Articles tagged with Mathematical Functions
Comprehensive exploration of living organisms, biological systems, and life processes across all scales from molecules to ecosystems. Encompasses cutting-edge research in biology, genetics, molecular biology, ecology, biochemistry, microbiology, botany, zoology, evolutionary biology, genomics, and biotechnology. Investigates cellular mechanisms, organism development, genetic inheritance, biodiversity conservation, metabolic processes, protein synthesis, DNA sequencing, CRISPR gene editing, stem cell research, and the fundamental principles governing all forms of life on Earth.
Comprehensive medical research, clinical studies, and healthcare sciences focused on disease prevention, diagnosis, and treatment. Encompasses clinical medicine, public health, pharmacology, epidemiology, medical specialties, disease mechanisms, therapeutic interventions, healthcare innovation, precision medicine, telemedicine, medical devices, drug development, clinical trials, patient care, mental health, nutrition science, health policy, and the application of medical science to improve human health, wellbeing, and quality of life across diverse populations.
Comprehensive investigation of human society, behavior, relationships, and social structures through systematic research and analysis. Encompasses psychology, sociology, anthropology, economics, political science, linguistics, education, demography, communications, and social research methodologies. Examines human cognition, social interactions, cultural phenomena, economic systems, political institutions, language and communication, educational processes, population dynamics, and the complex social, cultural, economic, and political forces shaping human societies, communities, and civilizations throughout history and across the contemporary world.
Fundamental study of the non-living natural world, matter, energy, and physical phenomena governing the universe. Encompasses physics, chemistry, earth sciences, atmospheric sciences, oceanography, materials science, and the investigation of physical laws, chemical reactions, geological processes, climate systems, and planetary dynamics. Explores everything from subatomic particles and quantum mechanics to planetary systems and cosmic phenomena, including energy transformations, molecular interactions, elemental properties, weather patterns, tectonic activity, and the fundamental forces and principles underlying the physical nature of reality.
Practical application of scientific knowledge and engineering principles to solve real-world problems and develop innovative technologies. Encompasses all engineering disciplines, technology development, computer science, artificial intelligence, environmental sciences, agriculture, materials applications, energy systems, and industrial innovation. Bridges theoretical research with tangible solutions for infrastructure, manufacturing, computing, communications, transportation, construction, sustainable development, and emerging technologies that advance human capabilities, improve quality of life, and address societal challenges through scientific innovation and technological progress.
Study of the practice, culture, infrastructure, and social dimensions of science itself. Addresses how science is conducted, organized, communicated, and integrated into society. Encompasses research funding mechanisms, scientific publishing systems, peer review processes, academic ethics, science policy, research institutions, scientific collaboration networks, science education, career development, research programs, scientific methods, science communication, and the sociology of scientific discovery. Examines the human, institutional, and cultural aspects of scientific enterprise, knowledge production, and the translation of research into societal benefit.
Comprehensive study of the universe beyond Earth, encompassing celestial objects, cosmic phenomena, and space exploration. Includes astronomy, astrophysics, planetary science, cosmology, space physics, astrobiology, and space technology. Investigates stars, galaxies, planets, moons, asteroids, comets, black holes, nebulae, exoplanets, dark matter, dark energy, cosmic microwave background, stellar evolution, planetary formation, space weather, solar system dynamics, the search for extraterrestrial life, and humanity's efforts to explore, understand, and unlock the mysteries of the cosmos through observation, theory, and space missions.
Comprehensive examination of tools, techniques, methodologies, and approaches used across scientific disciplines to conduct research, collect data, and analyze results. Encompasses experimental procedures, analytical methods, measurement techniques, instrumentation, imaging technologies, spectroscopic methods, laboratory protocols, observational studies, statistical analysis, computational methods, data visualization, quality control, and methodological innovations. Addresses the practical techniques and theoretical frameworks enabling scientists to investigate phenomena, test hypotheses, gather evidence, ensure reproducibility, and generate reliable knowledge through systematic, rigorous investigation across all areas of scientific inquiry.
Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
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.