Equations once used to predict whether populations of rabbits would boom, stabilize, or collapse are now being applied to something potentially even more complicated: romantic relationships.

According to mathematician Laurent Pujo-Menjouet of Claude Bernard University Lyon 1, the forces that determine whether a couple survives life’s inevitable stresses can be studied much like other complex systems. Attraction can strengthen or fade, outside pressures can push a relationship away from stability, and perhaps most importantly, there may be a critical mathematical threshold beyond which recovery becomes increasingly difficult.

In his new book, Love! Valour! Equations! The Mathematics of the Couple, published by CRC Press, Pujo-Menjouet draws on mathematical ecology, psychology, literature, and even film to explore why some couples weather years of conflict, stress, children, illness, and financial hardship while others gradually drift apart.

The goal isn’t to produce an equation that predicts who will fall in love with whom. Instead, Pujo-Menjouet treats relationships as dynamical systems—systems that change over time, respond to disturbances, and can move toward either stability or decline.

“There is no mysterious enchantment or magic potion. By now, that would be known,” Pujo-Menjouet writes in the book, which draws on mathematics, psychology, literature, and film. “Is all hope lost then? Certainly not. That is precisely where everything becomes interesting.”

From Rabbits to Relationships

The mathematical models Pujo-Menjouet uses originated in ecology. His work uses Malthusian growth models and the Lotka-Volterra equations, originally developed to describe population dynamics in animals such as rabbits. He also studies the Allee effect, a phenomenon that explains how populations struggle to recover if they drop below a particular size.

Pujo-Menjouet adapts these concepts to relationships, using the idea of a critical threshold to examine when a couple may become increasingly vulnerable to separation. He also draws on the research of psychologist John Gottman, who showed that relationship behaviors can be quantified as data.

“Just as we can predict population growth or endangered species, we can model the evolution of feelings within a couple,” Pujo-Menjouet explains. “We’re not trying to predict who you’ll fall in love with, we’re trying to understand why some couples remain stable despite life’s inevitable shocks while others slowly drift apart.”

A Threshold for Falling Apart

The basic idea is simple: a relationship may have a critical threshold, or minimum level of stability needed to keep the bond intact. Pujo-Menjouet’s model considers three main forces: mutual attraction, the gradual weakening of feelings over time, and each partner’s emotional response to the other.

“If your feelings fall below this threshold and stay there, the mathematics predicts an inevitable decline toward separation,” Pujo-Menjouet says. “However, understanding this threshold gives couples a powerful tool: they can recognize danger zones and take corrective action.”

These models emphasize how couples recover from drifting apart. The key question is not whether couples experience conflict, but whether they have the resilience to restore balance afterward.

“Life will always send its wolves: stress, illness, work, children, financial difficulties,” Pujo-Menjouet says, “mathematics helps us understand how to build the brick house rather than the straw one.”

Could AI Become Love’s Early-Warning System?

Researchers such as Pujo-Menjouet are considering whether they could combine these mathematical models with artificial intelligence to create an early-warning system for relationships. Such a system could detect the signs of instability before they become apparent to the people involved.

Pujo-Menjouet compares this method to a GPS for relationships, showing where a couple currently is, where its dynamics may be heading, and the various ways they could arrive at a healthier place. Although the models don’t decide who somebody will love, they can help explain how relationships evolve and what actions might help couples maintain their connection. Early detection of problems would allow partners to make changes before reaching a stage where recovery becomes unlikely.

Why Love Resists a Formula

Pujo-Menjouet admits that present-day mathematical models have limitations. Most of these models are based on data from Western relationships. In contrast, the factors that impact whether a relationship succeeds or fails can differ from one culture, religion, or generation to another. He points out that the model must account for additional factors to be applicable everywhere.

Human behavior also introduces unpredictability that mathematical models cannot fully account for. People can change their habits, strengthen their commitment, seek therapy, or otherwise alter the dynamics of a relationship in ways the equations cannot anticipate. The equations identify tendencies rather than determine an unavoidable outcome.

“Mathematics can illuminate patterns and provide guidance,” Pujo-Menjouet says, “but ultimately, the success of a relationship depends on two people choosing, every day, to nurture their connection. The equations can show you the path, but you still have to walk it together.”

Austin Burgess is a writer and researcher with a background in sales, marketing, and data analytics. He holds an MBA, a Bachelor of Science in Business Administration, and a data analytics certification. His work focuses on breaking scientific developments, with an emphasis on emerging biology, cognitive neuroscience, and archaeological discoveries.

The family has put together the Big Premise (a solar flare has flung Oak Street back to the Mesozoic era). The dad predicts, “God's not gonna let us die here.”

