I saw a project that use a laser pointer to point laser to a solar cell and that plays music on the speaker connected to the solar cell.   I am just confused in regards to the general concept behind how this would work. How is a laser light turned into unique sets of data such as music?  link:
I have to design a circuit in which I have to transfer data through lasers (serial transmission of data). Now what I was thinking was to check if the laser light is on then '1' is passed and when the laser is off '0' would be passed. Now I need to check if a 1 or a 0 was passed.   How would I check for this and another problem I'm facing is if it's on it may keep on passing 1's. How would I check for this? I though of using LDR's (Light Dependent Resistors)? Would this be okay or it there a better method?
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge? So I've been thinking through some test cases. If $a_n = n$ then $\sum_n \frac{a_{n+1} - a_n}{a_n}$ is the harmonic series which diverges. And if $a_n = \sum_{k=1}^n 1/k$ then $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverges like $\sum_n 1/(n \log n)$. So that got me thinking, if $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ necessarily diverge? Whenever I try to get somebody to follow me in Skyrim they something in the lives with "You already have a follower.". The problem is, I don't.   I have not, to my recollection, had a follower at any given point in the game.  The only thing I can think of is that I have (spoiler)      finished Anriel's Endeavors and gotten him as a summon creature.    Or do I have a hidden follower that I can't remember. A dog or a horse perhaps? Note that I do not have a dog or horse following me now. I talked to dog once, and had a horse that died.  Is this a common/known issue? Is there a work around?  Any tips? Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$ Find natural number $x$ so that $$\begin{align}x&amp;\equiv 9\pmod{10}\\ x&amp;\equiv8\pmod9\\ &amp;\ \ \vdots\\ x&amp;\equiv 1\pmod2\end{align}$$ Does C# have an equivalent to JavaScript's encodeURIComponent()? In JavaScript:  encodeURIComponent("©√") == "%C2%A9%E2%88%9A"   Is there an equivalent for C# applications? For escaping HTML characters I used:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"&amp;#" + ((int)m.Value[0]).ToString() + ";");   But I'm not sure how to convert the match to the correct hexadecimal format that JS uses. For example this code:  txtOut.Text = Regex.Replace(txtIn.Text, @"[\u0080-\uFFFF]",     m =&gt; @"%" + String.Format("{0:x}", ((int)m.Value[0])));   Returns "%a9%221a" for "©√" instead of "%C2%A9%E2%88%9A". It looks like I need to split the string up into bytes or something.  Edit: This is for a windows app, the only items available in System.Web are: AspNetHostingPermission, AspNetHostingPermissionAttribute, and AspNetHostingPermissionLevel. I have 14" 16:9 notebook and would like my Windows 10 taskbar have on the (left) side. Unfortunately, although I set it to small icons the bar is pretty wide. Do not you know how to make it thinner?  This is how I would like to have it: Locally bounded additive function is linear Let $T:\mathbb{R}^k\to\mathbb{R}^m$ is additive, i.e. $T(X_1+X_2)=T(X_1)+T(X_2)$. $T$ is locally bounded. Prove that $T$ is a linear transformation.  I know there is a relation between boundedness, convexity and scalar multiplicity. But not sure where to start or how to tie things together. How to merge multiple Internet connections into one? My PC has a total of 4 NICs, 2 wired Gigabit Ethernet network cards and also 2 wireless network cards. (One Broadcom with proprietary drivers and Ralink with open source software, which works much better than Broadcom.)  My cellphone can share its connection wirelessly to my PC, but I also have a wired Internet connection. So I have multiple Internet connections to access the Internet. How can I merge 2 or more connections together and balance them to enjoy one unified Internet experience that it is the sum of all Internet connections connected to it.  For example if I have a modem with an Internet connection of 1024kB/s and another one that offers 512kB/s and one small one that offers 128kB/s, after load balancing and merging all connections (Bonding or Teaming), I could download at a speed of 1664kB/s using all 3 Internet connections as one for example.  This question has always intrigued me. Retrieving Maxwell's equations from the minimum action principle I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps.  Starting with the action:  $$S = \int dt \int d^3 x \mathcal{L}_{\mathrm{EM}} = \int dt \int d^3 x \left( -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + j_\mu A^{\mu}\right).