News Flash (November 2020-April 2021)

November-December 2021

Mathematician suggests new approach to cooperative game

A mathematician from RUDN University developed a matrix representation of set functions that can be applied to cooperative game theory. The scientist obtained matrix expressions by transforming a derived set function expression. A derived function shows how a function transforms when its variables change. Having calculated a derived function, a specialist can give an accurate analysis of a certain situation. Specialists in cooperative game theory study methods of complex decision-making in situations with multiple criteria. In such a situation, groups (or coalitions) of players have to come up with a decision that is the most profitable for all of them. Set functions are one of the tools used to work with cooperative game theory. In these functions, the input data are sets of elements that can have different values. Simple explicit questions are quite rare in real life; therefore, the data on different elements can support or neutralize each other. Combinations of elements called coalitions can assume their own values.

Mathematicians specify the criteria for the emergence of Turing patterns

Turing patterns are mathematical expressions of the structures formed in chemical and biological systems, such as spots and stripes on the animal skin. A team of scientists from RUDN University found out that the traditional mathematical conditions of their existence failed to describe the whole range of real-life cases, and that the criteria of their emergence are more flexible. According to Turing's standard model, a system of two elements requires certain conditions for the patterns to emerge. One of the elements should self-activate whereas the second element should self-inhibit. Moreover, the mobility (or diffusion coefficient) of the latter should be higher than that of the former to a degree that depends on the values of other systemic parameters. However, this is not true for real-life chemical and biological systems, where the difference between the mobility of the activator and the inhibitor is usually very little. Therefore, there is only a narrow range of values that other systemic parameters can have for the structures to be formed.

A mathematical model facilitates inventory management in the food supply chain

The Diverfarming project's research group, in charge of designing and analyzing value chains, and directed by Dr. Francisco Campuzano-Bolarín has developed a mathematical model that facilitates decision making when planning distribution capacity, and achieves a balance between performance of the inventory and transport in a supply network, taking differing scenarios into account depending on the availability of vehicles.

The model developed is based on the methodology of system dynamics, a recognized way of dealing with problems related to dynamic processes, such as the supply chain. This set of equations, input data and relationships among variables is tested in a frozen products supply chain at national level. This enables managers to determine the best configuration of parameters to obtain the best decision alternative in terms of costs and inventory levels, optimizing the procedure with regard to costs and stock levels.

January 2021

What is a margin of error? This statistical tool can help you understand vaccine trials and political polling

How accurate is the Covid-19 test? How do scientists know the effectiveness of Covid-19 vaccine? These questions contain some uncertainty but some accurate predictions can be made only if we clearly understand the uncertainty. Margin of error is the tool used by statisticians to study and quantify uncertainty.

If a new medicine is being researched, then it will be somewhere 0 to 100% effective . But, this is not a helpful figure. It is the job of a statistician to narrow down this interval. Statisticians usually call this range a confidence interval, and it is the range of predictions within which statisticians are very confident the true number will be found. Confidence intervals are calculated using a mathematical formula that encompasses the sample size, the range of responses and the laws of probability. If you divide the confidence interval by 2, you would get margin error.

Imagine that researchers test the vaccine on 1000 people and it was effective in 700 of them. The efficiency rate is 70%. The confidence interval is 67% to 73% with margin error 3%. We could say that this vaccine is expected to be 70% effective, plus or minus 3%, for the entire population.

Stanford’s Sourav Chatterjee awarded prestigious mathematics prize

Chatterjee's significant contributions in pure and applied mathematics range from social networks to quantum mechanics.

Growing up in India, Chatterjee was always into maths and chess. With his mind boggling aptitude, he joined Stanford University as a professor of mathematics and statistics in the School of Humanities and Sciences in 2013. Chatterjee has received the Infosys Prize in Mathematical Sciences. The $100,000 award, which recognizes outstanding researchers and scientists of Indian origin, is presented by the Infosys Science Foundation, a nonprofit founded by Infosys, an Indian multinational digital services and consulting corporation.