Source

A University of West Bohemia (UWB)- led team of archaeologists has unearthed an ancient Czech ritual center linked to the movement of the Sun and Moon, predating Stonehenge by over 1,000 years.

The UWB-led team behind the discovery said the site’s 6,500-year-old age makes it one of the oldest monuments of Central Europe. Moving forward, the researchers plan to take soil samples from the enclosure and its surroundings to examine chemical traces left by the site’s ancient inhabitants.

Ancient Ritual Center Predating Stonehenge Tracks Sun and Moon Positions

According to a UWB statement, the newly discovered almost circular enclosure was found at present-day Chelby. Initial measurements set its diameter at 230 meters. The ritual center also featured a 2.5-meter-plus ditch and twelve entrances placed at irregular intervals.

Research team leader Petr Krištuf of UWB’s Department of Archaeology at the Faculty of Arts said circular enclosures like the Chelby structure are completely unknown in this region, making the site “exceptional.” However, Krištuf explained, when researchers began analyzing the positions of the asymmetrical entrances, “it became clear that their arrangement was not random.”

“Their geometry creates a system that made it possible to observe the most significant moments of the solar and lunar cycles,” the UWB researcher explained.

A more detailed survey of the newly discovered ritual center revealed two main observation points designed for specially timed observations of the Sun and Moon. The researchers said the first appears to be “associated with the Moon’s extreme positions on the horizon during its approximately 18-year cycle.”

The team said the second observation point identified during the survey connects the sunrise at the summer solstice, the longest day of the year, with sunset on the winter solstice, the shortest day.

Archaeologists Note Site’s Similar Astronomical Alignments to Famous Neighbor

Although the site is not the only ancient monumental structure in the region, the team used organic material to date the newly discovered enclosure to 6,500 years before present. For comparison, the relatively nearby Stonehenge monument, which also contains astronomical alignments connected to the Sun and Moon, was built over 1,000 years later.

Krištuf said the astronomical alignments found at the Chelby site are not unusual for prehistoric people. The researchers specifically highlighted the symbolic nature of sunrise and the summer solstice marking a beginning for prehistoric farming communities known to inhabit the region. They also noted the winter solstice “represented an ending” for these same ancient farmers.

“The same principle can be seen along Stonehenge’s main axis,” the researcher explained. “We can now see that the sanctuary at Chleby was designed similarly. Still, more than a thousand years earlier, as we have established from the dating of organic material.”

Additional evidence found at the site also suggests the newly discovered enclosure was a ritual center where people performed ceremonies celebrating astronomical events. For example, the team unearthed bull skulls and horns in the ditches near the entrances.

Archaeologist Jan Turek, who is involved in the research on behalf of Charles University, said the artifacts, which are similar to objects excavated near Stonehenge, suggest the ritual center’s ancient builders may have decorated the monumental gateways leading into the enclosure.

“The cult of the bull was an important religious symbol among the first farming communities and is known from many parts of prehistoric Europe,” Turek explained. 

Krištuf said their research also unearthed several iterations of the ritual center. The team leader said this feature sets it apart from its nearby, more well-known successor.

“While Stonehenge experienced repeated periods of renewed use and is still associated, for example, with Celtic druids, the first results from Chleby suggest the opposite development,” he explained. “By the Iron Age, the monument appears to have definitively lost its original significance. The ditch was gradually filled in, and an ordinary settlement was established on the site of the former sanctuary.”

Upcoming Soil Samples Could Fill in Missing Historical Blanks

The next step in the ancient ritual center’s excavation will include a detailed soil analysis. Jan Fišer of the University of Hradec Králové, who is analyzing soil samples from the enclosure and the immediate surrounding area, noted that chemical traces in the soil can complement artifacts and human remains.

“These can help us understand how this exceptional site was used during different periods of prehistory,” Fišer explained.

The new excavations and upcoming soil analysis are part of a greater international effort, Long-term Land Use Dynamics within the Areas of Prehistoric Ritual Places. That project focuses on changes in prehistoric ritual landscapes like Stonehenge and the new Chelby site.

Christopher Plain is a Science Fiction and Fantasy novelist and has spent the last six years as Associate News Editor and Head Science Writer at The Debrief. Follow and connect with him on X, learn about his books at plainfiction.com, or email him at christopher@thedebrief.org.

De acordo com o jornalista da Bloomberg, Mark Gurman, a Apple teria cogitado (e posteriormente descartado) um recurso bastante interessante para o Apple Upgrade: a transferência dos dados do iCloud do usuário para o novo aparelho antes mesmo de ele ser enviado para o assinante.

Revelada na última edição da sua newsletter “Power On”, a ideia — descrita como um recurso premium — seria especialmente bem-vinda para as trocas anuais de iPhones realizadas durante o período do serviço adquirido, livrando o usuário de ter que configurar seu aparelho ao ligá-lo pela primeira vez.

