Articles tagged with Mathematical Functions
Using an algorithm called the Krakencoder, researchers at Weill Cornell Medicine mapped how the brain's anatomical connections and activity patterns relate to behavior. The tool accurately predicted individual's functional connectome about 20 times more than previous approaches, also mapping age, sex, and cognitive performance scores.
Researchers introduced a novel approach to enhance reservoir computing, incorporating a generalized readout that offers improved accuracy and robustness compared to conventional methods. The new method uses a nonlinear combination of reservoir variables to uncover deeper patterns in input data.
Scientists at IISc have found a new series representation for pi that combines specific parameters in a way that rapidly arrives at the exact value of pi. This discovery could lead to practical applications in physics and potentially solve long-standing challenges in representing pi as a combination of mathematical components.
Researchers have successfully solved a problem in graph theory that has attracted attention from within the field. The team's research involves packing coloring, which deals with labelling parts of a graph to comply with certain rules and avoid specific conflicts.
A University of Ottawa study reveals that a diverse brain's ecosystem is key to maintaining normal function while responding to changes. This concept is inspired by Charles Darwin's idea that biodiversity is crucial for survival, suggesting cell-to-cell diversity helps prevent failures in brain circuits.
A study by the University of Geneva finds that adopting multiple perspectives on mathematical problems enhances proportional reasoning. Students who received lessons based on this approach outperformed those in traditional classes, regardless of socio-economic background.
An interdisciplinary team will uncover complex biological systems and develop tools to globally document coral reef health changes. The research aims to understand how herbivory rate at the ecosystem scale emerges and shapes the ecosystem, ultimately informing management of ecosystems.
A novel 'rational' neural network reveals underlying mathematical equations through Green's functions, enabling humans to understand machine-generated findings. This breakthrough in partial differential equation learning holds promise for advancing scientific exploration of weather systems, climate change, and more.
Researchers have established theorems that guarantee whether a given machine learning algorithm will work as it scales up on larger computers. This breakthrough solves a key problem of useability for quantum machine learning and takes an important step toward achieving quantum advantage.
Mathematicians from RUDN University and University of Munich introduced a new method for stationary solutions in three-dimensional Vlasov-Poisson equations, describing phenomena in stellar dynamics. The results provide insights into the interaction of gravitating particles and electromagnetic fields.
Researchers at Brigham Young University have created a new method called fluid carving to speed up the animation process for fluids. This technique allows animators to tweak and change animations on the fly without having to re-simulate entire sequences.
Researchers developed a new computational tool based on Graph theory to infer large-scale regulatory networks from healthy and pathological organs. They were able to pinpoint genes relevant to organ function and potential drivers of diseases, such as type 2 diabetes and Alzheimer's disease.
Researchers at UNC School of Medicine have developed a powerful algorithm to quickly categorize long non-coding RNAs (lncRNAs) based on their molecular makeup and predicted functions. The method, called SEEKR, uses protein-binding sequences to identify lncRNA communities with similar functions in humans and other species.
Researchers created a model of hybrid system with two unreliable servers, finding that heterogeneity improves data transmission speed and reliability. The new reliability measurement is introduced as the distribution function of failures within a given operation period.
Using Nobel Prize-winning methods, researchers developed a mathematical approach to predict human behavior in crowds, predicting distribution and mood based on density fluctuations. The approach could be applied to analyze population flows and provide early warnings for extreme crowding.
Researchers have found that swirling liquids, such as coffee, follow the same mathematical principles as transactions with cryptocurrencies like bitcoin. This discovery may lead to more advanced digital security methods and a deeper understanding of chaotic mixing in nature. The findings also suggest that cryptographic computations can...
Researchers from MIT's Computer Science and Artificial Intelligence Laboratory have developed a new system called Catena that uses Bitcoin's security machinery to defend against online identity theft and equivocation. The system requires the download of only about 40 megabytes of data, making it suitable for smartphones.
Researchers at MIT and Stanford develop Splinter, a system that disguises database queries to protect user privacy. The system uses function secret sharing to split queries across multiple servers, making it impossible for anyone other than the user to determine what query was executed.
Researchers at MIT have developed techniques to amplify minute motions in digital video, as well as smooth out small variations in digital images. The techniques can produce more polished images for graphic-design projects, while also disclosing structural defects and camouflaged objects.
Researchers have developed a new cutting-plane algorithm that improves upon existing methods, offering huge efficiency gains for specific optimization problems. The algorithm has been applied to various types of problems, including submodular minimization and semidefinite programming, resulting in significant speedups.
HMMER enables researchers to infer protein function and evolutionary history by identifying hundreds of thousands of related sequences. The new web interface offers fast and interactive visualization tools, making it easier to interpret results.
A team of mathematicians and optometrists developed a mathematical model to better understand the inner workings of tear film distribution over the eye's surface. Their findings suggest that it takes a blink to redistribute tear film, which may aid in the development of better treatments for dry eye disease.
A study by Andrea Giometto reveals that body sizes in aquatic microorganisms follow a mathematical expression common to all species, influencing size distributions and ecosystem balance. This finding could lead to new insights into population dynamics and the existence of universal laws governing natural ecosystems.
A NIH-funded study identifies fundamental math skills needed for functioning in adult life, including number system knowledge. Children who failed to acquire these basic math skills by first grade scored far behind peers by seventh grade on a test of mathematical abilities.
A mathematician has proven that a formula for mock modular forms, developed by Indian mathematician Srinivasa Ramanujan, can be computed just as he predicted. The discovery may unlock secrets about black holes and has implications for number theory.
A Stanford imaging study found that children with math anxiety show increased activity in fear centers and decreased activity in problem-solving regions of the brain. This suggests that math-specific fear interferes with the brain's information-processing capacity and ability to reason through math problems.
Professor Ingrid Daubechies of Duke University received the John von Neumann Lecture Prize for her fundamental work in developing the foundations and applications of wavelets. Her research focuses on time-frequency analysis, with contributions to mathematical sciences and engineering fields.
Researchers at University of Pittsburgh's Department of Mathematics will create computer models based on differential equations to predict patient responses to treatment. The models aim to improve therapies for neurological conditions like Parkinson's disease and deep brain stimulation.
Allan Spradling receives the 2008 Gruber Genetics Prize for groundbreaking discoveries about stem cell development in Drosophila melanogaster. His work has significantly contributed to understanding human genetics, development, and disease.
Dr. Nancy Kopell received the John von Neumann Lecture for her groundbreaking work on coupled nonlinear oscillators and their application to various biological systems. Her research focuses on understanding rhythmic behavior in networks of neurons and its role in filtering and transforming input patterns.
A NIST-developed image enhancement technique, APEX, successfully sharpened details on distant galaxies in Hubble images. The method overcame limitations of traditional deblurring techniques by leveraging mathematical simplifications.