### Plotting the sum of two points on an elliptic curve

I am doing an experiment to prove the associativity of the addition of points on an elliptic curve. So far, I have produced a code which allows me to move points on my curve.

To find their sum, I need to draw a line till it intersects a curve in the third point, then mirror this point around $x$ axis and put a dot there.

But I am completely stuck in this moment. I have tried using NSolve with InterpolatingPolynomial, but got no result.

Here is the code so far:

Extr = {x /. #, y /. #} &;
Att =
Extr[
NMinimize[{(x - #[[1]])^2 + (y - #[[2]])^2, x - x^3 + y^2 == 0}, {x, y}, AccuracyGoal -> 10, PrecisionGoal -> 8][[2]]] &;

DynamicModule[{loc1 = {0, 0}, pt1 = {0, 0}, pt2 = {1, 0}, loc2 = {1, 0}, pt3= {-1, 0}},
{
LocatorPane[Dynamic[{loc1, loc2}],
ContourPlot[{y^2 - x (x - 1) (x + 1) == 0}, {x, -2, 2}, {y, -2, 2},
AxesLabel -> Automatic, ImageSize -> 600,
Epilog -> {Red, PointSize[Large],
Point[Dynamic[pt1 = Att[loc1]]],
Green,
Point[Dynamic[pt2 = Att[loc2]]],
Yellow, Thick,
Dynamic[InfiniteLine[{pt1, pt2}]]
}
]
],
Dynamic[{pt1, pt2, pt3}];
}
]


How should I get a point of intersection into pt3 so it will be of the same type as pt1 and pt2?

### If/When to stop asking a client for clarification and just design

I am an in-house designer for a small tech start-up business. I create all of their advertising materials.

This is an issue I've run into many times with my point of contact from whom I get the design requests from.

for example they are asking me to create a backdrop for a trade show booth and they just asked for a "simple" background. After asking for more details they respond just make a "colored background" with our logo. At which I ask do you mean you want a solid colored background or an interesting pattern that will catch peoples attention?

So my question is: is there a time to stop asking questions and just design something to give them options. Because I feel many times I'm not sure if they know what they really want. Or should I just send them what they asked for a solid colored backdrop with their logo?

I also always direct the design requests to this google form:

to make the information gathering process more streamlined. But it seems the longer I've been using the form the less motivated my point of contact is to fill it with the most information.

Any tips on how teach the client the importance of information gathering?

### Finding specific activity of an enzyme from Km values for a reversible enzyme reaction

I have an enzymatic equation in the form:

$$E + S\xleftrightarrow[k_{-1} = 2.6\text{ x }10^{-2} \text{s}^{-1}]{k_1 = 3 \text{ x }10^8 \text{M}^{-1}\text{s}^{-1}} EX \xleftrightarrow[k_{-2} = 3.8\text{ x }10^{-8} \text{M}^{-1}\text{s}^{-1}]{k_2 = 1.45 \text{ x }10^3 \text{s}^{-1}} E + P$$

For the forward reaction, I have calcluated the $K_m$ value to be:

$${K_m}_f = \frac{k_{-1}+k_2}{k_1} = 4.83\text{ x }10^{-6}\text{M}$$

And for the reverse, I calculated $K_m$ to be:

$${K_m}_r = \frac{k_{-1}+k_2}{k_{-2}} = 3.82\text{ x }10^{-6}\text{M}$$

From this info, I need to somehow calculate the specific activity of the enzyme in both the forward and reverse reactions.

The weight of one enzyme unit is 50,000 kDa.

Specific activity is defined as the number of 'Units' per mg of protein.

One enzyme unit is defined as the amount of enzyme that catalyzes the formation of 1 μmol of product per min under optimal assay conditions, which are assumed for this question (saturation of substrate in forward reaction / saturation of product in reverse reaction).

Can anyone point me in the right direction? I have a feeling that this is related to the $V_{max}$ term in the Michaelis-Menten equation:

$$v = \frac{V_{max}\text{[S]}}{K_m + \text{[S]}}$$

In that $K_m = \text{[S] at}\frac{1}{2}V_{max}$.

So, $$[S]_{f} \text{ at } V_{max} = 2(4.83\text{ x }10^{-6}\text{M}) = 9.66\text{ x }10^{-6}\text{M}$$

So, $$[S]_{r} \text{ at } V_{max} = 2(3.82\text{ x }10^{-6}\text{M}) = 7.64\text{ x }10^{-6}\text{M}$$

but I dont know how to relate it to specific activity.

### Ping [computer] get strange IP address

On my local network, I have multiple computers that I connect to. I don't typically remember the IP address nor do I care. This morning, I went to RDP put "Sam" in the field and pressed enter. It wouldn't connect so I opened up a command prompt to see if I could ping her computer and got something I have never seen before.

