The solutions to these long-standing problems could further enhance our understanding of symmetries of structures and objects in nature and science, and of long-term behavior of various random processes arising in fields ranging from chemistry and physics to engineering, computer science and economics.

Pham Tiep, the Joshua Barlaz Distinguished Professor of Mathematics in the Rutgers School of Arts and Science’s Department of Mathematics, has completed a proof of the 1955 Height Zero Conjecture posed by Richard Brauer, a leading German-American mathematician who died in 1977. Proof of the conjecture — commonly viewed as one of the most outstanding challenges in a field of math known as the representation theory of finite groups — was published in the September issue of the Annals of Mathematics.

“A conjecture is an idea that you believe has some validity,” said Tiep, who has thought about the Brauer problem for most of his career and worked on it intensively for the past 10 years. “But conjectures have to be proven.I was hoping to advance the field. I never expected to be able to solve this one.”

In a sense, Tiep and his colleagues have been following a blueprint of challenges Brauer laid out for them in a series of mathematical conjectures posed and published in the 1950-60s.

“Some mathematicians have this rare intellect,” Tiep said of Brauer. “It’s as though they came from another planet or from another world. They are capable of seeing hidden phenomena that others can’t.”

In the second advance, Tiep solved a difficult problem in what is known as the Deligne-Lusztig theory, part of the foundational machinery of representation theory. The breakthrough touches on traces, an important feature of a rectangular array known as a matrix. The trace of a matrix is the sum of its diagonal elements. The work is detailed in two papers, one was published in Inventiones mathematicae, vol. 235 (2024), the second in Annals, vol. 200 (2024).

“Tiep’s high-quality work and expertise on finite groups has allowed Rutgers to maintain its status as a top world-wide center in the subject,” said Stephen Miller, a Distinguished Professor and Chair of the Department of Mathematics. “One of the great accomplishments in 20^th century mathematics was the classification of the so-called but perhaps misleadingly named ‘simple’ finite groups, and it is synonymous with Rutgers — it was led from here and many of the most interesting examples were discovered here. Through his amazing stretch of strong work, Tiep brings international visibility to our department.”

Insights from the solution are likely to greatly enhance mathematicians’ understanding of traces, Tiep said. The solution also provides insights that could lead to breakthroughs in other important problems in mathematics, including conjectures posed by the University of Florida mathematician John Thompson and the Israeli mathematician Alexander Lubotzky, he added.

Both breakthroughs are advances in the field of representation theory of finite groups, a subset of algebra. Representation theory is an important tool in many areas of math, including number theory and algebraic geometry as well as in the physical sciences, including particle physics. Through mathematical objects known as groups, representation theory also has been used to study symmetry in molecules, encrypt messages and produce error-correcting codes.

Following the principles of representation theory, mathematicians take abstract shapes that exist in Euclidean geometry — some of them extremely complex — and transform them into arrays of numbers. This can be achieved by identifying certain points that exist in each three- or higher-dimensional shape and converting them to numbers placed in rows and columns.

The reverse operation must work, too, Tiep said: One needs to be able to reconstitute the shape from the sequence of numbers.

Unlike many of his colleagues in the physical sciences who often employ complex devices to advance their work, Tiep said he uses only a pen and paper to conduct his research, which so far has resulted in five books and more than 200 papers in leading mathematical journals.

He jots down math formulas or sentences indicating chains of logic. He also engages in continual conversations — in person or on Zoom — with colleagues as they proceed step by step through a proof.

But progress can come from internal reflection, Tiep said, and ideas burst forth when he is least expecting it.

“Maybe I’m walking with our children or doing some gardening with my wife or just doing something in the kitchen,” he said. “My wife says she always knows when I’m thinking about math.”

On the first proof, Tiep collaborated with Gunter Malle of Technische Universität Kaiserslautern in Germany, Gabriel Navarro of Universitat de València in Spain and Amanda Schaeffer Fry, a former graduate student of Tiep’s who is now at the University of Denver.

For the second breakthrough, Tiep worked with Robert Guralnick of the University of Southern California and Michael Larsen of Indiana University. On the first of two papers that tackle the mathematical problems on traces and solve them, Tiep worked with Guralnick and Larsen. Tiep and Larsen are co-authors of the second paper.

“Tiep and coauthors have obtained bounds on traces which are about as good as we could ever expect to obtain,” Miller said. “It’s a mature subject which is important from many angles, so progress is hard — and applications are many.”