The main pillars of his research were probability and statistics. His work not only impacted mathematics, but also physics, technology and other various fields. Topics that have benefited from his mathematical insights include occurrences of rare events, the dynamics of social as well as technological networks, the behavior of magnets and efforts to further solidify a mathematical basis for quantum mechanics.

The jury of the Infosys Science Foundation, composed of academics from around the world, described Chatterjee as “one of the most versatile probabilists of his generation” and praised his “formidable problem-solving powers.”

Chatterjee appreciated the recognition of his fellow mates and thanked his mentors, teachers, family and friends for always supporting him and helping him to achieve the success that he has today.

ICMI calls for participation in the International Mathematics Day.

The ICMI [International Commission for Mathematical Instruction] calls for the participation in the International Day of Mathematics (14 March 2021). The theme for the same has been decided to be “Mathematics for a better world.” In the view of pandemic, it is highly likely that it will not be possible for the ICMI, to hold events for the general public. Hence, they have recommended that celebrations be planned in schools and colleges, during class times or as extra-curricular activities. They have enthusiastically invited all the schools and colleges to participate in the poster-making competition on the topic- ‘Mathematics for a better world.’

2021 Mathematics Art Exhibition Awards declared

The Mathematical Art Exhibition Award recognizes aesthetically pleasing works that combine mathematics and art. In 2008, an anonymous donor provided an endowment to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form. The exhibition takes place every January at the Joint Mathematics

Meetings. Three awards are made annually: One for best photograph, painting, or print ($400); one for best textile, sculpture, or other medium ($400); and one honourable mention ($200).

1. “Laura’s Flowerpot” by Debora Coombs and Duane Bailey, was awarded Best textile, sculpture, or other medium. This sculpture is a patch of Penrose tiling raised into the third dimension. It is built from a single shape, a golden rhombus orientated according to its equivalent self in two-dimensions.

2. “Eight -Ring Circus “by Margaret Kepner, was awarded Best photograph, painting, or print”. A partition of N is a set of positive integers that adds up to N. This work is an exploration of the 22 unique partitions of eight, and their representations and properties.

3. “Madar-i-Shah Reconstruction” by Phillip Webster, was awarded Honourable Mention. " This work is a manual re-creation of an especially elegant two-level Islamic geometric pattern found at the Madrassa Madar-i-Shah in Isfahan, Iran. The piece was drawn using nothing but pencil, straightedge and compass.

INDIAN MATHEMATICIAN NIKHIL SRIVASTAVA NAMED THE JOINT WINNER OF MICHEAL AND SHEILA HELD PRIZE

Nikhil Srivastava from the University of California, Berkeley, Adam Marcus, the Ecole polytechnic federale de Lausanne (EPFL) and Daniel Alan, Spielman from Yale University will receive the 2021

Michael and Sheila Held Prize, The national Academy of Sciences, said in the statement, for solving the long standing questions on the Kadison-Singer problem and on Ramanujan graphs. The prize consists of a medal and USD 100000.

They published new constructions on Ramanujan graphs, that

describe sparse, but highly connected networks, and a solution to

what is known as the Kadison-Singer problem, a detailed old problem that asks whether unique information can be gleaned from a system, in which only some of the features can be observed or measured. Mr. Srivastava is currently an Associate Professor of Mathematics, at the University of California. Their groundbreaking papers on the questions, solved problems that mathematicians had been working on for several decades, the National Academy of Sciences said. “Their proofs provided new tools to address several other problems, which have been embraced by several other computer scientists seeking to apply the geometry of polynomials to solve discrete optimization problems”

2021 New Horizons in Mathematics Prize declared

The Breakthrough Prize Foundation today announced the esteemed recipients of the 2021 Breakthrough Prize, recognizing a spectacular array of ground-breaking achievements in the Life Sciences, Fundamental Physics and Mathematics. Each year, the Prize is celebrated at a gala award ceremony, where the awards are presented by superstars of movies, music, sports and tech entrepreneurship. Due to the global pandemic, however, this year’s ceremony has been postponed until March 2021.

