Complex network has been a popular topic in the past decade and attracted the research interests of multiple disciplines, including computer science, social science, physical science and mathematical ...

Deep learning models have shown great potential in predicting and engineering functional enzymes and proteins. Does this prowess extend to other fields of biology as well? Contrary to expectations, a ...

Nonlinear dynamics investigates systems whose governing equations exhibit terms that are non-proportional or non-additive, giving rise to rich phenomena such as bifurcations, limit cycles, solitons ...

Building on ES_APPM 420-1, this course covers advanced perturbation and asymptotic methods. They may include methods for ordinary differential equations (e.g. WKB method), for integrals (e.g.

The Bernoulli shift map is a well-known chaotic map in chaos theory. For a binary system, however, the output is not chaotic and converges to zero instead. One way to prevent this is by perturbing the ...

A recent study, led by Sabre Kais, Distinguished Professor of Chemistry and professor of electrical and computer engineering at Purdue University, and IBM’s Barbara Jones, used a quantum computer to ...

This course teaches commonly used approximation methods in quantum mechanics. They include time-independent perturbation theory, time-dependent perturbation theory, tight binding method, variational ...

Understanding how neural circuit activity emerges from, and feeds back into, underlying molecular states is a central challenge in modern neuroscience.

Is it possible for a deterministic system to be unpredictable? Although counter-intuitive, the answer is yes. Such systems are called “chaotic systems,” which are characterized by sensitive dependence ...

Asymptotic expansions of integrals. Regular and singular perturbation methods for ordinary and partial differential equations. Boundary layer theory. Matched asymptotic expansions. Homogenization. Two ...