Tag: statistics

A number of pioneer discoveries in statistical mechanics arose from questioning the applicability of core abstract concepts to physical systems and experimental devices. A notable example is the ergodic hypothesis, which assumes that over time a system visits almost every available microstate of the phase space, and that the infinite time average of any measurable quantity of the system matches with its phase space average. In short, this is the reason why ice melts in a pot of water. And it will do so faster, if the water is hotter. Scientists have been figuring ways to verify the validity or the failure of the ergodic hypothesis based on finite-time measurements.

Led by Sergej Flach, IBS researchers have developed an efficient method to extract precise estimates of the time-scales for ergodicity (coined ergodization time). This method has herewith been successfully applied to classical networks of superconducting grains weakly coupled by Josephson junctions.

The team found that in these networks the ergodization time-scale quickly becomes huge — although staying finite — upon increasing the system temperature. Instead, the time-scales necessary for chaoticity to develop remain practically unchanged with respect to the ergodization one. This is highly surprising, as ergodicity is inextricably knotted to chaos, and one may expect that their respective time-scales must be also strictly related. In terms of the ice, it means that the hotter the water gets, the longer it takes for the ice cubes to melt. IBS researchers numerically showed that higher temperature fluctuations strongly hinder their own meandering through the system. Thus, a slower and slower process drastically delays the ergodization of the system. The team has labeled this discovery: dynamical glass.

“Upon increasing the temperature, our studies unravelled the emergence of roaming chaotic spots among frozen and seemingly inert regions. The name dynamical glass follows from this very fragmentation, as the word dynamical hints the quick development of chaos, while the word glass points at phenomena that require an extremely long — but finite — time-scale to occur,” explains Carlo Danieli, a member of the team.

“The understanding of the mechanism and the necessary time scales for ergodicity and chaoticity to develop is at the very core of a huge number of recent advancement in condensed matter physics. We expect this to pave the way to assess several unsolved issues in many body systems, from anomalous heat conductivity to thermalization,” enthuses the team.

IBS researchers expect that the observed dynamical glass is a generic property of networks of superconducting grains via Josephson coupling irrespective of their space dimensionality. Furthermore, it is conjectured that a broad set of weakly non-integrable many-body systems turn into dynamical glasses as they approach specific temperature regimes. An equally charming and challenging task is the team’s aspiration to demonstrate the existence of a dynamical glass in quantum many-body systems, and establish its connection with many-body localization phenomena.

As stated by Flach “We expect these findings open a new venue to assess and understand phenomena related to many-body localization and glassiness in a large number of weakly non-integrable many-body systems.”

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Materials provided by Institute for Basic Science. Note: Content may be edited for style and length.

Research shows that up to 80 percent of college students experience some form of statistics anxiety — and for students majoring in psychology, this anxiety often puts obstacles in their path to graduation.

“In my psychology statistics class, I once had a student take and fail the class two or three times,” said Michael Vitevitch, professor and chair of psychology at the University of Kansas. “He’d taken everything in the major, and this was the last class he needed. But he had high statistics anxiety. On one of the exams, he kind of froze and was staring at the paper. I took him into the hallway and said, ‘Relax, go splash some water on your face and come back when you’re OK.’ He did, but at the end of class, he was still staring at the paper. I asked him to come back to my office and finish it. That extra time was enough to get him through the test. Eventually, he passed the class and graduated that semester. It took him seven or eight years to complete his bachelor’s degree, and it was because of his problems in the statistics class. He went on to do occupational therapy and is really doing quite well, but it was a statistics class that was almost the barrier to having that future.”

Now, Vitevitch is the co-author of a new study that uses a questionnaire and an analytical technique called “network science” to determine precisely what factors contribute to this kind of statistics anxiety among psychology majors. The paper appears in the peer-reviewed journal Scholarship of Teaching and Learning in Psychology.

“We teach a statistics class in the psychology department and see many students put it off until senior year because they’re scared of this class,” Vitevitch said. “We’re interested in seeing if we could help students out of the statistics anxiety. There’s not a one-size-fits-all solution to get them to overcome their fears. You need to find out what their fear is and focus on that. For people who don’t think statistics are useful, you need to convince them it’s not just useful for psychology but for other things as well. For people fearful of math and statistics in general, you need to help lower their anxiety so they can focus on learning. We hope this gives us some understanding of our own students and statistical anxiety in general.”

Vitevitch’s collaborators on the new paper are Cynthia Siew of the University of Warwick and Marsha McCartney of the National University of Singapore. The researchers said a grasp of statistics is vital to academic achievement and a well-rounded understanding of the field of psychology.

“It’s a way of communicating with numbers instead of words,” Vitevitch said. “A picture is worth a thousand words. Numbers can convey a lot of information as well. Being able to compute those numbers and communicate that massive amount of information quickly and concisely is important. It’s also very important knowing what those numbers mean and not skipping over them in a paper in a peer-reviewed journal article.”