1. Bhargav Bhatt (University of Michigan) for his work in commutative geometry and arithmetic algebraic geometry.

2. Aleksandr Logonov (Princeton University) for his work on novel techniques for solutions of elliptical equations.

3. Song Sun (University of California) for his work on complex differential geometry and existence results for Kahler-Einstein metrics. FEBRUARY 2021

Institute Professor Emeritus Isadore Singer, renowned mathematician who united math and physics, dies at 96

Longtime MIT professor who laid the foundations for the development of index theory was a recipient of both the National Medal of Science and the Abel Prize

Institute Professor Emeritus Isadore M. Singer, an enormously influential figure in 20th-century science whose work united mathematics and physics, died on Feb. 11. He was 96. In a career that spanned more than 50 years, Singer not only profoundly affected the development of mathematics, but discovered connections between math and physics that led to the creation of a new field, index theory. Singer was the recipient of numerous awards and honors for his pioneering work, including the National Medal of Science and the Abel Prize, often considered the Nobel Prize of mathematics.

Among his greatest achievements, Singer and Richard Kadison formulated the Kadison-Singer Conjecture in 1959 as part of their work on formalizing the foundations of English physicist Paul Dirac’s quantum mechanics. In 1963, Singer and Michael Atiyah hit upon an even more profound connection with the Atiyah-Singer Index Theorem. This theorem deeply and irrecoverably tied together the mathematical fields of analysis, geometry, topology.

Even late into his career, Singer insisted on teaching undergraduates, volunteering to work for several semesters as a teaching assistant for the introductory calculus course for first-year students at MIT. He liked to say that empathy made him a good teacher.

The Ramanujan Machine: Researchers have developed a 'conjecture generator' that creates mathematical conjectures

Using AI and computer automation, Technion researchers have developed a 'conjecture generator' that creates mathematical conjectures, which are considered to be the starting point for developing mathematical theorems. They have already used it to generate a number of previously unknown formulas. The Technion researchers proposed and examined a new idea: The use of computer algorithms to automatically generate mathematical conjectures that appear in the form of formulas for mathematical constants.

A conjecture is a mathematical conclusion or proposition that has not been proved; once the conjecture is proved, it becomes a theorem.

The conjectures generated by the Technion's Ramanujan Machine have delivered new formulas for well-known mathematical constants such as pi, Euler's number (e), Apéry's constant (which is related to the Riemann zeta function), and the Catalan constant. Surprisingly, the algorithms developed by the Technion researchers succeeded not only in creating known formulas for these famous constants, but in discovering several conjectures that were heretofore unknown.

The research team has launched a website, RamanujanMachine.com, which is intended to inspire the public to be more involved in the advancement of mathematical research by providing algorithmic tools that will be available to mathematicians and the public at large.

Mathematicians develop new classes of stellar dynamics systems solutions

The Vlasov-Poisson equations describes very important physical phenomenon such as the distribution of the gravitating particles in interstellar space, high temperature plasma kinetics and the Landau damping effect. A joint team of scientists from the Mathematical institute of the University of Munich and the RUDN University suggested a new method to obtain stationary solutions for a system of Vlasov-Poisson equations in a three-dimensional case. The obtained solutions describe the phenomena of stellar dynamics. The results of the study were published in the Doklady Mathematics Journal.

"We have considered a three-dimensional stationary system of the Vlasov-Poisson equations concerning the distribution function of gravitating matter, local density, and Newtonian potential, and developed a new method for obtaining spherically symmetric stationary solutions. This was the result of our fruitful collaboration with renowned German scientists J. Batt and E. Joern," said Alexander Skubachevskii, a D Sc in Physics and Mathematics, and the Head of the Nikolskii Mathematical Institute of RUDN University.