$$  In the absence of any sources $j_\mu = 0$ and $c=1$, which after pulling in the negative sign implies  $$S = \frac{1}{2}\int dt \int d^3 x  \,\,\left(E^2 - B^2\right)$$ The next step is to take $\vec{E} = -\vec{\nabla} \phi + \partial_t \vec{A}$ and $\vec{B} = \vec{\nabla} \times \vec{A}$. Letting $\phi = 0$ and directly inserting these into the above yields:  $$S = \frac{1}{2} \int dt \int d^3 x  \,\left( (\partial_t \vec{A})^2 - (\vec{\nabla} \times \vec{A})^2 \right) $$  Now considering $\vec{A} = \vec{A}_0 + \delta \vec{A}$ as some minimal change in our vector potential, with $\vec{A}_0$ gives a minimum for the action and putting this into the above expression we have: $$\delta S = \int dt \int d^3 x \left(\partial_0 \vec{A}_0 \partial_0 \delta \vec{A} + \left(\vec{\nabla} \times \vec{A}_0\right)\cdot\left(\vec{\nabla} \times \delta \vec{A} \right) \right)+ \mathcal{O}(A^2)\,\,\,\,\,\,\, (1)$$ where I have the term  $$\mathcal{O}(A^2) = \int dt \int d^3 x \left( (\partial_0 \vec{A}_0)^2 + (\partial_0 \delta \vec{A})^2 - (\vec{\nabla}\times\vec{A}_0)^2-(\vec{\nabla}\times \delta\vec{A})^2\right)$$  The next step is where I lose our author and go from "Oh ok I get this" to "completely clueless". He rewrites $\delta S$ as:  $$\delta S =  \int dt \int d^3 (\delta x) \vec{A} \mathcal{F(\vec{A}_0)}+ \mathcal{O}(A^2)$$  where $\mathcal{F} = \frac{\delta S}{\delta A}$. What is the purpose of $x\to \delta x$ in the above expression? Is the functional derivative $\mathcal{F}$ a vector quantity? He has it bolded with a bolded $\vec{A}$ in the above expression. One last question takes the above expression further. We assume $\delta \vec{A}$ vanishes at infinity, as it should, and integration by parts yields:  $$\delta S =  -\int dt \int d^3 x \left( \partial^2_0 \vec{A}_0 - (\vec{\nabla} \times \vec{\nabla})\times \vec{A}_0  \right)\delta \vec{A}\,\,\,\,\,\,\,\, (2)$$ How exactly did we go from (1) to (2)? Thanks I appreciate your time! Why does the dock appear on the left when my screen is locked? The dock doesn't work correctly after I enter my password, either. Dealing with "java.lang.OutOfMemoryError: PermGen space" error Django Template Variables and Javascript When I render a page using the Django template renderer, I can pass in a dictionary variable containing various values to manipulate them in the page using {{ myVar }}.  Is there a way to access the same variable in Javascript (perhaps using the DOM, I don't know how Django makes the variables accessible)? I want to be able to lookup details using an AJAX lookup based on the values contained in the variables passed in. How Conditional Random Fields and Logistic Regression could be the same? If you have read  tutorial about CRF, on page 4 under the section Classification, it wants to relate CRF to Logistic Regression (or Maximum Entropy, as it is known by this name in NLP community).   The formulation of Logistic Regression is said to be  $ p(y|x) = \frac{1}{Z(X)}exp \{ \lambda_y + \sum_{j=1}^{K}\lambda_{y,j}x_{j}\} $.  On the other hand, on the Wikipedia  for logistic regression, the formulation is  $ f(t) = \frac{1}{1+e^{-t}} $  and the classifier's formulation is the explanation of this formulation which is derived from Logistic Function.  My question is, first, how Logistic Regression and Maximum Entropy Classifier are related to each other and are identical?   Second, the CRF tutorial says Logistic Regression (or Maximum Entropy Classifier) is simple CRF model, how? What are good strategies for booster drafts? I know that doing a booster draft can be somewhat complicated, because to really be good you need to know a lot about the set you're drafting (or be really good at evaluating cards quickly) and to pay attention to signal cards.    Besides going into the whole complicated strategies of knowing the set and paying attention to signal cards, what are some relatively simple/basic guidelines for drafting? I am in the process of redesigning an interface with a lot of Tabular data that is previously simply used as tables that look like the 19th century. I was a bit confused whether to switch it to a Card View sort of layout and present the data in that way, or to leave it in a Tabular View itself and instead just style around it.  I would like to know what could be the better approach when it comes to User Experience and what seems more at ease to the customer as I want the product to be easier for the customer to use rather than looking complicated to them.  The users of the product would be on the financial sides of the industry so, if needed please keep that into consideration. How does extra damage work for critical hits? Background:   Story: A colleague of mine told me about  and it seems good to me. I am always trying to use tools which Mac OS X itself gives me, so I've given the Keychain a try. It seems satisfying, but I don't know how to tell Google Chrome to use my specific keychain. I need it to separate saved stuff for work and for private (syncing private to work, but separated from work data).  Stuff:   Google Chrome 21.0.1180.57 (Fully updated) Mac OS X Lion (Fully updated) OS X Mountain Lion (Fully updated)   Question:  How do I tell to Chrome to use a specific keychain and to save data from/to this keychain? Update a field without changing the node I need to change a field in a node without altering the 'changed' timestamp. I know this was possible in Drupal 7 using field_attach_update(), but that has been removed since then.  I could use an update query and change the field directly in the database, but I was wondering if there is a better way (or a replacement for field_attach_update()). How to execute hostapd command in cli? I always got error. When i execute hostapd command. I was changed everything in my hostapd.conf file but i got error.  hostapd_cli wps_pbc Failed to connect to hostapd - wpa_ctrl_open: No such file or directory  Can anyone help to me.? PHP generate file for download then redirect Read only field not working in page layout I have custom object called candidate. I have created field name called first name which is read-only in the page layout. Once a record is created with first name field populated I am able to edit that field. Why I am able to edit (I mean getting pencil icon). Can anyone suggest me for this issue?