The team used a questionnaire called the Statistical Anxiety Rating Scale (STARS) to determine aspects of learning statistics causing the most anxiety and categorize students into groups of high- and low-anxiety students. Questions probed students’ feelings about the value of statistics, self-concepts about math ability, fear of statistics teachers, interpretation anxiety, test and class anxiety, and the fear of asking for help.

“People would answer and rate questions like, ‘Do you think this is a useless topic? Do you think you’ll never use statistics in your life? Do you think statistics professors aren’t human because they’re more like robots?'” Vitevitch said. “Hopefully something like ‘my statistics teacher isn’t human’ is something we can focus on — and I’m saying that as a former statistics teacher who is human.”

With the questionnaire results from 228 students, the KU researcher and his colleagues mapped results visually using an emerging analysis technique called network science, which puts the most important contributors or symptoms of statistical anxiety at the center of a visual diagram of connecting nodes.

“Network science maps a collection of entities that are somehow related to another,” Vitevitch said. “Most people think of a social network where the dots would be you and your friends and lines would be drawn between you and people you know. You might know someone and they might know someone, but you might not know that third person. If you sketch these friends out, you get this spider-web looking thing. People have been doing this with various psychopathologies — looking at symptoms of depression, for example. With statistics anxiety, it’s not just that you have symptoms, it’s how long you have them and which ones are more important? That’s not always captured by a laundry list of symptoms. But it does seem to be captured by a network approach. The most important symptoms are in the middle of that spider web.”

Whereas previous studies on the topic used a scale to measure the levels of students’ statistics anxiety, the application of network science to responses from the STARS questionnaire increased the researchers’ understanding of the nature of the anxiety itself. For instance, network science analysis revealed high- and low-anxiety networks have different network structures.

For students high in statistics anxiety, the chief symptoms included high agreement with the statements “I can’t even understand seventh- and eighth-grade math; how can I possibly do statistics?” and “statistics teachers are so abstract they seem inhuman.” For low-anxiety students, main symptoms included fear of “asking a fellow student for help in understanding a printout” and anxiety “interpreting the meaning of a table in a journal article.”

Vitevitch said he hoped the results would be used by instructors in university psychology departments to develop effective interventions to ease students’ statistics anxiety.

“This paper is targeted at people who teach psychology,” he said. “Hopefully we’ll turn our science on ourselves and find a better way to make sure we’re getting our points across to our students and helping those who need a little help. It might not be a matter of teaching remedial math, but more like helping them overcome fears or discomfort they have with this topic.”

The risk of extinction varies from species to species depending on how individuals in its populations reproduce and how long each animal survives. Understanding the dynamics of survival and reproduction can support management actions to improve a specie’s chances of surviving.

Mathematical and statistical models have become powerful tools to help explain these dynamics. However, the quality of the information we use to construct such models is crucial to improve our chances of accurately predicting the fate of populations in nature.

“A model that over-simplifies survival and reproduction can give the illusion that a population is thriving when in reality it will go extinct.,” says associate professor Fernando Colchero, author of new paper published in Ecology Letters.

Colchero’s research focuses on mathematically recreating the population dynamics by better understanding the species’s demography. He works on constructing and exploring stochastic population models that predict how a certain population (for example an endangered species) will change over time.

These models include mathematical factors to describe how the species’ environment, survival rates and reproduction determine to the population’s size and growth. For practical reasons some assumptions are necessary.

Two commonly accepted assumptions are that survival and reproduction are constant with age, and that high survival in the species goes hand in hand with reproduction across all age groups within a species. Colchero challenged these assumptions by accounting for age-specific survival and reproduction, and for trade-offs between survival and reproduction. This is, that sometimes conditions that favor survival will be unfavorable for reproduction, and vice versa.

For his work Colchero used statistics, mathematical derivations, and computer simulations with data from wild populations of 24 species of vertebrates. The outcome was a significantly improved model that had more accurate predictions for a species’ population growth.

Despite the technical nature of Fernando’s work, this type of model can have very practical implications as they provide qualified explanations for the underlying reasons for the extinction. This can be used to take management actions and may help prevent extinction of endangered species.

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Materials provided by University of Southern Denmark. Note: Content may be edited for style and length.

Joseph Lukens, Brian Williams, Nicholas Peters, and Pavel Lougovski, research scientists with ORNL’s Quantum Information Science Group, performed distinct, independent operations simultaneously on two qubits encoded on photons of different frequencies, a key capability in linear optical quantum computing. Qubits are the smallest unit of quantum information.

Quantum scientists working with frequency-encoded qubits have been able to perform a single operation on two qubits in parallel, but that falls short for quantum computing.

“To realize universal quantum computing, you need to be able to do different operations on different qubits at the same time, and that’s what we’ve done here,” Lougovski said.

According to Lougovski, the team’s experimental system — two entangled photons contained in a single strand of fiber-optic cable — is the “smallest quantum computer you can imagine. This paper marks the first demonstration of our frequency-based approach to universal quantum computing.”