How game theory could reduce the cost of PPE for frontline health care workers

Kingston University London researchers have used a mathematical model known as game theory to explore how the challenge of securing sufficient levels of vital personal protective equipment (PPE) for healthcare workers during the peak of the COVID-19 pandemic could have been mitigated.

In the study, the researchers simulated a variety of scenarios based on five different start dates for when stockpiling could have been initiated between January and March. These included when the first UK COVID-19 case was confirmed, when the European Union proposed a bulk-buying scheme to the UK and when COVID-19 was declared a global pandemic, with various increases in storage capacity up to 20 times higher than the estimated base level.

The results showed that a combination of early stockpiling and a large increase in storage capacity would have resulted in significant cost savings, with the model delivering a saving of 38 percent had stockpiling begun on February 7—the date the World Health Organisation warned of PPE shortages—and had storage capacity been increased tenfold. However, if storage capacity at regional NHS trusts was not increased, early stockpiling only had a negligible impact on cost. Across each of the simulated dates for beginning stockpiling, the team found that increasing PPE storage capacity by a factor of 15 would be required to considerably lower peak demand and effectively minimize the pressure on the NHS.

Researchers use mathematical modeling to identify factors that determine adaptive therapy success

The research team at H.Lee Moffitt Cancer Centre and Research Institute used mathematical modelling to determine how the cost of resistance is associated with adaptive therapy. They modelled the growth of drug sensitive and resistant cell populations under both continuous therapy and adaptive therapy conditions and compared their time to disease progression in the presence and absence of a cost of resistance.

The researchers showed that tumours with higher cell density and those with smaller levels of pre-existing resistance did better under adaptive therapy conditions. They also showed that cell turnover is a key factor that impacts the cost of resistance and outcomes to adaptive therapy by increasing competition between sensitive and resistance cells. To do so, they made use of phase plane techniques, which provide a visual way to dissect the dynamics of mathematical models.

To confirm their models, the researchers analysed data from 67 prostate cancer patients undergoing intermittent therapy treatment, a predecessor of adaptive therapy. While more studies are needed to understand how adaptive therapies may benefit patients, researchers are hopeful their data will lead to better indicators of which tumours will respond to adaptive therapy.

March 2021

Cybersecurity pioneers win the Abel Prize

The Abel Prize, which honours achievements in mathematics, was

awarded on 17 March, 2021 to Hungarian Laszlo Lovasz (right) and Israeli Avi Wigderson (left) for their contributions to computer security. The pair were

honoured for their foundational contributions to theoretical computer

science and discrete mathematics, and their leading role in shaping them into

central fields of modern mathematics, the jury said. Lovasz developed

the LLL algorithm, which has applications in areas such as number theory,

cryptography and mobile computing. The algorithm serves as the basis

for the only encryption systems that can withstand an attack by a

quantum computer. Avi Wigderson’s has widened and deepened the understanding of complexity theory & quot meanwhile. His research has led to advances in internet cryptography and serves as the basis for the

technology powering crypto-currencies such as bitcoin.

Classic math conundrum solved:Superb algorithm for finding the shortest route

When heading somewhere new, most of us leave it to computer

algorithms to help us find the best route, whether by using a car’s GPS,

or public transport and map apps on their phone. The best route can

suddenly be the slowest, e.g., because a queue has formed due to

roadworks or an accident.

People probably don’t think about the complicated math behind routing

suggestions in these types of situations. The software being used is

trying to solve a variant for the classic algorithmic shortest path

problem, the shortest path in a dynamic network. For 40 years,

researchers have been working to find an algorithm that can optimally

solve this mathematical conundrum. Now, Christian Wulff-Nilsen of the

University of Copenhagen Department of Computer Science has

succeeded in cracking the nut along with two colleagues.

