There have been many contributions to mathlib from Aristotle already, it’s a major use case for our users
352 karma · joined April 14, 2007
If you also think this is the future of programming and are interested in building it, please consider joining us: https://jobs.ashbyhq.com/Harmonic. We have incredibly interesting challenges across the stack, from infra to AI to Lean.
Yes, the government funds research, the benefit of which accrues to all of society. There is no credible alternative to government funding for public research; the scales are not the same. Private funding of basic research (internal R&D budgets) accrues benefits to the funders directly.
Knock-on effects to cutting the government funding include a decimation of future research leadership by the US by making it unattractive to study and do basic research here. Other countries are taking advantage of this (like any private sector company would if one of its competitors makes such a drastic mistake).
> Lastly you are implying that your graduate research was something that advanced some combination of science, humanity, the country...or maybe that the current work you do is of such value that the government should have paid your way to your current status.
You're overly indexing on the benefits any specific researcher gets from research funding. Research is currently done by humans; if we want more research done, then the people doing that research will necessarily get some of the benefits.
Also, since you're commenting on a software-focused web forum -- you should be aware that the compensation for government-funded researchers is a fraction of what these folks could make in the private sector. Framing it as some greedy theft of resources from the public is foolish and disingenuous to readers who don't know about how science funding works in the US.
Write an efficient, not brute force, python program that solves the following problem: suppose we have two unknown quantities x and y. If three time x plus two times y is twenty, and 2 times x plus three time y is ten, what are x and y?
To solve this problem efficiently, we can use linear algebra. We can represent the equations as a system of linear equations, and then use matrix operations to solve for the unknown quantities x and y.
First, we can represent the equations as follows:
3x + 2y = 20
2x + 3y = 10
Next, we can put the equations in matrix form:
| 3 2 | | x | | 20 |
| 2 3 | * | y | = | 10 |
To solve for x and y, we can use the inverse of the matrix on the left side to eliminate the coefficients. The inverse of a matrix is denoted as A^-1, and is calculated as follows:
A^-1 = (1/det(A)) * adj(A)
Where det(A) is the determinant of the matrix A, and adj(A) is the adjugate matrix of A. The determinant of a 2x2 matrix is calculated as follows:
det(A) = a * d - b * c
Where a, b, c, and d are the elements of the matrix A:
| a b |
| c d |
The adjugate matrix of a 2x2 matrix is calculated as follows:
adj(A) = | d -b |
| -c a |
We can then calculate the inverse of the matrix on the left side of the equations, and use it to solve for x and y:
| 3 2 |^-1 1 | 3 -2 |
| 2 3 | ----- * | -2 3 | = (1/5) * | 3 -2 | = | 3/5 -2/5 |
|-2 3 | |-2/5 3/5 |
| 3/5 -2/5 | | x | | 20 |
|-2/5 3/5 | * | y | = | 10 |
We can then solve for x and y by multiplying the inverse matrix with the vector on the right side of the equations:
| 3/5 -2/5 | | 20 |
|-2/5 3/5 | * | 10 | = | 6 |
| 7 |
Therefore, the values of x and y are 6 and 7, respectively.
Here is the complete Python program to solve this problem using linear algebra:
Calculate the determinant of a 2x2 matrix
def determinant(a, b, c, d):
return a * d - b * c
Calculate the adjugate matrix of a 2x2 matrix
def adjugate(a, b, c, d):
return [[d, -b], [-c, a]]
Calculate the inverse of a 2x2 matrix
def inverse(a, b, c, d):
det = determinant(a, b, c, d)
adj = adjugate(a, b, c, d)
return [[adj[0][0] / det, adj[0][1] / det], [adj[1][0] / det, adj[1][1] / det]]
Solve the system of linear equations
def solve(a, b, c, d, e, f):
inv = inverse(a, b, c, d)
return [inv[0][0] * e Write an efficient, not brute force, program that solves the following problem: suppose we have two unknown quantities x and y. If three time x plus two times y is twenty, and 2 times x plus three time y is ten, what are x and y?
