Mathematical computational biology (MCB) has proven fruitful for all three fields:
mathematics, computation, and biology. One approach to the intersection begins
with symbolic representations of models, so that high-level abstractions and
advantageous problem transformations can be applied computationally before
good numerical methods are called in to do the heavy work of simulation and optimization.
This is the potential advantage of “declarative” modeling. It opens up further connections
between applied mathematics, artificial intelligence (including current trends in hybrid
logical/statistical inference), and foundational mathematics including logic and type theory.
I will illustrate the possibilities with recent work in complex, multiscale computational
biology  including signal transduction in synapses and gene regulation/signaling networks
in  developmental biology, by means of stochastic model reduction, enriched graphical
models expressed using computer algebra, and declarative modeling languages for
multiscale heterogeneous dynamics.

A classical result of Khinchin says that for almost all real numbers α, the geometric mean of the first n digits ai(α) in the continued fraction expansion of α converges to a number K ≈ 2.6854520 . . . (Khinchin’s constant) as n → ∞. On the other hand, for almost all α, the arithmetic mean of the first n continued fraction digits ai(α) approaches infinity as n → ∞. There is a sequence of refinements of the AM-GM inequality, known as Maclaurin’s inequalities, relating the 1/kthpowers of the kth elementary symmetric means of n numbers for 1 ≤ k ≤ n. On the left end (when k = n) we have the geometric mean, and on the right end (k = 1) we have the arithmetic mean. We analyze what happens to the means of continued fraction digits of a typical real number in the limit as one moves f (n) steps away from either extreme. We also study the limiting behavior of such means for quadratic irrational α.

(Joint work with Francesco Cellarosi, Doug Hensley and Steven J. Miller)

We’ll introduce a common model framework for valuing and measuring risk for
options on pools of mortgages. In some market conditions this model does
not accurately match option market prices. Different ways of dealing with
this issue lead to different risk measurements. We’ll consider a “model
free” way of looking at risk through a local vol calculation, and use this
for comparison. As background we’ll introduce agency Mortgage Backed
Securities and some of their associated risk management issues.

Bio:

Without either car or money Michael Landrigan was compelled to bike all
the way from his home town in New Hampshire to study math at Irvine.

At UCI he got a solid training in logic, then in algebraic geometry,
before finally getting his PHD in mathematical physics, in 2001, that
earned a department's Kovalevsky outstanding PhD thesis award. In the
postdoctoral period his interests switched to financial math. Now he is
the head of risk and quantitative opportunities for Catalina Asset
Management, the investment arm for the non-life insurance consolidator
Catalina Holdings. Before Catalina Michael was a Director in Quantitative
Risk Control at UBS Investment Bank. He has also had positions in the
financial industry at MSCI, PIMCO and Rimrock Capital Management, and he
has had faculty positions at Idaho State University and UC Santa Barbara.
Prior to the UCI PhD he got a BA in mathematics at the University of
Chicago.