We have developed an algorithm, for which we now have mathematical

proof, that it is better than every other algorithm up to now -- and the

closest thing to optimal that will ever be, even if we look 1000 years into

the future, says Associate Professor Wulff-Nilsen. The results were

presented at the FOCS 2020 conference.

New tool can help predict the next financial bubble

An international team of interdisciplinary researchers has identified mathematical metrics to characterize the fragility of financial markets.

Their paper Network geometry and market instability sheds light on the higher-order architecture of financial systems and allows analysts to identify systemic risks like market bubbles or crashes.

Their paper abstracts the complexity of the financial market into a

network of stocks and employs geometry-inspired network measures to

gauge market fragility and financial dynamics. They analysed and

contrasted the stock market networks for the USA P500 and the

Japanese Nikkei-225 indices for a 32-year period (1985-2016) and for

the first time were able to show that several discrete Ricci curvatures are

excellent indicators of market instabilities. The work was recently

published in the Royal Society Open Science journal and allows analysts

to distinguish between business-as-usual periods and times of fragility

like bubbles or market crashes.

Mathematical modelling used to analyse dynamics of CAR T-cell therapy

Mathematical modelling has been used to help predict how CAR T cells

will behave after being infused back into patients; however, no studies

have yet considered how interactions between the normal T cells and

CAR T cells impact the dynamics of the therapy, in particular how the

nonlinear T cell kinetics factor into the chances of therapy success.

Moffitt researchers integrated clinical data with mathematical and

statistical modelling to address these unknown factors.

The researchers demonstrate that CAR T cells are effective because

they rapidly expand after being infused back into the patient; however,

the modified T cells are shown to compete with existing normal T cells,

which can limit their ability to expand.

Chimeric antigen receptor T-cell therapy, or CAR T, is a relatively new

type of therapy approved to treat several types of aggressive B cell

leukaemia and lymphomas. Many patients have strong responses to

CAR T; however, some have only a short response and develop disease

progression quickly. Unfortunately, it is not completely understood why

these patients have progression.

Sum of cubes: New math solution for 3

The equation x3+y3+z3=k is known as the sum of cubes problem. While

seemingly straightforward, the equation becomes exponentially difficult

to solve when framed as a "Diophantine equation" -- a problem that

stipulates that, for any value of k, the values for x, y, and z must each be

integers.

Over the years, mathematicians had managed through various means to

solve the equation, either finding a solution or determining that a solution

must not exist, for every value of k between 1 and 100 -- except for 42.

In September 2019, Booker and Sutherland, harnessing the combined

power of half a million home computers around the world, for the first

time found a solution to 42. The widely reported breakthrough

the team to tackle an even harder, and in some ways more universal

problem: finding the next solution for 3.

As decades went by with no new solutions for 3, many began to believe

there were none to be found. But soon after finding the answer to 42,

Booker and Sutherland's method, in a surprisingly short time, turned up

the next solution for 3:

5699368212219623807203 + (−569936821113563493509)3 + (−472715493453327032)3 = 3

April 2021

MATHEMATICIANS DISCOVERED A NEW TYPE OF PRIME NUMBER

In new research, mathematicians have revealed a new category of “digitally delicate” prime numbers. These infinitely long primes turn back to composites with a change of any individual digit. Mathematicians from the University of South Carolina have established an even more specific niche of the digitally delicate primes: widely digitally delicate primes. These are primes with added, infinite “leading zeros,” which don’t change the original prime, but make a difference as you change the 0s into other digits to test for delicacy. The mathematicians believe there are infinite widely digitally delicate primes, but so far, they can’t come up with a single real example. They’ve tested all the primes up to 1,000,000,000 by adding leading zeros and doing the math. South Carolina math professor Michael Filaseta and former graduate student Jeremiah Southwick worked together on the widely digitally delicate number research, publishing their findings in Mathematics of Computation . Even without specific examples, they proved the numbers exist in base 10 and that there are infinitely many. AUXIN MAKES THE SPIRALS IN GERBERA INFLORESCENCES FOLLOW THE FIBONACCI SEQUENCE

