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Kostia Zuev - Research
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Prospective Students

If you are interested in working with me in one of the research areas described on the right, or have your own project in mind that you would like to discuss, please send me an email to kostia [at] caltech [dot] edu. 

Jenna Birch (U of Liverpool)
Will Cunningham (Northeastern U)
Or Eisenberg (Northeastern U)
Alfredo Garbuño-Inigo (U of Liverpool)
Stephen Wu (Caltech, now at ETH) 


[16] [18]

Ivan Au (U of Liverpool)
James Beck (Caltech)
Ginestra Bianconi (QMUL)
Marián Boguñá (U de Barcelona)
Alexey Bolsinov (Loughborough U)
Alex DiazDelaO (U of Liverpool)
Lambros Katafygiotis (HKUST)
Dima Krioukov (Northeastern U)
Athanasios Pantelous (U of Liverpool)
Fragkiskos Papadopoulos

[7] [8] [9] [11] [17]
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[3] [5] [6] [7]
[12] [13] [15]

Erdös Number
My Erdös number is (at most) 4:

Google Scholar:

Research Areas

I am a mathematician with broad research interests. I like to branch out, learn new areas of math and applied science, and jump on new problems. I have written two completely independent Ph.D. dissertations and published papers being affiliated with departments of mathematics, physics, and civil engineering. So, according to Dyson's birds-and-frogs” classification, I am a frog which occasionally makes very long jumps. Most of my research falls under the umbrella of applied probability & statistics and has a strong geometric flavor. In particular, I am interested in complex networks, Markov chain Monte Carlo algorithms, rare event estimation, Bayesian inference, and integrable Hamiltonian systems.

- Somewhere in Hong Kong

Complex Networks

Networks are everywhere. Examples include networks of roads, railways, airline routes, electric power grids, the Internet, the World Wide Web, networks of friendship between individuals, business relations between companies, citations between papers, protein interaction networks, food webs, etc. Networks are different, but many have some structural properties in common. One of the fundamental problems in the study of complex networks is to identify evolution mechanisms that shape the structure and dynamics of large real networks.
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Markov Chain Monte Carlo
Markov chain Monte Carlo (MCMC) is a class of algorithms for sampling from complex probability distributions. These methods are based on constructing a Markov chain whose stationary distribution is the target distribution of interest. The most common application of MCMC is numerical calculation of multi-dimensional integrals, which is known to be a very important, yet difficult problem in applied mathematics.
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Rare Event Estimation
An event is rare if its occurrence is unlikely. Getting ten heads in ten flips of a fair coin, for example, is a rare event. In probabilistic terms, this means that the event occupies a tiny portion of the underlying sample space. If the occurrence of a rare event does not cause substantial consequences (say, you lose a dollar in the coin example), the event can be safely ignored, since it is both unimportant and statistically negligible. In many applications, however, there are events which, although rare, may lead to catastrophes.
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Bayesian Inference
A Bayesian approach to statistics views probability as a measure of the plausibility of a proposition when incomplete information does not allow us to establish its truth or falsehood with certainty. Bayesian probability theory was, in fact, originally developed by Laplace for statistical analysis of astronomical observations.
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Integrable Hamiltonian Systems
A Hamiltonian system is a system of differential equations which can be written in a very “nice” (Hamiltonian) form. Liouville integrability means that a system has sufficiently many first integrals in involution. In this case one can already make a strong qualitative conclusions on the trajectories’ behavior.
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