One way to solve this problem efficiently is to use the method of elimination. We can set up a system of equations as follows:
3x + 2y = 20
2x + 3y = 10
We can then multiply the first equation by 2 and the second equation by 3, to get:
6x + 4y = 40
6x + 9y = 30
We can then subtract the second equation from the first equation, to get:
-5y = 10
y = -2
We can then substitute this value of y into one of the original equations (for example, the first one), to get:
3x + 2(-2) = 20
3x - 4 = 20
3x = 24
x = 8
Therefore, the values of x and y are x = 8 and y = -2.Mr. Brian Simms, K.C. (Lennox Paton Counsel and Attorney-at Law) was appointed as provisional liquidator. Additionally, the powers of the directors of FDM have been suspended and no assets of FDM, client assets or trust assets held by FDM, can be transferred, assigned or otherwise dealt with, without the written approval of the provisional liquidator.
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Helm.ai is a rapidly growing seed-stage autonomous vehicle startup. Our deep learning approach to self-driving is uniquely data- and capital-efficient, allowing us to get to market quickly. Our team consists of researchers from top schools like Harvard, MIT, Stanford, and Caltech and engineers from companies like Google, Stripe, Quora, and more.
* Autonomous Vehicle Engineer - https://tinyurl.com/HelmAVE
* Software Engineer - https://tinyurl.com/HelmSWE
* Research Engineer (Perception) - https://tinyurl.com/HelmRE
* Systems Engineer - https://tinyurl.com/HelmSYSE
You can read recent articles published about Helm.ai below:
* Forbes, "Android of Self Driving Cars" - https://tinyurl.com/HelmForbes
* Medium, "Helm.ai Pioneers Breakthrough 'Deep Teaching' of Neural Nets" - https://tinyurl.com/HelmMedium
Helm.ai is a rapidly growing seed-stage autonomous vehicle startup. Our deep learning approach to self-driving is uniquely data- and capital-efficient, allowing us to get to market quickly. Our team consists of researchers from top schools like Harvard, MIT, Stanford, and Caltech and engineers from companies like Google, Stripe, Quora, and more.
* Autonomous Vehicle Engineer - https://tinyurl.com/HelmAVE
* Software Engineer - https://tinyurl.com/HelmSWE
* Research Engineer (Perception) - https://tinyurl.com/HelmRE
* Systems Engineer - https://tinyurl.com/HelmSYSE
You can read recent articles published about Helm.ai below:
* Forbes, "Android of Self Driving Cars" - https://tinyurl.com/HelmForbes
* Medium, "Helm.ai Pioneers Breakthrough 'Deep Teaching' of Neural Nets" - https://tinyurl.com/HelmMedium
1. They DO have cameras onboard with the exposure settings necessary to see the woman in the video, and have not released the video because it makes for bad PR.
2. They DO NOT have such cameras, in which case they should have their self-driving permit revoked because this failure mode is completely predictable to anybody working in this space. And anyway their LIDAR should've detected the person.
Starting with a founder population of genetically heterogeneous rats (N/NIH stock), we applied two-way artificial selection based on the magnitude of change in running capacity after completing 8 weeks of standardized aerobic treadmill training. After 15 generations of selection, rats bred as HRT increased maximal treadmill running distance from 646 to 869 m (change, 223 ± 20 m), whereas rats bred as LRT decreased from 620 to 555 m (change, −65 ± 15 m) after completing the same absolute amount of training (Koch et al. 2013).
This is a huge confounding variable. There is a very good chance these cells have an impact on these rats' ability to run long distances after training, so it's completely reasonable to expect that the cell growth would respond well to the very exercise the rats were selected for responding well to! It does not show that the same effect would happen in a normal rat (the LRT rats did not see a difference in this particular cell growth, but they were also nonrandom).