An Absent Word

There was a time when I relished these kinds of moments. Serene earthquakes, discolored skies, unfinished waterfalls. Staggered, tired, calm. There was always this other word that accompanied the mentioned; not this time, though. A word that made all the difference, and indicated the end and start of a new era of my life.

However, the absence of this word comes with a bittersweet sentiment. As if it were the collateral damage of a teared-down, century-old, mob house; I'm glad is gone, but, alas, the memories and, well, the damage is still damage.

This era doesn't have an expected end apparently, and I'm still not at peace of not knowing what that means in the long run. In the short, I'm obviously thrilled, like I always am (was?). Life, my life, it seems, is now a marathon, not a collection of sprints as it was at first. I now throttle, not run; big change for a man who changed his surroundings more times than he'd like to admit in less than a decade (as I finished writing this sentence, I found myself grinning from the fact that I used the word "man", without realizing, to describe me; big change indeed). This is the bitter part.

And it's fine, as much as I hate its indifferent connotations. I suppose that there comes a time in which the intensity of one's life should be degraded to a reward of accomplishments, instead of the whole of its drive. It's like a drug that helps you live better by making you feel better; it's dangerous when it becomes the end instead of the mean. Transcending that requirement of intensity signifies good judgement and, hell, a better person. This is the sweet part.

So, with that in mind, I forgo my thrive and drive, and I'll try to never be satisfied. Because, even though it does feel good to signal an era with the feeling of satisfaction, it also implies the feeling of abandonement of that era's pursuit. As a kid in a candy warehouse, jumping from one hall to the next, I never have actually felt "finished", even though that's the feeling I'm pursuing; as if it were the end of the mean.

It was a good feeling, though, feeling satisfied; alas, the memories. However, the damage is still damage, and the marathon I've been unknowingly running is catching up with me. I better start learning how to throttle.

My Erdős Number

EDIT (2023-12-31): A decade into my academic career, my Erdős Number is even smaller now.

EDIT (2014-01-08): It appears as though my Erdős Number is smaller than I first thought. Thanks Barry (my PhD supervisor) for your vanity.

Paul Erdős was a very prolific mathematician, and, although technically homeless, he lived with his collaborators, with his famous initial greeting "my mind is open", during their work together. When finished, he moved to the house of another collaborator. He thought of mathematical research as a social event.

As a type of homage, with some admitted humility from Erdős himself, friends of his gave themselves an "Erdős Number" that measured the "collaborative distance" from him. Erdős has the number 0 (and the only that has it), people that have co-authored with him have the number 1, co-authors of co-authors of Erdoős have the number 2, and so on. There's more information in the Wikipedia article on Erdős Number.

In any case, apparently I have one. In the following list of publications, the numbers in brackets are the author's corresponding Erdős number:

Aharoni, R.[1]; Erdős, P.[0]; Linial, N.; Optima of dual integer linear programs. Comb. 8(1): 13-20 (1988).

Aharoni, R.[1]; Herman, G.[2]; Kuba, A.; Binary vectors partially determined by linear equation systems. Discrete Mathematics. 171(1-3): 1-16 (1997).

Ceja, C.; Rascon, C.[3]; Garduño, E.; Carvalho, B; Herman, G.[2]; Smooth normals with blobs for surfaces from 3D binary images. Topology Proceedings. 61(2023): 239-267 (2022).

So, my Paul Erdős number is now 3. I think this the best I'll do; quite well though.

EDIT (2023-12-31): A decade before, a decade after. Two jumps. Not bad.

Borosh, I.; Chui, Charles K.[1]; Erdős, P. [0];, On changes of signs in infinite series. (Russian summary), Anal. Math. 4 (1978), no. 1, 3–12.

Chen, Guang Rong[1]; Chui, Charles K.[2], Design of near-optimal linear digital tracking filters with colored input., J. Comput. Appl. Math. 15 (1986), no. 3, 353–370.

Guan, Zhi-Hong; Chan, C. W.; Leung, Andrew Y. T.[3]; Chen, Guan Rong[2], Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations. (English summary), IEEE Trans. Circuits Systems I Fund. Theory Appl. 48 (2001), no. 8, 1011–1019.

Wang, X., Lennox, B.[4], Goulding, P.R. and Leung, Andrew Y.T.[3], (2000), ‘Practical application of principal component analysis’, Proceedings of the Chinese Control Conference, Honk Kong University, 595-599

Rascon, C. [5]; Lennox, B. [4]; Marjanovic, O. Recovering Independent Components from Shifted Data using FastICA and Swarm Intelligence. Applied Spectroscopy 63(10), Oct. 2009.

So, my Paul Erdős number is 5. Better.

EDIT (2014-01-14): Yet another way to get to the same number.

Alon, Noga[1]; Erdős, P[0]. An application of graph theory to additive number theory. European J. Combin. 6 (1985), no. 3, 201–203.

Alon, Noga[1]; Bradford, Phillip G.; Fleischer, Rudolf[2]. Matching nuts and bolts faster. Inform. Process. Lett. 59 (1996), no. 3, 123–127.

Fleischer, Rudolf[2]; Koga, Hisashi[3]. Balanced scheduling toward loss-free packet queueing and delay fairness. Twelfth Annual International Symposium of Algorithms and Computation. Algorithmica 38 (2004), no. 2, 363–376.

Fuentes, Gibran[4]; Koga, Hisashi[3]; Watanabe, Toshinori. Unsupervised Object Discovery from Images by Mining Local Features Using Hashing. Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications Lecture Notes in Computer Science Volume 5856, 2009, pp 978-985.

Pineda, Luis; Salinas, Lisset; Meza, Ivan; Rascon, Caleb[5]; Fuentes, Gibran[4]. SitLog: A Programming Language for Service Robot Tasks. International Journal of Advanced Robotic Systems, 2013, 10:538.


Erdős, P. [0]; Gerencsér, L.[1]; Máté, A. Problems of graph theory concerning optimal design. Combinatorial theory and its applications, I (Proc. Colloq., Balatonfüred, 1969), pp. 317–325. North-Holland, Amsterdam, 1970.

Gerencsér, László [1]; Rissanen, Jorma [2] Asymptotics of predictive stochastic complexity. New directions in time series analysis, Part II, 93–112, IMA Vol. Math. Appl., 46, Springer, New York, 1993.

Rissanen, J. [2]; Ljung, L. [3] Estimation of optimum structures and parameters for linear systems. Mathematical systems theory (Proc. Internat. Sympos., Internat. Centre Mech. Sci., Udine, 1975), pp. 92–110. Lecture Notes in Econom. and Math. Systems, 131. Springer, Berlin, 1976.

Hagenblad, Anna; Ljung, Lennart [3]; Wills, Adrian [4] Maximum likelihood identification of Wiener models. Automatica J. IFAC 44 (2008), no. 11, 2697–2705.

Heath, W. P. [5]; Wills, A. G. [4] Design of a cross-directional controllers with optimal steady state performance. Eur. J. Control 10 (2004), no. 1, 15–29.

Li, G.; Heath, W. P. [5]; Lennox, B. [6] Concise stability conditions for systems with static nonlinear feedback expressed by a quadratic program. IET Control Theory Appl. 2 (2008), no. 7, 554–563.

Rascon, C. [7]; Lennox, B. [6]; Marjanovic, O. Recovering Independent Components from Shifted Data using FastICA and Swarm Intelligence. Applied Spectroscopy 63(10), Oct. 2009.

So, my Paul Erdős number is 7. Not bad, I suppose.