A giant inflorescence is beneficial, as it is effective in attracting pollinators. The order of the florets in a flower head is not random. Instead, they are patterned into regular spirals whose number follows the Fibonacci sequence familiar from mathematics. Fibonacci numbers are the sum of the two preceding numbers in the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... In the flower head, the number of left- and right-winding spirals is always two consecutive Fibonacci numbers. Sunflower flower heads can have as many as 89 right-winding and 144-left winding spirals, while the gerbera, another much-studied plant from the Asteraceae plant family, has fewer spirals (34/55). The researchers found that the meristem of the gerbera is patterned on the molecular level already at a stage where no primordia or other changes are discernible by even an electron microscope. "During growth, auxin levels rise to the maximum simultaneously in several locations of the meristem. The number of these clustered spots, which are called auxin maxima, increases rapidly as the diameter of the meristem grows, following the Fibonacci numbers. A new auxin maximum is always formed between two neighbouring maxima and moves so that it is always closer to the older of the neighbours. This is why the spirals are regular even in meristems that are not entirely symmetric." The findings demonstrate that the expansion growth of the meristem is the factor that affects, for example, the eventual number of florets in the flower head. MATHEMATICAL EXPLANATIONS FOR THE PERIODICAL BRIGHTENING OF CERTAIN STARS

KAUST's Soumya Das and Marc Genton have now developed a method to bring this evolving periodicity within the framework of mathematically "cyclostationary" processes. Classic cyclostationary processes have an easily definable variation over time, like the sweep of a lighthouse beam or the annual variation in solar irradiance at a given location. Here, "stationary" refers to the constant nature of the periodicity over time and describes highly predictable processes like a rotating shaft or a lighthouse beam. However, when the period or amplitude changes slowly over many cycles, the mathematics for cyclostationary processes fails. "We call such a process an evolving period and amplitude cyclostationary, or EPACS, process," says Das. "Since EPACS processes are more flexible than cyclostationary processes, they can be used to model a wide variety of real-life scenarios. Das and Genton modeled the nonstationary period and amplitude by defining them as functions that vary over time. In doing this, they expanded the definition of a cyclostationary process to better describe the relationship among variables, such as the brightness and periodic cycle for a variable star. They then used an iterative approach to refine key parameters in order to fit the model to the observed process.

MATHEMATICS USED TO EXPLAIN HOW PAPER CRUMPLES

Mathematicians at Harvard University recently uncovered something wholly unexpected about these wads of balled-up paper. Their experiments in Nature Communications show the total length of each crease in the scrunched-up paper increases logarithmically as you compact and unfold the sheet over and over again—that is, the crumpling process follows a general, predictable rule. From conducting previous research, the mathematicians knew "the logarithmic growth of crease length was a robust phenomenon that could be reproduced over and over again but we were missing the physical basis for why this happens," Harvard's Jovana Andrejevic, the lead author of the new paper, said in a prepared statement. To uncover the physical explanation for why paper crumples in this unexpectedly predictable fashion, Andrejevic and her team focused on the flat sections (which they call "facets") of a crumpled sheet. Specifically, they studied how the facets in crumpled sheets of Mylar—a type of shiny, polyester film used in NASA spacesuits to protect astronauts from radiation—break up into increasingly smaller fragments as the surfaces are scrunched up again and again.Using Adobe Illustrator and Photoshop, Andrejevic hand-traced the patterns in 24 sheets. It took her hours, and sometimes days, to complete this process. On average, the 4x4-inch squares of Mylar each possessed 880 facets after a few rounds of crumpling, but one had a staggering 3,810 facets. The resulting images were stunning, not dissimilar to the abstract art you might otherwise see hanging on the walls at the Met. The facets in the crumpled sheets of paper sort of resemble the countries on colorized world maps.