Optimization algorithms are everywhere in engineering. Among other things, they’re used to evaluate design tradeoffs, to assess control systems and to find patterns in data. One way to solve a difficult optimization problem is to first reduce it to a related but much simpler problem, then gradually add complexity back in, solving each new problem in turn and using its solution as a guide to solving the next one.
Massachusetts Institute of Technology researchers have discovered a new mathematical...
Researchers have begun to describe theoretical...
From a mechanical perspective, granular materials are stuck between a rock and a fluid place, with behavior resembling neither a solid nor a liquid. Think of sand through an hourglass: As grains funnel through, they appear to flow like water, but once deposited, they form a relatively stable mound, much like a solid.
Scientists at Oak Ridge National Laboratory have made the first direct observations of a 1-D boundary separating two different, atom-thin materials, enabling studies of long-theorized phenomena at these interfaces. Theorists have predicted the existence of intriguing properties at 1-D boundaries between two crystalline components, but experimental verification has eluded researchers.
Most modern cryptographic schemes rely on computational complexity for their security. In principle, they can be cracked, but that would take a prohibitively long time, even with enormous computational resources. There is, however, another notion of security—information-theoretic security—which means that even an adversary with unbounded computational power could extract no useful information from an encrypted message.
A team led by Virginia Tech researchers studied cells found in breast and other types of connective tissue and discovered new information about cell transitions that take place during wound healing and cancer. They developed mathematical models to predict the dynamics of cell transitions, and by comparison gained new understanding of how a substance known as transforming growth factor triggers cell transformations.
What could the natural diversity and beauty of plant leaves have in common with the violin? Much more than you might imagine. Dan Chitwood of the Donald Danforth Plant Science Center in St. Louis is applying “morphometrics”, which statistically tests hypotheses about factors that affect shape, to changes in the shape of violins over time. His work revealed a strong degree of design transmission and imitation.
Metabolic networks are mathematical models of every possible sequence of chemical reactions available to an organ or organism, and they’re used to design microbes for manufacturing processes or to study disease. Based on both genetic analysis and empirical study, they can take years to assemble. Unfortunately, a new analytic tool suggests that many of those models may be wrong.
An improved theoretical model of photoabsorption of nitrous oxide, developed by scientists in Malaysia, could shed light on the atmospheric chemistry of ozone depletion. The new theoretical work unveils, through improvements in established calculation approaches, the actual dynamic of stratospheric catalytic ozone destruction.
Mathematicians from Brown Univ. have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. Ironically, allowing uncertainty into a mathematical equation that models fluid flows makes the equation much more capable of correctly reflecting the natural world, including the formation, strength, and position of air masses and fronts in the atmosphere.
Univ. of California, Santa Barbara’s Paul Atzberger, a professor in the Department of Mathematics and in mechanical engineering, often works in areas where mathematics plays an ever more important role in the discovery and development of new ideas. Most recently he has developed new mathematical approaches to gain insights into how proteins move around within lipid bilayer membranes.
Mathematics might be able to reduce the need for invasive biopsies in patients suffering kidney damage related to the autoimmune disease lupus. In a new study, researchers developed a math model that can predict the progression from nephritis, or kidney inflammation, to interstitial fibrosis, scarring in the kidney that current treatments cannot reverse. A kidney biopsy is the only existing way to reach a definitive diagnosis.
Calculating the pros and cons of a potential decision is a way of decision-making. But repeated engagement with numbers-focused calculations, especially those involving money, can have unintended negative consequences, including social and moral transgressions, says new study. Several experiments supported these findings and pointed to a “calculative mindset” that can take precedence in reaching conclusions.
The central mystery of quantum mechanics is that small chunks of matter sometimes seem to behave like particles, sometimes like waves. The traditional view holds that a single particle really is a wave that collapses only when observed. But John Bush, of the Massachusetts Institute of Technology, believes that another explanation, the pilot-wave theory, deserves a second look.