C:\Documents and Settings\wbeard52>ping sam
Pinging sam.WORKGROUP [67.215.65.132] with 32 bytes of data:
Reply from 67.215.65.132: bytes=32 time=51ms TTL=56


Obviously, I have a computer named "sam" on the local network and I cam RDP into her computer with her IP address (not the one listed here). I don't have anything in the routing table that I can see.

wbeard52>route print
===========================================================================
Interface List
0x1 ........................... MS TCP Loopback interface
0x2 ...00 0e 35 a5 6f b2 ...... Intel(R) PRO/Wireless 2200BG Network Connection
- Packet Scheduler Miniport
===========================================================================
===========================================================================
Active Routes:
Network Destination        Netmask          Gateway       Interface  Metric
0.0.0.0          0.0.0.0   192.168.52.208  192.168.52.152       10
127.0.0.0        255.0.0.0        127.0.0.1       127.0.0.1       1
192.168.52.0    255.255.255.0   192.168.52.152  192.168.52.152       10
192.168.52.152  255.255.255.255        127.0.0.1       127.0.0.1       10
192.168.52.255  255.255.255.255   192.168.52.152  192.168.52.152       10
224.0.0.0        240.0.0.0   192.168.52.152  192.168.52.152       10
255.255.255.255  255.255.255.255   192.168.52.152  192.168.52.152       1
Default Gateway:    192.168.52.1
===========================================================================
Persistent Routes:
None


What would be causing the ping to be sent to an IP address in San Francisco?

We're working on a new, responsive version of a large website and need to support the main navigation and sub-navigation that changes based on the department. Below is a mockup of how we are approaching this.

Main navigation goes under the hamburger menu while the local sidebar menu becomes a toggle at the top of the page. Is there a better approach? Are there any major pitfalls to this approach?

We are also trying to decide on the label for the submenu toggle. If, for example, this is for a university website and the department is "Financial Aid," should the label just be "Financial Aid" or "Financial Aid Links" or something more generic like "Additional Navigation"? If it just says "Financial Aid," is it still clear that the toggle is sub-navigation? Thanks for any input.

### Is there a way to reverse the order of anchors in a path?

Is there any way to reverse the order of anchors in a path? I don't want to redraw the path again. I want to change the starting anchor point from the starting point of any path to its end. reversing the order of the anchors I already drew has some benefits to me, like:

1. Applying an art brush without flipping the direction of the brush in the stroke options dialogue.
2. If I want my SVG to appear in any webpage in the order that I want, like a drawing stroke animation effect.

### How to approach potential PhD advisors

What is the correct way for a new PhD student to approach an interested faculty member to discuss becoming their student?

Is it better to come with a few thesis project ideas prepared to pitch? Or is it better to come in expecting to have the faculty member to pitch them to the student?

Typically, the student has a year or two after joining a group to formulate an actual research proposal - but at the beginning of the program, when approaching potential advisers, there is only limited time, and limited knowledge of the lab's current focus and planned future projects.

Of course, the answer depends very much on the actual faculty member in question. But in what ways does it depend? Are there any aspects to the decision that remain invariant?

I am in the physical sciences (biology) but to make the question useful to more users, perhaps it may be better if we could have answers covering the peculiarities and commonalities of this question for different fields.

### Non-tax advantaged investing over 401k situation

Is it worth bypassing a 401k in favor of a normal taxable investing account if you can contribute while in the 15% tax bracket and plan to retire in that bracket as well?

After crunching some numbers, it really doesn't matter if you pay the taxes now or later with a 401k unless you are going into a lower bracket.

My assumptions (or things to do before attempting this)

• Contributed to a 401k to bring down taxable income to 15% if not there already
• Have already maxed out a Roth
• Highly likely to retire into this bracket (which seems very reasonable without a mortgage)

Another possible quirk with this is that it also depends on capital gains being 0% when withdrawing in the 15% bracket. This is what I believe the law currently is, please correct me if I am wrong.

If I am looking at this properly it looks like a very good opportunity to have easier access to your money as well as cheaper investing options.

Are there any flaws in how I am looking at this?

### sforce.console.refreshPrimaryTabById is not refreshing feed publisher

have developed a VF form and put it in a quick action & assigned it to case page layout. I am refreshing the current case tab by using console integration toolkit at submit button's oncomplete event (note that I have 30 of this command because I was unable to obtain enclosing tab id from inside quick action VF, so I refresh all open tabs)

var primaryTabId_0 = 'scc-pt-0';
sforce.console.refreshPrimaryTabById(primaryTabId_0, true);


The problem is; console components of page layout and detail view of record refreshes successfully, but the feed actions remain unrefreshed. This VF form links an account to the case, and I cannot see this account prepopulated in one of "update case" quick actions, in the account lookup field. When I manually refresh the page or tab, this field is prepopulated.

Has this issue acknowledged as a bug yet, or is there any other code I can add that will allow me to refresh the feed view as well?

Cheers

### With link and button side by side, and the link is the more important action, how can I SHOW that it's the more important and frequent action?

In this question I asked about the appropriate label for viewing/editing an item in a list.

I settled on a different solution than any there given - that of using a link for the viewing/editing, and a button for the delete. The reason being that the link is more semantically correct - it will navigate you to the details of the item and there you can view, edit, etc.

However now I have another problem...the button seems more noticeable, and more prominent. I would like the link, which is the more frequently used action, to be more noticeable, enticing, and prominent. I want it to be the obvious first choice for a user.

When I have a link and button side by side, and the link is the more important action, how can I SHOW that it's the more important and frequent action?