The Apple Upgrade feature that never made it past the drawing board: a so-called white-glove component, where your new device each year would arrive at home ready to go, preloaded with all of your data via your iCloud backup. Here’s what happened. https://t.co/PZ4r8jEgvG

— Mark Gurman (@markgurman) August 9, 2026

Essa ideia, no entanto, esbarrou em um obstáculo importantíssimo: a privacidade do usuário, já que dados do iCloud só poderiam ser acessados pela Apple nos casos em que a Proteção Avançada de Dados (Advanced Data Protection) com criptografia de ponta a ponta não foi ativada. Isso, é claro, não inclui o Reino Unido, onde o recurso não pode ser mais acessado.

Como lembrou o 9to5Mac, o acesso remoto às definições de sistema de um iPhone obtido por meio do Apple Upgrade poderia ser associado ao Presto, um sistema proprietário de gerenciamento de atualizações baseado em hardware (empurrado especificamente por um Mac mini com um sistema customizado) para realizar o update de iPhones lacrados.

Anunciado no mês passado, o Apple Upgrade oferece o leasing de Apple Watches, iPhones, iPads e Macs para clientes dos Estados Unidos, com planos de até 36 meses dependendo do dispositivo escolhido.

As AI reshapes the way we communicate, researchers at Texas A&M University are developing an artificial intelligence-powered platform that could transform care for children with autism and older adults living with dementia. The technology learns each person’s unique communication style, behaviors, and preferences, enabling increasingly personalized support for caregivers, therapists, and families over time.

Called VoiceLove, it is one of three projects being developed with support from the Advanced Research Projects Agency for Health (ARPA-H).

At the core of the system is an AI engine that analyzes both speech and nonverbal behaviors documented through short videos recorded by caregivers or therapists during daily communications and interactions. Rather than comparing participants against a general model, the platform focuses on understanding each person’s individual patterns and communication style.

“Every child with autism is unique, and effective support should reflect that,” he said. “Our project leverages artificial intelligence to understand each child’s individual behaviors, communication styles, and preferences. The goal is to deliver personalized recommendations that help families, educators, and clinicians work together more effectively, enabling more responsive, data-driven care and improving the health and well-being of children with autism,” says Dr. Junhyoung Kim, associate professor in the School of Public Health, one of the principal investigators on the project, in a statement. 

The AI system was created to identify behavioral patterns in communication, interests, and responses across different situations. Based on its observations, the program provides personalized recommendations that could help therapists or caregivers create individualized intervention plans.

“The key innovation behind this platform is its ability to understand each child individually and learn their unique preferences, needs, communication styles, and strengths to deliver personalized recommendations,” Kim said. “For people living with dementia, the platform is designed to enhance person-centered care by helping residents communicate their needs, preferences, and daily experiences more effectively.”

Researchers say the technology could support a wide range of developmental goals, including improving communication skills, encouraging self-care, strengthening social engagement, and enhancing a person’s quality of life.

The same personalized approach could also benefit people living with dementia, where communication challenges often make it difficult for individuals to express their needs and wants. 

“Our vision is to create an AI platform that continuously learns from each child’s daily experiences,” Kim said. “As the system identifies patterns in behaviors, preferences, and responses to different activities, it can provide therapists and caregivers with personalized recommendations that evolve over time.”

“This adaptive approach helps explain why certain behaviors occur and supports more individualized, proactive care,” Kim added. 

VoiceLove is designed to keep learning. As caregivers continue using the app, the AI analyzes new interactions while also incorporating caregiver observations, experiences, and responses to daily prompts. 

The research team plans to begin with a small pilot study involving children with autism and older adults living with dementia after receiving Institutional Review Board approval.

Participants will use the platform for approximately one month while researchers evaluate its usability, feasibility, and overall user experience, and from there, insights derived from the pilot will help to inform a larger-scale study at some point in the future. 

Chrissy Newton is a PR professional and the founder of VOCAB Communications. She currently appears on The Discovery Channel and Max and hosts the Rebelliously Curious podcast, which can be found on YouTube and on all audio podcast streaming platforms. Follow her on X: @ChrissyNewton, Instagram: @BeingChrissyNewton, and chrissynewton.com. To contact Chrissy with a story, please email chrissy @ thedebrief.org.

Most of us experience data by looking at screens filled with charts, graphs and numbers. But what if you could actually feel your data instead of just seeing it? Researchers at the University of Adelaide have developed an experimental wearable glove called ThermoPhy that turns information into physical sensations. The glove uses heat, touch and […]

The post New wearable glove lets people feel their data through heat and touch appeared first on Knowridge Science Report.