Now, new research reveals that these tiny suitors are leveraging a flexible network of modular brain circuits to quickly adapt to different mating signals. The study, published in Nature, is the first to describe how diverse species of fruit flies plug new sensory inputs, such as pheromones, into a set of basic brain circuits without needing to develop new neural pathways from scratch.

The findings offer a larger framework for understanding how brain wiring can change to influence behavioral evolution. “The diversity of behaviors across the animal kingdom is enormous, but the underlying mechanisms of how nervous systems are shaped by evolution have been very difficult to unravel,” says Vanessa Ruta, head of the Laboratory of Neurophysiology and Behavior. “Here we uncovered what we believe is a key neural mechanism that gives brain circuits the flexibility to rewire across species.”

Plug-and-play

One of the great mysteries of behavioral evolution is how, as species diversify, brain circuits keep pace with the rapid changes in social signals that allow individuals to find their ideal mates. Courtship behaviors, for instance, evolve quickly, making it difficult to imagine that the fly brain completely reinvents itself every time a new pheromone enters the Drosophila repertoire.

But until now, it was not possible to identify where evolution acts in the nervous system to alter behavior, and so the key features of what makes such circuits so adaptable remained a mystery. Ruta’s group turned to fruit flies, where closely related species share similar brains but rely on vastly different cues for mating rituals. D. simulans, for instance, mainly relies on visual cues to find a mate, while D. yakuba evolved a novel capacity to use pheromones to find a mate even in complete darkness. These and other variations presented an opportunity to study how similar brains detect and perceive different social cues.

“We started looking for parts of the brain that might be primed for flexibility,” says Rory Coleman, first author on the study and a postdoctoral fellow in the Ruta lab. “We were searching for features that might make the circuit intrinsically adaptable, potential evolutionary hotspots driving behavioral diversification.”

After comparing pheromone-sensing circuits across multiple species — using behavioral assays, genetic tools, neuroimaging, and CRISPR genome editing — they ultimately singled out sensory neurons in the male forelegs and P1 neurons in the higher brain as key to modulating courtship across species. The team found that the basic neural building blocks of male mating behaviors, such as the P1 neurons, are present across species, but different sensory signals can be flexibly wired into this node. This allows fly species to develop different mating strategies without rewiring their entire brains.

For instance, the researchers found that P1 neurons were activated in response to entirely different types of pheromones in D. melanogaster and D. yakuba. Yet the role of P1 neurons in initiating courtship was still conserved across both species. “One important discovery from our work is that there are discrete nodes within the brains of each of these species that can flexibly integrate new sensory modalities,” Ruta says. “This flexibility allows conserved nodes like the P1 neurons to still initiate courtship in different species but respond to the distinct cues of their females.”

A social brain

This research falls under the umbrella of Rockefeller’s Price Family Center for the Social Brain, an initiative focusing on understanding the neuronal, cellular, and molecular foundations of social behavior. In addition to shedding light on flexibility in the face of new sensory inputs, the present work also illustrates an experimental approach for studying how social behaviors evolve across species. “Our results demonstrate that Drosophila is a powerful system for studying behavioral evolution,” Ruta says.

By examining how variations in neural circuits shape behaviors like mating, the lab hopes to advance our understanding of the complex interplay between brain function and social behaviors, providing a framework for understanding how social circuits are built to produce adaptive behaviors in the human brain. And while the brain structures of flies and humans differ substantially, it is likely some of the underlying principles of how neural circuits evolve and adapt are conserved across species

“We hope that comparative evolutionary studies like this one will reveal the core rules shaping how neural circuits have been built across the animal kingdom, including in humans,” Coleman says. “Many neurological disorders are thought to arise from the miswiring of circuits” Ruta adds. “By examining neural circuits through the lens of evolution, we hope to shed light on which neural motifs can change and how they can be altered, not through the ravages of disease, but as a consequence of evolutionary selection.”

With MS, the body’s immune system attacks myelin, the fatty, white substance that insulates and protects the nerves. MS is chronic and can be unpredictable and disabling.

“People with MS undergo an increased number of tests to monitor MS, making it more likely to detect other diseases,” said study author Emmanuelle Leray, PhD, of Rennes University in France. “We found an association between some types of cancer and MS which may have different explanations depending on a person’s age and the types of cancer. Overall, our study found the increased risk of cancer was quite small.”

