur over Amazon S3 or Azure? What benefit does  offer over , , etc. for image hosting?   Is it the simplicity of integration? The cost model? What's better about using a "gateway"? How do I insert a backslash inside a mathematical statement? I'm trying to write a set subtraction operation in an AMS formatted template.  In the end, what I want should look like A\B.  But I'm doing this in math-mode $A\B$ and this gives me errors.  I've also tried using the \diagdown symbol, but it doesn't work either.  Is there another way to do this? Lagrangian of an effective potential If there is a system, described by an Lagrangian $\mathcal{L}$ of the form   $$\mathcal{L} = T-V = \frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) + \frac{k}{r},\tag{1}$$   where $T$ is the kinetic energy and $V$ the potential energy, it is also possible to define the total energy $E$ of the system   $$ E = T + V =\frac{m}{2}\left(\dot{r}^2+r^2\dot{\phi}^2\right) - \frac{k}{r}.\tag{2}$$  If the angular momentum $M$ is defined by $$ M = m r^{2} \dot{\phi},\tag{3}$$ then $E$ can be written as  $$ E = \frac{m}{2}\dot{r}^2 + \underbrace{\frac{M^2}{2mr^2}-\frac{k}{r}}_{V_\textrm{eff}\left(r\right)},\tag{4}$$  where the last two terms are written as new, "effective" potential $V_\textrm{eff}\left(r\right)$.    In addition, using the definition of $M$, the Lagrangian $\mathcal{L}$ can be written as  $$ \mathcal{L} = \frac{m}{2}\dot{r}^2 + \underbrace{\frac{M^2}{2mr^2}+\frac{k}{r}}_{-V_\textrm{eff}\left(r\right)},\tag{5}$$  where the sign of $V_\textrm{eff}\left(r\right)$ has been changed, since $\mathcal{L} = T-V$. But from this argument, it appears that there are two different possible ways to construct the same effective potential. This seems to me contradictory. Where is my mistake? This book came out of the 1970s (early 1980's) at the latest. In it the protagonist, a not so diligent student, gets turned on to computer programming and creates (I think..) a weather program.   Eventually he moves on and years later the program contacts him. It has become an AI and he is its creator.  I forget what the setup is post contact which is not helpful at all.. How can I raise a soldiers hacking ability? My main specialist seems to have a hard time hacking stuff. How can I make him better at it? How to terminate a script? I am aware of the die() command in PHP which exits a script early.  How can I do this in Python? How does damage dealt increase as you level up I've recently taken over as GM in my group.  We are all new to RPGs except for our original GM, so they decided to run an adventure path so it would be easier to change GMs if they had to stop playing.  Along this path, we had one CR 4 encounter that took us an hour, almost killed our bloodrager and knocked our brawler unconscious. When we leveled up, our GM told us to increase the damage we did by "one level," so my 1d6 became 2d6 and my friend's 2d6 became 4d6.  I saw no problem with this as a player, but I was looking over the adventure path and later encounters that also have a CR of 4 could be ended in one turn by our bloodrager. This would make encounters really boring, and my goal is to avoid boredom.  My question is: As you level up, how does the damage you do increase? Does it go up like my GM said so that at level 3 my rapier does 3d6 and the bloodrager's earth breaker does 6d6, or does it go up by some other method?  I have read the PHB and I don't think that what the GM was saying is correct, but being a first-time player I wasn't sure if had just missed something, so I figured I should ask elsewhere. Is there any table or any other way(metadata/rest api) we can query the list views of a particular object that a user/group  has access.  Example:  SELECT Name FROM table_x WHERE UserOrGroupId = '1234..' AND  SobjectType = 'Account'   I can see an object named UserListView in workbench, but query on that returns no data. Is it deprecated?