## Statistical Physics of Coupled Oscillator Networks (GitHub)

This video shows the collective behavior of 65,536 noisy coupled
nonlinear two-cycle oscillators occupying each node of a 2D grid.
The oscillators lying within each black cluster are synchronized
with each other but are out-of-sync with the oscillators in surrounding white
clusters. We have shown that this collective behavior of a coupled
oscillator network is identical to the collective behavior of a
two-state magnetic spin system, such as iron, near a critical transition from permanent to
non-permanent magnetism and of certain liquid-vapor transitions.
These theoretical results are based on **large-scale Monte Carlo simulations**
optimized in **C++** and distributed over 192 cores of a High
Performance Computing Cluster. Over 100GB of simulated data were
analyzed and visualized in **Python (numpy, scipy, matplotlib)**.
Machine learning techniques used to perform statistical inference
on an **Undirected Graphical Model (or Markov Random Field)**. This
research is supported by an NSF
INSPIRE award,
jointly funded by the Directorates for Mathematical and Physical
Sciences (MPS) and Biological Sciences (BIO). We are in the process of applying for
additional funding in collaboration with Steve Strogatz and Dan
Stein.

**Noble, AE**, Machta,
J, and Hastings, A. (2015) Emergent
Long-range Synchronization of Oscillating Ecological Populations
Without External Forcing Described by Ising Universality. **Nature
Communications.** 6: 6664. (open source) [journal]

## Network Anomaly Detection (GitHub)

Detecting anomalies in big spatiotemporal data sets is vitally
important to many areas of industry, including the tech,
health, financial, and power sectors. Rapid detection and mitigation
capabilities are needed to prevent localized distruptions or outbreaks from propagating across
large networks. A **Principal Component Analysis (PCA)** is one approach to
the **de-noising** and **dimensional reduction** of existing spatiotemporal data in order to
establish a baseline against which anomalies can be detected on fast timescales. The
leading principal components are also key baseline statistics that predictive spatiotemporal
process models should be able to reproduce. I am collaborating with
Bryan
Grenfell and Ottar
Bjornstad on an investigation of how the PCA approach might
improve upon exisiting epidemiological models of measles outbreaks in the UK following World War II. The video above is a visualization of
a portion of that data. The diameter of each disk is proportional to
the number of measles cases reported biweekly for each of the sixty largest UK cities. A PCA
can also detect anomalies in 1GB of operations data from the San
Fransisco bike share program. All of
these analyses were performed in
**Python (numpy, scipy, pandas, matplotlib)**.

## Mutivartiate Stochastic Processes for Population Biology and Game
Theory

Nonlinear **stochastic processes** generally require a numerical
solution, and the numerical simulation of a multivariate stochastic
process can be computationally expensive. The figure here
illustrates a scenario in which the dynamics of a nonlinear
multivariate stochastic process (panel b) can be predicted based on the
much simpler analysis of a purely deterministic system of ordinary
differential equations (panel a). Numerical simulations were performed
in **Python (numpy, scipy)**; results were plotted in **Mathematica**. Matching
conditions for the stochastic process and deterministic system were
obtained from the construction and analysis of a nonlinear multivariate **Markov Chain**.

**Noble, AE**, Hastings,
A, and Fagan, WF. (2011) Multivariate
Moran Process with Lotka-Volterra Phenomenology. **Physical Review
Letters** 107: 228101. [journal][arXiv]

## Constraining Particle Physics Models of the Higgs Boson

My Ph. D. research in theoretical particle physics focused on
confronting models with data. Measurements from terrestrial colliders
and satellite observatories
can be combined to place tight constraints on hypothetical models for
new particles and forces. The figure shown here is based on Feynman
diagram calculations and least-squares **regressions** performed
in
**Mathematica**. White indicates the region of the two-dimensional
model parameter space that is consistent
with collider data at the 95% C.L. or better. Green and blue regions are
consistent at the 99% and 99.9% C.L., respectively. The narrow bands of
parameter space lying between each of two sets of dashed lines are
consistent, at the 95% C.L., with satellite-based constraints on the
density of dark matter in the universe. In contrast to many other
models for new physics, joint constraints from collider and satellite data
do not rule out the existence of a "heavy" Higgs - a tantalizing possibility of great
current interest in the particle physics community.

Hubisz,
J, Meade, P,
**AE Noble**, and Perelstein, M. (2005)
Electroweak Precision Constraints on the Littlest Higgs Model with T
Parity. **Journal of High Energy Physics** 74: 035002. [journal][inspire]