For the study, researchers reviewed 10 years of data in the French national health care database. Researchers identified 140,649 people with MS and matched them for factors such as age, sex and residence to 562,596 people without MS. All participants were cancer free three years before the study. They were followed for an average of eight years.

During the study, 8,368 people with MS and 31,796 people without MS developed cancer.

Researchers determined there were 799 cancers per 100,000 person-years for people with MS and 736 cancers per 100,000 person-years for people without MS. Person-years represent both the number of people in the study and the amount of time each person spends in the study.

Researchers found people with MS had a 6% increased risk of developing any type of cancer regardless of age, sex and residence. They also found cancer risk was higher in those under 55 and lower in people 65 and older when compared to people without MS.

Researchers then looked at cancer types. People with MS had a 71% increased risk for bladder cancer, a 68% increased risk for brain cancer and a 24% increased risk for cervical cancer. However, they also had a 20% lower risk of prostate cancer, a 10% lower risk of colorectal cancer and a 9% lower risk of breast cancer.

“While our study found a higher risk for brain cancer, it may be due in part to earlier detection in those with MS since they regularly have brain scans which may detect cancers earlier, before a person has symptoms,” said Leray. “Frequent urinary tract infections in people with MS and the use of immunosuppressant drugs may contribute to their higher risk of bladder and cervical cancers.”

Leray added, “The lower risk for colorectal and breast cancers may be due in part to fewer people with MS getting screened for cancer in older age when they may be experiencing more MS symptoms. More research is needed, including studies that look at more closely at how cancer screenings may play a role.”

A limitation of the study was that researchers were unable to adjust for factors such as education, income, smoking and alcohol consumption since this information was not available in the national database.

The study was supported by the Rennes Institute of Clinical Neurosciences and the EDMUS-ARSEP Foundation.

In a new Northwestern University-led study, microbiologists found that showerheads and toothbrushes are teeming with an extremely diverse collection of viruses — most of which have never been seen before.

Although this might sound ominous, the good news is these viruses don’t target people. They target bacteria.

The microorganisms collected in the study are bacteriophage, or “phage,” a type of virus that infects and replicates inside of bacteria. Although researchers know little about them, phage recently have garnered attention for their potential use in treating antibiotic-resistant bacterial infections. And the previously unknown viruses lurking in our bathrooms could become a treasure trove of materials for exploring those applications.

The study will be published Wednesday (Oct. 9) in the journal Frontiers in Microbiomes.

“The number of viruses that we found is absolutely wild,” said Northwestern’s Erica M. Hartmann, who led the study. “We found many viruses that we know very little about and many others that we have never seen before. It’s amazing how much untapped biodiversity is all around us. And you don’t even have to go far to find it; it’s right under our noses.”

An indoor microbiologist, Hartmann is an associate professor of civil and environmental engineering at Northwestern’s McCormick School of Engineering and a member of the Center for Synthetic Biology.

The return of ‘Operation Pottymouth’

The new study is an offshoot of previous research, in which Hartmann and her colleagues at University of Colorado at Boulder characterized bacteria living on toothbrushes and showerheads. For the previous studies, the researchers asked people to submit used toothbrushes and swabs with samples collected from their showerheads.

Inspired by concerns that a flushing toilet might generate a cloud of aerosol particles, Hartmann affectionately called the toothbrush study, “Operation Pottymouth.”

“This project started as a curiosity,” Hartmann said. “We wanted to know what microbes are living in our homes. If you think about indoor environments, surfaces like tables and walls are really difficult for microbes to live on. Microbes prefer environments with water. And where is there water? Inside our showerheads and on our toothbrushes.”

Diversity and opportunities

After characterizing bacteria, Hartmann then used DNA sequencing to examine the viruses living on those same samples. She was immediately blown away. Altogether, the samples comprised more than 600 different viruses — and no two samples were alike.

“We saw basically no overlap in virus types between showerheads and toothbrushes,” Hartmann said. “We also saw very little overlap between any two samples at all. Each showerhead and each toothbrush is like its own little island. It just underscores the incredible diversity of viruses out there.”

While they found few patterns among all the samples, Hartmann and her team did notice more mycobacteriophage than other types of phage. Mycobacteriophage infect mycobacteria, a pathogenic species that causes diseases like leprosy, tuberculosis and chronic lung infections. Hartmann imagines that, someday, researchers could harness mycobacteriophage to treat these infections and others.

