## Assorted Links (Economics)

*By dcerezo On 27/08/2012 · Leave a Comment · In economics, links*

- On Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary component: a hidden gem on one of the most celebrated results of the twentieth century.
- Why Central Planning?: some very interesting historical examples, but tyrants only caring about control? Really? Nah.
- US Monetary Policy since the Financial Crisis: the 2008 crisis was a liquidity crisis. And the Fed profited from the rescue.
- How Large is the Magnitude of Fixed-Mobile Substitution?
- Unveiling the Power Relationships within VC Firms

## To Err is CAS-possible

*By dcerezo On 26/08/2012 · Leave a Comment · In mathematics*

I was aware that there are too many errors on any CAS to be listed on the margin of their accompanying documentation. But finding the culprit after hours of debugging, a very simple bug but with a very high impact since other complex calculations are being based on its proper calculation, is a disturbing experience. It turns out that, in Mathematica,

**In[1]:= badIntegration ****= ****Integrate****[****1 ****/ (****2 ****+ ****Cos****[****x****])****, ****{****x, 0, y}, Assumptions ****-> ****y ****> Pi]**

**Out[1]:= 2(Pi+ ArcTan[Tan[y/2]/ Sqrt(3))/Sqrt(3)**

is symbolically evaluated as a discontinuous function, even if it must clearly be continuous, since the integrand is everywhere continuous, finite and positive. But the Weierstrass substitution method used internally when symbolically calculating integrals of inverse trigonometric functions sometimes produces discontinuities. Go figure.

Lesson learned: as a safety measure, always use multiple CAS programs (SAGE, Maple, …) to compare solutions when getting strange results.

### Archives

- September 2017
- February 2017
- April 2014
- March 2014
- December 2013
- November 2013
- July 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011

### Blogroll

- ACM Queue
- Asymco
- Bentham's Gaze
- Bristol Cryptography Blog
- Computational Complexity
- Cryptographic Engineering
- ECRYPT-EU
- Elliptic News
- ePrint IACR
- Financial Times Tech Blog
- Gödel's Lost Letter and P=NP
- IEEE Spectrum
- ImperialViolet
- InfoQ
- Jefferson's Wheel
- Lessons Learned
- Light Blue Touchpaper
- Marginal Revolution
- Musing on Markets
- Nature
- Nick Higham
- Outsourced Bits
- Quanta Magazine
- Renesys Blog
- Schneier on Security
- Science
- Telco 2.0
- The Economist
- The Leisure of the Theory Class
- The morning paper
- Tomasz Tunguz
- Turing’s Invisible Hand
- Unenumerated