10. How to Make Friends and Influence People at Conferences
By Nilima Nigam
In the May 2018 issue, Nilima Nigam gave a light-hearted yet very real account of the anxiety that accompanies networking and socializing at conferences. Many SIAM meeting attendees likely experience similar trepidations about meeting new people at conferences and the urge to “hide behind a plant” that Nigam so earnestly describes. Read the article!
9. Detecting Gerrymandering with Mathematics
By Lakshmi Chandrasekaran
In the July/August issue, Lakshmi Chandrasekaran described how researchers use a variety of mathematical techniques to detect gerrymandering, the practice by which a political party alters congressional districts in its favor via a process called redistricting. Such evidence has recently held in court. Partisan biases in redistricting come into play in the U.S. following the census count every ten years. Jonathan Mattingly of Duke University uses sampling methods to evaluate partisan gerrymanders. After estimating the entire population of admissible redistricting plans, his team characterizes the level of gerrymandering in a district by identifying ways in which a plan deviates from what is typical. Read the article!
8. Research Software Engineer: A New Career Track?
By Chris Richardson and Mike Croucher
In the March issue, Chris Richardson and Mike Croucher outlined a U.K. initiative spearheaded by the Software Sustainability Institute (SSI) to improve academic software reliability and reusability. By encouraging better software practices, offering collaborations workshops, and pushing for a unique research software engineering career track, the SSI is helping enhance research software in academia. Read the article!
7. Interpreting Deep Learning: The Machine Learning Rorschach Test?
By Adam S. Charles
In the July/August issue, Adam Charles explained that the quest for theoretical understanding of deep learning has intensified in recent years and interpretations comprise different analysis styles from various fields, such as learning theory, sparse signal analysis, physics, chemistry, and psychology. This search for meaning is essential to deep learning’s proper implementation. Multilayer or deep neural networks (DNNs)—which consist of many interconnected nodes grouped into layers with stunningly simple operations—have quickly become a centerpiece of the machine learning toolbox, where they are simultaneously one of the simplest and most complex methods. Charles argues that a convergence of the literature around DNN theory would go a long way towards validation. Read the article!
6. Sensitive Dependence on Network Structure: Analog of Chaos and Opportunity for Control
By Adilson E. Motter and Takashi Nishikawa
In the April Special Issue on Control and Systems Theory, Adilson Motter and Takashi Nishikawa report on the recent discovery that network dynamics often depends sensitively on network structure, especially when the structure is optimized for maximum stability of a desired behavior. After elaborating on what such sensitive dependence means, they explain how this property can be utilized to make networks more responsive to control. Read the article!
5. Reservoir Computing: Harnessing a Universal Dynamical System
By Daniel J. Gauthier
In March’s Dynamical Systems Special Issue, Daniel Gauthier described how a reservoir computer can train a “universal” dynamical system to predict the dynamics of a desired system. While artificial intelligence algorithms are in great demand to process massive data sets for classification tasks, learning a deterministic dynamical system is a worthwhile goal for applications such as weather forecasting and radio transmitter fingerprinting. Read the article!
4. Mathematical Modelling Disproves Decades-old Hypothesis
A Potential New Way to Treat Heart Disease
By Alona Ben-Tal
In June’s Life Sciences Special issue, Alona Ben-Tal described mathematics’ crucial role in offering clarity and insight in dispelling misconceptions in the biological sciences. Such misconceptions commonly arise in the study of living systems, which often display built-in redundancies—referred to as “plasticity”—enabling more than one mechanism to support the same function, leading to confusion as to which mechanism is most important. Read the article!
3. A Visual Way to Teach the Fast Fourier Transform
By Jithin D. George
In the November issue, Jithin George offered a visual perspective that captures the essential meaning of the fast Fourier transform, with the goal of conveying the simple yet beautiful geometric interpretation of the algorithm behind FFT. Through this analysis, George hopes to dispel the notion that one needs to completely understand the Fourier transform to comprehend the FFT. Read the article!
2. Self-organization in Space and Time
By Matthew R. Francis
In March’s Dynamical Systems Special Issue, Matthew Francis detailed the work of a team of mathematicians who developed a simple mathematical model for the simultaneous study of spatially-coordinated and synchronous behavior. While synchronization, or self-organization in time, and aggregation, or self-organization in space, are conceptually similar, they have so far largely been studied separately. The simple “swarmalator” model, as the researchers call it, is designed to study basic principles before application to real-world physical or biological systems. Read the article!
1. Differentiation With(out) a Difference
By Nicholas Higham
In the June issue, Nicholas Higham discussed an instance of the maxim by mathematician Jacques Hadamard, which states, ““The shortest and best way between two truths of the real domain often passes through the imaginary one.” Higham explained the interplay between truncation errors and rounding errors, which poses a fundamental tension in numerical analysis and endorses the complex-step approximation as an easy-to-appreciate example of the potential gains from “going complex.” Read the article!