“A lot of researchers are talking about quantum information processing with photons, and even using frequency,” said Lukens. “But no one had thought about sending multiple photons through the same fiber-optic strand, in the same space, and operating on them differently.”

The team’s quantum frequency processor allowed them to manipulate the frequency of photons to bring about superposition, a state that enables quantum operations and computing.

Unlike data bits encoded for classical computing, superposed qubits encoded in a photon’s frequency have a value of 0 and 1, rather than 0 or 1. This capability allows quantum computers to concurrently perform operations on larger datasets than today’s supercomputers.

Using their processor, the researchers demonstrated 97 percent interference visibility — a measure of how alike two photons are — compared with the 70 percent visibility rate returned in similar research. Their result indicated that the photons’ quantum states were virtually identical.

The researchers also applied a statistical method associated with machine learning to prove that the operations were done with very high fidelity and in a completely controlled fashion.

“We were able to extract more information about the quantum state of our experimental system using Bayesian inference than if we had used more common statistical methods,” Williams said.

“This work represents the first time our team’s process has returned an actual quantum outcome.”

Williams pointed out that their experimental setup provides stability and control. “When the photons are taking different paths in the equipment, they experience different phase changes, and that leads to instability,” he said. “When they are traveling through the same device, in this case, the fiber-optic strand, you have better control.”

Stability and control enable quantum operations that preserve information, reduce information processing time, and improve energy efficiency. The researchers compared their ongoing projects, begun in 2016, to building blocks that will link together to make large-scale quantum computing possible.

“There are steps you have to take before you take the next, more complicated step,” Peters said. “Our previous projects focused on developing fundamental capabilities and enable us to now work in the fully quantum domain with fully quantum input states.”

Lukens said the team’s results show that “we can control qubits’ quantum states, change their correlations, and modify them using standard telecommunications technology in ways that are applicable to advancing quantum computing.”

Once the building blocks of quantum computers are all in place, he added, “we can start connecting quantum devices to build the quantum internet, which is the next, exciting step.”

Much the way that information is processed differently from supercomputer to supercomputer, reflecting different developers and workflow priorities, quantum devices will function using different frequencies. This will make it challenging to connect them so they can work together the way today’s computers interact on the internet.

This work is an extension of the team’s previous demonstrations of quantum information processing capabilities on standard telecommunications technology. Furthermore, they said, leveraging existing fiber-optic network infrastructure for quantum computing is practical: billions of dollars have been invested, and quantum information processing represents a novel use.

The researchers said this “full circle” aspect of their work is highly satisfying. “We started our research together wanting to explore the use of standard telecommunications technology for quantum information processing, and we have found out that we can go back to the classical domain and improve it,” Lukens said.

Lukens, Williams, Peters, and Lougovski collaborated with Purdue University graduate student Hsuan-Hao Lu and his advisor Andrew Weiner. The research is supported by ORNL’s Laboratory Directed Research and Development program.

The presence of humans on the American continent dates back to at least 14,500 years ago, according to datings made at archaeological sites such as Monte Verde, in Chile’s Los Lagos Region. But the first settlers continued moving towards the southernmost confines of America.

Now, researchers from Argentina’s National Council for Scientific and Technical Research (CONICET) and two Spanish institutions (the Spanish National Research Council and the University of Burgos) have analyzed the relationships between mobility and technology developed by those societies that originated in the far south of Patagonia.

The study, published in the Royal Society Open Science journal, is based on an extensive database of all available archaeological evidence of human presence in this region, from the time the first groups arrived in the early Holocene (12,000 years ago) until the end of the 19th century.

This was followed by the application of machine learning techniques, a statistical system that allows the computer to learn from many data (in this case, big data from characteristic technological elements of the sites) in order to carry out classifications and predictions.

“It is by means of automatic classification algorithms that we have identified two technological packages or ‘landscapes’: one that characterizes pedestrian hunter-gatherer groups (with their own stone and bone tools) and the other characterizing those that had nautical technology, such as canoes, harpoons and mollusc shells used to make beads,” explains Ivan Briz i Godino, an archaeologist of the National Council for Scientific and Technical Research (CONICET) of Argentina and co-author of the work.

“In future excavations, when sets of technological elements such as those we have detected appear, we’ll be able to directly deduce the type of mobility of the group or the connections with other communities,” adds Briz.

The results of the study have also made it possible to obtain maps with the settlements of the two communities, and this, in turn, has made it possible to locate large regions in which they interacted and shared their technological knowledge. In the case of groups with nautical technology, it has been confirmed that they arrived at around the beginning of the Mid-Holocene (some 6,000 years ago) from the channels and islands of the South Pacific, moving along the coast of what is now Chile.

“Traditional archaeology identifies sites, societies and their possible contacts on the basis of specific elements selected by specialists (such as designs of weapon tips or decorative elements), but here we show that it is more interesting to analyse sets of technological elements as a whole, using artificial intelligence techniques that allow us to work with large data volumes and without subjective prejudices,” concludes Briz.