“We could envision taking these mycobacteriophage and using them as a way to clean pathogens out of your plumbing system,” she said. “We want to look at all the functions these viruses might have and figure out how we can use them.”

Most microbes ‘will not make us sick’

But, in the meantime, Hartmann cautions people not to fret about the invisible wildlife living within our bathrooms. Instead of grabbing for bleach, people can soak their showerheads in vinegar to remove calcium buildup or simply wash them with plain soap and water. And people should regularly replace toothbrush heads, Hartmann says. Hartmann also is not a fan of antimicrobial toothbrushes, which she said can lead to antibiotic-resistant bugs.

“Microbes are everywhere, and the vast majority of them will not make us sick,” she said. “The more you attack them with disinfectants, the more they are likely to develop resistance or become more difficult to treat. We should all just embrace them.”

The study, “Phage communities in household-related biofilms correlate with bacterial hosts but do not associate with other environmental factors,” was supported by Northwestern University.

The team from the Department of Cardiology at LMU University Hospital launched the MunichBREW I study at Munich Oktoberfest in 2015. Back then, the doctors, led by Professor Stefan Brunner and PD Dr. Moritz Sinner, studied the connection between excessive alcohol consumption and cardiac arrythmias — but only through an electrocardiogram (ECG) snapshot.

Now the scientists wanted to gain a more detailed picture, so they set out with their mobile equipment once again. Their destinations were various small parties attended by young adults with a high likelihood “that many of the partygoers would reach breath alcohol concentrations (BAC) of at least 1.2 grams per kilogram,” says Stefan Brunner. These were the participants of the MunichBREW II study — the world’s largest investigation to date of acute alcohol consumption and ECG changes in prolonged ECGs spanning several days.

Hearts out of sync — especially in recovery phase

Overall, the researchers evaluated the data of over 200 partygoers who, with peak blood alcohol values of up to 2.5 grams per kilogram, had imbibed quite a few drinks. The ECG devices monitored their cardiac rhythms for a total of 48 hours, with the researchers distinguishing between the baseline (hour 0), the drinking period (hours 1-5), the recovery period (hours 6-19), and two control periods corresponding to 24 hours after the drinking and recovery periods, respectively. Acute alcohol intake was monitored by BAC measurements during the drinking period. ECGs were analyzed for heart rate, heart rate variability, atrial fibrillation, and other types of cardiac arrythmia. Despite the festive mood of the study participants, the quality of the ECGs was almost universally high throughout.

“Clinically relevant arrhythmias were detected in over five percent of otherwise healthy participants,” explains Moritz Sinner, “and primarily in the recovery phase.” Alcohol intake during the drinking period led to an increasingly rapid pulse of over 100 beats per minute. Alcohol, it would seem, can profoundly affect the autonomous regulatory processes of the heart. “Our study furnishes, from a cardiological perspective, another negative effect of acute excessive alcohol consumption on health,” emphasizes Brunner. Meanwhile, the long-term harmful effects of alcohol-related cardiac arrythmias on cardiac health remains a subject for further research.

Mathematician and assistant professor of biology Nicholas Landry, an expert in the study of contagion, is exploring how the structure of human-interaction networks affect the spread of both illness and information with the aim of understanding the role social connections play in not only the transmission of disease but also the spread of ideas and ideology.

In a paper published this fall in Physical Review E with collaborators at the University of Vermont, Landry explores a hybrid approach to understanding social networks that involves inferring not just social contacts but also the rules that govern how contagion and information spread.

“With the pandemic, we have more data than we’ve ever had on diseases,” Landry said. “The question is, What can we do with that data and how much data do you need to figure out how people are connected?”

The key to making use of the data, Landry explained, is to understand their limitations and understand how much confidence we can have when using epidemic models to make predictions.

Landry’s findings suggest that reconstructing underlying social networks and their impacts on contagion is much more feasible for diseases like SARS-CoV-2, Mpox or rhinovirus but may be less effective in understanding how more highly infectious diseases like measles or chickenpox spread.

However, for extremely viral trends or information, Landry suggests it may be possible to track how they spread with more precision than we can achieve for diseases, a discovery that will better inform future efforts to understand the pathways of both contagion and misinformation.