Dr. John Carr, a scientist at the U.S. Naval Research Laboratory, is part of an international team that has found what they believe is evidence of a planet forming around a star about 335 light years from Earth. They made the chance discovery while studying the protoplanetary disk of gas around a distant forming star using a technique called spectro-astrometry, which allows astronomers to detect small changes in the position of moving gas.
Proofs are the key method of mathematics. Until now, it has mainly been humans who have verified whether proofs are correct. This could change, says Russian mathematician Vladimir Voevodsky, who points to evidence that, in the near future, computers rather than humans could reliably verify whether a mathematical proof is correct.
Researchers at the Univ. of Rochester have cleared up an apparent violation of quantum mechanics’ wave-particle duality that was announced in 2012 by a team of scientists in Germany. They replicated the experiment, which simultaneously determined a photon’s path and observed high contrast interference fringes created by the interaction of waves. But they also found an undiscovered source of bias sampling that explained the strange results.
Polymers come with a range of properties dictated by their chemical composition and geometrical arrangement. Yasuyuki Tezuka and his team at Tokyo Institute of Technology have now applied an approach to synthesize a new type of multicyclic polymer geometry. While mathematicians are interested because these structures have not been realized before, the geometry studies also provide insights for chemists.
It makes sense that the credit for science papers with multiple authors should go to the authors who perform the bulk of the research, yet that’s not always the case. Now a new algorithm developed at Northeastern’s Center for Complex Network Research helps sheds light on how to properly allocate credit.
A computer algorithm being developed by Brown Univ. researchers lets users instantly change the weather, time of day, season or other features in outdoor photos with simple text commands. Machine learning and a clever database make it possible. A paper describing the work will be presented at SIGGRAPH 2014.
Inspired by the Red Queen in Lewis Carroll’s "Through the Looking Glass", collaborators from Illinois and Singapore improved a 35-year-old ecology model to better understand how species evolve. The new model, called a mean field model for competition, incorporates the “Red Queen Effect,” which suggests that organisms must constantly increase fitness in order to compete with other ever-evolving organisms in an ever-changing environment.
Until now, computer simulations of habitable climates on Earth-like planets have focused on their atmospheres. Mathematicians and earth sciences experts in the U.K. have recently taken the next step, creating a computer-simulated pattern of ocean circulation on a hypothetical ocean-covered Earth-like planet. They hope to learn how different planetary rotation rates would impact heat transport with the presence of oceans taken into account.
The addition of elements to the surface of graphene can modify the material’s physical and chemical properties, potentially extending the range of possible applications. Recently performed theoretical calculations at RIKEN in Japan show that the addition of oxygen to graphene on copper substrates results in enhanced functionalization. The resulting structure, known as an enolate, make support applications that require catalytic response.
A decade of research by Rice Univ. scientists has produced a 2-D model to prove how gas hydrate, the “ice that burns,” is formed under the ocean floor. Gas hydrate has potential as a source of abundant energy, if it can be extracted and turned into usable form. It also has potential to do great harm.
Fully automated "deep learning" by computers greatly improves the odds of discovering particles such as the Higgs boson, according to a recent study. In fact, this approach beats even veteran physicists' abilities, which now consists of developing mathematical formulas by hand to apply to data. New machine learning methods are rendering that approach unnecessary.
A relic from long before the age of supercomputers, the 169-year-old math strategy called the Jacobi iterative method is widely dismissed today as too slow to be useful. But thanks to a Johns Hopkins Univ. engineering student and his professor, it may soon get a new lease on life. With just a few modern-day tweaks, the researchers say they’ve made the rarely used Jacobi method work up to 200 times faster.
Wrinkles, creases and folds are everywhere in nature, from the surface of human skin to the buckled crust of the Earth. They can also be useful structures for engineers. Wrinkles in thin films, for example, can help make durable circuit boards for flexible electronics. A newly developed mathematical model could help engineers control the formation of wrinkle, crease and fold structures in a wide variety of materials.
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