Toggle light / dark theme

In the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.

“I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework.”

The question asked whether the Conway knot — a snarl discovered more than half a century ago by the legendary mathematician John Horton Conway — is a slice of a higher-dimensional knot. “Sliceness” is one of the first natural questions knot theorists ask about knots in higher-dimensional spaces, and mathematicians had been able to answer it for all of the thousands of knots with 12 or fewer crossings — except one. The Conway knot, which has 11 crossings, had thumbed its nose at mathematicians for decades.

As expected, they discovered large fluctuations in the composition and daily changes of the human and mouse gut microbiomes. But strikingly, these apparently chaotic fluctuations followed several elegant ecological laws.

“Similar to many animal ecologies and complex financial markets, a healthy gut microbiome is never truly at equilibrium,” Vitkup says. “For example, the number of a particular bacterial species on day one is never the same on day two, and so on. It constantly fluctuates, like stocks in a financial market or number of animals in a valley, but these fluctuations are not arbitrary. In fact, they follow predictable patterns described by Taylor’s power law, a well-established principle in animal ecology that describe how fluctuations are related to the relative number of bacteria for different species.”

Other discovered laws of the gut microbiome also followed principles frequently observed in animal ecologies and economic systems, including the tendency of gut bacteria abundances to slowly but predictably drift over time and the tendency of species to appear and disappear from the gut microbiome at predictable times.

“It is amazing that microscopic biological communities—which are about six orders of magnitude smaller than macroscopic ecosystems analyzed previously—appear to be governed by a similar set of mathematical and statistical principles,” says Vitkup.

Laws allow identification of abnormal bacterial behavior.

These universal principles should help researchers to better understand what processes govern the microbial dynamics in the gut. Using the statistical laws, the Columbia researchers were able to identify particular bacterial species with abnormal fluctuations. These wildly fluctuating bacteria were associated with documented periods of gut distress or travel to foreign countries in humans providing data for the study. Thus, this approach may immediately allow researchers to understand and identify which specific bacteria are out of line and behave in a potentially harmful fashion.

Using mice data, the researchers also observed that microbiomes associated with unhealthy high fat diets drift in time significantly faster compared with microbiomes feeding on healthier high fiber diets. This demonstrates that ecological laws can be applied to understand how various dietary changes may affect and perhaps alleviate persistent microbiome instabilities.

Gut microbiome as miniature ecological laboratory.

The study by Columbia researchers also opens an exciting opportunity to use the gut microbial communities as a model system for exploring general ecological relationships. “Ecologists have debated for years why and how these natural ecological laws arise, without any clear answers,” says Vitkup. “Previous ecological research has been mostly limited to observational studies, which can take decades to perform for animals and plants. And some key experiments, such as additions or removal of particular species simply cannot be performed.”


The fluctuations of gut microbial communities follow ecological principles developed for animals and financial markets, which may help to predict disease biomarkers and effects of unhealthy diets.

Plant scientists have long known that crop yield is proportional to the dose of nitrogen fertilizer, but the increased use of fertilizers is costly and harmful to the environment. Until now, the underlying mechanisms by which plants adjust their growth according to the nitrogen dose has been unknown—a key finding that could help enhance plant growth and limit fertilizer use.

In a new study published in the Proceedings of the National Academy of Sciences (PNAS), plant genomic scientists at New York University’s Center for Genomics & Systems Biology discovered the missing piece in the molecular link between a plant’s perception of the nitrogen dose in its environment and the dose-responsive changes in its biomass.

Taking a novel approach, the NYU researchers examined how increasing doses of nitrogen created changes in ’ genome-wide expression as a function of time. They then used mathematical models to investigate the rate of change of messenger RNA (mRNA) for thousands of genes within the genome to this experimental set up.

Circa 2018


After 10 years, Prof. Raimar Wulkenhaar from the University of Münster’s Mathematical Institute and his colleague Dr. Erik Panzer from the University of Oxford have solved a mathematical equation which was considered to be unsolvable. The equation is to be used to find answers to questions posed by elementary particle physics. In this interview with Christina Heimken, Wulkenhaar looks back on the challenges encountered in looking for the formula for a solution and he explains why the work is not yet finished.

You worked on the solution to the equation for 10 years. What made this equation so difficult to solve?

It’s a non-linear integral equation with two variables. Such an equation is so complex that you do actually think there can’t possibly be any formula for a solution. Two variables alone are a challenge in themselves, and there are no established approaches for finding a solution for non-linear integral equations. Nevertheless, again and again during those 10 years there were glimmers of hope and as a result, and despite all the difficulties, I thought finding an explicit formula for a solution – expressed through known functions – was actually possible.

Rice University researchers have discovered a hidden symmetry in the chemical kinetic equations scientists have long used to model and study many of the chemical processes essential for life.

The find has implications for drug design, genetics and biomedical research and is described in a study published this month in the Proceedings of the National Academy of Sciences. To illustrate the biological ramifications, study co-authors Oleg Igoshin, Anatoly Kolomeisky and Joel Mallory of Rice’s Center for Theoretical Biological Physics (CTBP) used three wide-ranging examples: protein folding, enzyme catalysis and motor protein efficiency.

In each case, the researchers demonstrated that a simple mathematical ratio shows that the likelihood of errors is controlled by kinetics rather than thermodynamics.

Hundreds of books are now free to download.

Springer has released hundreds of free books on a wide range of topics to the general public. The list, which includes 408 books in total, covers a wide range of scientific and technological topics. In order to save you some time, I have created one list of all the books (65 in number) that are relevant to the data and Machine Learning field.

Among the books, you will find those dealing with the mathematical side of the domain (Algebra, Statistics, and more), along with more advanced books on Deep Learning and other advanced topics. You also could find some good books in various programming languages such as Python, R, and MATLAB, etc.